item: #1 of 258 id: pythagoras-10 author: None title: pythagoras-10 date: None words: 7890 flesch: 45 summary: A model for teacher knowledge as a basis for online courses for professional development of statistics teachers. ISSN: 2223-7895 (online) Teachers’ professional development needs in data handling and probability In This Original Research... Open Access • Abstract • Introduction    • Classroom practices, teacher knowledge, beliefs and confidence       • Profiling teachers • Research design    • Research approach    • Research method       • Research participants       • Measuring instrument       • Statistical analysis       • Reliability       • Validity       • Ethical considerations • Results    • Section 1: Preparation for teaching a unit in data handling and probability    • Section 2: Teaching practices, including materials or resources used by teachers and learners    • Section 3: The topics sample and average in data handling and probability    • Section 4: Teacher confidence in the teaching of data handling and probability    • Section 5: Beliefs about statistics in everyday life    • Section 6: Teacher comments on learner survey items to determine content knowledge and pedagogical content knowledge    • Sections 7 and 8: Teacher background and professional development • Discussion • Conclusions and recommendations • Acknowledgements    • Competing interests    • Authors’ contribution • References Abstract (Back to top) Poor Trends in International Mathematics and Science Study (TIMMS) results and widespread disappointing mathematics results in South Africa necessitate research-based and more efficient professional development for in-service mathematics teachers. keywords: confidence; data; development; education; knowledge; levels; mathematics; probability; professional; research; section; statistics; teachers; teaching cache: pythagoras-10.htm plain text: pythagoras-10.txt item: #2 of 258 id: pythagoras-100 author: Julie, Cyril title: Mathematical Literacy: Myths, further inclusions and exclusions date: 2006-10-20 words: 5610 flesch: 46 summary: In particular the National Curriculum Statement Grades 10 to 12: Mathematical Literacy is held in focus and somewhat mirrored against Critical Mathematical Literacy. In this paper the definition of Mathematical Literacy as in the region of the Critical Mathematical Literacy guided the interrogation of the South African National Curriculum Statement (NCS) (Grades 10-12 – General): Mathematical Literacy (Department of Education, 2006a) and some issues surrounding the implementation of this subject. keywords: action; contexts; department; education; grades; knowledge; learners; learning; literacy; mathematics; school; teaching cache: pythagoras-100.pdf plain text: pythagoras-100.txt item: #3 of 258 id: pythagoras-101 author: Office, Editorial title: Erratum date: 2006-10-20 words: 898 flesch: 54 summary: But once more John is using the ‘new’ (to him) signs in mathematical activities. Specifically, it is only after John has seen exemplars in the textbook of improper integrals and their evaluation, that he starts to use the improper integral in a way that is consonant with its definition. keywords: integral; john cache: pythagoras-101.pdf plain text: pythagoras-101.txt item: #4 of 258 id: pythagoras-102 author: Parker, Diane title: Official pedagogic identities from South African policy – some implications for mathematics teacher education practice date: 2006-10-20 words: 8586 flesch: 37 summary: The NSE together with the NCSM projects a symbolic image of what is expected of mathematics teachers in the new reformed system. This produces the possibility of focused qualifications designed to integrate highly specialised knowledge for developing mathematics teachers. keywords: curriculum; education; identities; knowledge; learning; mathematics; new; pedagogic; practice; south; teacher cache: pythagoras-102.pdf plain text: pythagoras-102.txt item: #5 of 258 id: pythagoras-104 author: Berger, Margot title: Making mathematical meaning: From preconcepts to pseudoconcepts to concepts date: 2006-10-20 words: 5239 flesch: 45 summary: In terms of this 1 The introduction of new mathematical objects through definitions is common practice in many South African universities and in certain British universities such as Warwick (Alcock and Simpson, 2001). notion, and as I argue later, the learner’s use of the mathematical signs in activity and communication is a necessary first step in the appropriation of mathematical meaning. In particular I argue that this theory can be used to explain how idiosyncratic usages of mathematical signs by students (particularly when just introduced to a new mathematical object) get transformed into mathematically acceptable and personally meaningful usages. keywords: concept; mathematical; object; signs; thinking; use; vygotsky cache: pythagoras-104.pdf plain text: pythagoras-104.txt item: #6 of 258 id: pythagoras-105 author: Mbekwa, Monde title: Teachers’ views on mathematical literacy and on their experiences as students of the course date: 2006-10-20 words: 5397 flesch: 44 summary: Because most of the teachers who will be required to teach mathematical literacy are not practising mathematics teachers, they will need both subject content knowledge and pedagogical content knowledge. 22-29 Teachers’ views on mathematical literacy and on their experiences as students of the course Monde Mbekwa School of Science and Mathematics Education, University of the Western Cape mmbekwa@uwc.ac.za keywords: cape; course; education; literacy; mathematics; students; teachers; teaching; understanding cache: pythagoras-105.pdf plain text: pythagoras-105.txt item: #7 of 258 id: pythagoras-106 author: de Villiers, Michael title: A generalisation of the Spieker circle and Nagel line date: 2006-10-20 words: 3389 flesch: 54 summary: Of note too is a specific Yahoo discussion group which is specifically dedicated to current research in triangle geometry and traditional Euclidean geometry. The rise, fall, and possible transfiguration of triangle geometry. keywords: circle; conic; geometry; line; nagel; point; spieker; triangle cache: pythagoras-106.pdf plain text: pythagoras-106.txt item: #8 of 258 id: pythagoras-107 author: Kotze, G. S.; Strauss, J. P. title: Contextual factors of the mathematics learning environment of grade 6 learners in South Africa date: 2006-10-20 words: 5071 flesch: 63 summary: The data concerning the age of learners also provide insight into initial enrolment at the officially prescribed age, regular attendance and the progression of most learners from one grade to another at the appropriate time so that everyone is able to complete the curriculum. Aim and problem statement The aim of this article is to provide insight into the individual characteristics and family backgrounds that mathematics learners bring to the learning process and how they interact with the resources and practices that characterise the schools they attend. keywords: africa; education; grade; home; learners; mathematics; school; south cache: pythagoras-107.pdf plain text: pythagoras-107.txt item: #9 of 258 id: pythagoras-109 author: Adler, Jill title: Mathematics for teaching: What is it and why is it important that we talk about it? date: 2005-10-20 words: 6390 flesch: 52 summary: At the same time, from years of experience in mathematics teacher education, both pre and in- service, I am aware that many practising teachers would be hard pushed to spontaneously answer questions like: “What mathematical question would you ask a learner who does …” or “What are three possible, different solution strategies for …”. Researching mathematics for teaching in mathematics teacher education. keywords: adler; courses; education; mathematics; research; tasks; teachers; teaching cache: pythagoras-109.pdf plain text: pythagoras-109.txt item: #10 of 258 id: pythagoras-110 author: Yushau, Balarabe; Mji, Andile; Wessels, Dirk C. J. title: The role of technology in fostering creativity in the teaching and learning of mathematics date: 2005-10-20 words: 7775 flesch: 48 summary: In a study, Westby and Dawson (1995) examined elementary school teachers’ impact on learner creativity and found that teachers’ ratings of their favourite learners were negatively correlated with creativity. Therefore, learner creativity was only fostered to the degree that learners could learn to channel their creativity into acceptable behaviours. keywords: computer; creativity; education; learners; learning; mathematics; problems; role; teachers; teaching; technology; thinking; time; use cache: pythagoras-110.pdf plain text: pythagoras-110.txt item: #11 of 258 id: pythagoras-111 author: Bennie, Kate title: Developing teachers, developing as a teacher: A story about a story date: 2005-10-20 words: 5988 flesch: 63 summary: The presentation I use is based on the work of Rowland − the account is presented in the form of personal reflections on a story written about playing the two different roles of teacher educator and classroom teacher. These extracts have been selected to illustrate my thinking while playing the two roles, teacher educator and classroom teacher. keywords: learners; mathematics; mathslearn; school; story; teacher; teaching cache: pythagoras-111.pdf plain text: pythagoras-111.txt item: #12 of 258 id: pythagoras-112 author: de Villiers, Michael title: A generalisation of the nine-point circle and Euler line date: 2005-10-20 words: 2516 flesch: 59 summary: For the sake of completeness, the nine-point conic theorem and Euler line generalisation are now formally stated, and a proof of the latter given. Further Euler line generalisation The above Euler line generalisation generalises even further as follows. keywords: euler; figure; line; point; triangle cache: pythagoras-112.pdf plain text: pythagoras-112.txt item: #13 of 258 id: pythagoras-113 author: Feza, Nosisi; Webb, Paul title: Assessment standards, Van Hiele levels, and grade seven learners’ understandings of geometry date: 2005-10-20 words: 7942 flesch: 64 summary: Introduction Internationally there appears to be widespread realisation that teaching in mathematics in general has failed to overcome a number of cognitive barriers to learner understanding (Carpenter & Fennema, 1988; Kempa, 1993; Peterson, 1998). Manipulatives were used during the interviews conducted in this study in an attempt to reveal a range and variety of learner understandings. keywords: education; group; hiele; learners; level; mathematics; rectangle; shapes; sides; square; teachers; van cache: pythagoras-113.pdf plain text: pythagoras-113.txt item: #14 of 258 id: pythagoras-114 author: van Etten, Bertus; Smit, Kosie title: Learning material in compliance with the Revised National Curriculum Statement: A dilemma date: 2005-10-20 words: 5407 flesch: 61 summary: We present examples of learner material to illustrate and motivate our point of view. A number of examples of this kind gradually familiarise the learner with the essential matters relating to linear functions: the form of the formula and the role of the coefficients for the gradient and the y-intercept. Context-rich mathematics For a developer of learner material in the spirit of TeleBel No. of minutes 0 100 200 300 500 800 1000 Cost (in Rands) 75 135 195 255 375 555 675 EasyPhone No. of minutes 0 100 200 300 500 800 1000 Cost (in Rands) 0 90 180 270 450 720 900 Table 2. keywords: airtime; context; curriculum; education; learners; learning; material; mathematics; table cache: pythagoras-114.pdf plain text: pythagoras-114.txt item: #15 of 258 id: pythagoras-116 author: Graven, Mellony title: Mathematics teacher retention and the role of Identity: Sam’s story date: 2005-10-20 words: 6758 flesch: 47 summary: Indeed these components provide the basis for the development of Sam’s strengthened mathematics teacher identity and his longer-term trajectory within the profession. The teachers therefore are not ‘typical’ of the general population of mathematics teachers. keywords: community; education; identity; learning; mathematics; participation; plesme; sam; teachers cache: pythagoras-116.pdf plain text: pythagoras-116.txt item: #16 of 258 id: pythagoras-117 author: Juter, Kristina title: Limits of functions – how do students handle them? date: 2005-10-20 words: 7095 flesch: 64 summary: 11-20 11 Limits of functions – how do students handle them? How do students respond to limits of functions? keywords: concept; course; definition; functions; limits; stage; students; tasks cache: pythagoras-117.pdf plain text: pythagoras-117.txt item: #17 of 258 id: pythagoras-118 author: Masehela, Kgabo title: Ten years of democracy: Translating policy into practice in mathematics and science education date: 2005-10-20 words: 5315 flesch: 54 summary: Ten years of democracy: translating policy into practice in mathematics and science education Kgabo Masehela Human Sciences Research Council Email: kmasehela@hsrc.ac.za Background This paper provides a 10-year (1994 – 2004) review of the state of mathematics and physical science education (SME) in South Africa with respect to participation and performance, and its relationship with policy implementation. Following the Department of Education’s strategy to improve mathematics and science, the deputy minister released the names of 102 dedicated mathematics and science high schools as part of a national strategy to improve mathematics and science in schools (Bot and Masehela, 2003). keywords: candidates; education; learners; mathematics; number; policy; science; table cache: pythagoras-118.pdf plain text: pythagoras-118.txt item: #18 of 258 id: pythagoras-119 author: Hockman, Meira title: Dynamic geometry: An agent for the reunification of algebra and geometry date: 2005-10-20 words: 7074 flesch: 53 summary: We discovered that both the algebraic method and the graphical method Algebraic Algebraic and Geometric Before After Before After Classification of problem 15 2 5 18 Understanding the Problem 16 3 4 18 Solving the problem 18 13 2 7 Table 2: Analysis of Rational Function Questionnaire. In a similar way mathematics students may learn to build equations and solve problems using variables and fixed constants. keywords: algebra; algebraic; geometry; problem; students; tool cache: pythagoras-119.pdf plain text: pythagoras-119.txt item: #19 of 258 id: pythagoras-120 author: Barnes, Hayley title: The theory of Realistic Mathematics Education as a theoretical framework for teaching low attainers in mathematics date: 2005-10-20 words: 10408 flesch: 35 summary: The theory of RME was subsequently selected as the theoretical framework to drive the design and implementation of the intervention and is being suggested as a possible way forward for working with low attaining learners. Improving teaching and learning mathematics for low attaining learners I therefore agree with Abel (1983), Baroody and Hume (1991) and Reusser (2000) and work on the assumption that the environmental aspects of the mathematics teaching and learning can affect a learner’s performance. keywords: attainers; education; knowledge; learners; learning; mathematics; mathematics education; problem; process; rme; teaching; theory; understanding; use cache: pythagoras-120.pdf plain text: pythagoras-120.txt item: #20 of 258 id: pythagoras-121 author: Breen, Chris title: Perturbating the assessment of individuals and groups: Listening for challenges to mathematics teacher educators date: 2004-10-20 words: 8357 flesch: 59 summary: Having done this, I turn my gaze onto one particular teacher education situation and explore student teacher assessment as they are prepared for a career in teaching. In describing some of the particular ways in which I try to heighten the awareness of this particular group of student teachers regarding assessment and evaluation, I reflect on the experience and pose questions for teacher educators in general to consider about their own practice. keywords: assessment; class; group; learning; listening; mathematics; session; student; teacher; way; work cache: pythagoras-121.pdf plain text: pythagoras-121.txt item: #21 of 258 id: pythagoras-122 author: Webb, Lyn; Webb, Paul title: Eastern Cape teachers’ beliefs of the nature of mathematics: Implications for the introduction of in-service mathematical literacy programmes for teachers date: 2004-10-20 words: 4537 flesch: 35 summary: This investigation was an attempt to explore the views of Eastern Cape teachers concerning the nature of mathematics and to ascertain whether there was any correlation between their espoused views of learning and how they teach mathematics in their classrooms. Webb Pythagoras 60, December, 2004, pp. 13-19 13 Eastern Cape teachers’ beliefs of the nature of mathematics: implications for the introduction of in-service mathematical literacy programmes for teachers Lyn Webb and Paul Webb Department of Science, Mathematics and Technology Education, University of Port Elizabeth Email: lyn.webb@upe.ac.za; paul.webb@upe.ac.za Various studies have shown that what teachers consider to be optimal ways of teaching mathematics is influenced by their beliefs about the nature of mathematics, and that it is advantageous to determine teachers’ conceptions of the nature of mathematics before developing curriculum interventions. keywords: beliefs; education; learning; mathematics; nature; practice; teachers; teaching cache: pythagoras-122.pdf plain text: pythagoras-122.txt item: #22 of 258 id: pythagoras-123 author: Watson, Anne title: Chanting as mathematical enculturation date: 2004-10-20 words: 5882 flesch: 54 summary: The teachers’ utterances are intended to be expert, and the creation of learner responses is intended to involve learning of some kind. It is important to take time over this because many learners will have images of fractions as parts of pizzas rather than numbers of any size, and he intends eventually that they should be able to predict whether multiplying by a particular fraction will increase or decrease a quantity. keywords: chanting; example; learners; learning; mathematics; teacher; unison; use cache: pythagoras-123.pdf plain text: pythagoras-123.txt item: #23 of 258 id: pythagoras-124 author: Mwakapenda, Willy title: Understanding student understanding in mathematics date: 2004-10-20 words: 4972 flesch: 52 summary: Data analysis In many concept mapping studies, the analysis of concept maps is predominantly quantitative and proceeds by scoring various aspects of student Figure 1: Angie’s concept map Figure 1: Angie’s concept map Willy Mwakapenda 31 maps such as the presence and accuracy of hierarchy levels, propositions, links and cross- links, and specific examples provided to illustrate links (Ruiz-Primo & Shavelson, 1996). An analysis of one student’s concept map Detailed analyses and findings related to students’ concept maps from the broad study have been presented elsewhere (see Mwakapenda, 2004; Mwakapenda & Adler, 2003). keywords: angie; concepts; education; knowledge; mapping; mathematics; students; understanding cache: pythagoras-124.pdf plain text: pythagoras-124.txt item: #24 of 258 id: pythagoras-125 author: Mudaly, Vimolan title: Modelling of real-world problems is often the starting point for proof date: 2004-10-20 words: 4913 flesch: 57 summary: Real world Mathematical system Real-world conclusions Mathematical conclusions abstraction experiments logical argument interpretation Figure 1. Although it may be difficult to replicate real- world conditions in a mathematics classroom, it is essential to expose learners to different real-world scenarios so that they learn mathematics in contexts that are familiar to them. keywords: desigan; learners; mathematics; modelling; proof; teacher; world cache: pythagoras-125.pdf plain text: pythagoras-125.txt item: #25 of 258 id: pythagoras-126 author: Mewborn, Denise S.; Huberty, Patricia D. title: A site-based model for professional development in mathematics at the elementary school level date: 2004-10-20 words: 3984 flesch: 47 summary: Conclusion As a field of inquiry, mathematics education suffers from a lack of research on professional development and teacher learning. Students change, curricula change, and schools change; thus there is always a need to grow as teachers. keywords: classroom; development; learning; mathematics; model; school; students; teachers; teaching cache: pythagoras-126.pdf plain text: pythagoras-126.txt item: #26 of 258 id: pythagoras-127 author: Schäfer, Marc title: World view theory and the conceptualisation of space in mathematics education date: 2004-10-20 words: 6500 flesch: 44 summary: Mathematical space, physical space and psychological space: Downs and Stea (1973) cite Lewin (another Gestalt psychologist), who stressed the relationship of and distinctions among mathematical space, physical space and psychological life space. World view theory and the conceptualisation of space in mathematics education (an abridged version of this paper was presented at the SAARMSTE Conference, Cape Town in January 2004) Marc Schäfer Rhodes University email: M.Schafer@ru.ac.za Introduction The cornerstone of current education trends that recognise prior knowledge as fundamental to the learning process, is the notion that beliefs and experiences that learners bring to the classroom influence their learning experiences in the classroom (Cobern, Gibson and Underwood, 1999). keywords: capacity; cobern; conceptualisation; education; mathematics; research; space; study; view; world; world view cache: pythagoras-127.pdf plain text: pythagoras-127.txt item: #27 of 258 id: pythagoras-128 author: Sethole, Godfrey title: Meaningful contexts or dead mock reality: Which form will the everyday take? date: 2004-10-20 words: 5365 flesch: 55 summary: Others are fairly critical but sympathetic (for example, Volmink, 1993; Vithal, 1997; Nyabanyaba, 1999) Arguments against the inclusion of the everyday in school mathematics, or which suggests that such an action is insignificant in relation to the way learners engage with mathematics, have also been cited. Good teachers are those who are considered reputable and efficient by the school community (the principal, colleagues and students) as well as other mathematics teachers in the area. keywords: aids; bulelwa; context; everyday; kevin; learners; mathematics; school; teachers cache: pythagoras-128.pdf plain text: pythagoras-128.txt item: #28 of 258 id: pythagoras-129 author: Fraser, Claire; Murray, Hanlie; Hayward, Brenda; Erwin, Pat title: The development of the common fraction concept in Grade Three learners date: 2004-10-20 words: 7013 flesch: 48 summary: The following are typical examples: Jwara's response: a. Correct definition. 37 A dynamic approach to quadrilateral definitions The Van Hiele theory of learning geometry also provided a useful conceptual framework for interpreting and analysing the student teachers' levels of understanding (see Burger & Shaughnessy, 1986). keywords: definitions; level; mathematics; properties; quadrilateral; rhombus; sides; students; teachers; understanding cache: pythagoras-129.pdf plain text: pythagoras-129.txt item: #29 of 258 id: pythagoras-13 author: None title: pythagoras-13 date: None words: 5932 flesch: 49 summary: ‘”Item reliability” has no traditional equivalent and low values indicate a narrow range of item measures, or a small sample’ (Linacre, 2008, p. 393). Despite criticisms offered against questionnaires, Pring (2005, p. 39) argues for the value of survey research, particularly as it pertains to the interpretation of questionnaire items, stating that ‘The meanings which the respondents attribute to the questions are not something private and subjective, but the meanings which anyone conversant with the language would attribute to them’. keywords: analysis; education; instrument; items; literacy; mathematics; rasch; research; scale; teachers cache: pythagoras-13.htm plain text: pythagoras-13.txt item: #30 of 258 id: pythagoras-130 author: Govender, Rajendran; de Villiers, Michael title: A dynamic approach to quadrilateral definitions date: 2004-10-20 words: 7013 flesch: 48 summary: The following are typical examples: Jwara's response: a. Correct definition. 