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Mathematics Education of Pre-Service
Teachers: As Reflected in Methods Course
Syllabus
Leslie Anne Unsworth1, Immaculate K. Namukasa2, Kinful L. Aryee3,
Donna Kotsopoulos4
Western University, Canada
Introduction
The Merriam- Webster’s dictionary defines syllabus as a summary, a course of study, or
an outline. Matejka and Kurke (1994) proposed that there are four key functions of a
syllabus. The syllabus represents a legal agreement between the instructor and the student,
the student and the university, and the instructor and the university; it is a communication
device regarding the learning outcomes and goals of a program of study; it is a plan or a
description of events to occur within the course; and it is a cognitive map outlining a way
in which knowledge will be shaped by the content of the course.
Burkhardt, Fraser, and Ridgway (1990) provide comprehensive definitions for
various kinds of curricula where the term ideal curriculum may add to the understanding
of the role of a syllabus. According to these authors,
The ideal curriculum is what experts propound; because it is not firmly grounded
in relevant experience. The ideal curriculum is fundamentally speculative but important
in defining directions for change that should be pursued. The implemented curriculum is
what teachers actually teach in the classroom; because teachers vary enormously in their
capabilities, hence, there is a wide distribution of implemented curricula. The achieved
curriculum is what the students actually learn; its distribution is even wider across many
variables. The tested curriculum is determined by the spectrum of tests which vary public
credibility, and through that, influence what happens in classrooms (Burkhardt et al.,
1990, p. 5).
A syllabus can be viewed as a representation of what Burkhardt, Fraser, and
Ridgway call “ideal curriculum” (Burkhardt et al., 1990, p. 5) and what Deng (2011)
refers to as one of the major constituents of programmatic curriculum. The syllabus is
therefore an important first glimpse for students to know what matters most to a discipline
and to their learning by providing information on the topics to be studied, and the planned
activities of the course.
The ideal curriculum is particularly important in mathematics teacher education.
It signals important theory to practice connections from research that are relevant for
advancing learning and understanding for students. In this paper, we concern ourselves
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with the course content in mathematics method courses, also referred to as mathematics
pedagogy and school mathematics. As we describe shortly, we specifically adopt a
framework of analysis that is derived from research literature in mathematics education.
The objective of this study is to examine the extent to which key opportunities to learn
mathematics method courses by pre-service mathematics teachers, as recommended by
researchers, is evidenced in course syllabi. The question guiding the research was: How
are recommendations derived from research for the mathematics education of pre-service
teachers reflected in mathematics methods course syllabi?
Some studies have attempted to identify ideal curriculum. For example, the recent
Teacher Education and Development Study (TEDS-M) (Tatto, 2013) provided cross-
national data and shared terminology on what, and how, teachers learn in teacher
education programs around the world (Tatto, Lerman, & Novotna, 2010; Blömeke, 2014).
Others have investigated specific components of teacher education such as mathematics
concepts and knowledge pre-services teachers need for teaching and the links between
these components (Hill, Rowan & Ball, 2005). This understanding contributes to
conversations on teacher knowledge and practices as well as to conversations on
improving the future teachers’ effectiveness in the classroom.
Certain studies have focused on areas such as course goal, course content, course
structure, instructional approaches, and assessment (see for examples, Little, 2009;
Monoranjan, 2015; Sinay, & Nahornick, 2016). TEDS-M also administered a content test
questionnaire to teacher candidates (Tatto, 2013). This questionnaire was administered to
determine the “effectiveness of a course/content arrangement” [in teacher education
programs] (Hsieh, Law, Shy, Wang, Hsieh, & Tang, 2011, p. 180) by focusing on
“organization of sequences, links of the course/content, and whether the courses/content
met the needs of future teachers” (Hsieh et al., p. 180).
TEDS-M not only studied the achieved curriculum by future teachers at the end
of their teacher-education programs (TEP), it also collected data on “syllabi and sample
assignments from teacher education mathematics curricular” (CMEC, 2010, p. 7).
Canãdas, Gómez, and Rico (2013) maintain that analyzing the content dimensions of the
syllabi of courses offered by teacher education institutions was a useful data source,
which was more important than using student and instructor self-reported data on the
learned curriculum. In certain studies, instructors investigated syllabi (e.g., Burton, 2003)
for the course which they taught, or syllabi at their institutions (e.g., Corlu, 2013), or
syllabi in their own countries (e.g., Canãdas et al., 2013). Also, Canãdas et al. (2013)
studied the content for Spanish primary teachers’ training programs. We found few
studies on syllabi of mathematics pedagogy or mathematics knowledge at the university
level that offered a comparative analysis on proposed ideal curriculum. Our research
hopes to contribute in this way.
This study serves three goals: (a) introducing an instrument that may be useful in
supporting the conceptual thinking of instructors when developing mathematics methods
course content, (b) providing an examination of the extent to which key assertions within
the field related to the mathematics education for future teachers materialize in course
content, and (c) serving as a study of recommended elements for teacher education. It
also has the potential to suggest ways to strengthen teacher preparation courses.
