3 Research Article 2021 39(4): 3-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Published by the UFS http://journals.ufs.ac.za/index.php/pie © Creative Commons With Attribution (CC-BY) TWENTY YEARS INTO THE NEW MILLENNIUM: HOW INTEGRATED IS MATHEMATICS, PHYSICS AND COMPUTER SCIENCE AT SECONDARY SCHOOL LEVEL? ABSTRACT Twenty years into the millennium, the world has been confronted with a pandemic that has had an immeasurable impact on the workplace, learning environment and related technologies. Technology and technological advancements are founded on three disciplines, namely Physics, Mathematics and Computer Science. Internationally, an integration of the curricula of these disciplines are promoted in the education space, as an effective way to achieve 21st century capabilities that lately includes computational thinking. This study explores the changes in the content and alignment of the three subjects in the South African secondary school system from an interdisciplinary framework perspective. Textbooks, curriculum documents and planning calendars provided the information for the content analysis. The content in Physics and Mathematics have remained basically the same, with a few topics removed from Physics and some added to Mathematics. Information Technology has replaced Computer Science, with significant changes in content in alignment with developments in computing technology. No clear indication of an alignment between the disciplines could be found, which, to a certain extent, puts South Africa outside the international frame. The basic education system appears to run an assessment-driven curriculum in Mathematics, Physical Sciences and Information Technology. This system produces poor results and seemingly does not allow for interdisciplinary skills development. Keywords: Physics and Mathematics education, computing integration, curriculum alignment, FET phase. 1. INTRODUCTION Science, Technology, Engineering and Mathematics (STEM), as a collective framework, focuses on issues and explores epistemological questions on generic skills and the curriculum structure that would support or underpin interdisciplinarity (Millar, 2020). To date, however, there seems to be real difficulties with such curricula, including issues about theoretical frameworks, specified content knowledge and multiple interpretations of what the acronym AUTHOR: Prof Ilsa Basson1 AFFILIATION: 1University of South Africa DOI: http://dx.doi. org/10.18820/2519593X/pie. v39.i4.2 e-ISSN 2519-593X Perspectives in Education 2021 39(4): 3-26 PUBLISHED: 6 December 2021 RECEIVED: 13 August 2021 ACCEPTED: 27 September 2021 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 http://www.statssa.gov.za/?p=11341 http://documents.worldbank.org/curated/en/530481521735906534/Overcoming-Poverty-and-Inequality-in-South-Africa-An-Assessment-of-Drivers-Constraints-and-Opportunities http://documents.worldbank.org/curated/en/530481521735906534/Overcoming-Poverty-and-Inequality-in-South-Africa-An-Assessment-of-Drivers-Constraints-and-Opportunities http://documents.worldbank.org/curated/en/530481521735906534/Overcoming-Poverty-and-Inequality-in-South-Africa-An-Assessment-of-Drivers-Constraints-and-Opportunities http://orcid.org/0000-0002-4578-4625 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 42021 39(4): 4-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Perspectives in Education 2021: 39(4) actually represents (Martín-Páez et al., 2019). One example is from Wells (2019), who emphasised that the STEM acronym does not promote solidarity but perpetuates the traditional approaches to the individual disciplines comprising this grouping. He specifically pointed to the “T” in STEM, opining that, since inception, it was understood to be represented by a discipline in itself, aiming at technological literacy for all and not just instructional technologies, as commonly reported on by STEM researchers. The acronym has even been extended to STEAM with the inclusion of the Arts in Korea (Drake & Reid, 2018). Moving away from STEM as being a grouping of separate subjects or merely a collective name, it is instead increasingly seen as a solution for a range of purposes and directed by a discourse of interdisciplinarity, common or generic skills development and lately the employability of a person (Millar, 2020). When thinking about developing integrated skills and preparing for the world of work, the digital nature of study and work came to the fore. The two decades prior and the two following the advent of the new millennium, took us through developments and events that had major impacts on the learning and working environments (Figure 1). By 1980 we have seen the birth of modern computing, with the production of the world’s first commercial microprocessor, the Intel 4004 (Guadin, 2011). It caused a digital revolution that resulted in a multitude of new applications such as the pocket calculator, the home or personal computer (PC), new operating systems, programming languages, as well as the founding of internetworking. The next twenty years, leading to the year 2000 (Y2K), saw the introduction of a multitude of applications, including fax machines, cell phones, laptops and the World Wide Web (WWW). Y2K ignited commercial and technical activities due to the fear of the impact that the digits, “2000”, could have had on computing systems all over the world (Uenuma, 2019). By 2020, we all knew of cloud computing (Griffith, 2020), the internet of things (Evans, 2011) and a new industrial revolution (Schwab, 2015). The work environment and the learning landscape became digital and increasingly complex, which has been further fuelled by the COVID-19 (C19) pandemic. Figure 1: Four decades influenced by major developments and events. Computing developed rapidly over four decades and the fields of Computer Science and Information Technology matured. Although computational thinking (CT) received increased attention as a basic skill (Wing, 2006; Nouri et al., 2020) and STEM research has grown substantially over the past two decades, we have not seen the inclusion of Computer Science or Information Technology in the STEM grouping. Lately, there have at least been endeavours to integrate CT, specifically into K-12 STEM education, as illustrated by a recent special issue of the Journal of Science Education and Technology (Lee et al., 2020). How integrated is Mathematics, Physics and Computer Science? theoretical frameworks, specified content knowledge and multiple interpretations of what the acronym actually represents (Martín-Páez et al., 2019). One example is from Wells (2019), who emphasised that the STEM acronym does not promote solidarity but perpetuates the traditional approaches to the individual disciplines comprising this grouping. He specifically pointed to the “T” in STEM, opining that, since inception, it was understood to be represented by a discipline in itself, aiming at technological literacy for all and not just instructional technologies, as commonly reported on by STEM researchers. The acronym has even been extended to STEAM with the inclusion of the Arts in Korea (Drake & Reid, 2018). Moving away from STEM as being a grouping of separate subjects or merely a collective name, it is instead increasingly seen as a solution for a range of purposes and directed by a discourse of interdisciplinarity, common or generic skills development and lately the employability of a person (Millar, 2020). When thinking about developing integrated skills and preparing for the world of work, the digital nature of study and work came to the fore. The two decades prior and the two following the advent of the new millennium, took us through developments and events that had major impacts on the learning and working environments (Figure 1). By 1980 we have seen the birth of modern computing, with the production of the world’s first commercial microprocessor, the Intel 4004 (Guadin, 2011). It caused a digital revolution that resulted in a multitude of new applications such as the pocket calculator, the home or personal computer (PC), new operating systems, programming languages, as well as the founding of internetworking. The next twenty years, leading to the year 2000 (Y2K), saw the introduction of a multitude of applications, including fax machines, cell phones, laptops and the World Wide Web (WWW). Y2K