37 A dynamic approach to quadrilateral definitions The Van Hiele theory of learning geometry also provided a useful conceptual framework for interpreting and analysing the student teachers' levels of understanding (see Burger & Shaughnessy, 1986). keywords: definitions; level; mathematics; properties; quadrilateral; rhombus; sides; students; teachers; understanding cache: pythagoras-130.pdf plain text: pythagoras-130.txt item: #31 of 258 id: pythagoras-132 author: None title: pythagoras-132 date: None words: 9437 flesch: 54 summary: This study concentrates on practising mathematics teachers who were students in an in-service programme. In unknown percentage problems, students first transform a given value into an associated z-score using the standardisation process. keywords: conversions; distribution; mathematics; question; score; statistics; students; transformations; treatments; value cache: pythagoras-132.htm plain text: pythagoras-132.txt item: #32 of 258 id: pythagoras-133 author: None title: pythagoras-133 date: None words: 6290 flesch: 55 summary: This may also be why many advocate gifted mathematics students being placed in ability groupings. Gifted students of mathematics are often made to feel bad by their peers because they excel in mathematics and other academic disciplines come easy for them. keywords: bibliotherapy; children; gifted; literature; mathematics; peers; people; students; teachers; use; young cache: pythagoras-133.htm plain text: pythagoras-133.txt item: #33 of 258 id: pythagoras-134 author: None title: pythagoras-134 date: None words: 9106 flesch: 51 summary: It seems to be that Anne expected a one-to-one correspondence between the content in mathematics teacher education modules and her view of school mathematics content. According to her, school mathematics content is something that exists ad hoc and can be addressed in the final year of the BEd programme in terms of preparation. keywords: content; education; mathematics; mathematics teaching; modules; psts; school; school mathematics; teacher; teaching; views cache: pythagoras-134.htm plain text: pythagoras-134.txt item: #34 of 258 id: pythagoras-14 author: None title: pythagoras-14 date: None words: 9002 flesch: 45 summary: The state of student conceptions of proof in the class, as described in the aforementioned summary (where naïve empiricism predominated), had been anticipated in the lesson plan and was consistent with findings of prior research on the issue. Similarly, if the teacher did not understand the taxonomy of student conceptions of proof and how its different components compare in terms of mathematical sophistication (cf. knowledge about students’ conceptions of proof), she would have had difficulty evaluating her students’ thinking at different stages during the intervention. keywords: example; intervention; knowledge; mathematics; problem; proof; research; students; stylianides; teacher; teaching cache: pythagoras-14.htm plain text: pythagoras-14.txt item: #35 of 258 id: pythagoras-140 author: None title: pythagoras-140 date: None words: 6719 flesch: 48 summary: Mathematics teachers’ reflective practice within the context of adapted lesson study In This Original Research... Open Access • Abstract • Introduction • Problem statement • Conceptual theoretical framework    • Symbolic interaction theory    • Social reconstructionist theory    • Mathematics teachers’ reflective practice    • Lesson study       • Research on lesson study and mathematics teaching       • Lesson study in the South African context • Empirical investigation    • Research design       • Participants       • Procedure       • Data collection       • Data analysis       • Trustworthiness       • Ethical considerations • Findings    • Findings from the analyses of the lesson plans    • Findings of lesson study group reflection after observing lessons    • Findings of final group reflection on the influence of lesson study on teaching mathematics • Discussion    • Limitations of the study    • Further research • Conclusion • Acknowledgements    • Competing interests • References Abstract Top ↑ There seems to be paucity of research in South Africa on mathematics teachers’ reflective practice. Findings of lesson study group reflection after observing lessons keywords: education; group; learners; lesson; lesson study; mathematics; participants; practice; reflection; research; study; teachers; teaching cache: pythagoras-140.htm plain text: pythagoras-140.txt item: #36 of 258 id: pythagoras-147 author: Office, Editorial title: Acknowledgement to reviewers  date: 2011-12-14 words: 552 flesch: 45 summary: Andile Mji Anthony Essien Belinda Huntley Benadette Ainemani Caroline Long Clement Dlamini Craig Pournara Dirk Wessels Dorit Patkin Erna Lampen Faaiz Gierdien Gary Sharp Gerrit Stols Hamsa Venkat Helena Miranda Helena Wessels Hennie Boshoff Hugh Glover Humphrey Atebe Jacques du Plessis Janine Hechter Jenny Campbell Jill Adler Johan Meyer John Malone Kerryn Vollmer Lindiwe Tshabalala Luckson Kaino Lyn Webb Lynn Bowie Maggie Verster Marc North Marc Schäfer Margot Berger Mark Jacobs Mellony Graven Michael de Villiers Nelis Vermeulen Paula Ensor Percy Sepeng Piera Biccard Piet Human Retha Van Niekerk Sharon McAuliffe Sizwe Mabizela Stanley Adendorff Verena Nolan Vimolan Mudaly Willy Mwakapenda Zane Davis Zonia Jooste In an effort to facilitate the selection of appropriate peer reviewers for manuscripts for Pythagoras, we ask that you take a moment to update your electronic portfolio on www. pythagoras.org.za, allowing us better access to your areas of interest and expertise, in order to match reviewers with submitted manuscripts. Reviewers advise the Editor on the scholarly merits of the manuscript to help him evaluate the manuscript and to decide whether or not to publish it. keywords: manuscript; pythagoras; quality; reviewers cache: pythagoras-147.pdf plain text: pythagoras-147.txt item: #37 of 258 id: pythagoras-15 author: None title: pythagoras-15 date: None words: 5797 flesch: 51 summary: The study was conducted amongst pre-service mathematics teachers, specialising in literacy activities designed to foster mathematics language. This article deals with an intervention unit which focused on the positive effect of integrating poems, stories and fables (the literary genre) for improving mathematical language, fostering the teaching of mathematics language, increasing satisfaction with the process and strengthening the relationship between use of daily language and mathematics language. keywords: activities; language; literacy; mathematics; mathematics language; meaning; students; teachers; teaching; words cache: pythagoras-15.htm plain text: pythagoras-15.txt item: #38 of 258 id: pythagoras-158 author: None title: pythagoras-158 date: None words: 8779 flesch: 43 summary: Morrison (2008) reminds, whilst talking about her experience with student teachers, that students may consider some classroom acts as undemocratic if they mistake positive freedom for negative freedom; in our case, the student teachers did not accept the necessity of putting an end to a classroom dialogue, probably thinking that the dialogue should continue until all issues related to it were settled. The current research sheds light on the pedagogic and didactic democratic acts in the mathematics classroom, as perceived by student mathematics teachers. keywords: acts; classroom; dialogue; education; equality; freedom; learning; mathematics; mathematics classroom; participants; pedagogic; students; teachers; teaching cache: pythagoras-158.htm plain text: pythagoras-158.txt item: #39 of 258 id: pythagoras-16 author: Engelbrecht, Johann; Harding, Ansie; Phiri, Patrick title: Are OBE‐trained learners ready for university mathematics? date: 2010-09-28 words: 4829 flesch: 51 summary: The sample This study is firstly based on a questionnaire completed by a number of experienced lecturers involved with the 2009 intake of mathematics students. General performance in university mathematics In Figure 2 we compare the Grade 12 marks of the 2009 group of students with their performance in Semester Test 1 and Semester Test 2.   Figure 2: Student performance in Grade 12 and in Semester Tests 1 and 2 From Figure 2 it is clear that there was a strong shift to the left from the Grade 12 marks to marks in Semester Test 1. keywords: figure; grade; mathematics; performance; semester; students; test; university cache: pythagoras-16.pdf plain text: pythagoras-16.txt item: #40 of 258 id: pythagoras-162 author: None title: pythagoras-162 date: None words: 7683 flesch: 62 summary: A person might, simultaneously, envisage different foregrounds that might contradict one another. Students’ foregrounds: Hope, despair, uncertainty In This Original Research... Open Access • Abstract • Introduction • Foreground • Multiple and collective foregrounds • Foregrounds and meaning • Dreams in cages • keywords: classroom; education; foreground; learning; mathematics; nthabiseng; person; possibilities; school; skovsmose; students cache: pythagoras-162.htm plain text: pythagoras-162.txt item: #41 of 258 id: pythagoras-163 author: None title: pythagoras-163 date: None words: 6180 flesch: 51 summary: (2005) define four domains of mathematical knowledge for teaching: common content knowledge (mathematical knowledge of the school curriculum), specialised content knowledge (mathematical knowledge teachers make use of in teaching), knowledge of students and content (knowledge that combines knowledge of content and learners – in this domain, teachers need to be able to anticipate learner errors and common misconceptions, interpret learners’ incomplete thinking and predict what learners are likely to do with specific tasks and what they will find interesting or challenging), and knowledge of teaching and content (knowledge about instructional sequencing of particular content, and about salient examples for highlighting mathematical issues). Granting learners an authentic voice in the mathematics classroom for the benefit of both the teacher and the learner. keywords: education; knowledge; learners; learning; listening; mathematics; teacher; teaching; understanding cache: pythagoras-163.htm plain text: pythagoras-163.txt item: #42 of 258 id: pythagoras-164 author: None title: pythagoras-164 date: None words: 13065 flesch: 41 summary: The economic dimension of democracy    • The socio-cultural dimension of democracy • Links between mathematics education and democracy    • Link 1: Mathematics education as a provider of critical mathematical skills    • Link 2: Mathematics education as a source of values and attitudes    • Link 3: Mathematics education as a social gatekeeper • Strategies to foster a democratic competence in students    • Fostering critical mathematical skills    • Fostering democratic values and attitudes • Tensions and difficulties inherent in mathematical education for democracy    • Link 3: Mathematics education as a social gatekeeper The third link that we have identified relates to the fact that mathematics education can function as a kind of social filter. keywords: conference; democracy; education journal; international; journal; literature; mathematical; mathematics education; proceedings; research; review; skovsmose; society; students; teachers; valero; values cache: pythagoras-164.htm plain text: pythagoras-164.txt item: #43 of 258 id: pythagoras-165 author: None title: pythagoras-165 date: None words: 5661 flesch: 40 summary: Findings    • Analysis and discussion of data • Conclusion • Acknowledgements    • Competing interests    • Authors’ contribution • References Abstract Top ↑ This article reports on an exploration of teachers’ views on the meaning of mathematical representations in a democratic South Africa. Mathematical representations, as vehicles of communication, play a central role in such classrooms. keywords: classroom; education; learners; mathematical; representations; research; responses; teachers; use cache: pythagoras-165.htm plain text: pythagoras-165.txt item: #44 of 258 id: pythagoras-166 author: None title: pythagoras-166 date: None words: 7566 flesch: 53 summary: Admittedly these are few, hence the reviewer’s concern, but the literature (Brodie, 2010) confirms our findings that when learners produce unexpected contributions, teachers usually do not entertain such responses even though this is critical for learner empowerment in a democratic classroom. Towards empowering learners in a democratic mathematics classroom: To what extent are teachers’ listening orientations conducive to and respectful of learners’ thinking? In This Original Research... Open Access • Abstract • Introduction    • Theoretical underpinnings    • Contextualising the problem of disempowerment • Methodology    • Participants    • Procedure       • Protocol 1 – Evaluative event       • Protocol 2 – Relatability of learner contributions       • keywords: article; classroom; contributions; education; empowerment; event; knowledge; learner; listening; mathematics; teacher cache: pythagoras-166.htm plain text: pythagoras-166.txt item: #45 of 258 id: pythagoras-169 author: None title: pythagoras-169 date: None words: 8178 flesch: 48 summary: In summary, analysis of teacher responses shows that although only one teacher employed distributional reasoning in one of the tasks, varying levels of reasoning – from iconic, to additive, to proportional reasoning – were found across the different tasks. The study described in this article focused on variability reasoning in a repeated sampling context of a different population, namely of in-service teachers. keywords: data; development; education; mathematics; question; reasoning; research; sampling; shaughnessy; statistical; task; teachers; variability cache: pythagoras-169.htm plain text: pythagoras-169.txt item: #46 of 258 id: pythagoras-17 author: Miranda, Helena; Adler, Jill title: Re‐sourcing mathematics teaching through professional development date: 2010-09-28 words: 7152 flesch: 58 summary: This paper reports on a project that explored this pedagogical challenge with mathematics teachers in Namibia. But it 1 This teacher professional development project was part of a larger research study (Miranda, 2009a), which explored innovative means of professional development for mathematics teachers with a particular focus on how to help learners realise the need to make adequate interpretations of algebra. keywords: algebra; learners; mathematics; resources; teachers; tiles; use cache: pythagoras-17.pdf plain text: pythagoras-17.txt item: #47 of 258 id: pythagoras-171 author: None title: pythagoras-171 date: None words: 9012 flesch: 45 summary: The expansion of school mathematics education and its particular unfolding in countries such as Colombia cannot be separated from the history of Spanish colonisation (from the 16th to beginning of the 19th century) and the formation of an independent national state (from the 19th to mid–20th century) (Meyer, Ramirez & Soysal, 1992). On the grounds of our work as researchers, teacher educators and teachers engaging with a socio-political approach in mathematics education in Colombia, we propose to understand democracy in terms of the possibility of constructing a social subjectivity for the dignity of being. keywords: children; colombia; curriculum; democracy; learning; mathematics; mathematics curriculum; mathematics education; new; research; school; school mathematics; social; space; students; subjectivity cache: pythagoras-171.htm plain text: pythagoras-171.txt item: #48 of 258 id: pythagoras-172 author: None title: pythagoras-172 date: None words: 7162 flesch: 49 summary: Number patterns presented as a sequence of pictorial terms have the potential to open up meaningful spaces for classroom exploration and discussion. Number patterns presented in the form of a sequence of pictorial terms are thus far more than simply a visual representation of a given numeric pattern. keywords: context; figure; generalisation; mathematics; pattern; process; sequence; squares; term; terry; visualisation cache: pythagoras-172.htm plain text: pythagoras-172.txt item: #49 of 258 id: pythagoras-174 author: None title: pythagoras-174 date: None words: 8318 flesch: 51 summary: These findings will continue to inform the ongoing design of learner clubs in our work. This initial conception of the ZPD was more in line with it being interpreted as a ‘physical space’ that existed in the learners themselves prior to club learning activities that took place. keywords: activities; club; data; design; development; learners; learning; mathematics; pilot; research; theory; zone; zpd cache: pythagoras-174.htm plain text: pythagoras-174.txt item: #50 of 258 id: pythagoras-178 author: None title: pythagoras-178 date: None words: 8300 flesch: 51 summary: Producing narratives       • Ethical considerations • Mathematics teachers’ narratives    • Sindiswe    • Aziz    • Nisha • Discussion    • Mathematics teachers’ experiences       • Foregrounds and experiences of learning mathematics       • Mathematics and development       • Images of mathematics teachers • Mathematics, foregrounds and development • Acknowledgements    • Competing interests • References • Footnotes Abstract Top ↑ Memory work (King, 2000; Onyx & Small, 2001) presented the means to do so as the inquiry required going back in time to recall how participants viewed the future and its relevance to their present status as mathematics teachers. keywords: aziz; development; education; experiences; foregrounds; future; learning; mathematics; narratives; nisha; school; sindiswe; teachers; teaching cache: pythagoras-178.htm plain text: pythagoras-178.txt item: #51 of 258 id: pythagoras-179 author: None title: pythagoras-179 date: None words: 8492 flesch: 46 summary: 0.05).It was found that Mathematics learners (average = 5.1949) are more likely than Mathematical Literacy learners (average = 4.8973) to like following instructions, to do whatever they are told to do and to prefer fixed structures (executive thinking style). Mathematics learners (average = 5.3095) are also more likely than Mathematical Literacy learners (average = 5.0713) to design and do things in their own ways (legislative thinking style). keywords: grade; learners; literacy; literacy learners; mathematics; mathematics learners; sternberg; styles; subject; teachers; thinking; thinking styles cache: pythagoras-179.htm plain text: pythagoras-179.txt item: #52 of 258 id: pythagoras-18 author: Linneweber‐Lammerskitten, Helmut; Schäfer, Marc; Samson, Duncan title: Visual technology for the autonomous learning of mathematics date: 2010-09-28 words: 4796 flesch: 45 summary: The project seeks to capitalise on the versatility and ubiquity of cellphone technology to provide a mathematics platform to store and disseminate short mathematical video clips that can be used both as teaching and motivational resources. The use of both videos and video clips as a medium of learning and teaching is nothing new to the mathematics classroom. keywords: clips; education; learners; learning; mathematics; mobile; south; technology; use; video cache: pythagoras-18.pdf plain text: pythagoras-18.txt item: #53 of 258 id: pythagoras-182 author: None title: pythagoras-182 date: None words: 6244 flesch: 50 summary: Hencke et al. (2009) concede upfront that whilst TIMSS assessments were developed to represent an agreed-upon framework with as much in common across countries as possible, it was inevitable that the match between test and curriculum would not be identical in all countries. Reliability was assured by the independent coding of the experts who were given copies of the relevant pages for the classification of TIMSS assessment objectives as they appear in Mullis et al. keywords: alignment; assessment; content; curriculum; grade; mathematics; objectives; porter; rncs; standards; timss; timss assessment cache: pythagoras-182.htm plain text: pythagoras-182.txt item: #54 of 258 id: pythagoras-186 author: None title: pythagoras-186 date: None words: 7518 flesch: 51 summary: In contrast with medical students, nursing students have historically received dosage calculation skills training. In an effort to improve student dosage competence further we aimed to enrich the interaction between learners and experts (whether teachers or more capable students) in our interventions. keywords: calculation; competence; dosage; drug; education; group; learning; level; skills; students; teacher; teaching; tuition; year cache: pythagoras-186.htm plain text: pythagoras-186.txt item: #55 of 258 id: pythagoras-188 author: None title: pythagoras-188 date: None words: 6930 flesch: 47 summary: Coherence and connections in teachers’ mathematical discourses in instruction In This Original Research... Open Access • Abstract • Introduction    • Describing transformation activity – a literature review    • Concepts and framing questions    • Episodes       • Episode 1       • Episode 2       • Episode 3       • Episode 4 • Discussion • Conclusions • Acknowledgements    • Competing interests    • Authors’ contributions • References • Footnote Abstract Top ↑ The literature-based concepts that we use are drawn from writing focused on transformation activity as a fundamental feature of mathematical activity. keywords: activity; coherence; education; episode; input; mathematics; problem; representation; teacher; teaching; transformation cache: pythagoras-188.htm plain text: pythagoras-188.txt item: #56 of 258 id: pythagoras-189 author: None title: pythagoras-189 date: None words: 5997 flesch: 42 summary: A critical relationship with democracy for mathematics education may involve directing and redirecting its purposes. But, we ask, what if the ‘choice’ to not participate in experiences of mathematics education, or in its (re)direction, were itself also a critical relationship with mathematics education? keywords: democracy; development; education; gus; mathematics; mathematics education; people; refusal; social; south; swanson cache: pythagoras-189.htm plain text: pythagoras-189.txt item: #57 of 258 id: pythagoras-19 author: None title: pythagoras-19 date: None words: 13788 flesch: 46 summary: Systemic provision of a large variety of test items and their diagnostic support material, together with informed and deliberative selection by committed teachers for classroom use, with facilities for electronic data capture and/or marking, are important strategies. All other methods (whether based on so-called traditional test theory or on so-called 2-parameter and 3-parameter structures for item responses) simply assume the summation is valid, even if there is demonstrable evidence that test items scores do not behave additively. keywords: ability; analysis; assessment; classroom; data; difficulty; instrument; items; learners; learning; level; measurement; model; person; proficiency; rasch; systemic; teaching; test; test instrument cache: pythagoras-19.htm plain text: pythagoras-19.txt item: #58 of 258 id: pythagoras-193 author: None title: pythagoras-193 date: None words: 6964 flesch: 53 summary: Geometric proof    • An alternative ‘algebraic’ proof    • Evolving geometric proofs in the seventeenth century: From icons to symbols. keywords: discovery; education; function; mathematics; problem; proof; result; students; villiers cache: pythagoras-193.htm plain text: pythagoras-193.txt item: #59 of 258 id: pythagoras-195 author: None title: pythagoras-195 date: None words: 8866 flesch: 55 summary: We propose that even if standards are sequenced and well explicated by examples, they do not disclose to teachers what instructional practice should look like or what constitutes acceptable coverage and cognitive demand of curriculum content. • Round 2 was a slightly abridged version of the curriculum mapping, due to time constraints, in which the teachers only mapped curriculum content and did not report on when and how they taught this content. keywords: assessment; content; curriculum; curriculum mapping; data; education; grade; groups; items; knowledge; mapping; round; teachers; test cache: pythagoras-195.htm plain text: pythagoras-195.txt item: #60 of 258 id: pythagoras-197 author: None title: pythagoras-197 date: None words: 7438 flesch: 55 summary: Examining mathematical discourse to understand in-service teachers’ mathematical activities. Examining mathematical discourse to understand in-service teachers’ mathematical activities In This Original Research... Open Access • Abstract • Introduction • Research goal • Background    • The structure of the course • Commognitive framework    • Overview    • Elements of mathematical discourse       • Words       • Visual mediators       • Narratives       • Routines • Vignette and its background       • Task       • Pedagogical purpose of task    • Description and analysis       • Saming the unsame and endorsing the meta-rule of hand sketching       • Representing an undefined point       • Endorsing the meta-rule of hand sketching       • keywords: asymptote; discourse; eva; geogebra; mathematics; students; tom; use cache: pythagoras-197.htm plain text: pythagoras-197.txt item: #61 of 258 id: pythagoras-2 author: Pillay, Shunmugam; Pillay, Poobhalan title: Equipartitioning and balancing points of polygons date: 2010-07-04 words: 3738 flesch: 60 summary: The uniqueness of the equipartitioning point also can be used to argue that for any triangle all three medians go through the same point, namely, it’s equipartitioning point. The kite Use appropriate software again to determine whether kites have equipartitioning points. keywords: abcd; bisects; equipartitioning; figure; mass; point cache: pythagoras-2.pdf plain text: pythagoras-2.txt item: #62 of 258 id: pythagoras-20 author: None title: pythagoras-20 date: None words: 7853 flesch: 54 summary: A