Our study examines syllabi for mathematics teacher-education courses in six
countries. Cross-national studies are particularly important in an international climate of
educational reform that emphasizes the need to promote learning for all students (Tatto
et al., 2010). In short, we examine trends identified in course syllabi that signal what is
deemed as important across the discipline. Our analysis provides these findings as well
as commentary on areas that appear to be underrepresented.
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Theoretical Framework
Cross-national comparative studies on mathematics teacher education have only
emerged in the past decade. It is, therefore, commonplace for a study on this topic to
develop its own framework for analysis (Blömeke, 2014). In line with the framework
development, Blömeke, Suhl, Kaiser, and Döhrmann (2012) raised its importance and a
need to review research internationally to discuss such issues.
Variations seem to exist in the literature among the components of pedagogy
courses. For instance, Tatto et al. (2013) developed a framework on teacher education
using data from 20 countries to analyze approaches to content in teacher education
programs. Their framework which classified the overall curricular structure of teacher
education, specifically inquiring whether mathematics content knowledge (CK),
pedagogical content knowledge (PCK), or pedagogical knowledge (PK), were
successfully addressed in the programs. On the question of content and pedagogy,
Canãdas et al. (2013) following TEDS-M, considered four major categories of CK that
should be taught to teachers in teacher preparation programs–school mathematics content
knowledge, tertiary mathematics content knowledge, mathematics pedagogy and general
pedagogy. These four categories of CK were considered the content categories of the
seven broad opportunities to learn (OTL) for teachers (Tatto, 2013; Tatto & Senk, 2011).
The seven OTLs identified altogether were: Mathematics content knowledge (MCK)–
school and tertiary, mathematics education, general education pedagogy, teaching for
diversity, reflection on practice, school experiences and the field experience, as well as
overall coherence of the teacher education program. Table 1 summarizes categories
identified in TEDS-M, Blömeke (2014), NCTM (2012), and Wang and Tang (2013)
alongside the categories identified in our study of course syllabi.
Table 1: Classification of mathematics pedagogical (content) knowledge, MPCK
Mathematics education (Blömeke 2014; Monroe,
1984; NCTM 2012; Tatto, 2013; Tatto & Senk, 2011;
Wang & Tang, 2013).
This study & MTEd
Teaching issues (e.g., planning, reflection, and
foundations of mathematics)
Pedagogical content
knowledge
Curriculum (e.g., school content and assessment)
Content knowledge
Assessment
Learning issues (e.g., development of mathematics
thinking, planning),
Technology
Mathematical tasks
Contexts (e.g., equity and diversity)
Policy and politics of
mathematics education
Equity and diversity
Affective issues (e.g., motivational issues)
Affective issues in
pedagogy and content
Professional competencies (e.g., teacher inquiry)
Reflection
Lesson as unit of study
Field Experiences and Clinical Practices
Theory and practice
connections
Blömeke et al. (2012) and Hsieh (2013) argue that examination of both teaching
and assessment of future teachers would generate more insight into the relationship
between teacher-education programs and teacher learning. Furthermore, it is clear from
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studies using TEDS-M data that opportunities to learn (together with teacher
backgrounds), were closely positively correlated to teacher performance on the tests of
mathematics knowledge and mathematics pedagogical knowledge (Canãdas et al., 2013).
Still other distinctions such as teacher learning, and teacher quality are possible
(Blömeke, 2014).
This current research is an extension of a study that proposed an evaluative tool,
the Mathematics Teacher Educator (MTEd) Instrument (see Appendix A; Kotsopoulos,
Morselli, & Purdy, 2011). The MTEd Instrument includes 11 categories of research
related to mathematics pre-service teacher education and the rationale for these derives
from the literature as described above and outlined in Table 1. These 11 are: reflection,
mathematical tasks, lesson study, assessment, theory and practice connections, policy
and politics of mathematics education, equity and diversity, affect, content knowledge,
pedagogical content knowledge, and technology. We state up front, that other categories
or classifications likely exist. Several of these categories also appeared independently in
the TEDS-M framework. Given the contributions we hope to make in this paper, these
categories are viewed by us as broad and yet encompassing enough to capture this field
area of research. Our literature review consists of brief overviews of each of the 11
categories. More robust reviews are contained within the citations in each category.
Literature Review
Reflection
Artzt and Armour-Thomas (2002) contended that for teachers to develop their
teaching practice, they must engage in reflection before, during, and after implementing
a lesson. In the same way, prospective teachers must participate in those same forms of
reflection throughout their teacher preparation program (Chung-Shu, 2006; García,
Sánchez, & Escudero, 2007). Researchers argue that reflection helps teacher candidates
to: Become active learners; think about mathematics; improve their professional skills;
contribute to their understanding, especially of teachers’ professional knowledge; and
serve as teaching for diversity. Although reflection on practice in the TEDS-M framework
was conceptualized to be outside of the opportunity in mathematics pedagogy, we argue
that reflection is an integral component [tool] of pre-service mathematical methods
courses.
Mathematical Tasks
NCTM (2012) breaks content into content knowledge and mathematical practices.