ignited commercial and technical activities due to the fear of the impact that the digits, “2000”, could have had on computing systems all over the world (Uenuma, 2019). By 2020, we all knew of cloud computing (Griffith, 2020), the internet of things (Evans, 2011) and a new industrial revolution (Schwab, 2015). The work environment and the learning landscape became digital and increasingly complex, which has been further fuelled by the COVID-19 (C19) pandemic. Figure 1: Four decades influenced by major developments and events. http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 52021 39(4): 5-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Basson How integrated is Mathematics, Physics and Computer Science The focus of the international push towards STEM education in recent years has been on the curriculum being interdisciplinary, but it has different implications at the various education levels (Millar, 2020). Secondary schooling as the gateway to employment and further education has been selected as the level of attention for the purpose of this paper. In South Africa the Further Education and Training (FET) phase is specifically important as it represents the final three years of formal schooling (grades 10 to 12). It seems as if STEM refers to collectiveness rather than integration locally (Kahn, 2013; Tikly et al., 2018). FET content, alignment and possible integration will be probed in this paper to comment on preparedness for the post school environment. 2. CONCEPTUAL FRAMING Three disciplines, Physics, Mathematics and Computer Science, constitute the base of the technological advancements that we experienced during the 1980–2020 era. By 1980, Computer Science was established as a discipline for university and technical studies and as an additional subject at the secondary school level. Typical of the time, the three disciplines, Physics, Mathematics and Computer Science, existed independently (Figure 2), with some interaction among scholars and practitioners in these fields. This was particularly notable when curricula were designed to teach school learners and university students for studies in these disciplines and to prepare them for the work environment. Figure 2: Mathematics, Physics and Computer Science presented as independent disciplines at the university and secondary school levels During the twenty years leading to Y2K, physicists and mathematicians teaching mainly at the university level, realised the shortcomings and challenges confronting students when studying in these areas. We experienced an exponential growth in Physics and Mathematics educational research (PER-Central, 2021) that contributed to our understanding of how students could learn better and how curricula could be structured to facilitate improved learning (Van den Akker, 2004). Experiences and ideas developed that Mathematics and Physics (or science) could be presented as part of a continuum (Figure 3), as opposed to stand-alone subjects (Figure 2). Figure 3: Illustration of the Mathematics–Physics integration continuum (Basson, 2002) How integrated is Mathematics, Physics and Computer Science? Computing developed rapidly over four decades and the fields of Computer Science and Information Technology matured. Although computational thinking (CT) received increased attention as a basic skill (Wing, 2006; Nouri et al., 2020) and STEM research has grown substantially over the past two decades, we have not seen the inclusion of Computer Science or Information Technology in the STEM grouping. Lately, there have at least been endeavours to integrate CT, specifically into K-12 STEM education, as illustrated by a recent special issue of the Journal of Science Education and Technology (Lee et al., 2020). The focus of the international push towards STEM education in recent years has been on the curriculum being interdisciplinary, but it has different implications at the various education levels (Millar, 2020). Secondary schooling as the gateway to employment and further education has been selected as the level of attention for the purpose of this paper. In South Africa the Further Education and Training (FET) phase is specifically important as it represents the final three years of formal schooling (grades 10 to 12). It seems as if STEM refers to collectiveness rather than integration locally (Kahn, 2013; Tikly et al., 2018). FET content, alignment and possible integration will be probed in this paper to comment on preparedness for the post school environment. 2. Conceptual framing Three disciplines, Physics, Mathematics and Computer Science, constitute the base of the technological advancements that we experienced during the 1980–2020 era. By 1980, Computer Science was established as a discipline for university and technical studies and as an additional subject at the secondary school level. Typical of the time, the three disciplines, Physics, Mathematics and Computer Science, existed independently (Figure 2), with some interaction among scholars and practitioners in these fields. This was particularly notable when curricula were designed to teach school learners and university students for studies in these disciplines and to prepare them for the work environment. Figure 2: Mathematics, Physics and Computer Science presented as independent disciplines at the university and secondary school levels During the twenty years leading to Y2K, physicists and mathematicians teaching mainly at the university level, realised the shortcomings and challenges confronting students when studying in these areas. We experienced an exponential growth in Physics and http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 62021 39(4): 6-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Perspectives in Education 2021: 39(4) Interaction improved between Mathematics and Physics educators, but this did not extend to Computer Science educators, although the Association for Computing Machinery’s (ACM) Special Interest Group on Computer Science Education have been in existence for more than 50 years (SIGCSE, 2021). Examples of the integration of Mathematics and Physics with Computer Science are limited, with exceptions mostly found in very specific courses designed to provide certain pedagogical benefits. An example of such a course is presented by Pruski and Friedman (2014), who reported on a course for first level students, where they integrated calculus-based Physics with Computing using mathematical modelling. The objective was for seamless integration of the three areas: the course should neither be a Mathematics course, with components of Physics and Computing, nor a Physics or Computing one, with elements of the other two. They used MATLAB as the computing environment and introduced some basic concepts of computer programming. The course did not replace existing courses in any of the disciplines. It was aimed at developing critical thinking and enhancing conceptual understanding, while also providing experiences that illustrated that the subjects are not separate and disjointed entities. Physicists promoted their discipline as the foundation of nature and the physical world, added Mathematics as the vehicle or “language” to describe it in numbers and symbols, and used computers and programming to speed up calculations, analyse data, simulate systems, etc. The teaching/learning landscape became more complex (Figure 4) and more challenging to navigate as the boundaries between these disciplines blurred. Then came 2006, when Jeanette Wing (2006) reminded us of the riddle of machine intelligence, “What can humans do better than computers?” and “What can computers do better than humans?”. She re-introduced the concept “computational thinking” (CT) and emphasised that it “is a fundamental skill for everyone” and that we should add it – as we do for reading, writing and arithmetic – “to every child’s analytical ability” (Nouri et al., 2020: 3). By 2010, there were already examples of the integration of CT at all levels of formal education: primary, secondary and tertiary (Qualls & Sherrell, 2010). One year later, Barr and Stephenson (2011) reported on a process to establish an operational definition for CT and the meaning for K-12. They published a table of the core CT concepts and capabilities, with examples of how to embed it in activities of various disciplines such as Computer Science, Mathematics, Science, social studies, languages and arts. Most of the nine capabilities, such as data collection, analysis and representation, problem decomposition, abstraction and simulation, could also be associated with “mathematical thinking” or “physics thinking”. These capabilities stretched across disciplines and have opened up the space for collaboration. Figure 4: Complexity of a Physics-Mathematics-Computer Science teaching/learning landscape. 