modelling approach therefore allows one to detect learner beliefs in an authentic learning environment. Through a design research approach, 12 learners working in groups solved three modelling problems, and transcriptions of learner interactions, questionnaires and informal interviews revealed that learner beliefs improved over this short period when exposed to modelling tasks. keywords: beliefs; competencies; learners; learning; lesh; mathematics; modelling; problem; research; study; tasks; teaching cache: pythagoras-20.htm plain text: pythagoras-20.txt item: #63 of 258 id: pythagoras-200 author: None title: pythagoras-200 date: None words: 13209 flesch: 41 summary: Firstly, the question of whether mathematics education can be a preparation for democracy and include a concern for development, is discussed by drawing on conceptual tools of critical mathematics education and allied areas in a development context. Mathematics education, democracy and development: keywords: africa; conflict; curriculum; democracy; development; dialogue; knowledge; learners; mathematics; mathematics education; new; pedagogy; question; school; social; society; south; teachers; truth cache: pythagoras-200.htm plain text: pythagoras-200.txt item: #64 of 258 id: pythagoras-207 author: None title: pythagoras-207 date: None words: 2256 flesch: 35 summary: Poverty and its related issues (e.g. youth unemployment), which have many implicit and explicit connections to mathematics education, do not seem to feature strongly in mainstream mathematics education research, literature, conferences and in theorising mathematics teaching and learning, even though they have major policy implications. Mathematics education, democracy and development: A view of the landscape. keywords: democracy; development; education; mathematics; skovsmose; world cache: pythagoras-207.htm plain text: pythagoras-207.txt item: #65 of 258 id: pythagoras-209 author: Office, Editorial title: Acknowledgement to reviewers date: 2012-12-21 words: 816 flesch: 39 summary: In an effort to facilitate the selection of appropriate peer reviewers for manuscripts for Pythagoras, we ask that you take a moment to update your electronic portfolio on www. pythagoras.org.za, allowing us better access to your areas of interest and expertise, in order to match reviewers with submitted manuscripts. Reviewers advise the Editor on the scholarly merits of the manuscript to help him evaluate the manuscript and to decide whether or not to publish it. keywords: acknowledgement; changes; editor; manuscript; pythagoras; reviewers; reviewing cache: pythagoras-209.pdf plain text: pythagoras-209.txt item: #66 of 258 id: pythagoras-212 author: None title: pythagoras-212 date: None words: 6263 flesch: 53 summary: In such cases, learners stick to the prototype example which entails applying non-critical attributes to the rest of concept examples. The Van Hiele theory       • Critical attributes and non-critical attributes       • Examples and non-examples       • Prototype and non-prototype       • Typical position and non-typical position • Methodology    • Research objectives    • Research population    • Research tools       • keywords: attributes; children; cylinder; examples; non; position; pyramid; solid cache: pythagoras-212.htm plain text: pythagoras-212.txt item: #67 of 258 id: pythagoras-216 author: None title: pythagoras-216 date: None words: 7060 flesch: 47 summary: For example, it should be possible to develop isiZulu technical and theoretical terminology that is acceptable, appropriate and correct for use in numeracy education teaching and learning. ‘They say we are crèche teachers’: Experiences of pre-service mathematics teachers taught through the medium of isiZulu. keywords: education; english; isizulu; language; mathematics; medium; module; mother; numeracy; teachers; teaching; tongue cache: pythagoras-216.htm plain text: pythagoras-216.txt item: #68 of 258 id: pythagoras-22 author: None title: pythagoras-22 date: None words: 7117 flesch: 50 summary: The researchers built on the models of Barmby et al. and of Businskas so that their coding of teacher representations: • level 0 (DR0) denotes a representation of a mathematical connection in the DR category that was faulty or incorrect • level 1 (DR1) denotes a representation of a mathematical connection in the DR category that was mathematically correct but superficial or routinely algorithmic, with no further explanation or justification • level 2 (DR2) denotes a representation of a mathematical connection in the DR category that was more than just mathematically correct; justification and/or further explanation follow. The researchers felt that conceptualising mathematical representations, as Barmby et al. suggested, left an important gap because, whilst it captured weak and strong mathematical reasoning, it did not seem to capture faulty connections or reasoning. keywords: article; connections; excerpt; learners; mathematics; quality; representations; researchers; teacher; term; understanding cache: pythagoras-22.htm plain text: pythagoras-22.txt item: #69 of 258 id: pythagoras-220 author: None title: pythagoras-220 date: None words: 5627 flesch: 49 summary: In some cases item difficulties are presented – item refers to the subsection of each examination question. Very little attention is paid to other diagnostic statistics, such as the discrimination indices and item difficulties taking into consideration partial scores examinees achieve on items. keywords: analysis; difficulty; examination; examinees; item; learners; mathematics; number; patterns; rasch; terms cache: pythagoras-220.htm plain text: pythagoras-220.txt item: #70 of 258 id: pythagoras-232 author: None title: pythagoras-232 date: None words: 6472 flesch: 45 summary: The purpose of the current investigation was to investigate the level of Technological Pedagogical Content Knowledge (TPACK) of mathematics teachers, and how TPACK attributes contribute towards more effective Grade 8 mathematics teaching in South African schools, using the TPACK conceptual framework. The results indicate that the TPACK of mathematics teachers contributes towards more effective Grade 8 mathematics teaching in South African schools. keywords: content; education; ict; knowledge; learning; mathematics; sites; south; teachers; teaching; tpack; use cache: pythagoras-232.htm plain text: pythagoras-232.txt item: #71 of 258 id: pythagoras-233 author: None title: pythagoras-233 date: None words: 7351 flesch: 59 summary: With regard to teacher education, both literature and empirical evidence suggest that teacher educators have a legal, professional, moral and civic obligation to provide their student teachers with models of teaching that work in their contexts. From that perspective, it can be argued that this article could be of benefit to teacher education in that it explores a model of teaching mathematics that has been tried and tested elsewhere and locally and which might be considered for further trials with student teachers. keywords: difference; discernment; learners; learning; rule; teacher; unit; variation cache: pythagoras-233.htm plain text: pythagoras-233.txt item: #72 of 258 id: pythagoras-234 author: None title: pythagoras-234 date: None words: 7016 flesch: 49 summary: The development and application of a framework for the detailed analysis of student understanding of proportional comparison has enabled a systematic description of the range of student experiences in the process of gaining a full understanding of the concept. Preliminary observations From a preliminary examination of student responses it was clear that most students had not reasoned about percentage change in the way we had expected. keywords: change; concepts; data; framework; literacy; percentage; question; reasoning; responses; students; threshold; understanding cache: pythagoras-234.htm plain text: pythagoras-234.txt item: #73 of 258 id: pythagoras-235 author: None title: pythagoras-235 date: None words: 8671 flesch: 55 summary: Rasch (1960/1980) extended the model for dichotomously scored items to include a model for test items with more than two response categories, with possible scores of 0, 1, 2, … m4. FIGURE 16: Person item threshold distribution post-rescoring. keywords: figure; fit; item; learners; location; model; person; rasch; rescoring; score; test cache: pythagoras-235.htm plain text: pythagoras-235.txt item: #74 of 258 id: pythagoras-237 author: None title: pythagoras-237 date: None words: 7322 flesch: 47 summary: The effectiveness of a teacher professional learning programme: The perceptions and performance of mathematics teachers. The effectiveness of a teacher professional learning programme: The perceptions and performance of mathematics teachers In This Original Research... Open Access • Abstract • Introduction • Conceptual framing of RME as a TPL approach    • Rationale for using a learning theory as a framework for the design of TPL    • Criticisms of the RME approach    • Principles of an RME pedagogy       • Activity principle       • Reality principle       • Level principle       • Intertwinement principle       • Interactivity principle       • Guidance principle • Research methodology    • Research approach    • keywords: approach; development; education; learning; level; mathematics; participants; principle; rme; students; study; tasks; teachers; teaching cache: pythagoras-237.htm plain text: pythagoras-237.txt item: #75 of 258 id: pythagoras-238 author: None title: pythagoras-238 date: None words: 8712 flesch: 53 summary: Related to these practices I suggest three tasks that foreground the key ideas of compound interest whilst simultaneously exemplifying key mathematical ideas: • Strategic choices for interest rates that do and do not lead to a recurring decimal value in relation to the compounding period. In Grade 11 the notions of nominal and effective interest rates are introduced, together with problems involving changes in interest rates and depreciation. keywords: compound; compound interest; compounding; formula; growth; interest; knowledge; mathematics; period; rate; teachers; teaching cache: pythagoras-238.htm plain text: pythagoras-238.txt item: #76 of 258 id: pythagoras-24 author: None title: pythagoras-24 date: None words: 5957 flesch: 49 summary: The blended learning DVD approach used in the 2007 ISP    • Instructional design of the DVDs    • Production of the DVDs    • The Saturday programme • Research design    • Research method       • Participants       • Action research       • Validity and reliability       • Ethical considerations • Results and discussion    • Themes which arose from the data       • New experience       • DVD as a resource       • The blended learning environment    • Facilitators’ observations    • Improvement in marks    • Case study • Conclusion • Acknowledgements    • The blended learning DVD approach used in the 2007 ISP A blended learning approach was adopted in these ISP deliveries. keywords: approach; dvd; dvds; grade; isp; learners; learning; mathematics; research; teaching; technology cache: pythagoras-24.htm plain text: pythagoras-24.txt item: #77 of 258 id: pythagoras-240 author: None title: None date: None words: 9084 flesch: 45 summary: Schoenfeld (2007) warns that the type of assessment items generally given in tests of larger scale may often work against the type of problem solving process, extended and thorough in nature, advocated by Polya (1957). For the assessment community a bank of items covering a range of question types was to provide a solution to the increasing demand for the construction of assessment items. keywords: assessment; bloom; classroom; component; curriculum; dimensions; items; knowledge; mathematics; problem; taxonomy; teachers; teaching; test; understanding cache: pythagoras-240.htm plain text: pythagoras-240.txt item: #78 of 258 id: pythagoras-244 author: None title: pythagoras-244 date: None words: 7577 flesch: 44 summary: Number sense The notion of number sense embodies the most important concepts, skills and attitudes that learners should acquire in primary school as a foundation for further studies in mathematics and the development of quantitative literacy. Number sense is complex and can best be described by the skills and understandings that a person with number sense demonstrates: a concrete sense of quantity, including multi-digit whole numbers, fractions and decimals and their different representations, an understanding of the relative magnitude of an amount, an ability to compare quantities using benchmark numbers such as 0, or 100, automatic recall of basic facts, procedures and strategies and the application of this knowledge to operations and to solve problems, flexibility in performing mental calculations and the ability to judge the reasonableness of an answer. keywords: education; knowledge; mathematics; number; number sense; psts; questionnaire; research; school; sense; teachers; understanding cache: pythagoras-244.htm plain text: pythagoras-244.txt item: #79 of 258 id: pythagoras-246 author: None title: pythagoras-246 date: None words: 7740 flesch: 56 summary: An improved understanding of varying levels of understanding of contextual rules will also help teachers and teacher educators understand ‘what makes the learning of specific topics easy or difficult’ (Shulman, 1986, p. 9), thereby contributing to the development of our (ML educators’) pedagogical content knowledge (PCK) of ML. Secondly contextual rules are bound to the context and need to be interpreted by the learner. keywords: income; income tax; rule; study; task; tax; teachers; understanding; use cache: pythagoras-246.htm plain text: pythagoras-246.txt item: #80 of 258 id: pythagoras-25 author: None title: pythagoras-25 date: None words: 4858 flesch: 50 summary: All participating teachers signed a document acknowledging the fact that they were aware that their responses would be used for research purposes. TABLE 2: General scoring rubric for teacher responses. Figure 2 shows two examples of teacher responses for Item 1 and Item 2 that were scored as 1; these teachers demonstrated just a partial understanding of the concepts being tested. keywords: conceptualisations; gradient; item; knowledge; mathematics; responses; study; teachers cache: pythagoras-25.htm plain text: pythagoras-25.txt item: #81 of 258 id: pythagoras-250 author: None title: pythagoras-250 date: None words: 9547 flesch: 52 summary: In this article I elaborate four instances of mathematical knowledge for teaching annuities. I show how these involve mathematical knowledge, pedagogical knowledge and contextual knowledge of finance. keywords: annuities; annuity; formula; interest; knowledge; mathematics; payment; teachers; teaching; time; value cache: pythagoras-250.htm plain text: pythagoras-250.txt item: #82 of 258 id: pythagoras-252 author: None title: None date: None words: 7537 flesch: 66 summary: Learner responses to Question 2 (N = 30). The incorrect addition strategy was also observed in learner responses. keywords: eel; equation; incorrect; learner; people; question; ratio; strategy cache: pythagoras-252.htm plain text: pythagoras-252.txt item: #83 of 258 id: pythagoras-253 author: Office, Editorial title: Acknowledgement to reviewers date: 2014-01-16 words: 720 flesch: 41 summary: In an effort to facilitate the selection of appropriate peer reviewers for manuscripts for Pythagoras, we ask that you take a moment to update your electronic portfolio on www. http://pythagoras.org.za, allowing us better access to your areas of interest and expertise, in order to match reviewers with submitted manuscripts. Reviewers advise the Editor on the scholarly merits of the manuscript to help him evaluate the manuscript and to decide whether or not to publish it. keywords: changes; editor; pythagoras; reviewers cache: pythagoras-253.pdf plain text: pythagoras-253.txt item: #84 of 258 id: pythagoras-254 author: None title: pythagoras-254 date: None words: 7703 flesch: 47 summary: Learning about learner errors in professional learner communities. Toward a discursive framework for learner errors in mathematics. keywords: analysis; answer; criteria; criterion; education; error; explanations; knowledge; learners; mathematics; teachers; texts cache: pythagoras-254.htm plain text: pythagoras-254.txt item: #85 of 258 id: pythagoras-259 author: None title: None date: None words: 7536 flesch: 58 summary: Watson and Fitzallen (2010) posit that bar-like representations are of three major types (value bar graphs, distribution bar graphs and histograms), which are presented as historically developing from one into the other in that order. Furthermore, in the case of the distribution bar graphs, bars of approximately equal height indicate great variability, whereas for value bar graphs, the same visual display of approximately equal bar heights indicates little variability. keywords: axis; bar; bar graph; data; figure; graph; learners; number; value cache: pythagoras-259.htm plain text: pythagoras-259.txt item: #86 of 258 id: pythagoras-260 author: None title: pythagoras-260 date: None words: 8071 flesch: 55 summary: The minimum value of 7.00 suggests that learners have a good understanding of the behaviour of trigonometric graphs with the aid of dynamic online technology. Learners were not given repeated chances to complete the worksheets: learners completed each worksheet only once. keywords: environment; graphs; learners; learning; mathematics; online; software; teacher; teaching; technology; tools; trigonometric; use cache: pythagoras-260.htm plain text: pythagoras-260.txt item: #87 of 258 id: pythagoras-261 author: None title: None date: None words: 7436 flesch: 57 summary: This study is focused on errors students made when solving coordinate geometry problems in the final Grade 12 examination in South Africa. The study used a content analysis technique in which each question was analysed according to the content it contained (students errors). keywords: errors; geometry; group; hiele; knowledge; level; mathematics; question; students; van; van hiele cache: pythagoras-261.htm plain text: pythagoras-261.txt item: #88 of 258 id: pythagoras-263 author: None title: pythagoras-263 date: None words: 7457 flesch: 53 summary: These include engaging in error analysis continuously in order to enrich knowledge of teaching, familiarisation with student errors and error analysis from the literature, as some errors in mathematics are shared across contexts, and making an effort to gain an understanding about learning theories, in particular the constructivist views as they are concerned with how knowledge is constructed by the learner. Teacher knowledge of error analysis in differential calculus. keywords: analysis; error analysis; errors; knowledge; mathematics; students; study; teachers; teaching cache: pythagoras-263.htm plain text: pythagoras-263.txt item: #89 of 258 id: pythagoras-273 author: None title: None date: None words: 7448 flesch: 51 summary: The relational nature of rational numbers In This Original Research... Open Access • Abstract • Introduction • Transitions from whole to rational number understanding • Rational numbers as relations Top ↑ Relational comparisons in the common introduction to rational numbers It is still common practice (Kilpatrick, Swafford & Swindell, 2001; Lamon, 2007) for children to be introduced to rational numbers by working with parts of wholes. keywords: children; learning; line; nature; number; number learning; research; teaching; unit cache: pythagoras-273.htm plain text: pythagoras-273.txt item: #90 of 258 id: pythagoras-275 author: None title: None date: None words: 4402 flesch: 56 summary: Certain beliefs with respect to mathematical problem-solving sometimes have negative influences on learners’ mathematical thinking, such as: mathematics problems have only one correct answer; there is only one correct way to solve a mathematics problem; only a few learners understand mathematics – other learners are supposed to memorise and apply what they have learnt without understanding; learners who have understood the mathematics they learnt will be able to solve any problem in five minutes or less (Schoenfeld, 1992). Problem solving, metacognition and sense making in mathematics. keywords: grade; group; learners; mathematics; model; problem; solving; teaching cache: pythagoras-275.htm plain text: pythagoras-275.txt item: #91 of 258 id: pythagoras-28 author: None title: pythagoras-28 date: None words: 4612 flesch: 46 summary: The issue of statistics training of pre-service teachers is addressed by universities and teacher training centres, as they are starting to incorporate statistics education courses into their formal teacher training courses (Wessels, 2008). Opportunities and challenges for statistics education in South Africa. keywords: africa; curriculum; education; international; level; mathematics; school; south; statistics; teachers; year cache: pythagoras-28.htm plain text: pythagoras-28.txt item: #92 of 258 id: pythagoras-281 author: None title: None date: None words: 9403 flesch: 49 summary: I use the term arithmetic mean to refer to the mathematical structure of the mean algorithm and the use of the mean in other than statistical contexts. Multiplicative conceptions of arithmetic mean. keywords: algorithm; average; discourse; everyday; mean; meaning; middle; research; statistics; students; teachers; value cache: pythagoras-281.htm plain text: pythagoras-281.txt item: #93 of 258 id: pythagoras-285 author: None title: None date: None words: 8808 flesch: 26 summary: Since it is only in the esoteric domain of mathematical practice that learners are exposed to the generative, regulative and evaluative principles that define and structure legitimate knowledge and participation in the discipline of mathematics, successful apprenticeship in school mathematics is only possible if participants engage in and with esoteric domain practices (Dowling, 1998, p. 140). However, herein lies a contradiction: even though apprenticeship in esoteric domain mathematics practices is entirely absent, the fact that all of the examination questions are able to be categorised in the domains of mathematical practice schema signifies that legitimate participation and practice in the examinations are regulated by mathematical structures and principles. keywords: domain; domain practices; dowling; esoteric; examinations; literacy; mathematical; participation; practices; principles; subject cache: pythagoras-285.htm plain text: pythagoras-285.txt item: #94 of 258 id: pythagoras-288 author: None title: None date: None words: 8620 flesch: 52 summary: Using grounded theory as a qualitative research strategy, we analysed student responses and written reflections according to the sequence of their experiential realities: practical and textual experiences. Some students created the actual space in which seating would take place and exchanged seats, while other students recorded or counted the number of possible seating permutations. keywords: arrangements; concept; explanation; factorial; learning; mathematics; people; problem; students; thinking; understanding; ways cache: pythagoras-288.htm plain text: pythagoras-288.txt item: #95 of 258 id: pythagoras-292 author: None title: pythagoras-292 date: None words: 7363 flesch: 47 summary: Less than 10% of all candidates in the cohort analysed attained the Proficient benchmark level in MAT tests (i.e. obtained scores of 62% or more using the 2009 benchmarks, which were in place for test candidates in 2012). Specifically, we focus on identification of mathematical errors made by those who have performed in the upper third of the cohort of test candidates. keywords: assessment; candidates; education; errors; information; learners; learning; mathematics; national; results; school; teachers; tests cache: pythagoras-292.htm plain text: pythagoras-292.txt item: #96 of 258 id: pythagoras-293 author: None title: None date: None words: 7374 flesch: 59 summary: A teacher's engagement with learner errors in her Grade 9 mathematics classroom. A teacher's engagement with learner errors in her Grade 9 mathematics classroom In This Original Research... Open Access • Abstract • Introduction • Slips, errors and misconceptions • How teachers deal with misconceptions • Research design and methodology • keywords: errors; knowledge; learners; lessons; mathematics; misconceptions; table; teacher cache: pythagoras-293.htm plain text: pythagoras-293.txt item: #97 of 258 id: pythagoras-294 author: None title: None date: None words: 6742 flesch: 46 summary: Student mathematical activity as a springboard to developing teacher didactisation practices. Student mathematical activity as a springboard to developing teacher didactisation practices In This Original Research... Open Access • Abstract • Introduction • Didactisation and mathematical work of teaching framework • Active students as a theoretical construct in teaching • keywords: activity; classrooms; development; didactisation; learning; mathematics; practices; students; teachers; teaching cache: pythagoras-294.htm plain text: pythagoras-294.txt item: #98 of 258 id: pythagoras-297 author: None title: None date: None words: 6825 flesch: 44 summary: By combining the two approaches, the researchers could merge findings in order to develop new theory presented as guidelines for ICT PD of mathematics teachers (Sechrest & Sidana, 1995). The extracted factors had a reliability level higher than 0.8, which indicates the items in the questionnaire are significant to address the research problem and the questionnaire is valid for ICT PD. keywords: analysis; data; education; factor; ict; mathematics; questionnaire; research; researchers; school; stage; teachers cache: pythagoras-297.htm plain text: pythagoras-297.txt item: #99 of 258 id: pythagoras-298 author: None title: None date: None words: 6535 flesch: 51 summary: Before expanding the intake range, however, it would be useful to know the success rate of TRP students in future courses. The aim of this case study is to show how a tutored reassessment programme (TRP or ‘boot camp’) can be implemented to improve student success in ‘gatekeeper’ service courses. keywords: courses; education; engineering; examination; learning; mathematics; pass; programme; students; success; trp; university cache: pythagoras-298.htm plain text: pythagoras-298.txt item: #100 of 258 id: pythagoras-3 author: Mwakapenda, Willy; Dhlamini, Joseph title: Integrating mathematics and other learning areas: Emerging tensions from a study Involving four classroom teachers date: 2010-07-04 words: 5194 flesch: 51 summary: Figure 5: The Science teacher’s use of mathematics Clearly mathematics concepts are seen to be useful for solving problems in science. She noted that they sometimes relied on other teachers as well as learners for assistance with integration. keywords: arts; concept; connections; curriculum; integration; learning; mathematics; science; teacher cache: pythagoras-3.pdf plain text: pythagoras-3.txt item: #101 of 258 id: pythagoras-304 author: None title: pythagoras-304 date: None words: 7791 flesch: 61 summary: If these are not used, learners would view the relationship between area and perimeter as the result of the application of the intuitive rule ‘Same A – Same B’ (Same perimeter – Same area; Same area – Same perimeter). This process produces the kind of learner who is independent, able to think, able to express ideas and to solve problems, representing a shift to a learner-centeredness, that is, learners as knowledge developers and users, rather than storage systems and performers. keywords: area; concepts; knowledge; learners; misconceptions; perimeter; square; understanding cache: pythagoras-304.htm plain text: pythagoras-304.txt item: #102 of 258 id: pythagoras-307 author: None title: pythagoras-307 date: None words: 6742 flesch: 54 summary: This article explores the conceptions that student teachers have about nominal and effective interest rates. To help understand how students think about mathematics processes and objects, the author of this article, who is a lecturer to these students, uses this methodology to inform good preparation for teaching of student teachers. keywords: conceptions; interest; learners; mathematics; nominal; object; participant; process; rates; students; teachers cache: pythagoras-307.htm plain text: pythagoras-307.txt item: #103 of 258 id: pythagoras-311 author: Office, Editorial title: Acknowledgement to reviewers date: 2015-07-31 words: 689 flesch: 44 summary: In an effort to facilitate the selection of appropriate peer reviewers for manuscripts for Pythagoras, we ask that you take a moment to update your electronic portfolio on www. http://pythagoras.org.za, allowing us better access to your areas of interest and expertise, in order to match reviewers with submitted manuscripts. Reviewers advise the Editor on the scholarly merits of the manuscript to help him evaluate the manuscript and to decide whether or not to publish it. keywords: changes; manuscripts; pythagoras; reviewers cache: pythagoras-311.pdf plain text: pythagoras-311.txt item: #104 of 258 id: pythagoras-314 author: None title: pythagoras-314 date: None words: 7000 flesch: 47 summary: Tasar reflected that a fall in inflation rate is an example of a decreasing rate of increase, that is, the prices are increasing by a smaller percentage, contrary to the misunderstanding that it indicates a fall in prices. Usually, inflation rate figures are reported on a monthly basis. keywords: calculation; change; equation; inflation; inflation rate; mathematics; percentage; rate; teachers; year cache: pythagoras-314.htm plain text: pythagoras-314.txt item: #105 of 258 id: pythagoras-317 author: None title: pythagoras-317 date: None words: 7364 flesch: 48 summary: Factors affecting the difficulty of proportional reasoning problems Tourniaire and Pulos (1985) and Lamon (2007) reviewed the numerous studies of factors that influence the difficulty of proportional reasoning problems. Two factors that we have seen to affect the difficulty of proportional reasoning problems are the context and structure of the question. keywords: candidates; context; education; literacy; performance; problems; question; reasoning; research; students; value cache: pythagoras-317.htm plain text: pythagoras-317.txt item: #106 of 258 id: pythagoras-322 author: None title: pythagoras-322 date: None words: 12073 flesch: 51 summary: Every square that is offered by a student is different from every other square offered by the student and by other students and so the series of phenomenally generated squares constitute a series of individuals. Such students used the lengths and angle measures to adjust their quadrilaterals so that the definition of a square was satisfied. keywords: construction; drawing; geometry; lecturer; markers; mathematics; pedagogic; series; square; students; terms cache: pythagoras-322.htm plain text: pythagoras-322.txt item: #107 of 258 id: pythagoras-33 author: Mogari, David; Kriek, Jeanne; Stols, Gerrit; Iheanachor, Ogbonnaya U. title: Lesotho's students' achievement in mathematics and their teachers' background and professional development date: 2009-09-01 words: 7422 flesch: 42 summary: For instance, some of the studies focused on teacher qualifications (e.g., Darling-Hammond, 2000; Rice, 2003; Wenglinsky, 2000), some others on teacher subject major (e.g., Wilson & Floden, 2003), some others on teacher teaching experience (e.g., Betts, Zau, & Rice, 2003), and some others on teacher professional development (e.g., Franke, 2002; Kennedy, 1998; Varella, 2000). For example, Wilson and Floden (2003) established that students of mathematics teachers with mathematics degrees as majors tend to demonstrate higher academic achievement in mathematics. keywords: achievement; background; development; experience; learning; mathematics; professional; relationship; students; subject; teachers; teaching; years cache: pythagoras-33.pdf plain text: pythagoras-33.txt item: #108 of 258 id: pythagoras-331 author: None title: pythagoras-331 date: None words: 8294 flesch: 55 summary: Teacher knowledge of error analysis Studies on teacher knowledge, in the field of mathematics education, agree that there is a professional knowledge of mathematics for teaching (Adler, 2011; Anderson & Clark, 2012; Ball et al., 2005; Bertram, 2011; Grossman, 1990; Rowland & Turner, 2008; Shalem, 2013; Shulman, 1986). Learning about learner errors in professional learner communities. keywords: analysis; content; errors; interviews; knowledge; learners; load; mathematics; teachers; teaching cache: pythagoras-331.htm plain text: pythagoras-331.txt item: #109 of 258 id: pythagoras-333 author: None title: pythagoras-333 date: None words: 8247 flesch: 54 summary: Along the top row are the number of missing items for each group. Investigation and treatment of missing item scores in test and questionnaire data. keywords: analysis; contestants; data; difficulty; item; mathematics; person; rasch; selection; table cache: pythagoras-333.htm plain text: pythagoras-333.txt item: #110 of 258 id: pythagoras-334 author: None title: pythagoras-334 date: None words: 9035 flesch: 65 summary: In South Africa, there has been a resurgence in the focus on learner errors and error analysis in mathematics in recent years (Brodie, 2014; Brodie & Berger, 2010; Herholdt & Sapire, 2014; Makonye & Luneta, 2014; Shalem, Sapire, & Sorto, 2014). It was found that more learners were achieving low marks, fewer were scoring very high marks and there was little change in the kinds of errors learners made (Hodgen, Brown, Coe & Küchemann, 2012). keywords: algebra; errors; grade; items; learners; letters; mathematics; performance; research; test cache: pythagoras-334.htm plain text: pythagoras-334.txt item: #111 of 258 id: pythagoras-335 author: None title: pythagoras-335 date: None words: 4585 flesch: 44 summary: School background Focusing on school background, the inclusion of an interaction term (Quintile 5 × Race Focusing on race and its mediated effect on graduation based on the type of mark recorded for Mathematics and English, the results given in Table 10 indicate for both subjects that Black African students significantly underperform when being compared with non-Black African students. keywords: english; mathematics; probability; school; students; table; university cache: pythagoras-335.htm plain text: pythagoras-335.txt item: #112 of 258 id: pythagoras-338 author: None title: pythagoras-338 date: None words: 6133 flesch: 51 summary: The use of ‘degree’ as the unit for measuring angles (the Babylonian astronomers’ unit, Emerson, 2005) and use of the unit ‘radian’, commonly used when graphing trigonometric functions, would remain a mystery to most mathematics learners. Mathematical understandings of a number of different big ideas are important ideas that students need to learn because they contribute to an understanding of the bigger picture of mathematics. keywords: education; learners; learning; mathematics; picture; questioning; tall; teacher; teaching; world cache: pythagoras-338.htm plain text: pythagoras-338.txt item: #113 of 258 id: pythagoras-342 author: None title: pythagoras-342 date: None words: 10192 flesch: 45 summary: Predicting teacher computer use: A path analysis. (2013) investigated the level of technological pedagogical content knowledge (TPACK) of mathematics teachers and how TPACK contributes towards more effective Grade 8 mathematics teaching in South African schools. keywords: beliefs; computers; education; ict; internet; learning; mathematics; schools; statistics; study; table; teachers; teaching; technology; use cache: pythagoras-342.htm plain text: pythagoras-342.txt item: #114 of 258 id: pythagoras-343 author: None title: pythagoras-343 date: None words: 7900 flesch: 52 summary: Training of mentor teachers in each school would be the most appropriate solution to the problem. Mentoring as professional development intervention for mathematics teachers: A South African perspective. keywords: classroom; development; education; learners; lesson; mathematics; mentor; mentoring; programme; south; teachers; teaching; time cache: pythagoras-343.htm plain text: pythagoras-343.txt item: #115 of 258 id: pythagoras-347 author: None title: pythagoras-347 date: None words: 8794 flesch: 46 summary: Language learners need feedback on their utterances. This brings us back to the third condition of mathematics learning, namely that language learners need feedback on their utterances (Van Eerde et al., 2008). keywords: acquisition; esl; input; interaction; language; learners; learning; mathematics; output; strategies; teachers; teaching cache: pythagoras-347.htm plain text: pythagoras-347.txt item: #116 of 258 id: pythagoras-350 author: None title: pythagoras-350 date: None words: 8251 flesch: 47 summary: The research results agree with previous studies which showed that CoRT creativity programme positively affected students’ performance in creativity (e.g. Al-Edwan, 2011; Park & Kwon, 2006). The research results indicated that 35% of the variance in mathematical creativity scores could be predicted by the studied variables. keywords: achievement; cort; cort programme; creativity; creativity scores; differences; group; programme; research; scores; students; thinking cache: pythagoras-350.htm plain text: pythagoras-350.txt item: #117 of 258 id: pythagoras-355 author: None title: pythagoras-355 date: None words: 9561 flesch: 46 summary: While the NSC largely determines whether school-leavers are ready to leave the school system, the NBTs are based on the assumption that prospective higher education students are ready to leave the school system with a higher education pass, and the tests attempt to determine to what extent these prospective students are ready for the demands of higher education. Since these are therefore prospective higher education students, for the sake of brevity we will from now on refer to them as ‘students’ (see Table 5 for some demographic characteristics of the sample). keywords: education; figure; literacy; mathematics; national; nbt; nsc; performance; ql scores; scores; students; test cache: pythagoras-355.htm plain text: pythagoras-355.txt item: #118 of 258 id: pythagoras-36 author: Gierdien, Faaiz title: Musings on multiplication tables and associated mathematics and teaching practices date: 2009-09-01 words: 9780 flesch: 54 summary: On modal multiplication tables teaching practice in schools The format or layout of multiplication tables in schools and the associated teaching practice impact on what mathematics students learn and in turn how they learn. The idea of the paper is therefore to throw multiplication tables into “fresh combinations” (Whitehead, 1929/1951) with other branches of the mathematics curriculum. keywords: figure; grade; mathematics; multiplication; multiplication tables; numbers; students; tables; tabular; teachers; teaching cache: pythagoras-36.pdf plain text: pythagoras-36.txt item: #119 of 258 id: pythagoras-363 author: None title: pythagoras-363 date: None words: 6896 flesch: 40 summary: In all the studies, teacher learning was attributed to participation and collaboration in teacher learning communities. The findings cited above highlight how teacher communities can support teacher professional learning in terms of understanding and addressing problems of practice, understanding learners’ thinking, developing new teaching practices, and deepening knowledge of mathematics and the curriculum. keywords: communities; community; errors; knowledge; learners; learning; mathematics; professional; teachers cache: pythagoras-363.htm plain text: pythagoras-363.txt item: #120 of 258 id: pythagoras-364 author: None title: pythagoras-364 date: None words: 8586 flesch: 50 summary: In response to these identified problems, we propose to design a professional development (PD) intervention to support mathematics teachers in teaching problem solving. Effective professional development for teachers Our objective for the main study is to design an effective PD intervention that can be used to support mathematics teachers in the teaching of mathematical problem solving. keywords: design; development; education; intervention; learners; learning; mathematics; pedagogy; problem; research; solving; teachers; teaching cache: pythagoras-364.htm plain text: pythagoras-364.txt item: #121 of 258 id: pythagoras-367 author: None title: pythagoras-367 date: None words: 9011 flesch: 54 summary: Teachers’ explanations of learners’ errors in standardised mathematics assessments. The management of quality assurance of school based assessment at national level in South Africa. keywords: assessment; education; grade; learners; mathematics; moderation; participants; quality; sba; school; south; study; tasks; teachers cache: pythagoras-367.htm plain text: pythagoras-367.txt item: #122 of 258 id: pythagoras-37 author: Long, Caroline title: From whole number to real number: Applying Rasch measurement to investigate threshold concepts date: 2009-09-01 words: 6582 flesch: 53 summary: The shift from the “conceptualization of the ratios of integers from relations between numbers to numbers [themselves]” is necessary for understanding the threshold concept rational number (Vamvakoussi & Vosniadou, 2007, p. 266, my emphasis). From whole number to real number Usiskin (2005) highlighted the critical mathematical developments that take place during the “transition years”, most notably the transition from whole number1 to real number. keywords: concepts; fraction; item; learners; mathematics; number; percent; rasch; ratio; understanding; | | cache: pythagoras-37.pdf plain text: pythagoras-37.txt item: #123 of 258 id: pythagoras-371 author: None title: pythagoras-371 date: None words: 7976 flesch: 56 summary: On the model for growth in mathematical understanding, this task is pitched at the level of formalising understanding in that it required learners to notice and work with the property of similar triangles that corresponding sides have equal ratios. We were guided by Pirie and Kieren’s (1994) dynamic theory for the growth of mathematical understanding and Martin’s (2008) elaboration of Pirie and Kieren’s process of folding back to track two groups of learners from one Grade 10 class. keywords: angles; folding; intervention; layer; learners; lebogang; lesiba; mathematics; reasoning; teacher; understanding cache: pythagoras-371.htm plain text: pythagoras-371.txt item: #124 of 258 id: pythagoras-373 author: None title: pythagoras-373 date: None words: 8174 flesch: 51 summary: As was observed with their own learning, the two participants value the generation of number pattern and relating that to layers and total number of cubes. Teachers’ learning and assessing of mathematical processes with emphasis on representations, reasoning and proof. keywords: cubes; layer; learning; mathematics; number; pattern; pyramid; reasoning; teachers cache: pythagoras-373.htm plain text: pythagoras-373.txt item: #125 of 258 id: pythagoras-376 author: None title: pythagoras-376 date: None words: 6159 flesch: 48 summary: The effect of Van Hiele theory-based teaching educational package on achievement goal orientation of student teachers. Entry level mathematics education students were informed of the purpose of the test and a request for voluntary participation was made. keywords: concepts; education; geometry; mathematics; matriculants; performance; students; study; teaching; terminology; understanding cache: pythagoras-376.htm plain text: pythagoras-376.txt item: #126 of 258 id: pythagoras-377 author: None title: pythagoras-377 date: None words: 7952 flesch: 50 summary: The Data Informed Practice Improvement Project of Brodie (2013) focused on teachers engaging with misconceptions and errors resulting from learners’ responses to examination items. This is followed up when quadratic functions of the form indicated for Grade 10 are taught and items related to quadratic inequalities are included in the year-end examination as indicated in Figure 2. FIGURE 2: Examination item on the quadratic function (the quadratic inequality item is 6.1.4). keywords: achievement; assessment; curriculum; education; end; examination; grade; learners; mathematics; project; research; school; stakes; teachers; teaching; year cache: pythagoras-377.htm plain text: pythagoras-377.txt item: #127 of 258 id: pythagoras-378 author: None title: pythagoras-378 date: None words: 8498 flesch: 46 summary: In order to compare textbook content on linear functions pitched at a similar level for purposes of this comparison, the English stream Grade 9 textbook, Classroom Mathematics Grade 9 (CM) was therefore paired with the German stream Grade 7 textbook, Elemente der Mathematik 3 (EDM). Ten categories were used to differentiate the purpose of textbook content: narrative, related narrative, unrelated instructional narrative, related graphic, unrelated graphic, exercise set, unrelated exercise set, activity, worked example, and other. keywords: analysis; content; functions; knowledge; linear; mathematics; representations; tasks; textbooks; understanding cache: pythagoras-378.htm plain text: pythagoras-378.txt item: #128 of 258 id: pythagoras-38 author: Venkat, Hamsa; Graven, Mellony; Lampen, Erna; Nalube, Patricia title: Critiquing the mathematical literacy assessment taxonomy: Where is the reasoning and the problem solving? date: 2009-09-01 words: 7688 flesch: 41 summary: The difficulty essentially, therefore, lies not in the choice of problem contexts, but in the design of the questions within them, which seem to be designed to mimic the taxonomy in their unfolding. This definition alongside the broader description of the new subject’s aims in this document places emphasis on the need to develop life-oriented competences for a range of everyday situations in which mathematical reasoning and mathematical tools can be brought to bear productively to aid informed decision making and problem solving. keywords: assessment; development; level; literacy; mathematical; paper; problem; procedures; questions; reasoning; solving; taxonomy cache: pythagoras-38.pdf plain text: pythagoras-38.txt item: #129 of 258 id: pythagoras-380 author: None title: None date: None words: 2882 flesch: 46 summary: Concluding remark I highly recommend this book for mathematics education researchers, teachers and teacher educators interested in increasing the impact of research on teaching and learning, particularly in contexts of social inequality and economic disadvantage, and to those with an ethical commitment to navigating emergent tensions such as the production of deficit narratives of teacher practices. While I agree that this book is relevant to these agents I found the book particularly useful for secondary teachers and teacher educators because it provides powerful illumination of how theory can and does inform practice in concrete ways – thus addressing the challenge of many pre-service and in-service teacher conceptions of theory being largely irrelevant to the day-to-day practice of teaching. keywords: book; mathematics; research; researchers; teachers cache: pythagoras-380.htm plain text: pythagoras-380.txt item: #130 of 258 id: pythagoras-381 author: Office, Editorial title: Acknowledgement to reviewers date: 2017-06-01 words: 745 flesch: 42 summary: In an effort to facilitate the selection of appropriate peer reviewers for manuscripts for Pythagoras, we ask that you take a moment to update your electronic portfolio on http:// www.pythagoras.org.za, allowing us better access to your areas of interest and expertise, in order to match reviewers with submitted manuscripts. Reviewers advise the Editor on the scholarly merits of the manuscript to help him evaluate the manuscript and to decide whether or not to publish it. keywords: changes; manuscripts; pythagoras; reviewers cache: pythagoras-381.pdf plain text: pythagoras-381.txt item: #131 of 258 id: pythagoras-384 author: Office, Editorial title: Acknowledgement to reviewers date: 2017-06-08 words: 752 flesch: 40 summary: In an effort to facilitate the selection of appropriate peer reviewers for manuscripts for Pythagoras, we ask that you take a moment to update your electronic portfolio on http:// www.pythagoras.org.za, allowing us better access to your areas of interest and expertise, in order to match reviewers with submitted manuscripts. It is good practice as a reviewer to update your personal details regularly to ensure contact with you throughout your professional term as reviewer to Pythagoras Please do not hesitate to contact me if you require assistance in performing this task. keywords: changes; editor; manuscript; pythagoras; reviewers cache: pythagoras-384.pdf plain text: pythagoras-384.txt item: #132 of 258 id: pythagoras-39 author: du Toit, Stephan; Kotze, Gary title: Metacognitive strategies in the teaching and learning of mathematics date: 2009-09-01 words: 6785 flesch: 51 summary: Metacognitive components of instructional research with problem learners. Teachers used metacognitive strategies to a greater extent than the learners, as the teachers’ metacognitive mean of 3,28 as compared to the learners’ metacognitive mean of 2,72 indicates. Conclusion and recommendations From our experience of teaching, many mathematics learners do not like mathematics because they regard it as too difficult, and they cannot see the relevance of mathematics for their everyday or future lives. keywords: education; learners; learning; mathematics; problem; solving; strategies; teachers; teaching; thinking; use cache: pythagoras-39.pdf plain text: pythagoras-39.txt item: #133 of 258 id: pythagoras-393 author: None title: pythagoras-393 date: None words: 10505 flesch: 47 summary: In practice, this implies that learner performance results reported with the intention of enhancing teaching and learning must, at a very minimum, provide information on what learners at a particular point know and can do and, at the same time, what they are potentially ready to learn (Vygotsky, 1962). Beyond test scores: A framework for reporting mathematics assessment results to enhance teaching and learning. keywords: assessment; data; framework; information; learners; learning; level; mathematics; performance; reporting; results; school; standards; teachers; use cache: pythagoras-393.htm plain text: pythagoras-393.txt item: #134 of 258 id: pythagoras-396 author: None title: pythagoras-396 date: None words: 8318 flesch: 44 summary: Mathematical imagination and embodied cognition. In mainstream mathematics, the holder of a rational view will need to reflect on the cognitive demands of the problem and the associated tenets of the imaginative capabilities to solve circle geometry problems that are non-routine and open-ended in nature. keywords: awareness; case; circle; cognition; ideas; imagination; learner; mathematics; participants; problem; solving; visualisation cache: pythagoras-396.htm plain text: pythagoras-396.txt item: #135 of 258 id: pythagoras-4 author: Berger, Margot; Bowie, Lynn; Nyaumwe, Lovemore J. title: Taxonomy matters: Cognitive levels and types of mathematical activities in mathematics examinations date: 2010-07-04 words: 6479 flesch: 47 summary: Different taxonomies Within mathematics, a number of different taxonomies have been developed for various purposes. Thus mathematical complexity level refers to an attribute of a task which measures the level of thinking required to complete the task. keywords: complexity; doe; examination; level; mathematics; porter; procedures; question; sagm; taxonomies; taxonomy cache: pythagoras-4.pdf plain text: pythagoras-4.txt item: #136 of 258 id: pythagoras-40 author: Brijlall, Deonarain; Maharaj, Aneshkumar title: Using an inductive approach for definition making: Monotonicity and boundedness of sequences date: 2009-09-01 words: 6393 flesch: 54 summary: Generalising the description of monotonically increasing infinite real sequences Now write out a statement which you would adopt to describe (define) an arbitrary infinite real sequence  1nnx : Bounded sequences The following extract from the worksheet, modeled on the construction of a concept at the inductive reasoning level (Cangelosi, 1996), indicates the task based on examples and non-examples which the students engaged with: Sorting The following are examples of infinite real sequences which are bounded below: 1.  