It includes a distinct category of professional knowledge and skills about teachers
continuing to learn. Pre-service teachers need to engage in mathematical tasks that allow
them to develop a deeper understanding of mathematical content and student learning
processes (Ching-Shu, 2006; Watson & Sullivan, 2008; Zaslavsky, 2007). Watson and
Sullivan distinguish between classroom tasks for students, that is, “questions, situations
and instructions teachers might use when teaching students” (p. 109) and tasks for
teachers, that is, “the mathematical prompt” (p. 109) that teachers employ to increase
their knowledge levels. Mathematical tasks for teachers serve as a basis for providing
meaningful help to pre-service teachers to develop a blend of mathematical and
pedagogical knowledge (Chapman, 2007).
Lesson Study
Teachers increasingly engage in inquiry or research to obtain reliable and updated
information for their lessons. Teacher engagement in inquiry involves avenues such as
collaborative inquiry, communities of inquiry, design research, lesson study and learning
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study (Lerman, 2014). In this study, we focus on lesson study, which is a process that is
aimed at improving teaching practices among pre-service teachers by allowing them to
collaboratively plan lessons, [to] observe one or more teachers while teaching the jointly
planned lessons, and [to] collectively reflect upon the lessons (Dumm & Mojeed , 2015;
Post & Varoz, 2008; Stigler & Hiebert, 1999).
Assessment
Generally accepted in mathematics education is the need for pre-service teachers
to engage in assessment practices through the act of analyzing students’ level of
mathematization. Additionally, it is important for teachers to engage in a variety of
assessment strategies (Cunningham & Bennett, 2009; Ketterlin-Geller & Yovanoff, 2009)
since authentic assessment practices can encourage and support further student learning
and teachers’ own understanding of students’ mathematical thinking.
Theory and Practice
Through theory-to-practice activities pre-service teachers make connections
between research and practice when learning to teach (McDonnough & Matkins, 2010;
Tsafos, 2010). They are given opportunities to engage in research that allows them to
make practical connections between educational theory and practice.
Policy and Politics
Policy documents and educational reforms (e.g., the New Math reform of the Post-
Sputnik era) pervade mathematics education. Curriculum and teaching standards and
guidelines for teacher preparation programs (NCATE, 2008; NCTM, 2000), the
institutional curriculum (Deng, 2011) that according to Doyle (1992) guides
programmatic curriculum for teacher education. Apple (1992) and Johnston (2007) have
verified the importance of pre-service teachers exploring and engaging with policy
documents as a means of becoming familiar with regional and educational standards.
Further, mathematics by itself according to Gutiérrez (2013), “operates with a kind of
formatting power on our lives” and critical mathematics education researchers underscore
the importance of engaging preservice teachers in exploring the politics of teaching
mathematics.
Equity and Diversity
Numerous factors have been identified as contributing to the marginalization of
certain populations of students, such as: pedagogical factors (Esmonde, 2009),
Eurocentric mathematics (D'Ambrosio, 1985; Skovsmose, 1990), and teacher
preparation (Sleeter, 2001). This research points to some serious deficiencies in the
learning environments of several students, specifically when it comes to how teachers are
prepared during their pre-service teacher education (Bartolo, Smyth, Swennen, & Klink,
2008). As a result, prospective teachers need to explore concepts of equity and diversity,
so that they learn strategies for meeting the needs of diverse learners. The TEDS-M
framework adequately addresses this concern by making ways of teaching diverse
students an integral part of mathematics method courses for pre-service teachers.
Affect
Goldin (2002) stresses that the affective system is not merely an auxiliary to
cognition; it is central to what the cognitive represents. Traditionally, four key
components of affect are studied: emotions, beliefs, conceptions, and attitudes. Beliefs
about teaching and learning mathematics deeply influence teachers’ instructional practice
(Philipp, 2007; Thompson, 1992). Affect influences teaching practice as much as the
social context and the teachers’ level of thought and reflection (Ernest, 1989) to the extent
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that, sometimes, it is difficult to distinguish beliefs from knowledge because “teachers
treat their beliefs as knowledge” (Thompson, 1992, p. 127). Therefore, it is important for
pre-service teachers to become aware of and begin to challenge and potentially change
any unhelpful beliefs during their teacher preparation programs.
Content Knowledge
Over the last decade, numerous scholars have attempted to articulate the sorts of
content knowledge required by future mathematics teachers, where the outgrowth of this
research has become known as mathematics for teaching (MfT) (Adler & Davis, 2006;
Ball, Hill, & Bass, 2005; Ball, Thames, & Phelps, 2008). Stylianides and Stylianides
(2009) define MfT as the “mathematical content that is important for teachers to know
and be able to use in order to manage successfully the mathematical issues that come up
in their practices” (p. 161). MKfT allows pre-service teachers to know, implement
mathematical content, and also solve mathematical problems (Ball & Bass 2000;
Stylianides & Stylianides, 2009). The reason for acquiring the content knowledge is that
most elementary teachers are noted to “have had little or no mathematics [education]
since high school, and have found their high school mathematics difficult” (Jonker, 2008,
p. 328). Therefore, to improve the effectiveness of teaching and students work,
mathematics knowledge for teaching (Hurrell, 2013) would be an important aspect of pre-
service teachers’ education.