3. FRAMEWORKS There are various ways or forms to represent curricula (Van den Akker, 2004). Curriculum development and planning encompasses various levels. In curriculum design a distinction is made between the macro (system/society/nation), meso (school/institution), micro (classroom) and nano (individual/personal) levels. Van den Akker (2004) opines that a distinction should be made between curricula as “intended” (ideal, formal), “implemented” (perceived, operational) and “attained” (experiential, learned). For this paper, the focus will be on the macro and micro http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 72021 39(4): 7-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Basson How integrated is Mathematics, Physics and Computer Science levels, in conjunction with the intended and implemented forms associated with the curriculum. In South Africa, we identify the macro level as the National Department of Basic Education (DBE), with the current Curriculum and Assessment Policy Statement (DBE, 2011) as the intended curriculum. At the micro level, the focus is on the implemented curriculum, here represented by the content presented in textbooks and in the annual planning documents forwarded from national or provincial levels to teachers for classroom implementation. Emphasising the development of 21st century capabilities and an integrated curriculum as an effective way of achieving these capabilities, Drake and Reid (2018) offered a continuum for constructing such a curriculum. The span includes transdisciplinary, interdisciplinary, multidisciplinary and fusion as ways for integration. They proposed the Know, Do, Be (KDB) framework for constructing an integrated curricula. “Know” takes the focus away from memorising facts to conceptual thinking, “Do” shifts from lower-order skills to more complex interdisciplinary capabilities such as critical thinking, and “Be” adds character building that includes aspects such as mental health, values and attitudes. Michelsen (2015) proposed a didactical framework for interdisciplinary teaching between Mathematics and Physics, based on two aspects. The first is a didactical model for coordination and interaction between Mathematics and Natural Science subjects, consisting of two phases. The model starts with a phase of horizontal linking, when concepts and process skills from the two disciplines are connected by thematic integration, utilising modelling activities. Next, conceptual anchoring of the concepts that constitute a vertical structuring phase. This phase allows learners to move about analytically and logically within Mathematics and the Natural Science subject(s) in the interacting or an interdisciplinary context. The second aspect of the framework is the conception of modelling as an interdisciplinary competency. It stems from an interpretation that modelling is a Mathematics as well as a Science competence: “competency development can be seen as a lynchpin for interdisciplinary activities” (Michelsen, 2015: 493). Here, computing could be included based on modelling as a vehicle for development of skills. In addition to the above, Weintrop et al. (2016) proposed a taxonomy comprising four categories as a possible definition of CT for Science and Mathematics. The taxonomy describes the categories as “practices as opposed to skills or concepts in order to emphasise that engaging in scientific investigation requires not only skill but also knowledge that is specific to each practice” (Weintrop et al., 2016: 134). The four categories are data, modelling and simulation, computational problem solving and systems thinking practices, with each category consisting of five to seven CT subsets. An overview of the frameworks is provided to offer a window to the international landscape, with a view of considering the South African context. 4. RESEARCH QUESTIONS Given international trends and efforts to promote 21st century skills with STEM education and incorporating computational thinking (CT) in curricula, certain concerns have come to the fore regarding the South African secondary school system. To explore this, the following three questions have been formulated: 1. What were the changes in the content of the syllabi of Mathematics, Physics and Computer Science (Information Technology) over four decades at the FET level? http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 82021 39(4): 8-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Perspectives in Education 2021: 39(4) 2. Is there alignment and/or integration between Mathematics, Physics and Computer Science content in the current FET curriculum? 3. Would the alignment or integration equip a learner at the Grade 12 exit level to utilise 21st century CT skills when navigating the complex world of work or future study? 5. METHOD In this study an exploratory research design was adopted to examine whether there has been any meaningful changes in what has been taught in South African schools in the three disciplines, over the past four decades, using content analysis of representative current textbooks, and of the years around 1980, to detect changes over time. This would depict the implemented curriculum at the meso-micro levels (Van den Akker, 2004). Alignment of the three disciplines was explored by comparing the sequencing of topics in the current syllabi of Mathematics, Information Technology and the Physics part of Physical Sciences. It was done to check for interdisciplinary horizontal linking and vertical structuring (Michelson, 2015) of the final three years of school, namely Grades 10, 11 and 12. In addition, the 2020 “Suggested Planning of Teaching and Assessment” documents of one of the provinces in South Africa (WCED, 2020) was consulted. It provided an additional window to the current interpretation of the intended curriculum as it plays out at the classroom level. The syllabi cover large numbers of topics in all three subjects. For this paper it was not possible to investigate all topics in detail, something that could follow in future. A topic from Physics was selected as an example of alignment. Physics as application domain relies on Mathematics as a “language” and Computer Science or Information Technology as a “tool” (Figure 4). After 40 years “Motion” in Physics still is the first topic encountered by learners in Mechanics (Table 1). It is a topic that poses serious learning challenges (Hake, 1987; Halloun & Hestenes, 1985; McDermott et al., 1987) and relies on crucial pre-knowledge in Physics and Mathematics (Basson, 2002) with Computer Science included here. Curriculum and syllabi documents were scanned to reveal possible CT integration or a similar CT integrated taxonomy (Weintrop, 2016). 