This study focused on advanced mathematical thinking required for the concepts of monotonicity and boundedness of infinite real sequences. keywords: boundedness; concept; examples; following; group; mathematics; sequence; students cache: pythagoras-40.pdf plain text: pythagoras-40.txt item: #137 of 258 id: pythagoras-403 author: None title: pythagoras-403 date: None words: 8610 flesch: 50 summary: The question we address is: to what extent are high school mathematics learners able to see mathematics in non-mathematical reading texts? A sociological analysis of school mathematics texts. keywords: animal; domains; education; excerpts; farm; language; learners; learning; mathematics; reading; school; study; texts cache: pythagoras-403.htm plain text: pythagoras-403.txt item: #138 of 258 id: pythagoras-409 author: None title: pythagoras-409 date: None words: 5509 flesch: 43 summary: Professional development networks: From transmission to co-construction. Building on ideas of learning organisations (Senge, 1990), communities of practice (Lave & Wenger, 1991) and professional learning communities (Brodie, 2013, 2016; Chauraya & Brodie, 2018; Tam, 2015), the process of professional development (Loucks-Horsley, Love, Stiles, Mundry, & Hewson, 2003) is regarded as a cultural practice engaged in by participants of various communities, a collaborative praxis in which participants are involved in negotiating meaning and developing improved understandings in professional communities of learning. keywords: brodie; communities; concept; development; education; learning; networks; process; research; southwood; space cache: pythagoras-409.htm plain text: pythagoras-409.txt item: #139 of 258 id: pythagoras-41 author: Huntley, Belinda; Engelbrecht, Johann; Harding, Ansie title: Can multiple choice questions be successfully used as an assessment format in undergraduate mathematics? date: 2009-09-01 words: 6856 flesch: 47 summary: Since sub-question (1.3) requires the cognitive skills of identifying and applying the principle of Mathematical Induction to arrive at a solution, (1.3) assesses within the problem solving mathematics assessment component. Table 2: Mathematics assessment component taxonomy and cognitive level of difficulty Mathematics assessment components Cognitive level of difficulty 1. keywords: assessment; component; crqs; format; good; mathematics; mathematics assessment; prqs; quality; question; taxonomy cache: pythagoras-41.pdf plain text: pythagoras-41.txt item: #140 of 258 id: pythagoras-410 author: Office, Editorial title: Acknowledgement to reviewers date: 2017-12-21 words: 812 flesch: 38 summary: In an effort to facilitate the selection of appropriate peer reviewers for manuscripts for Pythagoras, we ask that you take a moment to update your electronic portfolio on http:// www.pythagoras.org.za, allowing us better access to your areas of interest and expertise, in order to match reviewers with submitted manuscripts. It is good practice as a reviewer to update your personal details regularly to ensure contact with you throughout your professional term as reviewer to Pythagoras Please do not hesitate to contact us if you require assistance in performing this task. keywords: changes; interest; manuscript; pythagoras; reviewers cache: pythagoras-410.pdf plain text: pythagoras-410.txt item: #141 of 258 id: pythagoras-42 author: Bansilal, Sarah title: The use of real life contexts in the CTA: Some unintended consequences date: 2009-09-01 words: 7714 flesch: 63 summary: In particular, I am concerned about the ways in which certain learners could be disadvantaged by some unintended consequences brought about by, the design of the tasks and/or assumptions about learners experiences. The second vignette was intended to draw our attention to the fact that certain learners tend to rely on their everyday experience when answering tasks set within real life contexts. keywords: assessment; contexts; cta; learners; life; mathematics; paper; tasks; teachers; use cache: pythagoras-42.pdf plain text: pythagoras-42.txt item: #142 of 258 id: pythagoras-424 author: None title: pythagoras-424 date: None words: 7935 flesch: 51 summary: In mathematics classrooms, the context conditions discussed in this section are the type of problems learners solve, as well as the classroom environment. A context analysis will then answer the question: What features of mathematical modelling support learner choice and contribute to sense-making? keywords: analysis; choice; classrooms; education; learners; learning; making; mathematics; modelling; problem; sense; teacher; understanding cache: pythagoras-424.htm plain text: pythagoras-424.txt item: #143 of 258 id: pythagoras-43 author: Essien, Anthony A. title: An analysis of the introduction of the equal sign in three Grade 1 textbooks date: 2009-09-01 words: 4749 flesch: 60 summary: The learner is left to believe that equal sign means “makes” as in “one plus one makes two” used in the earlier introduction of the addition symbol. Middle school mathematics teachers’ knowledge of students’ understanding of core algebraic concepts: Equal sign and variable. keywords: addition; introduction; learners; mathematics; sign; teacher; textbooks cache: pythagoras-43.pdf plain text: pythagoras-43.txt item: #144 of 258 id: pythagoras-431 author: None title: pythagoras-431 date: None words: 10468 flesch: 43 summary: Technological pedagogical content knowledge: A framework for teacher knowledge. In addition, Leendertz, Blignaut, Nieuwoudt, Els, and Ellis (2013) found that mastery of TPACK by mathematics teachers contributed to more effective mathematics teaching in South African schools. keywords: content; cpd; development; icts; knowledge; learning; mathematics; mathematics teachers; programmes; teachers; teaching; technology; tpack; use cache: pythagoras-431.htm plain text: pythagoras-431.txt item: #145 of 258 id: pythagoras-438 author: None title: pythagoras-438 date: None words: 12260 flesch: 54 summary: Achieving our aim of presenting the empirical detail of the how, when and why of learner thinking about linear equations in this article requires an explanation of (1) the detail of the key inter-related concepts we use from Sfard, and (2) how we put these to work in a framework for analysing learner discourse specifically about linear equations. However, the article shows that learner discourse is a rich resource for teachers to understand the extent to which learners are thinking exploratively, and offers suggestions for how their thinking can be shifted. keywords: discourse; equations; grade; learners; linear; mathematics; narratives; realisation; sfard; thinking; use cache: pythagoras-438.htm plain text: pythagoras-438.txt item: #146 of 258 id: pythagoras-44 author: Mogari, David; Coetzee, Hanlie; Maritz, Riette title: Investigating the status of supplementary tuition in the teaching and learning of mathematics date: 2009-09-01 words: 5934 flesch: 48 summary: The last question, namely, “who takes supplementary tuition?” mainly determined the gender and ratio of mathematics learners to those who take mathematical literacy. In general, the proportion of mathematics learners who wanted supplementary tuition was significantly (t = 5,27, df = 288, p < 0,0005) More school time for mathematics/mathematical literacy 0% 10% 20% 30% 40% 50% 60% Mathematics Mathematical Literacy Total Yes No Unsure The status of supplementary tuition in mathematics 42 more than that of mathematics literacy. keywords: education; learners; literacy; mathematics; school; study; teachers; teaching; time; tuition cache: pythagoras-44.pdf plain text: pythagoras-44.txt item: #147 of 258 id: pythagoras-441 author: None title: pythagoras-441 date: None words: 6902 flesch: 50 summary: High residual correlations between items can be resolved by forming a subset, essentially a super-item, where the two items contribute to the score (Andrich & Kreiner, 2010). The test items showed good fit to the model; however, response dependency and high residual correlation within sets of items was detected. keywords: figure; fractions; instrument; item; knowledge; measurement; model; number; proficiency; rasch; students; test cache: pythagoras-441.htm plain text: pythagoras-441.txt item: #148 of 258 id: pythagoras-45 author: Nyaumwe, Lovemore J.; Mtetwa, David K. title: In-service mathematics teacher's effective reflective actions during enactment of social constructivist strategies in their teaching date: 2009-09-01 words: 6389 flesch: 43 summary: Effective reflections during teaching enhances in-service teachers to consciously think about pedagogical actions at the time they are being enacted, interpret learner actions, and appropriately shape successive teaching using multiple pedagogical approaches in order to promote learner understanding (Schon, 1987). Dewey (1933) noted that during reflection teachers examine their teaching performance by critically analyzing what, how and why they did what they did in their teaching with an ultimate goal of improving learner understanding. keywords: actions; knowledge; learners; learning; mathematics; reflection; service; service teachers; teachers; teaching cache: pythagoras-45.pdf plain text: pythagoras-45.txt item: #149 of 258 id: pythagoras-458 author: None title: pythagoras-458 date: None words: 12219 flesch: 52 summary: Comparison of geometric proof development tasks as set up in the textbook and as implemented by teachers in the classroom. Pythagoras, 40(1), a458. https://doi.org/10.4102/pythagoras.v40i1.458 Original Research Comparison of geometric proof development tasks as set up in the textbook and as implemented by teachers in the classroom Lisnet Mwadzaangati Received: 12 Oct. 2018; Accepted: 10 Nov. 2019; Published: 10 Dec. 2019 Copyright: keywords: circle; figure; learners; level; mathematics; proof; proof development; proof tasks; proving; set; tasks; teachers; textbook cache: pythagoras-458.htm plain text: pythagoras-458.txt item: #150 of 258 id: pythagoras-462 author: Office, Editorial title: Acknowledgement to Reviewers date: 2018-12-11 words: 674 flesch: 37 summary: In an effort to facilitate the selection of appropriate peer reviewers for Pythagoras, we ask that you take a moment to update your electronic portfolio on https://pythagoras. org.za for our files, allowing us better access to your areas of interest and expertise, in order to match reviewers with submitted manuscripts. Reviewers’ comments serve two purposes, guided by two inter-dependent objectives: • Pythagoras wishes to publish only original manuscripts of the highest possible quality, making a meaningful contribution to the field. keywords: changes; manuscript; pythagoras; reviewers cache: pythagoras-462.pdf plain text: pythagoras-462.txt item: #151 of 258 id: pythagoras-464 author: None title: pythagoras-464 date: None words: 186 flesch: 41 summary: In the author list of this article published earlier, Marthie van der Walt’s first name and ORCID were unintentionally misprinted as ‘Martha’ and ‘https://orcid.org/0000-0002-6057-8352’. About the Author(s) Divan Jagals School for Professional Studies in Education, Faculty of Education Sciences, North-West University, South Africa Marthie van der Walt School for Science and Technology Education, Faculty of Education Sciences, North-West University, South Africa Citation Jagals, D., & Van der Walt, M. (2019). keywords: education cache: pythagoras-464.htm plain text: pythagoras-464.txt item: #152 of 258 id: pythagoras-466 author: Office, Editorial title: Table of Contents Vol 39, No 1 (2018) date: 2018-12-24 words: 485 flesch: -41 summary: Olivier Stellenbosch University (retired), South Africa Associate Editors Anthony Essien University of the Witwatersrand, South Africa Faaiz Gierdien Stellenbosch University, South Africa Rajendran Govender University of the Western Cape, South Africa Dirk Wessels Stellenbosch University, South Africa Editorial Board Jill Adler University of the Witwatersrand, South Africa Bill Barton University of Auckland, New Zealand Marcelo Borba São Paulo State University, Brazil Doug Clarke Australian Catholic University, Australia Jeremy Kilpatrick University of Georgia, United States of America Gilah Leder La Trobe University, Australia Stephen Lerman Southbank University, United Kingdom Frederick Leung University of Hong Kong, SAR, China Liora Linchevski Hebrew University of Jerusalem, Israel John Malone Curtin University, Australia Andile Mji Tshwane University of Technology, South Africa Willy Mwakapenda Tshwane University of Technology, South Africa John Olive University of Georgia, United States of America David Reid University of Bremen, Germany Paola Valero Stockholm University, Sweden Renuka Vithal University of KwaZulu-Natal, South Africa Anne Watson Oxford University, United Kingdom Volume 39 Number 1 December 2018 ‘Islamic geometric patterns’. PYTH 39(1)_Table of contents.indd Open keywords: africa; learning; south africa; united; university cache: pythagoras-466.pdf plain text: pythagoras-466.txt item: #153 of 258 id: pythagoras-475 author: None title: pythagoras-475 date: None words: 8683 flesch: 49 summary: Most CPD initiatives have to contend with at least one of these two sites, in which university-based mathematics educators and school teachers can have different and at times overlapping ways of talking about the same mathematics. Continuous professional learning community of mathematics teachers in the Western Cape: Developing a professional learning community through a school-university partnership. keywords: algebraic; conversation; design; educator; mathematics; minus; problem; set; site; teachers; turn; university cache: pythagoras-475.htm plain text: pythagoras-475.txt item: #154 of 258 id: pythagoras-48 author: None title: pythagoras-48 date: None words: 1016 flesch: 55 summary: What I anticipated then was a do-it-yourself job where we would upload Pythagoras articles on our own do-it-yourself website (the so-called ‘green route’), becausethe increased costs of outsourcing the production of Pythagoras to a professional publishing house (the so called ‘golden route’) That means that when somebody searches for a key word, the probability that relevant Pythagoras articles are listed and accessed is now much higher. keywords: access; authors; pythagoras cache: pythagoras-48.htm plain text: pythagoras-48.txt item: #155 of 258 id: pythagoras-480 author: None title: pythagoras-480 date: None words: 8125 flesch: 52 summary: The use of semiotic representations in reasoning about similar triangles in Euclidean geometry. Pythagoras, 40(1), a480. https://doi.org/10.4102/pythagoras.v40i1.480 Original Research The use of semiotic representations in reasoning about similar triangles in Euclidean geometry Ifunanya Ubah, Sarah Bansilal Received: 27 Mar. 2019; Accepted: 08 Nov. 2019; Published: 13 Dec. 2019 Copyright: © 2019. keywords: celo; education; geometry; mathematics; question; representation; sabelo; similarity; students; study; triangles cache: pythagoras-480.htm plain text: pythagoras-480.txt item: #156 of 258 id: pythagoras-484 author: None title: pythagoras-484 date: None words: 9330 flesch: 53 summary: Students provided four categories of definitions of anti-derivatives that are personal concept definitions From the 117 students’ responses about the definition of anti-derivative, 111 yielded four categories: an anti-derivative is the integral of a function (67 students – 60% of students including interviewees S41, S59, S96 and S100); an anti-derivative is the integration of a function (34 students – 31% of students including interviewees S12, S42, S48 and S101); an anti-derivative is the function that undoes (change, reverse) the derivative (7 students – 6% of students including interviewees S25 and S52); an anti-derivative is the function that when derived gives the original function (3 students – 3% of students including interviewees S66 and S67). Students related a function to its anti-derivative with multiple interpretations The two questions that required students to explicitly relate a function to its anti-derivative are Question 2 and Question 7. keywords: anti; concept; derivative; differentiation; function; indefinite; integral; integration; students; study cache: pythagoras-484.htm plain text: pythagoras-484.txt item: #157 of 258 id: pythagoras-487 author: None title: pythagoras-487 date: None words: 11177 flesch: 50 summary: Teaching number: Advancing children’s skills and strategies (2nd ed.). As a result, the introduction of formal written methods ought to be delayed until use of written number symbols and spoken number names is secure. keywords: addition; break; caps; children; digit; framework; learning; mathematics; number; strategies; strategy; swa; teaching; tmu cache: pythagoras-487.htm plain text: pythagoras-487.txt item: #158 of 258 id: pythagoras-493 author: None title: pythagoras-493 date: None words: 9701 flesch: 46 summary: Develop a teacher competency assessment framework (related to mathematics), for Foundation and Intermediate Phase, for student teachers graduating from Initial Teacher Education (ITE) programmes. Teams of professionals from across South African universities are collaborating on assessing the mathematics knowledge of student teachers when they enter the Bachelor of Education (B.Ed.) programme in their first year, and again when they exit at fourth-year level. keywords: assessment; education; figure; knowledge; mathematics; performance; primted; reporting; scores; skills; standards; students; test; university; year cache: pythagoras-493.htm plain text: pythagoras-493.txt item: #159 of 258 id: pythagoras-5 author: Molefe, Nico; Brodie, Karin title: Teaching mathematics in the context of curriculum change date: 2010-07-04 words: 7154 flesch: 52 summary: This paper looks at teacher practices in the context of South African high schools and our new curriculum. Our interest was in exploring teacher practices in the ongoing flow of mathematics lessons. keywords: answers; learners; learning; mathematics; practices; reform; ronaldo; teachers; teaching; thinking cache: pythagoras-5.pdf plain text: pythagoras-5.txt item: #160 of 258 id: pythagoras-50 author: None title: pythagoras-50 date: None words: 8337 flesch: 53 summary: It was, however, noticed that during interviews students saw a possible use for the information they received from the lesson, to advise friends who deal with gambling. Albanian students participating in the first interviews expressed great interest in a secure future economic situation and upward mobility in life; thus connectedness of real-life situations to their future interests is a possible mechanism for preference. keywords: albanian; context; grade; interviews; life; mathematics; preferences; research; school; situations; students; study; topic cache: pythagoras-50.htm plain text: pythagoras-50.txt item: #161 of 258 id: pythagoras-515 author: None title: pythagoras-515 date: None words: 7490 flesch: 53 summary: In a review essay that critically examined mathematics teacher change, Goos and Geiger (2010, p. 505) found that a common thread in the literature on teacher change was the role of ‘productive tensions in creating opportunities for mathematics teacher change’. Clark and Hollingsworth’s model of teacher change provided the theoretical framework necessary to understand teacher change. keywords: change; development; domain; learners; lessons; mathematics; model; problem; professional; research; study; teachers; teaching cache: pythagoras-515.htm plain text: pythagoras-515.txt item: #162 of 258 id: pythagoras-519 author: None title: pythagoras-519 date: None words: 187 flesch: 52 summary: About the Author(s) Anthea Roberts Schools Development Unit, University of Cape Town, Cape Town, South Africa Kate le Roux Academic Development Programme, University of Cape Town, Cape Town, South Africa Citation Roberts, A., & Le Roux, K. (2019). https://doi.org/10.4102/pythagoras.v40i1.519 Note: DOI of original article: https://doi.org/10.4102/pythagoras.v40i1.438 Erratum Erratum: A commognitive perspective on Grade 8 and Grade 9 learner thinking about linear equations Anthea Roberts, Kate le Roux Published: 05 Dec. 2019 Copyright: © 2019. keywords: cape cache: pythagoras-519.htm plain text: pythagoras-519.txt item: #163 of 258 id: pythagoras-52 author: None title: pythagoras-52 date: None words: 10546 flesch: 47 summary: Overall, the enablements and affordances of Sketchpad software enable one to create a static graphic, static symbolic (algebraic), and static numeric (table of values) representations of the function on the one hand, and a dynamic graphic (animated point), dynamic symbolic (for curves or lines which vary their position), and dynamic numeric (table of values) representation on the other. Competing interests M.d.V. is a South African agent for Key Curriculum Press, promoting and selling Sketchpad software and curriculum materials. keywords: change; constraint; derivative; function; graph; line; mathematics; menu; plot; point; rate; sketchpad; slope; students; tangent; teacher cache: pythagoras-52.htm plain text: pythagoras-52.txt item: #164 of 258 id: pythagoras-520 author: None title: pythagoras-520 date: None words: 11455 flesch: 48 summary: This article reports on Grade 12 peer tutors’ views on their role in motivating Grade 8 and Grade 9 learners to learn mathematics in relation to the four categories of learner motivation, namely attention, relevance, confidence and satisfaction (ARCS). Purpose of the study This article reports on a study (Roberts, 2019) with the purpose of establishing the views peer tutors hold with regard to their role in motivating Grade 8 and Grade 9 learners to learn mathematics in relation to the four categories of learner motivation, namely attention, relevance, confidence and satisfaction, adapted from Keller (1987). keywords: attention; confidence; grade; keller; learners; learning; mathematics; motivation; peer; peer tutors; relevance; research; role; tutoring cache: pythagoras-520.htm plain text: pythagoras-520.txt item: #165 of 258 id: pythagoras-523 author: Office, Editorial title: Acknowledgement to reviewers date: 2019-12-17 words: 797 flesch: 38 summary: No. of manuscripts currently in review 7 1.Accepted after one round of review, with ‘minor’ changes as specified by reviewers and Editor. 