Pedagogical Content Knowledge
Much of TEDS-M study research focused on the knowledge of content learned in
mathematics pedagogy courses. Shulman (1986) defined two different components of
teachers’ knowledge: content knowledge, also known as MfT as stated earlier, and
pedagogical content knowledge (PCK). MfT and PCK are complementary pieces of the
knowledge puzzle necessary for teaching mathematics. It appears that prospective pre-
service teachers need opportunities to examine, develop, and analyze various pedagogical
strategies to gain knowledge about the components of MfT and PCK including
instructionally sound representations and how to approach students’ learning difficulties
(Shulman,1986).
Technology
According to Niess (2005), research regarding technology integration in
mathematics teacher education has focused primarily on ways of using technology to
enhance teaching and learning. Mistretta (2005) noted that this integration has brought a
lot of enhancement into the teaching and learning environments. Freiman (2014) breaks
down learning technologies into: Microworlds, Virtual Learning Communities,
Applications and Task Designs, Mobile Learning, and Games. Educational reforms
around technology have promoted the integration of various facets of these technologies
into all classrooms (Greenhow, Robelia, & Hughes, 2009; Jonassen, Howland, Marra, &
Crismond, 2008; Xiao & Carroll, 2007). Some of the teacher education practices
championed in classroom technology include: a professor demonstrating or modeling the
use of mathematics technology (Picha, 2018; Sturdivant, Dunham, & Jardine, 2009),
opportunities for pre-service teachers to study mathematics technology (da Ponte,
Oliveira, & Varandas, 2002), and to engage in authentic implementation of mathematics
technology (Lin, 2008). Studies have shown that when pre-service teachers are provided
with the opportunity to observe, investigate and implement technology, they maximize
their current knowledge of technology integration in a mathematics classroom (Blubaugh,
2009; Niess, 2001). Even though this category did not appear in the TEDS-M, as
evidenced in the review above, it is a major category in mathematics education research.
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Methods
Participants
Mathematics methods course syllabi (English only) for pre-service teachers were
solicited from professors/instructors of mathematics teacher education courses through
two listserv mailing lists: The Psychology of Mathematics Education (PME) Listserv and
the Canadian Mathematics Education Study Group (CMESG) Listserv. In total, 147
syllabi were submitted. Although our intent was to obtain syllabi from every continent,
we were unable to do so despite numerous invitations.
The full syllabus set underwent a preliminary filtering to exclude (a) syllabi that
were not consistent with the methods courses under investigation in this research (e.g.,
syllabi related to practicum/field experience, enrichment mathematics, mathematic
content exclusive of pedagogy, graduate courses that had a narrow/conceptual focus), and
(b) syllabi with less than 30 or more than 49 hours of instructional time. Hours of
instruction were bracketed to ensure that appropriate comparisons were made across
courses of similar length versus short courses or full year courses. This considerably
reduced the data set. Multiple syllabi from one institution were not excluded, given that
differences existed between the syllabi when examined; that is, different instructors
prepared different versions of mathematics methods courses reflecting differing
perspectives on essential components. Two researchers and one graduate student coded
the syllabi and analyzed the data. The two researchers are specialists in mathematics
education. Interrater reliability was determined by independently reviewing coding by
two coders and any disagreements were resolved.
Data Sources
In total 31 syllabi were analyzed from six different countries, three of which–
Canada, Malaysia, United States—also participated in TEDS-M. The mean length of the
syllabi in the final sample was 9.3 pages and the mean number of course hours was 37.9
hours. Each of these courses spanned one academic term (approximately 12 to 13 weeks)
and was deemed to be as close an approximation of similar hours as possible. To maintain
anonymity for the course instructors, the syllabi were referred to by country and a
sequential number (e.g., Canada 1, Canada 2, etc.).
The final syllabus data set was then broken down into two categories, elementary
and secondary. Elementary refers to syllabi used in courses that prepare teachers to teach
kindergarten to grade eight. Secondary refers to syllabi used in courses that prepare
teachers to teach grades nine through to twelve. This grade breakdown between
elementary and secondary reflects common groupings in Canada. The final dataset
included 19 elementary syllabi and 12 secondary syllabi (see Table 2).
Table 2: Final Syllabus Dataset Sorted by Country (elementary vs. secondary)
Country
Syllabi
Level
Elementary Secondary
Australia
Canada
Italy
5
6
2
5
6
1
0
0
1
Malaysia
New Zealand
United States of
America
1
3
14
0
2
5
1
1
9
Total 31 19 12
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Materials
The MTEd instrument used in this study is an analytical rubric that uses level one
through to level four, to evaluate the extent to which the categories emphasized in the
mathematics education literature and research in the literature review is evidenced in a
syllabus. Low, moderate, and high tags were assigned to each syllabus based upon the
cumulative level of the syllabus obtained using the MTEd Instrument. In a similar
manner, Corlu (2013) developed and applied an analytical rubric to assess STEM courses
at a university. The cumulative level was determined by adding up the levels from each
of the individual categories, with one point for each level one, two points for each level
two, three points for each level three, and four points for each level four. A syllabus was
tagged as showing low evidence of research if it scored below 22 (total of one point for
each of the 11 categories), moderate evidence of research if it scored between 22 and 32
(range of potential points if all categories scored below a level three), and high evidence
of research if it scored higher than 32 (range of potential scores reflecting inclusion of
one or more categories at a level four).