6. RESULTS AND DISCUSSION 6.1 Subject content spanning forty years Prior to Y2K, learners in South Africa received focused tuition in two languages and a minimum of four subjects of choice in their final two school years (Grades 11 and 12). Since then, they have to study two languages, Life Orientation and Mathematics or Mathematical Literacy as compulsory subjects, in conjunction with a minimum of three subjects of choice over the final three years of school (Grades 10, 11 and 12) (DBE, 2021). This is a significant difference in approach and regarding what is expected of learners. The second major difference is that Physics and Chemistry used to be combined as Science in Grade 10, and separated for Grades 11 and 12, presenting Physics only in Grade 11 and Chemistry only in Grade 12. Currently, the Physics and Chemistry content is presented in all three grades as Physical Sciences (DBE, 2011). Table 1 shows the content of the Physical Sciences textbooks, representative of the early and latter parts of the forty-year period. The basic Physics content stayed the same over this period. A couple of topics were removed – these relate to aspects of “Heat” (heat capacity, latent heat and thermionic emission), http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 92021 39(4): 9-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Basson How integrated is Mathematics, Physics and Computer Science “two-dimensional projectile and circular motion” and “nuclear reactions”. The “Doppler Effect” seems to be the topic expanded on in the current syllabus, including “frequency calculations”, while having only descriptions about shock waves before. Similar to Physics, the basic content of Mathematics remained the same (Table 2). The difference being that some content was added and seemingly nothing removed. The new content covers aspects of “Financial Mathematics”, “Statistics” and “Probability” in all three grades, as well as “Linear programming” in Grade 11, and “Differential calculus” in Grade 12. Linear programming was introduced a couple of years ago and in the meantime removed, but it still appears in some textbooks as a topic. During the same time, the implemented Computer Science curriculum changed substantially, with the introduction of Information Technology (IT) at the school level as a replacement for Computer Science. The topics changed from the “Classification of numbers”, “Arithmetic operations”, “Boole algebra”, “Data handling” and “Fortran as programming language”, to the inclusion of aspects related to the “Internet”, “World Wide Web”, “Algorithms” and “Data base design”, among a spectrum of topics with a wide choice of tools to navigate the digital space (Table 3). Computing hardware advanced phenomenally and, with that, the development of applications and software. The introduction of “Coding”, even at primary school level, also receives attention (Khoza, 2021). The value adding objective seems to be questioned and under consideration and discussion (Van der Velden, 2019). 6.2 Sequence of topics related to “motion” To ascertain the level of alignment, requires that there be a closer look at the sequencing of topics, as prescribed or presented. Table 4 shows the details pertaining to “Motion”, as the selected critical topic. It was taught previously as continuous arrangement of subtopics in Grade 11 only. Currently, the subtopics are intertwined with other Physics topics, as well as Chemistry topics, which are spread over Grades 10–12 (Table 1). Apart from the concepts related to “circular and parabolic motion”, which have been removed (green in Table 4), all the subtopics seem to be presented in a similar sequence, although it spans over three years, compared to one year previously. Tables 2 and 3 provide an overview of the content in Mathematics and Information Technology (marked with a hash) that supports the topic, “Motion”. When compared with the results of a previous study (Basson, 2002), the Mathematics content is adequate and appropriate. The concern is the alignment of topics that span over the three years. An example is that aspects of “Functions”, “Analytical geometry” and “Trigonometry”, studied in Grade 11 Mathematics, would be required for Grade 10 Physics topics related to vectors, when studying “Motion”. “Functions” in Grade 10 Mathematics provides an introduction to the linear function showing the effect of varying the gradient and y-intercept and to the quadratic function dealing with shape, vertical shift and the turning point. In Grade 11 the linear function is part of Analytical Geometry when the concepts of inclination and parallel and perpendicular lines are discussed. The quadratic function though remains a “Functions” topic and learners are introduced to a different form of this function as well as the average gradient concept. Learners studying Motion in Grade 10 could benefit from all of these Grade 11 Mathematics topics. In Trigonometry, trigonometric ratios, special angles and the Cartesian plane are introduced to assist with determining lengths in Grade 10. But Grade 11 trigonometric identities and some of the reduction formulae and the area rule would be useful tools when Motion is introduced. http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 102021 39(4): 10-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Perspectives in Education 2021: 39(4) Other examples are the introduction of “Calculus” and “Pythagoras’ theorem”, towards the end of Grade 12. These are indispensable for Physics, but at this point, it is too late to contribute towards the initial learning of complex concepts, for example, velocity, acceleration and projectile movement in a unit about “Motion”. It is more difficult to observe the relation with IT. The concepts that would be appropriate to encounter before or along with the teaching of motion deal with programming. These, together with the necessary skills, appear in the “practical” units of IT. The advantage would only be meaningful in Grade 12, after completion of all these units. Table 1. Content of Physical Sciences textbooks, representative of the years, 1980 (Myburgh et al., 1978; Pienaar & Walters, 1975; Prinsloo, et al., 1976) and 2020 (Siyavula, 2020). The focus is on the Physics part, indicated by the colour, yellow. The red text shows the topics that have been removed. 1980 Physics and Chemistry Textbooks 2020 Physical Sciences Textbooks Grade 10 Science (Physics and Chemistry) Grade 10 Physical Sciences 1 Light (sources, energy, speed, reflection, refraction, colour) 1 Skills for science 2 Sound (sources, waves, speed, reflection, refraction, intensity, shock waves) 2 Classification of matter 3 Heat, work and energy (phases of matter, heat transfer, heat capacity, latent heat) 3 States of matter and kinetic molecular theory 4 Electricity (current, resistance, heat & magnetic effects of current, induction, transformer) 4 The atom 5 Structure of the atom 5 Periodic table 6 Atomic models 6 Chemical bonding 7 Model of electron arrangement 7 Transverse pulses and waves 8 Chemical bonding 8 Longitudinal waves and sound 9 Chemical reactions 9 Electromagnetic radiation 10 Acids, bases and salts 10 Particles that atoms are made of 11 Chemical reactions and electricity 11 Physical and chemical change 12 Ionic reactions 12 Representing chemical change Grade 11 Physics 13 Magnetism 1 Mathematical relationships 14 Electrostatics 2 Motion and vectors 15 Electric circuits 3 Uniform and accelerated motion 16 Reactions in aqueous solution 4 Free fall and equations of motion (projectile motion) 17 Quantitative aspects of chemical change 5 Force and motion (Newton I, acceleration, momentum, weight) 18 Vectors and scalars (applications mainly forces) 6 Forces in equilibrium 19 Motion in one dimension (speed, velocity, acceleration, equations of motion) 7 Newton’s law of gravitation (gravitational force, circular motion, orbits) 20 Mechanical energy (potential and kinetic energy, conservation of mechanical energy) 8 Conservation of momentum (impulse, momentum, Newton III, action and reaction) 21 The hydrosphere http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 112021 39(4): 11-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Basson How integrated is Mathematics, Physics and Computer Science 1980 Physics and Chemistry Textbooks 2020 Physical Sciences Textbooks 9 Work, energy, power (potential, kinetic, energy conservation) Grade 11 Physical Sciences 10 Electrostatics 1 Vectors in two dimensions (context of forces) 11 Electric field and potential difference 2 Newton’s laws ( Newton I, II, III, gravitation, weight) 12 Electrical current and electromagnetism 3 Atomic combinations 13 Force between electrical currents, magnetic induction 4 Intermolecular forces 14 Resistance in electrical circuits 5 Geometrical optics 15 Electrical energy and power 6 2D and 3D wave fronts 16 Alternating current and the transformer 7 Ideal gases 17 Thermionic emission 8 Quantitative aspects of chemical change 18 Waves and their properties 9 Electrostatics 19 Wave nature of light 10 Electromagnetism (field, current, Faraday’s law) 20 Electromagnetic waves 11 Electric circuits (Ohm’s law, power, energy) 21 Electrons & positive current (deflection, photoelectric effect) 12 Energy and chemical change 22 Wave particle duality 13 Types of reaction 23 Atomic nucleus 14 The lithosphere 24 Nuclear reactions Grade 12 Physical Sciences Grade 12 Chemistry 1 Momentum and impulse 1 Periodic table and electron configuration 2 Verticle projectile motion in one dimension 2 Chemical bonding 3 Organic molecules 3 Chemical calculations 4 Work, energy and power (conservation of energy) 4 Gases, liquids and solids 5 Doppler effect 5 Speed of chemical reactions 6 Rate and extent of reaction 6 Electrolytes 7 Chemical equilibrium 7 Redox reactions 8 Acids and bases 8 Hydrogen, oxygen and water 9 Electric circuits (series, parallel, internal resistance) 9 Alkali and earth metals 10 Electrodynamics (motors, generators, alternating current) 10 Halogens and transition elements 11 Optical phenomena and properties of matter (photoelectric effect, spectra) 11 Elements of groups 4-6 12 Electrochemical reactions 12 Organic chemistry 13 Chemical industry http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 122021 39(4): 12-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Perspectives in Education 2021: 39(4) Table 2. Content of Mathematics textbooks, representative of the years 1980 (Dekker et al., 1984; Kruger & Ahlers, 1975; Van der Schyf et al., 1975) and 2020 (Siyavula, 2020). The blue shows algebra and the green new content. Content supporting the topic, “Motion”, in Physics is marked with a hash #. 