2.Accepted after two or more rounds of review, with ‘major’ changes specified by reviewers and Editor. Acknowledgement to reviewers In an effort to facilitate the selection of appropriate peer reviewers for Pythagoras, we ask that you take a moment to update your electronic portfolio on https:// pythagoras.org.za for our files, allowing us better access to your areas of interest and expertise, in order to match reviewers with submitted manuscripts. keywords: changes; manuscripts; pythagoras; reviewers cache: pythagoras-523.pdf plain text: pythagoras-523.txt item: #166 of 258 id: pythagoras-524 author: None title: pythagoras-524 date: None words: 11973 flesch: 55 summary: Abstract Introduction Theory of image functions Literature review Part 1: The Image Functions Intervention and its theoretical evaluation Part 2: A first attempt at determining the Image Functions Intervention’s viability Discussion and conclusions Acknowledgements References About the Author(s) Christiaan Venter Department of Mathematics and Applied Mathematics, Faculty of Natural and Agricultural Science, University of the Free State, Bloemfontein, South Africa Citation Venter, C. (2020). Keywords: function concept; image functions; APOS theory; genetic decomposition; mathematics. keywords: concept image; dubinsky; function; function concept; ifi; image; image function; learning; level; mathematics; process; student; understanding cache: pythagoras-524.htm plain text: pythagoras-524.txt item: #167 of 258 id: pythagoras-525 author: None title: None date: None words: 1979 flesch: 48 summary: The debate that centres on the interpretation (p. 14) of the meaning of ‘realistic’ in RME terms is interesting. There are numerous RME terms that may not be familiar to educators, thus educators who are new to RME may find a glossary of terms at the end of the book quite useful. Significance of the book This book not only aligns favourably to other books written on RME – such as that of Koeno Gravenmeijer (1994), titled Developing Realistic Mathematics Education, and Marja van den Heuvel-Panhuizen’s (ed., 2001) keywords: authors; book; education; mathematics; rme cache: pythagoras-525.htm plain text: pythagoras-525.txt item: #168 of 258 id: pythagoras-527 author: Office, Editorial title: Table of Contents Vol 40, No 1 (2019) date: 2019-12-19 words: 475 flesch: -5 summary: Olivier Stellenbosch University (retired), South Africa Associate Editors Anthony Essien University of the Witwatersrand, South Africa Faaiz Gierdien Stellenbosch University, South Africa Michael Murray University of KwaZulu-Natal, South Africa Rajendran Govender University of the Western Cape, South Africa Editorial Board Jill Adler University of the Witwatersrand, South Africa Bill Barton University of Auckland, New Zealand Marcelo Borba São Paulo State University, Brazil Doug Clarke Australian Catholic University, Australia Jeremy Kilpatrick University of Georgia, United States of America Gilah Leder La Trobe University, Australia Stephen Lerman Southbank University, United Kingdom Frederick Leung University of Hong Kong, SAR, China Liora Linchevski Hebrew University of Jerusalem, Israel John Malone Curtin University, Australia Andile Mji Tshwane University of Technology, South Africa Willy Mwakapenda Tshwane University of Technology, South Africa John Olive University of Georgia, United States of America David Reid University Bremen, Germany Paola Valero Stockholm University, Sweden Renuka Vithal University of the Witwatersrand, South Africa Anne Watson Oxford University, United Kingdom Volume 40 Number 1 December 2019 ‘Semiregular tiling 3-4-6-4 (Small rhombitrihexagonal)’ PYTH 40(1)_Contents.indd Open keywords: africa; south; south africa; university cache: pythagoras-527.pdf plain text: pythagoras-527.txt item: #169 of 258 id: pythagoras-532 author: None title: pythagoras-532 date: None words: 10533 flesch: 52 summary: Reflective inquiry as a means of teacher PD is recommended by Muir and Beswick (2007), who advocate that to improve teachers’ classroom practice, emphasis should be placed on teachers’ learning and self-reflection. This particular project comprised a PD component that focused on assisting mathematics teachers from a local school district to improve their capability to design and enact mathematical problem-solving activities. keywords: context; intervention; learners; learning; mathematics; meaning; mpsp; problem; research; solving; south; study; teachers; teaching cache: pythagoras-532.htm plain text: pythagoras-532.txt item: #170 of 258 id: pythagoras-538 author: None title: pythagoras-538 date: None words: 9982 flesch: 55 summary: The following two research questions are answered in this study: Are certain types of isiXhosa compare type problem easier for learners to solve than others? In this study the influence of these two dimensions is explored for isiXhosa compare type problems. keywords: compare; english; formulation; isixhosa; learners; matching; problems; question; situation; type; type problems; word; word problems cache: pythagoras-538.htm plain text: pythagoras-538.txt item: #171 of 258 id: pythagoras-54 author: None title: pythagoras-54 date: None words: 8089 flesch: 56 summary: Mathematics teachers, especially, are sceptical about the feasibility of teaching the same curriculum within the same time frame to all learners (Naidoo, 2006), regardless of the inequitable distribution of resources (Adler, 2001; Reddy, 2005). The use of visual tools in the classroom • Theoretical framework • Methodology    • Introduction    • Participants       • Master teachers       • Learners    • Ethical considerations    • Research instruments or methods    • Reliability and validity • Findings and discussion    • Why do master teachers use visual tools?       • Making mathematics easier to remember       • Making mathematics more interesting and fun       • Making mathematics more concrete, accessible and comprehensible    • How do master teachers use visual tools in?       • Level 1: Organising the learning environment       • Level 2: Exploring teacher-learner interaction       • Level 3: The use of representational tools • Conclusion    • Limitations and recommendations for future work    • Implications for professional development • Acknowledgements    • Competing interests • References Abstract Top ↑ Research has shown that the use of visual tools in mathematics classrooms is beneficial, but what we do not know is how South African teachers negotiate the use of visual tools (e.g. diagrams, gestures, the use of colour, et cetera) in classrooms. keywords: education; learners; learning; lesson; master; master teachers; mathematics; study; teachers; teaching; tools; use cache: pythagoras-54.htm plain text: pythagoras-54.txt item: #172 of 258 id: pythagoras-545 author: None title: pythagoras-545 date: None words: 7629 flesch: 51 summary: In the ongoing effort to investigate learner performance in school mathematics, various researchers have identified factors associated with learner performance (Graven, 2014; Howie, 2003; Maree et al., 2006; Mji & Makgato, 2006; Ogbonnaya & Awuah, 2019; Ramohapi, Maimane, & Rankhumise, 2015; Spaull & Kotze, 2015). The model presents factors related to learner performance in school mathematics within the South African context in terms of inputs, processes and outputs in the education system. keywords: cape; district; education; examination; learners; marks; mathematics; nsc; performance; quantile; regression; schools; south; study cache: pythagoras-545.htm plain text: pythagoras-545.txt item: #173 of 258 id: pythagoras-55 author: Office, Editorial title: Acknowledgement to reviewers date: 2011-09-28 words: 326 flesch: 45 summary: Reviewer Acknowledgement Pythagorashttp://www.pythagoras.org.za Acknowledgement to reviewers The Pythagoras editorial team recognises the value and importance of peer reviewers in the overall publication process – not only in shaping individual manuscripts, but also in shaping the credibility and reputation of our journal. It is good practice as a reviewer to update your personal details regularly to ensure contact with you throughout your professional term as reviewer to Pythagoras. keywords: pythagoras; reviewers cache: pythagoras-55.pdf plain text: pythagoras-55.txt item: #174 of 258 id: pythagoras-552 author: None title: pythagoras-552 date: None words: 9946 flesch: 44 summary: This indicates that the GC-supported learning modelled by Kutzler’s (2000) and Kenney’s (2014) problem-solving strategies afforded learners of the experimental group opportunities to explore quadratic inequality problems by linking strategies such as making a model or diagram, using table of values, linking verbal and symbolic representations and using logical reasoning to infer the meaning within the context of the problem. Learners’ perceptions of graphing calculator use in quadratic inequality problem solving The results of the in-depth interviews of the two learners from the experimental group showed that the GC availability had a positive effect on their learning of contextual quadratic inequality problems. Pythagoras, 41(1), a552. https://doi.org/10.4102/pythagoras.v41i1.552 Original Research The effect of graphing calculator use on learners’ achievement and strategies in quadratic inequality problem solving Levi Ndlovu, Mdutshekelwa Ndlovu Received: 30 Apr. 2020; Accepted: 08 Oct. 2020; Published: 18 Nov. 2020 Copyright: keywords: control; group; inequalities; inequality; learners; learning; mathematics; problem; research; solving; strategies; study; test; use cache: pythagoras-552.htm plain text: pythagoras-552.txt item: #175 of 258 id: pythagoras-56 author: Naidoo, Inderasan; Huntley, Belinda title: Procepts and proceptual solutions in undergraduate mathematics  date: 2010-09-28 words: 6239 flesch: 58 summary: Example 1 Consider the lines with vector equations : 8, 14, 7 2, 1, 5 and : 41, 8, 7 1,4,1 . We also mention that the direct (vector) solutions presented allow greater access to such type of problems and deeper applications of vector concepts in the sciences and engineering undergraduate Linear Algebra courses. keywords: equation; lines; mathematics; matrix; solution; vector cache: pythagoras-56.pdf plain text: pythagoras-56.txt item: #176 of 258 id: pythagoras-560 author: None title: pythagoras-560 date: None words: 5090 flesch: 56 summary: Keywords: Multilingual classrooms; linear programming; home languages; mother tongue; mathematics tasks; translated tasks. Complexities of translating mathematics tasks from English to learners’ home languages. keywords: education; english; home; languages; learners; mathematics; study; tasks; translation; use cache: pythagoras-560.htm plain text: pythagoras-560.txt item: #177 of 258 id: pythagoras-567 author: None title: pythagoras-567 date: None words: 9737 flesch: 58 summary: ST13: There are many methods of solving series limit questions for example, the integral test, ratio test, comparison series test, root test, alternating series test etc. A plethora of research on the limit concept is available and suggests that the concept is on record as being difficult for students to learn and comprehend. keywords: conception; convergence; infinite; level; limit; process; responses; series; students; task; test cache: pythagoras-567.htm plain text: pythagoras-567.txt item: #178 of 258 id: pythagoras-568 author: None title: pythagoras-568 date: None words: 9557 flesch: 43 summary: New empirical research may also assist in determining further noteworthy experiences of postgraduate mathematics education students on the use of digital platforms for the learning of mathematics. The experiences of postgraduate mathematics education students, as discussed in this article, focuses on their use of digital platforms for learning within the COVID-19 pandemic era. keywords: cop; discussion; education; learning; mathematics; mathematics education; online; participants; platforms; students; study; technology; use cache: pythagoras-568.htm plain text: pythagoras-568.txt item: #179 of 258 id: pythagoras-569 author: None title: pythagoras-569 date: None words: 11342 flesch: 48 summary: More specifically, NGP content promotes the possibility of learners’ generalisations from arithmetic to algebra (Kieran, 2004). Investigating the strength of alignment between Senior Phase mathematics content standards and workbook activities on number patterns. keywords: alignment; content; content standards; dbe; grade; knowledge; levels; mathematics; ngp; patterns; spmcs; study; webb; workbook activities cache: pythagoras-569.htm plain text: pythagoras-569.txt item: #180 of 258 id: pythagoras-57 author: Mtetwa, David; Mudehwe, Lazarus; Munyira, Sheunesu title: Learning mathematics for personal understanding  and productions: A viewpoint  date: 2010-09-28 words: 3915 flesch: 49 summary: Fuller understanding of mathematical concepts and methods is achieved through personal mathematising by the learner her/himself. One of the key characteristics of mathematics is that of abstraction, described by Damerow (2007, p. 22) as a ‘meta-cognitive construct’ that is necessary for the production of mathematical concepts, or as a deliberate effort requiring coordination of a variety of, often parallel, (mental) actions – a description that builds on Piagetian conceptualisations (Dubinsky, 1991; von Glasersfeld, 1999). keywords: concepts; learner; learning; mathematics; problem; thinking; understanding cache: pythagoras-57.pdf plain text: pythagoras-57.txt item: #181 of 258 id: pythagoras-572 author: None title: pythagoras-572 date: None words: 11959 flesch: 49 summary: Boaler (2016) develops these notions in relation to mathematics, arguing that successful mathematics learners hold growth beliefs about themselves and about the nature of mathematics and their role in it. For example, in the extra-mathematical tasks, justifications would be constrained to local, immediate reasoning and would fall completely in the everyday space, while mathematics tasks where reasoning is constrained to isolated, rote-learned claims would fall completely in the mathematics space. keywords: agency; club; curriculum; education; everyday; identities; identity; knowledge; learners; mathematical; proficiency; reasoning; school; spaces; support; tasks cache: pythagoras-572.htm plain text: pythagoras-572.txt item: #182 of 258 id: pythagoras-573 author: None title: None date: None words: 2270 flesch: 48 summary: Book Review Pedagogical narratives in mathematics education in South Africa Book title: The Pedagogy of Mathematics in South Africa: Is There a Unifying Logic? Author: István Lénárt; Patrick Barmby; Karin Brodie; Mellony Graven; Fritz Hahne; Stephen Lerman; Mogege Mosimege; Werner Olivier; Nicky Roberts; Anna Rybak Paul Webb and Nicky Roberts (Eds). ISBN: 978-1-928341-11-6 Publisher: MISTRA (Mapungubwe Institute for Strategic Reflection) and Real African Publishers, Johannesburg, 2017, 282 pages, *R310 *Book price at time of review Review title: Pedagogical narratives in mathematics education in South Africa Reviewer: Charles R. Smith1 Affiliation: 1School of Science and Mathematics Education, Faculty of Education, University of the Western Cape, Cape Town, South Africa Corresponding author: Charles Smith, smithcharlesraymond@gmail.com How to cite this book review: Smith, C.R. (2020). keywords: africa; book; chapter; education; mathematics; south cache: pythagoras-573.htm plain text: pythagoras-573.txt item: #183 of 258 id: pythagoras-575 author: None title: pythagoras-575 date: None words: 8806 flesch: 50 summary: Children’s difficulties with mathematical word problems. Recognition of students’ difficulties in solving mathematical word problems from the viewpoint of teachers. keywords: design; education; learners; learning; mathematics; mmr; mwps; order; problems; research; solving; teachers; teaching; terms; udl; word cache: pythagoras-575.htm plain text: pythagoras-575.txt item: #184 of 258 id: pythagoras-578 author: None title: pythagoras-578 date: None words: 9941 flesch: 50 summary: The types of problems learners are exposed to suggest an orientation that is more content centred. The particular focus is on mathematics problems featured in tests used by two Grade 10 teachers in each school and teachers’ marking of learners’ test scripts. keywords: class; content; evaluation; expression; learners; marking; mathematics; mathematics problems; orientation; pedagogic; problems; school; solution; test; topic cache: pythagoras-578.htm plain text: pythagoras-578.txt item: #185 of 258 id: pythagoras-58 author: Office, Editorial title: Acknowledgment to reviewers  date: 2010-09-28 words: 394 flesch: 47 summary: Acknowledgment.doc 2 Acknowledgment to Reviewers  The quality of the papers in Pythagoras crucially depends on the expertise and commitment of our peer reviewers. We would like to sincerely thank the following people who have recently acted as reviewers for Pythagoras. keywords: manuscript; pythagoras; reviewers cache: pythagoras-58.pdf plain text: pythagoras-58.txt item: #186 of 258 id: pythagoras-586 author: None title: pythagoras-586 date: None words: 6474 flesch: 49 summary: Activity theory can form a solid basis for developing online mathematics games that create concerted learning conditions, for example networks of practices, where mathematics learners cooperate with different subjects, articles and instruments of the online mathematics game, under stated guidelines, and make networks through division of labour. Abstract Introduction Literature overview and conceptual framework Research design and methods Statement 1: Do you think learning without online mathematics games is boring? Statement 2: Do you feel comfortable playing online mathematics games? keywords: algebra; games; learners; learning; mathematics; mathematics games; online; online mathematics; research; statement; study; understanding cache: pythagoras-586.htm plain text: pythagoras-586.txt item: #187 of 258 id: pythagoras-588 author: Office, Editorial title: Acknowledgement to Reviewers date: 2020-12-21 words: 435 flesch: 33 summary: Alwyn Olivier André du Plessis Aneshkumar Maharaj Anita L. Campbell Anthea Roberts Anthony Essien Belinda Huntley Benita P. Nel Carol Macdonald Caroline Long Cerenus Pfeiffer Deonarain Brijlall Duan van der Westhuizen Duncan Mhakure Eunice K. Moru George Ekol Hamsa Venkatakrishnan Helen Sidiropoulos Iben M. Christiansen Ifunanya J.A. Ubah Ingrid E. Mostert Jacques du Plessis Joseph Baidoo Kabelo Chuene Kakoma Luneta Karen E. Junqueira Lyn Webb Marc North Marie Joubert Mdutshekelwa C. Ndlovu Michael Murray Michael D. de Villiers Michael K. Mhlolo Million Chauraya Mohammad F. Gierdien Neil Eddy Nokulunga S. Ndlovu Patrick Barmby Paul Mokilane Piera Biccard Rina Durandt Rose S. Maoto Sarah Bansilal Shaheeda Jaffer Sheena Rughubar-Reddy Tarun K. Tyagi Vanessa Scherman Vasuthavan Govender Yip-Cheung Chan Zingiswa M.M. Jojo Zwelithini B. Dhlamini http://www.pythagoras.org.za� https://pythagoras.org.za� https://pythagoras.org.za� https://pythagoras.org.za� https://pythagoras.org.za� https://pythagoras.org.za/index.php/pythagoras/user https://pythagoras.org.za/index.php/pythagoras/user https://pythagoras.org.za/index.php/pythagoras/user mailto:publishing@aosis.co.za http://www.pythagoras.org.za Open Access Page 1 of 1 Reviewer Acknowledgement Acknowledgement to reviewers In an effort to facilitate the selection of appropriate peer reviewers for Pythagoras, we ask that you take a moment to update your electronic portfolio on https:// pythagoras.org.za for our files, allowing us better access to your areas of interest and expertise, in order to match reviewers with submitted manuscripts. keywords: access; https://pythagoras.org.za/index.php/pythagoras/user; pythagoras; reviewer cache: pythagoras-588.pdf plain text: pythagoras-588.txt item: #188 of 258 id: pythagoras-59 author: None title: pythagoras-59 date: None words: 7832 flesch: 58 summary: The next step is to look for unique misspellings of mathematics words which have not yet been encountered. Remembering that not all words that remain after stop word processing are, in fact, mathematics terms, it was not a simple matter of just taking the best choice for the word. keywords: conversations; lingo; mathematics; model; mxit; phase; processing; research; stop; terms; topic; tutors; words cache: pythagoras-59.htm plain text: pythagoras-59.txt item: #189 of 258 id: pythagoras-593 author: None title: pythagoras-593 date: None words: 11166 flesch: 56 summary: We located our investigation in current debates about the extent to which disciplinary knowledge can be linked to learners’ out-of-school experiences. We articulate the complexities and nuances involved in bridging powerful knowledge and lived experience and thus contribute to debates on how to teach powerful knowledge in relation to learners’ lifeworlds. keywords: class; covid-19; deaths; everyday; information; knowledge; learners; mathematics; question; relation; school; tasks; teacher cache: pythagoras-593.htm plain text: pythagoras-593.txt item: #190 of 258 id: pythagoras-597 author: Office, Editorial title: Table of Contents Vol 41, No 1 (2020) date: 2020-12-23 words: 401 flesch: 22 summary: Reviewer Acknowledgement Pythagoras | Vol 41, No 1 | a588 | 21 December 2020 69 82 94 110 125 141 Book Review Pedagogical narratives in mathematics education in South Africa Charles R. Smith Pythagoras | Vol 41, No 1 | The effect of graphing calculator use on learners’ achievement and strategies in quadratic inequality problem solving Levi Ndlovu, Mdutshekelwa Ndlovu Pythagoras | Vol 41, No 1 | a552 | 18 November 2020 Original Research Learner performance in the 2009 to 2014 final Grade 12 mathematics examination: A quantile regression approach Nombuso Zondo, Temesgen Zewotir, Delia North Pythagoras | Vol 41, No 1 | a545 | 30 November 2020 Original Research Postgraduate mathematics education students’ experiences of using digital platforms for learning within the COVID-19 pandemic era Jayaluxmi Naidoo Pythagoras | keywords: pythagoras; vol cache: pythagoras-597.pdf plain text: pythagoras-597.txt item: #191 of 258 id: pythagoras-599 author: None title: pythagoras-599 date: None words: 13580 flesch: 56 summary: Reflecting on dilemmas in digital resource design as a response to COVID-19 for learners in under-resourced contexts. Original Research Reflecting on dilemmas in digital resource design as a response to COVID-19 for learners in under-resourced contexts Pamela Vale, Mellony H. Graven Received: 19 Jan. 2021; Accepted: 19 Aug. 2021; Published: 09 Nov. 2021 Copyright: © 2021. keywords: access; africa; department; design; education; learners; learning; lockdown; mathematics; number; process; research; resources; schools; south; tasks; use; work cache: pythagoras-599.htm plain text: pythagoras-599.txt item: #192 of 258 id: pythagoras-6 author: Maharaj, Aneshkumar title: An APOS Analysis of students’ understanding of the concept of a limit of a function date: 2010-07-04 words: 6946 flesch: 52 summary: The question analysis indicating number of student choices and the percentage (correct to one decimal place) for each of the four questions are indicated in Tables 1 to 4 below. Then lim A) is 5 B) is 3 C) is 6 D) does not exist E) is none of these Table 1: Question 1 analysis of student choices ( 868 A B C D* E Omit index Bad index 99 keywords: analysis; apos; concept; function; limit; process; question; schema; structures; students; teaching cache: pythagoras-6.pdf plain text: pythagoras-6.txt item: #193 of 258 id: pythagoras-60 author: None title: pythagoras-60 date: None words: 6121 flesch: 46 summary: Simple translations were provided for phrases that are often used in mathematical word problems to simplify the meaning of these problem statements. We investigated the situation in terms of the problem-solving performance of Grade 9 learners with English as their second language, using a pre-test to establish how the learners solved mathematics word problems and what problems they might have mathematically. keywords: comparison; discussion; group; intervention; learners; mathematics; problems; solving; study; test; word cache: pythagoras-60.htm plain text: pythagoras-60.txt item: #194 of 258 id: pythagoras-602 author: None title: pythagoras-602 date: None words: 9647 flesch: 53 summary: Learners have a partial understanding of a fraction as part-of-a-whole The equality of fraction parts Most learners used words such as ‘sharing’, ‘dividing’ and ‘cutting’ when defining a fraction; 50% of the learners defined a fraction as a part of a whole, and L15 explained it as ‘a piece of something complete’. Grade 9 learners’ understanding of fraction concepts: Equality of fractions, numerator and denominator. keywords: concepts; fraction; grade; knowledge; learners; misconceptions; number; numerator; parts; study; understanding cache: pythagoras-602.htm plain text: pythagoras-602.txt item: #195 of 258 id: pythagoras-61 author: Olivier, Alwyn title: Pythagoras is going places … date: 2008-10-10 words: 580 flesch: 58 summary: We will start by re-building a database of reviewers and streamlining our procedures