Data Analysis
Each of the syllabi contained in the final syllabus data set (n = 31) were coded
using the MTEd Instrument. Items on the syllabus could be coded as representing two
different categories or multiple instances of the same category. If multiple pieces of
evidence were found for one category within one syllabus, then the highest level noted
for that category was recorded. If no pieces of evidence were found for a category within
one syllabus, then the category was given a level one. A ten percent reliability test of
coding was conducted, and inter-rater reliability was 90%.
Descriptive statistics were computed to summarize overall levels across the eleven
research areas analyzed. Qualitative examples of categories were identified. Correlation
analysis was conducted to examine the relationship between category levels and overall
levels assigned to each syllabus in elementary-only and secondary-only. Finally, a Mann-
Whitney U test was conducted between two groups found in the final data set, elementary
and secondary, to see if the distribution of levels varied in a statistically significant way.
Results
An overall level of high was achieved by eight syllabi since their overall score
was 33 or higher. An overall level of moderate was achieved by nineteen syllabi since
their overall score was between 22 and 32. An overall level of low was achieved by four
syllabi since their overall score was 21 or lower. The overall score assigned to the syllabi
ranged from 17.0 to 38.0. Of the eight syllabi that scored high, six were elementary, and
two were secondary. Of the four syllabi that scored low, one was elementary, and three
were secondary. Consequently, the evidence of research in the course syllabi was
moderate overall.
Descriptive analysis (see Table 3) of the 31 course syllabi revealed variation
across the research areas identified on the MTEd Instrument. Mathematical tasks (M =
1.77, SD = 0.80) and affect (M = 1.68, SD = 0.87) were the lowest represented on the
syllabi. Additionally, equity (M = 2.94, SD = 1.41) and technology (M = 3.84, SD = 1.44)
had the greatest amount of variance. Conversely, the three categories that showed low
variance were: theory (M = 2.61, SD = 0.67), policy (M = 3.03, SD = 0.75), and content
(M = 2.71, SD = 0.64).
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Table 3: Overall Descriptive Statistics of Syllabi (n = 31)
Range
N M SD Min. Max.
Course Hours 31 37.94 5.31 30.00 49.00
MTEd Categories
Reflection 31 2.52 1.03 1.00 4.00
Tasks 31 1.77 0.80 1.00 4.00
Lesson
Study 31 2.71 1.07 1.00 4.00
Assessment 31 2.16 0.90 1.00 4.00
Theory 31 2.61 0.67 2.00 4.00
Policy 31 3.03 0.75 1.00 4.00
Equity 31 2.94 1.41 1.00 4.00
Affect 31 1.68 0.87 1.00 4.00
Content 31 2.71 0.64 1.00
3.00
Pedagogy 31 3.03 1.02 1.00 4.00
Technology 31 3.84 1.44 1.00 4.00
Overall Score 31 28.00 5.28 17.00 38.00
Qualitative examples of the cells of the MTEd Instrument are provided in Table
4. The table does not distinguish between elementary and secondary examples. As we
will show later, differences in means across cells between elementary and secondary
syllabi were not significant except for content. Therefore, only one table of examples is
provided.
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Table 4: Qualitative Examples of MTEd Instrument Cells
Categories Level 1 Level 2 Level 3 Level 4
Reflection
(no
reference to
reflection)
“[teaching
assignment]
Comments will focus
on how successful
the sequence of
lessons was
including in areas for
improvement, and
possible directions of
future lessons.”
(Australia 4)
(only one type of
reflection – posteri)
“[teaching
assignment] Following
your peer teaching
session you will view
your lesson on tape
and write a 2-3-page
self-analysis/reflection
paper using feedback
from the instructor and
students in the class.”
(USA 13)
(two types of reflection
– initeri while
watching tape and
posteri after viewing)
“[assignment] …weekly reflective journal”
(Canada 1)
(a weekly journal is ongoing and thus
requires all 3 types of reflection – priori,
initeri, and posteri)
Mathematic
al Tasks
(no reference
to
mathematical
tasks)
“[lesson planning
assignment] At least
two examples of how
to solve the problem
you have chosen for
the main part of the
lesson. Solutions
(showing various
approaches) to the
questions you are
assigning for work-
time and/or
“[assignment] Activity
of problem solving to
find an operation that
is commutative and
not associative.
Activity of problem
solving: the sum of the
first 100 numbers.
Activity of problem
solving: the magic
square.”
(Italy 1 - translated)
“[assignment] Three problem-solving
assignments will be given to you to complete.
The main goals of these assignments are for
you to become a better problem solver
yourself, to identify and develop strategies
for solving problems…to reflect on your own
approach and style in problem solving.”
(USA 4)
(extensive opportunity to engage in
mathematical tasks)
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homework.” (Canada
6)
(opportunity to
engage in only pupil
level tasks)
(some opportunity to
engage in
mathematical tasks)
Lesson
Study
(no reference
to lesson
planning)
“[assignment]
…developing a unit
of mathematics study
(individually)…
include…lesson
plans (minimum of
five)” (Canada 1)
(individual planning
lessons but they are
not enacted or
reflected upon)
“[course objectives]
Design and implement
a mathematics lesson
in collaboration with
practicum teacher.”