1980 Mathematics Textbooks 2020 Mathematics Textbooks Grade 10 Algebra Grade 10 Mathematics 1 Products 1 Algebraic expressions: Real, rational and irrational numbers, rounding off, estimating surds, products, factorisation, simplification of fractions# 2 Decomposition in factors 2 Exponents: Revision of exponent laws, rational exponents, exponential equation# 3 Algebraic fractions 3 Number patterns: Describing sequences 4 Equations and inequalities: linear and quadratic 4 Equations and inequalities -Solving linear, quadratic equations & simultaneous equations, word problems, literal equations, solving linear inequalities# 5 Formulas: prisms, cylinders 5 Trigonometry: Similarity of triangles, trigonometric and reciprocal ratios, special angles, trigonometric equations, ratios in Cartesian plane# 6 Functions: linear, half circle, hyperbola, parabola with b=0 6 Functions: Linear, quadratic, hyperbolic, exponential and trigonometric functions, interpretation of graphs# 7 Systems of linear equations 7 Euclidean geometry: Triangles, quadrilaterals, mid-point theorem 8 Exponents 8 Analytical geometry: Cartesian plane, distance between two points, gradient & mid-point of a line# Grade 10 Geometry 9 Finance and growth 9 Euclidian geometry: quadrilaterals, parallelograms, triangles 10 Statistics 10 Trigonometry: angles, Cartesian plane, six trig functions, right-angled triangle 11 Measurements: polygon, right prisms, cylinders, right pyramids, right cones & spheres Grade 11 Algebra 12 Probability (union, intersection, Venn diagrams) 1 Factors, biggest common denominator, least common multiple and fractions 2 Union and intersections Grade 11 Mathematics 3 Real number system 1 Exponents and surds: Rational exponents and surds, solving surd equations, applications of exponentials 4 Venn diagrams 2 Equations and inequalities: Completing the square, quadratic formula, substitution, finding the equation, nature of roots, quadratic inequalities, simultaneous equations# 5 Relations and functions 3 Number patterns: Quadratic sequences 6 The rest statement (cubic polynomials) 4 Analytical geometry: Equation and inclination of a line, parallel and perpendicular lines# http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 132021 39(4): 13-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Basson How integrated is Mathematics, Physics and Computer Science 1980 Mathematics Textbooks 2020 Mathematics Textbooks 7 Linear functions, equations and inequalities 5 Functions: Quadratic, hyperbolic & exponential functions, Sine, cosine & tangent 8 Hyperbola and circle 6 Trigonometry: Trigonometric identities, reduction formula, trigonometric equations, area, sine & cosine rules# 9 Exponents, powers and square roots 7 Measurement: Area of a polygon, right prisms, cylinders pyramids, and cones, spheres 8 Hyperbola and circle 8 Euclidean geometry: Circle geometry 9 Exponents, powers and square roots 9 Finance, growth and decay Grade 11 Geometry 10 Probability 10 Locus 11 Statistics 11 Circle and cords of the circle 12 Linear programming - Introduction 12 Angles in a circle 13 Tangent to a circle Grade 12 Mathematics 14 Intersection 1 Sequences and series 15 Relations and proportionality 2 Functions: Functions & relations, inverse, linear, quadratic & exponential functions# 16 Analytical geometry 3 Finance Grade 12 Algebra 4 Trigonometry: Compound & double angle identities, solving equations, applications of trigonometric functions# 1 Exponential and logarithmic functions 5 Polynomials: Cubic polynomials, remainder theorem, factor theorem, solving cubic 2 Logarithms 6 Differential calculus: Limits, differentiation, differentiation rules, equation of tangent to curve, second derivative, sketching graphs, applications# 3 Quadratic equations with one unknown 7 Analytical geometry: Equation of a circle and of a tangent to a circle 4 Quadratic functions, quadratic inequalities and the nature of the roots 8 Euclidean geometry: Ratio and proportion, polygons, triangles, similarity, Pythagorean theorem# 5 Two equations with two unknowns, quadratic and linear 9 Statistics 6 Interpretation of graphs 10 Probability 7 Relations and proportionality 8 Sequences and series 9 Real number system II Grade 12 Geometry and Trigonometry 10 Naming triangles, positive & negative angles 11 Trigonometric functions 12 Natural & logarithmic tables of trig relations 13 Trigonometric relations of angles in any quadrant 14 Relations of sides and angles of any triangle http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 142021 39(4): 14-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Perspectives in Education 2021: 39(4) 1980 Mathematics Textbooks 2020 Mathematics Textbooks 15 Function values of specific angles 16 Relations between trigonometric ratios 17 Trigonometric formulas compound angles 18 Graphs of trigonometric functions 19 Identities and trigonometric equations Table 3. Content of Computer Science books, representative of the years 1980 (Computer Science Notes, no textbook prescribed at the time) and 2020 (DBE, 2020a). Content supporting the topic, “Motion”, in Physics is marked with a hash #. 1980 Computer Science Notes 2020 Information Technology Textbooks Grade 11 and 12 Computer Science Grade 10 Information Technology 1 Computer science history and careers 1 Basic concepts of computing# 2 Classification of decimal numbers 2 Data representation storage and social implications 3 Conversion of number systems 3 Practical: Algorithms, Delphi, variables, components, solving basic mathematical problems using Delphi# 4 Arithmetic operations, binary system and alpha numeric characters 4 Basic concepts of hardware 5 Arithmetic calculations and the binary system 5 Basic concepts of system software 6 Data 6 Networks 7 Flow charts 7 Electronic communications 8 Flow charts and Fortran 8 Practical: Decision making, algorithms, Boolean expressions & operators, If-then & Nested if-then statements# 9 Boole algebra 9 Computer management 10 Input, output and storage media 10 The internet and World-Wide Web 11 Program storage computers 11 PracticalL Repetition, Do loop, string manipulation# 12 SAMOS machine 12 Internet services 13 Fortran programming language 13 Practical: practical assessment task – Assignment statement Grade 11 Information Technology – Input and output 1 Hardware - cache, memory – Program execution and development 2 Software - operating systems, compilers – Do statement 3 Networks and social implications – Subscripted variables 4 Practical: Functions and nested loops# – Functions and subroutines 5 Computer management – Case studies 6 Electronic communications 7 Database management and design 8 Practical: arrays, string and date manipulation# 9 Database management and design 10 Internet and www 11 Internet services technologies 12 Practical: text files, procedures, functions, user interfaces, databases# http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 152021 39(4): 15-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Basson How integrated is Mathematics, Physics and Computer Science 1980 Computer Science Notes 2020 Information Technology Textbooks Grade 12 Information Technology 1 Database Management - collection, warehousing, mining 2 Database design concepts 3 Practical: Programming fundamentals, procedures and function in Delphi libraries, user-interface, databases# 4 Hardware - mobile technologies, performance of computers 5 Software - cloud computing, viral and augmented reality 6 Practical: OO-oriented programming, 2-dim arrays# 7 Internet services, networks 8 E-communication 9 Social implications 10 Practical - Databases and SQL Table 4. Details and sequence of the topic, “Motion” (green shows subtopics removed). 