and policies … Council has voted that we establish a little office for Pythagoras in my building, with a little infra- structure and administrative support. I underestimated the amount of time that needs to be invested to just manage the day-to-day editor’s task – acknowledging receipt of submissions, finding suitable reviewers, distributing the papers to reviewers, following up reviewers, chewing on different evaluations, giving feedback to authors. keywords: pythagoras cache: pythagoras-61.pdf plain text: pythagoras-61.txt item: #196 of 258 id: pythagoras-613 author: None title: pythagoras-613 date: None words: 9338 flesch: 51 summary: In particular, regardless of the syntactic obstruction, nearly all the errors made by Spanish students are reversals, while South African students barely commit reversal errors but errors consisting of equations that do not make sense in the situation stated in the problem statement, such as additive or inverse proportionality relationships. Therefore, in respect of the explanatory power of the static comparison as a model for the reversal error, firstly, our results point out that when taking together statements with and without syntactic obstruction, the rate of reversal errors among South African students is very low regardless of the type of magnitude (Table 3). keywords: african; comparison; context; error; matching; order; reversal; reversal error; south; spanish; students; word cache: pythagoras-613.htm plain text: pythagoras-613.txt item: #197 of 258 id: pythagoras-618 author: None title: pythagoras-618 date: None words: 9684 flesch: 37 summary: A non-parametric test (Wilcoxon Signed Ranks test) was used to evaluate the change in attitudes of student teachers towards mathematical modelling after exposure to a series of mathematical modelling activities, and a parametric test (one-sample t-test) was used to determine the effectiveness of the methodological design. Design principles to consider when student teachers are expected to learn mathematical modelling. keywords: activities; competencies; cycle; data; design; education; mathematics; modelling; participants; research; student; study; sub; teachers cache: pythagoras-618.htm plain text: pythagoras-618.txt item: #198 of 258 id: pythagoras-62 author: Barnes, Hayley; Venter, Elsie title: Mathematics as a social construct: Teaching mathematics in context date: 2008-10-10 words: 6615 flesch: 52 summary: Mathematical Literacy: What does it mean for school mathematics. It is therefore necessary in training mathematics teachers to teach in context, to develop the skills needed to be able to relate mathematics and context (Brown & Schafer, 2006) in a more problem-solving or inquiry oriented approach. keywords: approach; context; education; knowledge; language; learners; mathematics; problem; south; teaching; theory cache: pythagoras-62.pdf plain text: pythagoras-62.txt item: #199 of 258 id: pythagoras-623 author: None title: pythagoras-623 date: None words: 11597 flesch: 51 summary: However, the majority of the existing literature on dialogic teaching stems from studies conducted in Asian, European, and North American countries, whereas systematic research on dialogic teaching across international contexts remains limited. Analysis of transcripts using the notion of dialogic teaching as a theoretical lens revealed that there was little evidence of Nox’s attempts to use talk to make learning of equivalent fractions a cumulative process. keywords: approach; classroom; data; dialogic; dialogic teaching; education; fractions; ideas; knowledge; learners; learning; mathematics; nox; research; study; talk; teacher; teaching; understanding cache: pythagoras-623.htm plain text: pythagoras-623.txt item: #200 of 258 id: pythagoras-624 author: None title: pythagoras-624 date: None words: 9834 flesch: 52 summary: Moreover, expert teachers anticipated unpredictable incidents in their planning and possible learner misconceptions whereas novice teachers did not anticipate such contingencies in their planning (Borko & Livingston, 1989). In terms of instruction, expert teachers delivered coherent lessons whereas novice teachers tended to deliver mostly disjointed lessons (Borko & Livingston, 1989). keywords: cassandra; expert; learner; lesson; mathematics; moment; novice; offers; question; response; tara; teachers; teaching cache: pythagoras-624.htm plain text: pythagoras-624.txt item: #201 of 258 id: pythagoras-63 author: Stols, Gerrit; Mji, Andile; Wessels, Dirk title: The potential of teacher development with Geometer’s Sketchpad date: 2008-10-10 words: 4344 flesch: 53 summary: The importance of technology notwithstanding, it is worth noting that mathematics teachers, and not technological tools, are the key change agents needed to bring about reform in mathematics teaching. The findings revealed that teachers had a better understanding of the same geometry that they initially disliked. keywords: geometer; geometry; mathematics; sketchpad; teachers; teaching; technology; test cache: pythagoras-63.pdf plain text: pythagoras-63.txt item: #202 of 258 id: pythagoras-630 author: None title: pythagoras-630 date: None words: 12257 flesch: 44 summary: Furthermore, in probability education research, there is a need for developing a unified model that involves several probabilistic conceptions. Based on this historical development of probability education research, some areas for future study have been identified; one of these concerns is developing a unified framework that models several conceptions of probability (Chernoff & Russell, 2014; Jones, Langrall, & Mooney, 2007; Shaughnessy, 1992). keywords: birth; context; die; education; international; knowledge; mathematics; outcome; probabilistic; probability; psmts; reasoning; research; statistics; students; study; teachers; teaching; thinkers cache: pythagoras-630.htm plain text: pythagoras-630.txt item: #203 of 258 id: pythagoras-633 author: None title: pythagoras-633 date: None words: 6471 flesch: 60 summary: These are examples of student responses: I instantly visualized the problem and tried to picture what kind of quadrilateral it could be. The findings point to the fact that teachers could try to influence how students think during the problem-solving process by encouraging them to engage with mental images. keywords: diagram; mathematics; problem; process; question; solution; solving; students cache: pythagoras-633.htm plain text: pythagoras-633.txt item: #204 of 258 id: pythagoras-64 author: Likwambe, Botshiwe; Christiansen, Iben M. title: A case study of the development of in-service teachers’ concept images of the derivative date: 2008-10-10 words: 6160 flesch: 56 summary: Theoretical Framework In the research, we drew on Zandieh’s theoretical framework for the derivative (1997; 2000), which draws on the notion of concept images (Tall & Vinner, 1981; Thompson, 1994), Sfard’s (1991) work on the process-object duality of mathematical concepts and work on concept representations (Goldin & Shteingold, 2001; Gravemeijer, Lehrer, van Oers, & Verschaffel, 2003; Vinner & Dreyfus, 1989). A theoretical framework for analyzing student understanding of the concept of derivative. keywords: concept; derivative; images; layer; limit; ratio; representation; slope; students cache: pythagoras-64.pdf plain text: pythagoras-64.txt item: #205 of 258 id: pythagoras-641 author: None title: pythagoras-641 date: None words: 8683 flesch: 53 summary: It is recommended that universities create a sound educational partnership with mentor teachers. Analysis of results Separated data were categorised and merged into main themes, seven of which emerged from the data about the experiences of novice mentors while mentoring student teachers: communication and collaboration between novice mentors and lecturers, guidance given to mentor teachers, mentoring skills, pedagogical competence, commitment to the mentoring process, matching of mentor and mentee, and motivation of novice mentors. keywords: education; learners; learning; mathematics; mentees; mentoring; mentors; novice; practice; teachers; teaching; wenger cache: pythagoras-641.htm plain text: pythagoras-641.txt item: #206 of 258 id: pythagoras-644 author: None title: pythagoras-644 date: None words: 6477 flesch: 48 summary: Exploring low-tech opportunities for higher education mathematics lecturers in an emergency techno-response pedagogy. Original Research Exploring low-tech opportunities for higher education mathematics lecturers in an emergency techno-response pedagogy Antonia Makina, Langton Kadzere Received: 04 Aug. 2021; Accepted: 05 Feb. 2022; Published: 22 Apr. 2022 Copyright: keywords: emergency; ert; face; framework; learning; lecturer; lesson; mathematics; microsoft; onenote; students; teaching cache: pythagoras-644.htm plain text: pythagoras-644.txt item: #207 of 258 id: pythagoras-646 author: None title: pythagoras-646 date: None words: 7100 flesch: 44 summary: Grade R numeracy also predicts Grade 1 achievement since mathematics concepts have been shown to develop hierarchically (Bezuidenhout, 2018; Clements & Sarama, 2014; Fritz, Ehlert, & Balzer, 2013). After identifying these four factors as critical contributors for Grade 1 numeracy from the literature, we designed an experiment to investigate predictive correlations between Grade R numeracy, mathematics-specific vocabulary, executive functions and logical reasoning, and numeracy attainment at the beginning of Grade 1. keywords: children; development; executive; functions; grade; grade r; home; language; mathematics; number; numeracy; reasoning; vocabulary cache: pythagoras-646.htm plain text: pythagoras-646.txt item: #208 of 258 id: pythagoras-65 author: de Villiers, Michael title: Generalizing the Nagel line to circumscribed polygons by analogy and constructive defining date: 2008-10-10 words: 5181 flesch: 53 summary: Other analogies may help learners to remember results, e.g. a ‘negative times a negative is positive since magnets of same polarity repel each other’, but provides no explanation why the result is true. Generalizing the Nagel line to Circumscribed Polygons by Analogy and Constructive Defining Michael de Villiers School of Science, Mathematics & Technology Education, University of KwaZulu-Natal profmd@mweb.co.za This paper first discusses the genetic approach and the relevance of the history of mathematics for teaching, reasoning by analogy, and the role of constructive defining in the creation of new mathematical content. keywords: analogies; analogy; line; mathematics; nagel; point; quadrilateral; villiers cache: pythagoras-65.pdf plain text: pythagoras-65.txt item: #209 of 258 id: pythagoras-655 author: None title: pythagoras-655 date: None words: 9990 flesch: 50 summary: On the one hand, a study by Kabi (2016) found that despite strides made by the Department of Basic Education to address inequalities in education, learner mathematics and physical science performance has not improved but has dropped over time. It is expected that resilience plays a deciding role in learners’ foreground with the potential to affect learner mathematics achievement in constrained environments positively. keywords: achievement; context; data; education; environment; foreground; grade; journal; learners; learning; mathematics; research; resilience; school; skovsmose; south; study; teachers; use cache: pythagoras-655.htm plain text: pythagoras-655.txt item: #210 of 258 id: pythagoras-659 author: None title: pythagoras-659 date: None words: 9163 flesch: 43 summary: Commognition uses four elements that characterise mathematical discourse and the difference between ritualistic and explorative discourses to explain how one displays mastery of mathematical problem-solving. Wang (2016) combined these two theories (commognition and Van Hiele) with a focus on the elements of mathematical discourses, but this article takes a different approach by focusing on the type of discourse participation. keywords: commognition; discourse; geometry; hiele; learning; level; mathematics; participation; psts; sfard; thinking; van cache: pythagoras-659.htm plain text: pythagoras-659.txt item: #211 of 258 id: pythagoras-66 author: Webb, Lyn; Webb, Paul title: A snapshot in time: Beliefs and practices of a pre-service mathematics teacher through the lens of changing contexts and situations date: 2008-10-10 words: 5913 flesch: 48 summary: There has been extensive research in recent years on the relationships between the beliefs of mathematics teachers and their actual practice in the classroom (Brodie, 2001; Ensor, 1998; Ernest, 1989, 1991; Hoyles, 1992; Lerman, 1986, 2002; Pehkonen & Törner, 2004; Thompson, 1992; Skott, 2001a, 2001b, 2004; Speer, 2005; Wilson & Cooney, 2002). The forced autonomy of mathematics teachers. keywords: beliefs; learning; mathematics; practices; problem; sarah; solving; teachers; teaching cache: pythagoras-66.pdf plain text: pythagoras-66.txt item: #212 of 258 id: pythagoras-666 author: None title: pythagoras-666 date: None words: 12628 flesch: 52 summary: Meta-didactical transposition Meta-diactical transposition (MDT) is highly relevant to describing present actions and interactions among researchers and mathematics teachers relating to the MERLO pedagogy after participation in workshop training sessions (Arzarello et al., 2014; Robutti, 2018). Theme 2: Development of mathematics teachers praxeologies keywords: african; assessment; classroom; education; items; learners; learning; lesson; lis; mathematics; meaning; merlo; research; south; study; teachers; teaching cache: pythagoras-666.htm plain text: pythagoras-666.txt item: #213 of 258 id: pythagoras-667 author: None title: pythagoras-667 date: None words: 8917 flesch: 53 summary: Examples can also provide context, while the variation in examples can help learners distinguish essential from incidental features and, if well selected, the range over which that variation is permitted. For example, there was a special issue of ZDM Mathematics Education devoted to investigations on examples in mathematical thinking and learning (Antonini, Presmeg, Mariotti, & Zaslavsky, 2011) and, more recently, a special section in the Journal of Mathematical Behavior has focused on the roles and uses of examples in conjecturing and proving (Zaslavsky & Knuth, 2019). keywords: examples; functions; learners; learning; lesson; mathematics; teacher; teaching; variation cache: pythagoras-667.htm plain text: pythagoras-667.txt item: #214 of 258 id: pythagoras-669 author: None title: pythagoras-669 date: None words: 8864 flesch: 48 summary: Mathematics classroom language: Form, function and force. Mathematics teaching in Australian multilingual classrooms: Developing an appropriate approach to the use of classroom languages. keywords: africa; classrooms; education; english; language; learning; mathematics; mathematics education; papers; policy; pythagoras; research; south; teaching cache: pythagoras-669.htm plain text: pythagoras-669.txt item: #215 of 258 id: pythagoras-67 author: Brijlall, Deonarain title: Collaborative learning in a multilingual class date: 2008-10-10 words: 6787 flesch: 65 summary: This same sentiment was echoed by other learners who were unhappy working in groups. The two tasks were presented in the form of word problems and the classroom comprised of multilingual learners. keywords: answer; group; language; learners; mathematics; problem; question; solving cache: pythagoras-67.pdf plain text: pythagoras-67.txt item: #216 of 258 id: pythagoras-670 author: Office, Editorial title: Acknowledgement to reviewers date: 2021-12-21 words: 405 flesch: 37 summary: http://www.pythagoras.org.za Open Access Page 1 of 1 Reviewer Acknowledgement Acknowledgement to reviewers In an effort to facilitate the selection of appropriate peer reviewers for Pythagoras, we ask that you take a moment to update your electronic portfolio on https:// pythagoras.org.za for our files, allowing us better access to your areas of interest and expertise, in order to match reviewers with submitted manuscripts. It is good practice as a reviewer to update your personal details regularly to ensure contact with you throughout your professional term as reviewer to Pythagoras. keywords: https://pythagoras.org.za/index.php/pythagoras/user; pythagoras; reviewer cache: pythagoras-670.pdf plain text: pythagoras-670.txt item: #217 of 258 id: pythagoras-672 author: Office, Editorial title: Table of Contents Vol 42, No 1 (2021) date: 2021-12-30 words: 447 flesch: 15 summary: PYTH_V42(1)_2021_Contents.indd http://www.pythagoras.org.za Open Access Table of Contents Original Research Early career teacher’s approach to fraction equivalence in Grade 4: A dialogic teaching perspective Benjamin Shongwe Pythagoras | Vol 42, No 1 | a623 | 15 November 2021 Original Research Insights into the reversal error from a study with South African and Spanish prospective primary teachers Calos Soneira, Sarah Bansilal, Reginald Govender Pythagoras | Vol 42, No 1 | a613 | 25 November 2021 Original Research Constructing mental diagrams during problem-solving in mathematics Vimolan Mudaly Pythagoras | Vol 42, No 1 | a633 | 29 November 2021 Original Research Novice and expert Grade 9 teachers’ responses to unexpected learner offers in the teaching of algebra Julian Moodliar, Lawan Abdulhamid Pythagoras | Vol 42, No 1 | a624 | 15 December 2021 Original Research Reasoning under uncertainty within the context of probability education: A case study of preservice mathematics teachers Samah G.A. Elbehary Pythagoras | Vol 42, No 1 | a630 | 17 December 2021 57 71 82 90 103 Original Research Acknowledgement Pythagoras | Vol 42, No 1 | a670 | 21 December 2021 149 Vol 42, No 1 (2021) keywords: vol cache: pythagoras-672.pdf plain text: pythagoras-672.txt item: #218 of 258 id: pythagoras-677 author: None title: pythagoras-677 date: None words: 5998 flesch: 56 summary: Learners’ use of probability models in answering probability tasks in South Africa. The objective is to understand the distribution of the cognitive demand levels of PCP learning tasks that are in the DT introduced earlier in the previous section of this study. keywords: demand; grade; learners; learning; mathematics; pcp; probability; study; tasks; teachers cache: pythagoras-677.htm plain text: pythagoras-677.txt item: #219 of 258 id: pythagoras-678 author: None title: pythagoras-678 date: None words: 11650 flesch: 55 summary: At the start of the session the facilitator Carol (who was highly experienced in the use of the SLF for supporting teacher reflection on videos) provided some orienting comments that included an explicit statement about the importance of noticing mathematical over general aspects of lessons, such as: ‘Our focus is on the mathematics, so we try to talk less about generic aspects such as the teacher’s voice or the teacher’s body language; these things are interesting [but] … our focus is to talk about the mathematics. Promoting teacher reflection in second language education: A framework for TESOL professionals. keywords: education; learners; lesson; mathematics; practice; psts; reflections; rop1; rop2; sessions; teacher; teaching; video cache: pythagoras-678.htm plain text: pythagoras-678.txt item: #220 of 258 id: pythagoras-68 author: Setati, Mamokgethi; Barwell, Richard title: Making mathematics accessible for multilingual learners   date: 2008-10-11 words: 2526 flesch: 44 summary: In this issue we publish six papers by authors all of who work in multilingual mathematics classrooms in Southern Africa. Furthermore the work that is already published in this area of study is not easily accessible to practicing school mathematics teachers. keywords: english; language; learners; mathematics; research; teaching cache: pythagoras-68.pdf plain text: pythagoras-68.txt item: #221 of 258 id: pythagoras-686 author: None title: pythagoras-686 date: None words: 8072 flesch: 45 summary: In B. Kaur & L.N. Hoe (Eds.), Empowering mathematics learners (pp. 99–115). Orchestrating mathematical classroom discourse about various solution methods: A case study of a teacher’s development. keywords: classroom; control; discourse; education; group; ideas; instruction; learners; learning; mathematics; proficiency; study; teacher; teaching; test cache: pythagoras-686.htm plain text: pythagoras-686.txt item: #222 of 258 id: pythagoras-69 author: Dlamini, Clement title: Policies for enhancing success or failure?  A glimpse into the language policy dilemma of one bilingual African state  date: 2008-10-11 words: 6214 flesch: 52 summary: English language has become the linguistic capital (Barwell, 2002; Zevenbergen, 2000) in Anglophone countries and a legitimate medium of instruction in schools. That is, government policy states that a child who fails English language is deemed to have failed the grade level and should not proceed to the next grade. keywords: credit; education; english; grades; instruction; language; learners; mathematics; policies; proficiency; school cache: pythagoras-69.pdf plain text: pythagoras-69.txt item: #223 of 258 id: pythagoras-691 author: None title: pythagoras-691 date: None words: 6859 flesch: 48 summary: Bond et al. (2020) used three indicators of student cognitive engagement: purposeful, critical thinking and self-regulation. However, student engagement is a broad concept (Attard, 2012), and studying it is problematic during this pandemic. keywords: desmos; education; engagement; figure; geogebra; learning; mathematics; self; students; tasks; teachers; teaching; time cache: pythagoras-691.htm plain text: pythagoras-691.txt item: #224 of 258 id: pythagoras-696 author: None title: pythagoras-696 date: None words: 8325 flesch: 48 summary: The set of examples teachers introduced across the different lessons can be described in terms of the following patterns of invariance and variation: in all the examples we find an equation in the form ‘y = f(x)’, together with an equation in the form ‘y = a.f(x)+q’, as stipulated in the Curriculum and Assessment Policy Statements (CAPS). The commognitive theory also allowed for rich descriptions and discussion of teachers’ ways of teaching functions, through its focus on the contextual, cultural, dialogical and dynamic nature of participants’ discourses in mathematics. keywords: effect; examples; functions; learners; learning; lessons; mathematics; parameters; research; teachers; teaching cache: pythagoras-696.htm plain text: pythagoras-696.txt item: #225 of 258 id: pythagoras-7 author: Atebe, Humphrey U.; Schäfer, Marc title: Beyond teaching language: Towards terminological primacy in learners’ geometric conceptualisation date: 2010-07-04 words: 7366 flesch: 52 summary: These results further buttress our earlier claim that on average, South African learners involved in this study have a better knowledge of basic geometric terminology than their Nigerian counterparts. Another interpretation, and perhaps one more tenable, is that South African learners had a more comprehensive understanding of basic geometric terminology than their Nigerian counterparts and hence obtained a higher mean score in the TPGT. keywords: african; geometry; grade; hiele; learners; mathematics; mean; nigerian; score; south; study; teaching; terminology; tpgt; van cache: pythagoras-7.pdf plain text: pythagoras-7.txt item: #226 of 258 id: pythagoras-70 author: Setati, Mamokgethi; Molefe, Terence; Langa, Mampho title: Using language as a transparent resource in the teaching and learning of mathematics in a Grade 11 multilingual classroom  date: 2008-10-11 words: 9492 flesch: 62 summary: Code-switching in a senior primary class of second language learners. Supporting the participation of English language learners in mathematical discussions. keywords: classrooms; education; electricity; english; home; home languages; language; learners; learning; mathematics; resource; teaching; terence; tshivenda; use cache: pythagoras-70.pdf plain text: pythagoras-70.txt item: #227 of 258 id: pythagoras-71 author: Webb, Lyn; Webb, Paul title: Introducing discussion into multilingual mathematics classrooms: An issue of code switching?  