(USA 7)
(collaborative lesson
planning and
implementing those
lessons but no
reflection piece)
“[assignment] Plan and teach a mathematics
lesson…collaborate with your mentor
teacher on a lesson that you will be
responsible to teach. After conducting your
lesson, you need to write a reflection on your
assessment of the lesson”
(USA 4)
(planned collaboratively, presented, and
reflected upon)
Assessment
(no
reference to
engaging in
assessment)
“[student outcomes]
…by the end of this
course, students
should be able to
describe a variety of
formative and
summative
assessment
techniques” (Canada
1)
(limited opportunity
to analyze student
level work because
the candidate is only
required to describe
assessment
techniques)
“[course content]
Assessment of
children’s
mathematical
understanding,
performance, and
disposition.”
(USA 4)
(some opportunity to
analyze the different
aspects of student level
work)
“[student outcomes] Developing
understanding of curriculum in context by
assessing students’ work, mathematical
problems and/or texts.”
(USA 10)
(extensive opportunity to analyze student
level work and other aspects of the
mathematics program)
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Theory and
Practice
Connections
(reference
only to
textbook and
no other
research)
“[assignment]
…article and reading
summary
paragraph.”
(Canada 1)
(limited opportunity
to engage with
research since highly
structured
introduction to
research literature)
“[assignment]
…assume
responsibility for
reading, reporting on,
and presenting three
practitioners’
articles…presentation
should include an
overview of the
concepts…along with
the group’s critique or
reflections.”
(USA 7)
(some opportunity to
engage with research
through course being
grounded in research
but no chance to
engage in their own
inquiry/research)
“[section under each class schedule with
research links] Linking Theory and Practice”
(Canada 3)
“[inquiry project assignment] … engage in
teacher/action research…actively involved in
asking questions aimed at understanding or
improving teaching.” (Canada 3)
(extensive and authentic engagement in
research with links to current research and
engagement in their own inquiry/research)
Policy and
Politics of
Mathematic
s Teaching
(no reference
to curriculum
documents or
political
aspect of
education)
“[course
description] The
course provides
participants the
opportunity to be
familiar with the
organization of
mathematics through
the BC’ s math
curriculum” (Canada
1)
(limited evidence of
policy exploration
“[lesson topic]
…familiarization with
the content standards
of NCTM, the Ontario
Curriculum, and
additional Ministry
documents (e.g.,
Expert Panel reports
and support
documents).” and a list
of supplementary
journal readings
(Canada 6)
“[course objective] Critique national
assessment practices and tasks for
mathematics” and a list of supplementary
journal readings
(Australia 1)
(extensive evidence of policy exploration due
to additional readings and critique of
national standards)
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since curriculum
document stated but
no extra journal
readings required)
(some evidence of
policy exploration due
to additional readings
and one class
discussion)
Equity and
Diversity
(no reference
to the
exploration of
equity and
diversity
issues)
“[learning
objectives]
…developed an
understanding
of…suitable teaching
approaches for
addressing anxiety
and other
mathematical
phobias.”
(Australia 5)
(limited evidence of
equity exploration
due to narrow focus
on mathematics
specific phobias and
not the diverse needs
of contemporary
students)
“[lesson topic]
Multicultural
Mathematics”
(Canada 1)
(a topic for a class but
not an overriding
concept for the entire
course)
“[course objectives] …apply their
understanding of student differences and
needs in the classroom to promote quality
mathematics for all students.”
(USA 9)
(equity statement and an overriding concept
for the entire course)
Affect
(no reference
to addressing
affect issues)
“[course assignment]
Mathematics
Autobiography…
write your ideas,
attitudes and beliefs
about
mathematics…”
(USA 13)
“[generic skill]
Students will
develop… confidence
in addressing personal
conceptual and skill-
based knowledge of
mathematics during
class activities.”
(Australia 4)
“[course framework] Reflecting
Professionally - How does my relationship to
math, my math thinking, and my teaching
change over time?”
(Canada 2)
(addresses, challenges, and potentially
changes affect)
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(addresses affect but
does not try to
challenge or
potentially change it
(addresses affect and
challenges students’
confidence, but it does
not try to potentially
change affect)
Content
Knowledge
(no reference
to content
knowledge
exploration)
“[course schedule]
Algebraic Thinking
[and] Geometry”
(USA 10)
(engaged in only two
selective components
of content
knowledge)
“[course schedule]
Geometry and
Measurement [and]
Number Concepts and
Operations [and]
Patterns and Place
Value, Fractions [and]
Percent, and Decimals,
Statistics and
Probability Data
Analysis.”
(Canada 1)
(engaged in content
knowledge at student
grade level but not
taken beyond it)
(no syllabi received on this level since none
evidenced engagement in broader ranges of
content knowledge beyond the level of
instruction of the students)
Pedagogical
Content
Knowledge
(no reference
to
pedagogical
discussion)
“[learning outcomes]
…on successful
completion of this
course, students
should be able to
access strategies to
implement…relevant
pedagogy.”
(Australia 2)
(examine
pedagogical
“[course description]
…pragmatic activities
involving the
development and
implementation of
effective teaching and
learning strategies.”