1980 Physics topic MOTION 2020 Physics topic MOTION Grade 11 Grade 10 1 Motion and vectors 1 Vectors and scalars (note: applications mainly forces) – Path length,distance and displacement, direction – Introduction – Speed and velocity – Properties of vectors – Scalars and vectors – Techniques of vector addition – Adding of displacements and velocities 2 Motion in one dimension – Decomposition of vectors – Reference frame 2 Uniform and accelerated motion – Speed and velocity – Uniform motion in a straight line – Acceleration – Uniform velocity & acceleration, displacement and velocity time graphs – Instantaneous velocity and speed – Description of motion 3 Free fall and equations of motion – Equations of motion – Free fall and air resistance Mechanical energy – Gravitational acceleration 3 – Potential energy – Equations of motion and calculations – Kinetic energy – Acceleration at an angle with the direction of motion – Mechanical energy – Horizontal and upward projection (two dimensions) – Conservation of mechanical energy 4 Force and motion – Nature of force Grade 11 – Uniform motion without force 4 Vectors in two dimensions (note: context of forces) – Newton’s first law – Resultant and perpendicular vectors – Inertia and mass – Components of vectors – Force and acceleration 5 Newton’s laws http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 162021 39(4): 16-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Perspectives in Education 2021: 39(4) – Momentum – Force – Weight and measurement of mass – Newton’s laws 5 Forces in equilibrium – Forces between masses – Vector nature of force (Newton’s law of universal gravitation, weight and mass) – Equilibrant and resultant of forces – Parallelogram, triangle, polygon of forces Grade 12 – Decomposition of forces 6 Momentum and impulse 6 Newton’s law of gravitation – Momentum – The moon in free fall – Newton’s second law revisited – Gravitational force at a distance and on a mass – Conservation of momentum – Law of gravitation and constant – Impulse – Centripetal force and acceleration – Physics in action: impulse – Circular motion 7 Vertical projectile motion in one dimension – Effects of centripetal force, mass, radius on speed of object – Introduction – Orbit and period of a satellite – Vertical projectile motion 7 Conservation of momentum 8 Work, energy and power – Impulse and momentum – Work – Changes in and total momentum – Work-energy theorem – Conservation of momentum during a collision – Conservation of energy – Newton’s third law, Action and reaction – Power 8 Work, energy and power – Work – Potential, kinetic and forms of energy – Power – Conservation of mechanical energy 6.3 Physics, Mathematics and Computer Science alignment The “Suggested Planning of Teaching and Assessment” documents for Grades 10–12 (WCED, 2020), of the 2020 secondary school year (Tables 5 to 7, respectively), show that the planning calendar provided for 42 weeks of learning and assessment activities. In these tables, it is notable that the content is split into chunks of alternating subtopics, in relation to all three disciplines. In Mathematics, bits of “Algebra” alternate with bits of “Geometry” and “Trigonometry”, with the new content, “Statistics” and “Finance”, presented towards the end of the school year. In Physical Sciences, bits of “Physics” and “Chemistry” alternate, but even within “Physics”, some “Mechanics”, “Electricity”, “Magnetism” and “Optics” alternate through the grades. Within the topic of “Motion”, for example in Grade 10, “Energy” ideas go hand in hand with “Speed” and “Velocity”. Coherence is lost when these subtopics are detached and presented with six weeks of “Chemistry” in between. Information Technology shows less fragmentation, but it appears that theoretical aspects are separated from practical programming tasks. The National Curriculum Statement (NCS) emphasises progression of content and context as one of the guiding principles (DBE, 2021). It seems to be achieved in the lower to higher grades, but none of the curriculum documents referenced provided an explanation or justification for the chunking of the content and for the specific sequencing of the bits, as described above and shown in the tables. Further exploration of these aspects would http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 172021 39(4): 17-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Basson How integrated is Mathematics, Physics and Computer Science be required to get a better understanding of how it could benefit or affect the learning of FET learners. It should also be explored in light of the reality that learners write separate Physics and Chemistry papers in Grade 12, and that “Algebra”, “Functions”, “Finance” and “Differential Calculus” form part of Mathematics Paper 1, which is separate from “Geometry”, “Trigonometry” and “Statistics”, assessed in Mathematics Paper 2. The topic of “Motion” is revisited to ascertain alignment of the topic across the three disciplines. Tables 5 to 7 show the subtopics in green for Physics and the supporting Mathematics topics in blue and for Information Technology in orange. The Mathematics required comes in the first half of the year for Grade 10 and in this way supports the introduction of “Motion”, presented in the second half. Information Technology subtopics run parallel with Mathematics and could be useful by the time “Loops” are introduced later. Inspection of the details of the planning calendar for Grade 11 does not bode well for Grade 11 learners. “Analytical geometry”, “Trigonometry” and aspects of “Euclidian geometry” follow on “Vectors” in two dimensions, “Force and free body diagrams” and “Newton’s laws” in Physics. Ideally, these Mathematics subtopics should be pre-knowledge for the topics covered in Physics. Similarly for Grade 12, “Functions” and “Differential calculus” should come before “Momentum”, “Projectile motion”, “Work” and “Energy”, or these subtopics should even rather be taught in Grade 11. The first reference to computational thinking was found in Grade 11 Information Technology within seven weeks of “Application development” and “Event driven programming”. It appears with specific reference to dataset handling and therefore no immediate link to physics. The same applies to Grade 12 Information Technology, where the focus and context is “SQL” and the “Internet”. The NCS (DBE, 2021) aims to “produce learners that are able to demonstrate an understanding of the world as a set of related systems by recognising that problem solving contexts do not exist in isolation”. Neither the macro nor the meso/micro levels seem to support this aim of achieving alignment across the disciplines, or with aspects of interdisciplinarity as a possible framework or objective. 