date: 2008-10-11 words: 5203 flesch: 53 summary: The approach used in this study emulates the strategy used by Mercer (1995) towards dialogic learning, i.e., understanding and encouraging learner talk and discussion so that their reasoning becomes visible. Incomplete Journeys: Code switching and other language practices in mathematics, science and English language classrooms in South Africa. keywords: classrooms; code; discussion; english; language; learners; mathematics; reasoning; talk; teachers cache: pythagoras-71.pdf plain text: pythagoras-71.txt item: #228 of 258 id: pythagoras-714 author: None title: pythagoras-714 date: None words: 474 flesch: 41 summary: For example, the article ‘Exploring low-tech opportunities for higher education mathematics lecturers in an emergency techno-response pedagogy’ puts forth a conceptual framework for emergency remote teaching of mathematics in higher education environments that could enable academics and students to better prepare for future pandemics that may affect physical access to the classroom. The contestation of the role of home language in the learning of mathematics is ongoing, and this volume brings to the fore the benefits that accrue when learners’ home languages are taken into account in mathematics teaching and learning. keywords: education; mathematics cache: pythagoras-714.htm plain text: pythagoras-714.txt item: #229 of 258 id: pythagoras-72 author: Vorster, Hannatjie title: Investigating a scaffold to code‐switching as strategy in multilingual classrooms  date: 2008-10-11 words: 6330 flesch: 57 summary: It poses problems even for first language learners because of the specific structure of the mathematics register (Pimm, 1991), and all the more so for second language learners. Thabo was more non-committal and commented on the code-switching: “It was very interesting” and on the notes and Setswana terminology: “it was not a problem to have two languages.” keywords: code; english; language; learners; mathematics; school; setswana; switching; teaching; terminology; use cache: pythagoras-72.pdf plain text: pythagoras-72.txt item: #230 of 258 id: pythagoras-724 author: Office, Editorial title: Acknowledgement to reviewers date: 2022-12-19 words: 523 flesch: 39 summary: http://www.pythagoras.org.za Open Access Page 1 of 1 Reviewer Acknowledgement Acknowledgement to reviewers In an effort to facilitate the selection of appropriate peer reviewers for Pythagoras, we ask that you take a moment to update your electronic portfolio on https://pythagoras. org.za for our files, allowing us better access to your areas of interest and expertise, in order to match reviewers with submitted manuscripts. It is good practice as a reviewer to update your personal details regularly to ensure contact with you throughout your professional term as reviewer to Pythagoras. keywords: journal; pythagoras; reviewers cache: pythagoras-724.pdf plain text: pythagoras-724.txt item: #231 of 258 id: pythagoras-73 author: Bohlmann, Carol; Pretorius, Elizabeth title: Relationships between mathematics and literacy: Exploring some underlying factors  date: 2008-10-11 words: 9112 flesch: 51 summary: Thirdly, there was a trend of a slightly lower correlation between NS language and NS reading than there was between English language and English reading. Thirdly, we note again the large gaps between achievement in NS language and reading, as also the slightly smaller gaps in English language and English reading. keywords: ability; education; english; grade; language; learners; learning; literacy; mathematics; performance; proficiency; reading; school; teachers cache: pythagoras-73.pdf plain text: pythagoras-73.txt item: #232 of 258 id: pythagoras-734 author: Office, Editorial title: Table of Contents Vol 43, No 1 (2022) date: 2022-12-31 words: 484 flesch: 7 summary: August 2022 Original Research Grade 10 teachers’ example selection, sequencing and variation during functions lessons Hlamulo W. Mbhiza Pythagoras | Vol 43, No 1 | a696 | 30 August 2022 Original Research The intersect of early numeracy, vocabulary, executive functions and logical reasoning in Grade R Hanrie S. Bezuidenhout, Elizabeth Henning Pythagoras | Vol 43, No 1 | a646 | 15 September 2022 Original Research Investigating the cognitive demand levels in probability and counting principles learning tasks from an online mathematics textbook George Ekol, Simphiwe Mlotshwa Pythagoras | Vol 43, No 1 | a677 | 16 September 2022 Original Research Vol 43, No 1 | a724 | 19 December 2022 64 74 85 93 101 111 126 Editorial Research Resilience in the COVID era Rajendran Govender Pythagoras | Vol 43, No 1 | a714 | 15 December 2022 Review Article Complexities of translating mathematics tasks from English to learners’ home languages Nkosinathi Mpalami Pythagoras | Vol 43, No 1 | a560 | 18 January 2022 Review Article Language and multilingualism in the teaching and learning of mathematics in South Africa: A review of literature in Pythagoras from 1994 to 2021 Kathryn McLachlan, Anthony A. Essien Pythagoras | Vol 43, No 1 | a669 | 22 July 2022 Review Article Exploring the relationship between commognition and the Van Hiele theory for studying problem-solving discourse in Euclidean geometry education Sfiso C. Mahlaba, Vimolan Mudaly Pythagoras | Vol 43, No 1 | a659 | 29 July 2022 Original Research Exploring low-tech opportunities for higher education mathematics lecturers in an emergency techno-response pedagogy Antonia Makina, Langton Kadzere Pythagoras | Vol 43, No 1 | a644 | 22 April 2022 Original Research Weathering the storm: keywords: pythagoras; vol cache: pythagoras-734.pdf plain text: pythagoras-734.txt item: #233 of 258 id: pythagoras-74 author: Kazima, Mercy title: Mother tongue policies and mathematical terminology in the teaching of mathematics  date: 2008-10-11 words: 6340 flesch: 53 summary: al.’s study is that, where one teacher translated mathematics word problems including mathematical terms into the learners’ local languages, the learners found the terms harder to understand than when presented in English. The influence of English-Korean bilingualism in solving mathematics word problems. keywords: chichewa; english; language; learners; malawi; mathematics; meanings; problems; teaching; terminology; terms; word cache: pythagoras-74.pdf plain text: pythagoras-74.txt item: #234 of 258 id: pythagoras-75 author: Brodie, Karin title: Dialogue in mathematics classrooms: Beyond question-and- answer methods date: 2007-10-14 words: 7894 flesch: 68 summary: Initiation moves are often in the form of questions, and a number of researchers have focused on teacher questions. Example 1: Questions and answers One of the main reasons why teacher questions are considered insufficient to ensure genuine particip- ation and mathematical thinking is that teachers often ask very low-level questions (Boaler & Brodie, 2004; Hiebert & Wearne, 1993; Jina, 2007) keywords: equations; example; learners; mathematics; questions; teacher; teaching cache: pythagoras-75.pdf plain text: pythagoras-75.txt item: #235 of 258 id: pythagoras-76 author: Schäfer, Marc title: Thank you ... from the editor date: 2007-10-14 words: 396 flesch: 54 summary: Appropriate dissemination (and consumption) of good quality Mathematics Education research in South Africa is an issue of concern. This points to an active Mathematics Education research community, and an increased commitment to research dissemination in South Africa. keywords: pythagoras cache: pythagoras-76.pdf plain text: pythagoras-76.txt item: #236 of 258 id: pythagoras-77 author: Vermeulen, Nelis title: Does Curriculum 2005 promote successful learning of elementary algebra? date: 2007-10-14 words: 10310 flesch: 44 summary: Elementary algebra can therefore not be taught in a simple linear fashion, as was often the case with the traditional approach (letter symbols Does Curriculum 2005 promote successful learning of elementary algebra? Use S for the number of students and P for the number of professors.” keywords: algebra; algebraic; arithmetic; curriculum; expressions; learners; learning; mathematics; properties; verdict cache: pythagoras-77.pdf plain text: pythagoras-77.txt item: #237 of 258 id: pythagoras-78 author: Maharaj, Aneshkumar title: Using a task analysis approach within a guided problem-solving model to design mathematical learning activities date: 2007-10-14 words: 4864 flesch: 53 summary: Task analysis has two useful functions (Usability First, 2005): The second point indicates that task analysis has the potential to serve a predictive function, such as identifying possible impediments to learning. keywords: knowledge; learners; learning; mathematics; problem; solving; task cache: pythagoras-78.pdf plain text: pythagoras-78.txt item: #238 of 258 id: pythagoras-79 author: Samson, Duncan; Schäfer, Marc title: An analysis of the influence of question design on learners’ approaches to number pattern generalisation tasks date: 2007-10-14 words: 5610 flesch: 51 summary: Secondly, because the three consecutive terms give a physical Stage Questions Next (Stage 1) 10th (Stage 2) 50th (Stage 3) Total 1–5: Single pictorial term; dependent and independent variable mentioned. There are numerous pictorial and practical contexts in which pattern questions can be set, among the most obvious being dot patterns, tiling patterns, matchstick patterns as well as two- and three-dimensional building block patterns. keywords: context; generalisation; learners; pattern; question; stage; strategy; terms cache: pythagoras-79.pdf plain text: pythagoras-79.txt item: #239 of 258 id: pythagoras-8 author: Mudaly, Vimolan title: Thinking with diagrams whilst writing with words date: 2010-07-04 words: 7625 flesch: 62 summary: New knowledge in the form of visual images (as they worked on Sketchpad) was constantly replacing the old untested hypotheses. An investigation into learner understanding of the properties of selected quadrilaterals using manipulatives in a grade eight mathematics class. keywords: figure; images; learners; mathematics; mind; mudaly; new; point; problem; quadrilateral; reasoning; solution; triangle; visual cache: pythagoras-8.pdf plain text: pythagoras-8.txt item: #240 of 258 id: pythagoras-80 author: Austin, Pam; Webb, Paul title: Developing inquiry-based teaching and learning in Family Maths programme facilitators date: 2007-10-14 words: 6304 flesch: 38 summary: Comparison of facilitator mean scores with regard to inquiry learning belief versus practice. The participants were predominantly in-service teachers and teacher educators in the Departments of Education in the Developing inquiry-based teaching and learning in Family Maths programme facilitators 54 Western and Eastern Cape. keywords: education; facilitators; family; inquiry; learning; maths; novice; participants; programme; veteran cache: pythagoras-80.pdf plain text: pythagoras-80.txt item: #241 of 258 id: pythagoras-81 author: Mudaly, Vimolan title: Proof and proving in secondary school date: 2007-10-14 words: 7591 flesch: 68 summary: Inductive reasoning used while working with the computer software Sketchpad assists learners in arriving at and testing their conjectures. A study by Suydam (1985: 483) showed that about 50% of learners saw no need to prove what they considered obvious. keywords: explanation; learners; mathematics; point; proof; researcher; result cache: pythagoras-81.pdf plain text: pythagoras-81.txt item: #242 of 258 id: pythagoras-82 author: Venkat, Hamsa title: Mathematical Literacy – mathematics and/or literacy: What is being sought? date: 2007-10-14 words: 5601 flesch: 50 summary: In the body of this paper I present two excerpts of Mathematical Literacy teaching drawn from research exploring the implementation of Mathematical Literacy in schools, in which I have been involved through the Marang Centre at Wits University. In contrast, I will argue here that the empirical data from Mathematical Literacy lessons point to ways in which ‘tweaking’ the flow of questions and activities can allow for a productive integration of mathematical and literacy-oriented agendas, with each agenda working to bolster, rather than distract from, the other. keywords: agenda; bmi; class; education; freddy; learners; literacy; mathematical; teaching cache: pythagoras-82.pdf plain text: pythagoras-82.txt item: #243 of 258 id: pythagoras-83 author: Murimo, Adelino Evaristo; Forgasz, Helen title: Depictions of females and males in Mozambican and Victorian (Australia) primary mathematics textbooks date: 2007-10-14 words: 7151 flesch: 47 summary: Appropriate depictions of females and males in mathematics textbooks are important because pictures and text that depict gender stereotyped roles and occupations and gender-biased language can send implicit messages to females and males that they incorporate into their understandings of life around them, and their place in it. Forgasz’ (1996) recommendations to ensure that mathematics textbooks are gender equitable were generally evident in the Victorian textbooks examined; however, further improvements are needed. keywords: education; females; gender; learning; mathematics; mozambican; mozambique; roles; study; textbooks; victorian cache: pythagoras-83.pdf plain text: pythagoras-83.txt item: #244 of 258 id: pythagoras-85 author: Horsthemke, Kai; Schäfer, Marc title: Does ‘African mathematics’ facilitate access to mathematics? Towards an ongoing critical analysis of ethnomathematics in a South African context date: 2007-10-14 words: 5688 flesch: 43 summary: 2-9 Does ‘African mathematics’ facilitate access to mathematics? After providing an account of the African origins of mathematics (Seepe, 2000: 125-128; see also Van Sertima, 1999: 314-316; both writers seem to vacillate between an account of the “African origins of mathematics” and that of the “origins of African mathematics”), Sipho Seepe defends the desirability for a “culturally informed mathematics”, an ethnomathematics approach as part of the ‘democratisation’ of curricula (Seepe, 2000: 131-133). keywords: african; curriculum; education; ethnomathematics; knowledge; mathematics; practices; skills; south; truth cache: pythagoras-85.pdf plain text: pythagoras-85.txt item: #245 of 258 id: pythagoras-86 author: Stols, Gerrit title: Designing mathematical-technological activities for teachers using the Technology Acceptance Model date: 2007-10-14 words: 5087 flesch: 56 summary: • Determine the effective duration and nature of a full basic course for GSP teachers. Hu, Clark and Ma (2003) used the Technology Acceptance Model (TAM) to examine the use of PowerPoint by school teachers. keywords: activities; development; geometry; gsp; learners; teachers; technology; use; workshops cache: pythagoras-86.pdf plain text: pythagoras-86.txt item: #246 of 258 id: pythagoras-87 author: Zewotir, Temesgen; North, Delia title: Focus on the statistical education of prospective engineers in South Africa date: 2007-10-14 words: 4164 flesch: 49 summary: An overview of the current engineering statistics in South Africa Bear in mind that at most South African universities and technikons, engineering students’ first encounter with statistics courses are at third year level. Despite the effort that instructors of Engineering Statistics devote to the course, many students experience anxiety when they are required to take statistics courses, as these courses are rumoured to be difficult to pass. keywords: courses; education; engineering; engineers; rate; south; statistics; students; teaching cache: pythagoras-87.pdf plain text: pythagoras-87.txt item: #247 of 258 id: pythagoras-88 author: Kotzé, Gary S.; Strauss, Japie. P. title: An investigation into the mathematics performance of Grade 6 learners in South Africa date: 2007-10-14 words: 4783 flesch: 58 summary: Gender and learner achievement reveal that the modal achievement for mathematics is level 2 (emergent numeracy). The modal achievement of school location and learner achievement reveal the following: learners from both isolated/rural and small town schools are level 2 (emergent numeracy) achieved by 59.6% and 46.9% of the learners respectively. keywords: achievement; africa; grade; learners; levels; mathematics; south; test cache: pythagoras-88.pdf plain text: pythagoras-88.txt item: #248 of 258 id: pythagoras-89 author: Stols, Gerrit; Olivier, Alwyn; Grayson, Diane title: Description and impact of a distance mathematics course for Grade 10 to 12 teachers date: 2007-10-14 words: 4983 flesch: 61 summary: Impact of the course on teachers In 2002, twenty-seven teachers of grades 10 to 12 mathematics enrolled for the Mathematics for Teachers course. What is needed if mathematics teachers are to become more effective are professional develop- ment opportunities to strengthen their conceptual knowledge and problem-solving skills. keywords: course; knowledge; learners; mathematics; problem; skills; teachers; teaching cache: pythagoras-89.pdf plain text: pythagoras-89.txt item: #249 of 258 id: pythagoras-90 author: Sanni, Rasheed title: Teaching geometry in schools: An investigative rather than instructive process date: 2007-10-14 words: 4383 flesch: 58 summary: • Generate and use mathematical equations to compute surface areas of plane shapes and other possible variables in them Materials needed • Three cardboard boxes of 3 different sizes – A: 5 × 4 × 6 cm; B: 2 × 3 × 5 cm; and C: 4 × 4 × 7 cm – and their nets, for different learner groups. Then comes the third stage, explain, where oppor- tunities are provided for learner groups to present solutions or answers to the inquiry question(s), giving justifications and explanations for their claims. keywords: activities; area; learners; learning; mathematics; surface; teacher; teaching; tiles cache: pythagoras-90.pdf plain text: pythagoras-90.txt item: #250 of 258 id: pythagoras-91 author: Fox, Tracey D; Vos, Natasha B; Geldenhuys, Johanna L title: The experience of cross-cultural peer teaching for a group of mathematics learners date: 2007-10-14 words: 5637 flesch: 56 summary: Summary of peer learners’ and helpers’ responses to interviews 50 Tracey D Fox, Natasha B Vos and Johanna L Geldenhuys low-achieving learners are more effective as peer helpers. The peer helpers and peer learners responded very favourably to the peer teaching and 100% of them believed in the sustainability of peer tutoring. keywords: group; helpers; learners; mathematics; peer; peer teaching; research; school; teaching; township cache: pythagoras-91.pdf plain text: pythagoras-91.txt item: #251 of 258 id: pythagoras-92 author: Gierdien, M. Faaiz title: From ‘proofs without words’ to ‘proofs that explain’ in secondary mathematics date: 2007-10-14 words: 6914 flesch: 62 summary: Proofs that explain From ‘proofs without words’ to ‘proofs that explain’ in secondary mathematics M Faaiz Gierdien Stellenbosch University Email: faaiz@sun.ac.za Introduction From the mid 1970s onwards in almost every issue of the undergraduate mathematics journals Mathematics Magazine and College Mathematics Journal there is at least one ‘proof without words’ (Nelsen, 1993). For example, “competence descriptions” for learners by the end of grade 12 include “being able to critically analyse and compare mathematical arguments and proofs” and being able to “demonstrate an understanding of proof in local axiomatic systems” (Department of Education, 2003: 83). keywords: + +; + =; = +; mathematical; n +; proof; visualisation; words cache: pythagoras-92.pdf plain text: pythagoras-92.txt item: #252 of 258 id: pythagoras-93 author: Vithal, Renuka; Bishop, Alan J. title: Mathematical Literacy: A new literacy or a new mathematics? date: 2006-10-20 words: 2489 flesch: 34 summary: They point to the challenges of preparing teachers who do not having the requisite mathematical skills and knowledge choosing to become mathematical literacy teachers. As South Africa begins to implement a new Mathematical Literacy curriculum this year for all learners from grades 10-12 who do not take the subject ‘Mathematics’, there is much discussion about what exactly is mathematical literacy and issues about how it can be realised have emerged. keywords: curriculum; education; literacy; mathematics; research; south cache: pythagoras-93.pdf plain text: pythagoras-93.txt item: #253 of 258 id: pythagoras-94 author: Christiansen, Iben Maj title: Mathematical Literacy as a school subject: Failing the progressive vision? date: 2006-10-20 words: 5570 flesch: 51 summary: In Proceedings of the 6th National Congress of the Association for Mathematics Education of South Africa: The Beauty of Mathematics. There is an existing body of research in mathematics education which addresses how learners can learn mathematical modelling and thereby experience the power of mathematics in addressing complex issues (see for instance the ICTMA publications such as Matos et al. (2001)). keywords: christiansen; education; knowledge; learners; mathematics; mathematics education; modelling; ncs; role; skovsmose; society; south cache: pythagoras-94.pdf plain text: pythagoras-94.txt item: #254 of 258 id: pythagoras-95 author: Venkatakrishnan, Hamsa; Graven, Mellony title: Mathematical Literacy in South Africa and Functional Mathematics in England: A consideration of overlaps and contrasts date: 2006-10-20 words: 9181 flesch: 43 summary: Brombacher (2006) argues that Mathematical Literacy programmes across the world essentially develop out of two pressures, which he describes in the following terms: there is pressure to provide greater access to mathematics for more people – the democratisation of mathematics. Mathematical Literacy qualifications at FET level have been available within the adult learning sector since 2001, but this paper focuses primarily on the current school-based introduction of Mathematical Literacy, incorporating the more general aspects of critiques that have been undertaken of the programme on offer in the adult sector. keywords: africa; curriculum; department; education; england; learners; learning; level; literacy; mathematics; phase; policy; skills; south cache: pythagoras-95.pdf plain text: pythagoras-95.txt item: #255 of 258 id: pythagoras-96 author: Bowie, Lynn; Frith, Vera title: Concerns about the South African Mathematical Literacy curriculum arising from experience of materials development date: 2006-10-20 words: 5676 flesch: 39 summary: Similarly, Mathematical Literacy learners will have to develop a good grasp of these contexts and herein lies a host of problems. Mathematical Literacy teachers will not only be required to understand mathematics, but also voting systems, mortgages, retirement funding, HIV/AIDS, global positioning systems, socially responsible trade (to name but a few of the contexts suggested in the current curriculum). keywords: assessment; content; contexts; curriculum; education; learners; learning; literacy; mathematics; national cache: pythagoras-96.pdf plain text: pythagoras-96.txt item: #256 of 258 id: pythagoras-97 author: Vithal, Renuka title: Developing Mathematical Literacy through project work: A teacher/teaching perspective date: 2006-10-20 words: 5910 flesch: 44 summary: Project work processes and activities give teachers access to background knowledge as well as foreground information, about the dreams and aspirations of learners that can guide their intervention in particular projects. Microsoft Word - 64 Front Cover final.doc Pythagoras 64, December, 2006, pp. 37-44 37 Developing Mathematical Literacy through project work: A teacher/teaching perspective1 Renuka Vithal Faculty of Education, University of KwaZulu-Natal vithalr@ukzn.ac.za The implementation of the new Mathematical Literacy curriculum in South Africa is assuming several different conceptions of mathematics and therefore also being realised through a range of different pedagogies. keywords: education; learners; literacy; mathematics; problem; project; project work; school; teacher; vithal; work cache: pythagoras-97.pdf plain text: pythagoras-97.txt item: #257 of 258 id: pythagoras-98 author: Brown, Bruce; Schäfer, Marc title: Teacher education for Mathematical Literacy: A modelling approach date: 2006-10-20 words: 4643 flesch: 52 summary: The process of identifying and then using relevant mathematics to analyse and make decisions about contexts showed many similarities to that of mathematical modelling. But the basic approach of mathematical modelling could just as easily be applied to the use of elementary mathematics for modelling more everyday contexts (PISA, 2003). keywords: context; groups; literacy; mathematics; modelling; teachers cache: pythagoras-98.pdf plain text: pythagoras-98.txt item: #258 of 258 id: pythagoras-99 author: Frith, Vera; Prince, Robert title: Reflections on the role of a research task for teacher education in data handling in a Mathematical Literacy education course date: 2006-10-20 words: 6841 flesch: 47 summary: We adopt the following definition of mathematical literacy, in which all three approaches to the description (contexts, content and reasoning) are embedded: Mathematical literacy is the ability to manage situations or solve problems in practice, and involves responding to quantitative (mathematical and statistical) information that may be presented verbally, graphically, in tabular or symbolic form; it requires the activation of a range of enabling knowledge, behaviours and processes and it can be observed when it is expressed in the form of a communication, in written, oral or visual mode. The introduction of the subject “Mathematical Literacy” in the Further Education and Training band from 2006 has created an urgent need for large numbers of teachers to be educated about the nature of mathematical literacy and to become effective teachers of it. keywords: curriculum; data; education; literacy; mathematical; practice; research; research task; task; teachers cache: pythagoras-99.pdf plain text: pythagoras-99.txt