(USA 12)
(examine and develop
pedagogical strategies
but no analysis of
“[course objectives] Be immersed in, discuss
when and how, and implement the use of
different instructional strategies appropriate
for teaching mathematics, including whole
class, small group, cooperative learning, and
individual instruction.”
(USA 7)
(examine, develop, and analyze pedagogical
strategies)
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strategies but no
development or
analysis of
pedagogical
strategies)
pedagogical
strategies)
Technology (no reference
to the use of
technology)
“[course topic]
Technology”
(Canada 5)
(didactic method of
technology
investigation since
technology is limited
to a course topic to
be covered by the
professor)
“[assignment]
…lesson plans…one
based on the use of
technology”
(Canada 1)
(some evidence of
investigation into
technology but limited
to one lesson plan
opposed to integrating
technology into an
entire unit)
“[technology use statement] Utilize
technology as a resource for your own
learning and the learning of children.”
(USA 4)
(extensive evidence of investigation into
technology since it is an overriding concept
for the entire course)
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Correlations in the Elementary Syllabus Data Set
Correlation analysis of elementary syllabi revealed a statistically significant very
strong positive relationship between technology and overall score (r = .841, p = .000).
Additionally, numerous statistically significant strong positive relationships were found
including: reflection and pedagogy (r = .492, p = .016), reflection and overall score (r =
.484, p = .018), lesson study and assessment (r = .571, p = .005), lesson study and
technology (r = .418, p = .038), lesson study and overall score (r = .666, p = .001),
assessment and technology (r = .477, p = .020), assessment and overall score (r = .649, p
= .001), theory and policy (r = .520, p = .011), policy and overall score (r = .521, p =
.011), equity and technology (r = .586, p = .004), equity and overall score (r = .575, p =
.005), and pedagogy and overall score (r = .579, p = .005). Finally, a statistically
significant moderate positive relationship was found between policy and pedagogy (r =
.392, p = .048)
Correlation analysis of elementary syllabi also revealed statistically significant
strong negative relationships including: course hours and lesson study (r = -.446, p =
.028), course hours and assessment (r = -.459, p = .024), mathematical tasks and equity
(r = -.490, p = .017), and mathematical tasks and content (r = -.403, p = .044). Therefore,
mathematical tasks were negatively related to a focus on equity and content, and more
course hours did not suggest more lesson study or more evidence of assessment.
Important to note, course hours and overall score were negatively related and not
statistically significant (r = -2.99, p = n.s.).
Correlations in the Secondary Syllabus Data Set
Correlation analysis of secondary syllabi revealed a statistically significant very
strong positive relationship between technology and overall score (r = .772, p = .002).
Additionally, numerous statistically significant strong positive relationships were found
including: course hours and theory (r = .507, p = .046), course hours and affect (r = .510,
p = .045), reflection and lesson study (r = .641, p = .012), reflection and overall score (r
= .600, p = .020), lesson study and assessment (r = .647, p = .012), lesson study and
overall score (r = .562, p = .029), assessment and theory (r = .554, p = .031), assessment
and policy (r = .514, p = .044), assessment and overall score (r = .664, p = .009), policy
and overall score (r = .586, p = .023), equity and pedagogy (r = .553, p = .031), equity
and technology (r = .555, p = .031), equity and overall score (r = .499, p = .049), and
pedagogy and technology (r = .635, p = .013).
Correlation analysis of secondary syllabi also revealed statistically significant
strong negative relationships between mathematical tasks and theory (r = -.696, p = .046)
and mathematical tasks and affect (r = -.507, p = .046). More evidence of mathematical
tasks was negatively related to evidence of theory or affect components to the syllabi.
Important to note, course hours and overall score were not related and not statistically
significant for secondary syllabi as well (r = .084, p = n.s.).
Mann-Whitney U
A Mann-Whitney U test was conducted between the elementary data-set and the
secondary data-set and the results indicated that evidence of content was greater in the
elementary syllabi (Mean Rank = 18.11) than in the secondary syllabi (Mean Rank =
12.67), U = 74.00, p = 0.18, r = .42 and this was statistically significant. There were no
other statistically significant differences found across any of the other MTEd Instrument
categories. Therefore, other than around content, evidence of research representing the
MTEd Instrument categories across both the elementary and secondary syllabi was
consistent.
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Discussion
Results suggest that only moderate levels of the dominant areas of research in
mathematics teacher education were found in the syllabi that were analyzed in this
research. Technology and assessment were the only categories correlated across both
datasets to overall score. The elementary and secondary course syllabi only differed in
content, where elementary syllabi were shown to have a higher overall level. Finally,
course hours were not related to overall score. This implies that secondary courses likely
include more content, and this perhaps makes intuitive sense. These findings also imply
that an overall score, which would suggest high levels of evidence of the categories
explored in this research, are not influenced by simply more classroom time.
It is important to note from this study’s result that while the analysis of course
syllabi showed moderate or no evidence of correlations between certain categories, such
as course hours and tasks, opportunities to learn these may still emerge when instructors
connect to them in classroom practices in the implemented curriculum. However, the
absence of this evidence has led to questions about the importance of transparency of
course content for students. Numerous scholars have argued that this sort of transparency
is essential and that it may indeed be why some institutions have policy statements
regarding course syllabi (Matejka & Kurte, 1994). Conversely, it is important to also note
that certain items may be stated in a syllabus but may not necessarily be implemented in
the classroom, while other items may be implemented that may not be stated at the onset
of the syllabus.