6.4 Assessment driven system The intension of this study at the onset was not to consider assessment per se. While analysing the sequencing of the weekly learning activities (Tables 5 to 7), it became inevitable to observe and comment on the emphasis on formal assessment (tests and examinations as per the planning calendars) in Grades 10 to 12. The South African secondary school system at the FET level seems to be driven by a rigid, prescribed assessment scheme, as shown by an analysis (Table 8) of the activities indicated in Tables 5 to 7. In 2020, learners spent, on average, about 30% of the 42-week school year in Grades 10 and 11 on formal assessments. This number increases astoundingly to about 50% in Grade 12. To put it explicitly, learners devote only half of their time learning and developing new concepts and skills in their final year of school. In spite of the focus on assessments, especially in Grade 12, the results are not in support of the tremendous effort spent to prepare for tests and examinations. Figure 5 shows the Grade 12 final examination results for Mathematics and Physical Sciences. Over the five-year period 2016–2020, on average, only 22% of candidates obtained 50% or more in Mathematics and 28% in Physical Sciences. It is alarming to note that about half of the learners do not even reach the 30% mark in Mathematics and only a fifth gets above 50%! There is unfortunately no data in the diagnostic reports of the DBE for Information Technology. http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 182021 39(4): 18-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Perspectives in Education 2021: 39(4) Table 5. Grade 10 planning calendar (grey shows assessment activities). Week no. Grade 10 Planning Calender 2020 Mathematics Physical Sciences Information Technology 1 Alg: rational/irrational numbers, surds, rounding, multiply bi- with trinomial Revise matter and classification Basic concepts of computing 2 Alg: factorisation (grouping, quadratic, sum & difference of cubes), simpl fract States of matter and kinetic molecular theory Experiment 1 Basic concepts of computing: algorithms 3 Alg: exponents (laws, simplify, solve equations) The atom basic building block Data representation: bits, bytes, number systems, data types 4 Equations and inequalities: quadratic Periodic table Algorithms: flow charts, trace tables 5 Equations and ineq: quadratic, simultaneous linear equations Chemical bonding Data representation: file naming and types 6 Eq and ineq: word problems, literal eq’s, linear inequalities Transverse pulses on a string or spring Variables: naming, assigning values, data types 7 Euclidean geometry: kite, parallelogram, rectangle, rhombus, square, trapesium Longitudianal waves Functions: random, round, sq root, calculations 8 Eucl geo: line segements joining midpoints of two sides of triangle Sound Social implications; licence, copyright, ethics, legal 9 Trigonometry: Trig ratios, reciprocals, special ratios Electromagnetic radiation Applying algorithms, swapping values, isolate digits 10 Trigonometry: solve simple eq’s, use diagrams to determine ratios Indiginous knowledge systems - folklore Event handling 11 Analytical geom: Distance formula, gradient of line, coordinates midpoints Magnetism Extend use of variables, nested if’s, relational operators 12 Applications of week 11 Electrostatics Boolean logic, operators 13 Number patterns: linear Electric circuits Strings: methods and operations 14 Functions: concept of a func, basic graphs x^2, 1/x, b^x Electric circuits String operations, system software 15 Functions: sketching of x^2, 1/x, b^x Particles substances are made of Events and validation 16 Functions: finding eq of the form x^2, 1/x, b^x Physical and chemical change Debugging and networks 17 Functions: trigonometry graphs Representing chemical change e-Communication and implications 18 Examination Revision Problem solving 19 Examination Examination Examination 20 Examination Examination Examination 21 Examination Examination Examination 22 Trigonometry graphs problems in 2 dim Vectors and scalars Iteration constructs: loops http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 192021 39(4): 19-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Basson How integrated is Mathematics, Physics and Computer Science Week no. Grade 10 Planning Calender 2020 Mathematics Physical Sciences Information Technology 23 Trigonometry graphs problems in 2 dim Motion in one dimension Loops and computer management 24 Statistics Motion in one dimension Computer management 25 Statistics Instantaneous speed and velocity String handling 26 Probability Equations of motion Experiment 2 Internet and WWW, implement algorithms 27 Probability Reaction in acqueous solution Internet and WWW, application development 28 Finance growth Reaction in acqueous solution Application development 29 Finance growth Reaction in acqueous solution Application development 30 Measurement: Volume and surface areas Quantitative aspects of chemical change Solution development 31 Measurement: Volume and surface area spheres, pyramids, cones Quantitative aspects of chemical change Practical Assessment Task (PAT) 32 Measurement: Volume and surface area spheres, pyramids, cones Quantitative aspects of chemical change PAT 33 Eucl geo: appl quadrilateral theorems Energy Internet services technology 34 Eucl geo: appl quadrilateral theorems Energy potential and kinetic Solution development 35 Revision Energy potential and kinetic PAT 36 Revision The hydrosphere PAT 37 Revision Revision Revision 38 Examination Examination Revision 39 Examination Examination Examination 40 Examination Examination Examination 41 Examination Examination Examination 42 Examination Examination Examination Table 6. Grade 11 planning calendar (grey shows assessment activities). Week no. Grade 11 Planning Calender 2020 Mathematics Physical Sciences Information Technology 1 Exponents and surds Vectors in 2 dimensions Hardware 2 Exponents and surds Newtons laws, kinds of forces Loops: nested 3 Equations and inequalities: quadratic, factors Newtons laws, force diagrams and free body Arrays as data structure 1D 4 Equations and inequalities: quadratic inequalities Newtons laws, applications 1,2,3 Arrays basic operations 5 Equations and inequalities: simultaneous eq’s, nature of roots Newtons laws, applications 1,2,3 Arrays searching and sorting 6 Euclidian geometry: circle Newtons laws, applications 1,2,3 Experiment 1 Arrays parallel and nested loops http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 202021 39(4): 20-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Perspectives in Education 2021: 39(4) Week no. Grade 11 Planning Calender 2020 Mathematics Physical Sciences Information Technology 7 Eucl geom: apply theorems to geometry sketches with angles given as variables Newtons laws, universal gravitation String manipulation 8 Eucl geom: apply theorems to geometry sketches with angles numerical Molecular structure Computer management 9 Trig: tan, square identities, reduction formulae Intermolecular forces Methods string manipulation 10 Trig: neg angles, values for which identities hold Control test Problem solving: algorithms for string manipulation 11 Anal geometry: equation of line Geometrical optics: refraction Input and output text and file 12 Anal geometry: inclination of line Geometrical optics: Snell’s law Electronic communication 13 Number patterns Geometrical optics: Critical angle Functions, arguments vs parameters 14 Number patterns Wave fronts 2D and 3D: Diffraction Social implications 15 Functions: parabola Ideal gases, thermal properties Software engineering principles 16 Functions: a/(x+p), ab^(x+p) Ideal gas law Practical Assessment Task (PAT) 17 Functions: exam questions integrating weeks 15 and 16 Quantitative aspects of chemical change Practical Assessment Task (PAT) 18 Examination Quantitative aspects of chemical change Examination 19 Examination Examination Examination 20 Examination Examination Examination 21 Examination Examination Examination 22 Functions: effect of parameters in sin, cos, tan Coulomb’s law PAT database management 23 Measurement: revise grade 10 Electric field, electromagnetism PAT database design 24 Trigonometry: sin and cos rules Magnetic field and Faraday’s law Database design 25 Trigonometry: area rules Ohm’s law Experiment 2 Database design, social implications 26 Trigonometry: problems in 2D applying weeks 24 and 25 Ohm’s law power and energy Application development 27 Statistics Energy and chemical change PAT application development 28 Statistics Types of reaction: acid-base Appl dev: computational thinking & software eng 29 Probability Types of reaction: acid-base Appl dev: computational thinking & software eng 30 Probability Types of reaction: redox Appl dev: computational thinking & software eng 31 Finance growth and decay Control test Appl dev: use of algorithms http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 212021 39(4): 21-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Basson How integrated is Mathematics, Physics and Computer Science Week no. Grade 11 Planning Calender 2020 Mathematics Physical Sciences Information Technology 32 Finance growth and decay Control test Practical Assessment Task (PAT) 33 Finance growth and decay Oxidation number Database design 34 Finance growth and decay Exploiting lithosphere or earth’s crust Database design and GUI 35 Revision Exploiting lithosphere or earth’s crust Internet and WWW and GUI 36 Revision Revision Internet solutions and GUI 37 Revision Examination Social implications and PAT 38 Examination Examination Practical Assessment Task (PAT) 39 Examination Examination Examination 40 Examination Examination Examination 41 Examination Examination Examination 42 Examination Examination Examination Table 7. Grade 12 planning calendar (grey shows assessment activities). Week no. Grade 12 Planning Calender 2020 Mathematics Physical Sciences Information Technology 1 Number patterns, sequences & series Skills for practical investigations Database design and concept 2 Number patterns, sequences & series Newton law 2 and momentum OOP and hardware 3 Number patterns, sequences & series Impuls OOP and software 4 Euclidian geometry: ratio, proportionality theorem & appl Conservation of momentum SQL 5 Euclidian geometry: similarity theorem & appl Vertical projectile motion Practical Assessment Task (PAT) 6 Trig: compound angle, double angle Organic molecular structure SQL and networks 7 Trig: identities involving week 6 IUPAC naming and formulae SQL and e-Communication 8 Trig: eqs involving week 6 Applications of organic chemistry SQL and social implications 9 Trig: graphs and solutions of triangles in 3D involving week 6 Plastics and polymers Sotware engineering principles 10 Anal geom: circle with centre (a,b) Control test Sotware engineering principles 11 Anal geom: eq. of tangent to circle Work def & work-energy theorem Practical Assessment Task 12 Functions: definition and inverse of linear, x^2 and b^x Conservation of energy non- conserv forces Computer management and PAT 13 Func: def of log, inverse of exp and log Doppler effect Arrays 2D as datastructure 14 Func: polynomials 3rd degree Rates of reaction Arrays 2D as datastructure http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 222021 39(4): 22-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Perspectives in Education 2021: 39(4) Week no. Grade 12 Planning Calender 2020 Mathematics Physical Sciences Information Technology 15 Differential calculus: limit, gradiet, find derivative Chemical equilibrium Softw eng: algorithmic thinking 16 Diff calc: stas points & concavity, sketch func’s & its deriv, eq. of func Equilibrium constant Practical Assessment Task (PAT) 17 Differential calculus: applications Acid-base reactions Practical Assessment Task (PAT) 18 Examination Acid-base reactions Examination 19 Examination Examination Examination 20 Examination Examination Examination 21 Examination Examination Examination 22 Finance growth & decay Gr 11 Elec and Magn revision PAT and software engineering 23 Finance growth & decay Electrical machines motors and generators PAT and software engineering 24 Statistics Electrical machines alternating current PAT and Internet and WWW 25 Statistics Electrolytic and galvanic cells Internet services and social implications 26 Counting & Probability Electrode potentials and oxidatiton numbers Database design concepts 27 Counting & Probability Fertiliser industry PAT and appl development 28 Revision Photoelectric effect Application development 29 Internal examination Internal examination Application development 30 Internal examination Internal examination Internal examination 31 Internal examination Internal examination Internal examination 32 Internal examination Internal examination Internal examination 33 Revision Revision Assessment tasks 34 Revision Revision Assessment tasks 35 Revision Revision Examination 36 Examination Revision Examination 37 Examination Examination Examination 38 Examination Examination Examination 39 Examination Examination Examination 40 Examination Examination Examination 41 Examination Examination Examination 42 Examination Examination Examination Table 8. Percentage of time spent on assessment activities for the 2020 school year. Subject Grade 10 Grade 11 Grade 12 Mathematics 29 29 45 Physical Sciences 24 31 43 Information Technology 31 29 55 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 232021 39(4): 23-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Basson How integrated is Mathematics, Physics and Computer Science Figure 5. Grade 12 Mathematics and Physical Sciences examination results 2016–2020 (DBE, 2020b). 7. CONCLUSIONS Twenty years into the millennium, the basic Physics and Mathematics content of the FET phase remained the same, while that of Information Technology has changed completely. When analysing syllabi, textbooks and planning schedules, there was no clear indication of whether there has been any consideration given to the alignment of the content of the three disciplines or how this will be realised. Without alignment and no integration of disciplines including aspects of computing, STEM could locally still be viewed as a collective term for the four subject areas represented by the acronym. It puts South Africa, to an extent, on the outside of the international frame regarding multi- or interdisciplinarity given STEM frameworks. Chunking of content, as observed in this study, indicates neither alignment nor integration. At least two aspects should be clarified when further studies are pursued, preceding integration: (1) the impact and/or benefit of chunked content presented as alternating Physics and Chemistry topics in Physical Sciences, and alternating Algebra with Geometry-Trigonometry in Mathematics, given that no clear motive was found for it; (2) the need for spreading the content of critical topics over three years, compared to continuously per year, could shed light on the nature of vertical anchoring. The South African basic education system appears to run an assessment-driven FET curriculum in Mathematics, Physics and Information Technology, with poor results as outcome. Such a system, seemingly, does not allow space for proper, integrated, interdisciplinary, 21st century skills development. 8. ACKNOWLEDGEMENT Dr Vreda Pieterse is thanked for discussion and presentation of the complexity of a Physics- Mathematics-Computer Science teaching/learning landscape (Figure 4). REFERENCES Barr, V. & Stephenson, C. 2011. Bringing computational thinking to K-12: What is involved and what is the role of the computer science education community? Association for Computing Machinery (ACM) Inroads, 2(1): 48–54. https://doi.org/10.1145/1929887.1929905 How integrated is Mathematics, Physics and Computer Science? Table 8. Percentage of time spent on assessment activities for the 2020 school year. Subject Grade 10 Grade 11 Grade 12 Mathematics 29 29 45 Physical Sciences 24 31 43 Information Technology 31 29 55 Figure 5. Grade 12 Mathematics and Physical Sciences examination results 2016–2020 (DBE, 2020b). 7. Conclusions Twenty years into the millennium, the basic Physics and Mathematics content of the FET phase remained the same, while that of Information Technology has changed completely. When analysing syllabi, textbooks and planning schedules, there was no clear indication of whether there has been any consideration given to the alignment of the content of the three disciplines or how this will be realised. Without alignment and no integration of disciplines including aspects of computing, STEM could locally still be viewed as a collective term for the four subject areas represented by the acronym. It puts South Africa, to an extent, on the outside of the international frame regarding multi- or interdisciplinarity given STEM frameworks. Chunking of content, as observed in this study, indicates neither alignment nor integration. At least two aspects should be clarified when further studies are pursued, preceding integration: (1) the impact and/or benefit of chunked content presented as alternating Physics and Chemistry topics in Physical Sciences, and alternating Algebra with http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 https://doi.org/10.1145/1929887.1929905 242021 39(4): 24-26 http://dx.doi.org/10.18820/2519593X/pie.v39.i4.2 Perspectives in Education 2021: 39(4) Basson, I. 2002. Physics and Mathematics as interrelated fields of thought development using acceleration as example. International Journal of Mathematical Education in Science and Technology, 33(5): 679–690. https://doi.org/10.1080/00207390210146023 Department of Basic Education (DBE). 2011. Curriculum and Assessment Policy Statement Grades 10-12 Physical Sciences. 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