The categories of mathematical tasks and affect have the lowest mean levels and
are thus the two categories least represented on mathematics teacher educators’ syllabi.
It has been proposed that pre-service teachers engage in mathematical tasks to develop a
deeper understanding of content and learning processes (Chapman, 2007; Watson &
Sullivan, 2008). Yet, this does not appear to be widely evident on the syllabi examined.
This finding is worth sharing because mathematical tasks is one of the important attributes
to assist teachers in engaging students in a meaningful learning. One possible reason for
the lack of representation of mathematical tasks on mathematics teacher education syllabi
might be that research on pre-service education in this area is still at an early stage. This
is not to say that there is no historical research on the importance of mathematical tasks,
but rather that current research is focusing more on pre-service mathematical tasks, and
giving consideration to the importance of both student-and teacher-level mathematical
tasks (Watson & Sullivan, 2008).
In contrast, research on affect is robust and stretches across many years, which
makes it unusual that so few syllabi reference affect. Interestingly, affect is proposed to
influence teaching practice as much as the social context and the teachers’ level of thought
and reflection (Ernest, 1989; Watson & Sullivan, 2008). Perhaps the only justification for
the lack of representation of affect in mathematics teacher education syllabi is that
sometimes it becomes difficult to distinguish beliefs from knowledge, because most
“teachers treat their beliefs as knowledge” (Thompson, 1992, p. 127). As a result, it could
be inferred that mathematics teacher educators overlook affect when planning their pre-
service teacher preparation programs because the syllabi already represents, at least
implicitly, their orientation towards affect.
Equity and technology have the greatest amount of variance in terms of the levels
received from syllabus to syllabus, and this is not surprising. This may be because most
syllabi either mentioned equity and/or technology once in their overriding course goals
section or not at all. Conversely, the three categories that showed the least amount of
variance about the levels received from syllabus to syllabus were theory, policy, and
content. The low variance of levels received suggests that mathematics education is a
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political endeavor that is closely prescribed by policy and needs to be followed by
teachers and taught to pre-service teachers.
Mathematics teacher education research around content knowledge has been
extensive and vigorous, particularly over the past decade (Adler & Davis, 2006; Ball,
2000; Ball et al., 2005; Ball & Grevholm, 2008; Stylianides & Stylianides, 2009). As
stated in the literature review, numerous scholars have attempted to articulate the sorts of
content knowledge required by future mathematics teachers. Many outgrowths of this
have occurred (Ball & Grevholm, 2008; Blömeke 2014; NCTM, 2012; Tatto, 2013; Wang
& Tang, 2013). Overall, the extensive research available on theory-to-practice
connections and content knowledge may explain why pre-service teacher educators
include these areas of research in their program and thus, why these two categories
showed the least amount of variance about the levels received from syllabus to syllabus.
Content knowledge was the only category on the MTEd Instrument that displayed
a statistically significant difference between elementary and secondary syllabi (i.e.,
content knowledge was observed more on elementary syllabi than on secondary syllabi).
This may be due in part because secondary teachers likely have more background in
mathematics education discipline and thus, mathematics teacher educators may assume
that content knowledge is not necessarily a crucial aspect of their teacher education
program. This finding is in line with research which notes that elementary teachers, on
the other hand, tend to have a smaller number of mathematics courses, and rather explore
more content knowledge and in ways that make it less difficult (Jonker, 2008).
The literature on assessment points out that opportunities for pre-service teachers
to engage in the analysis of student level diagnostic, formative, and summative
assessment tasks allow them to gain the necessary knowledge and understanding needed
to teach mathematics (Cunningham & Bennett, 2009; Ketterlin-Geller & Yovanoff,
2009; Xu & Liu, 2009). It could be argued then that assessment weaves through many
stages of the teaching and learning processes and thus, an explanation for the relationship
between assessment and overall score can begin with the realization that assessment is
embedded into some of the eleven categories on the MTEd Instrument (e.g., lesson study,
pedagogy, equity).
Educational reforms around technology have endorsed the advantages of
integrating information and communication technologies (ICT) into all classrooms
(Chai, Koh, & Tsai, 2010; Greenhow et al., 2009; Jonassen et al., 2008; Tan et al., 2006;
Xiao & Carroll, 2007). This type of mass adoption of technology into all facets of
teaching and learning is a relatively new and an evolving concept as it is still in its
formative stages as stated by Tsai and Tsai (2019). One can therefore conclude that a
mathematics teacher education course that integrates technology into its program
demonstrates an approach to pre-service teacher education that is grounded in current
research. Moreover, pre-service mathematics teacher education courses that incorporate
technology into the classroom may also incorporate other educational reforms into their
program and thus, a high degree of current research in their pre-service teacher education
course syllabi may also be evident.
Another surprising result was that no statistically significant positive correlations
(at p = .01 or below) existed between course hours and overall score. An increase in
course hours did not potentially yield high score or more lesson study according to this
research. Whereas this result may be interpreted that more time spent in a course may
not necessarily lead to greater opportunities to learn for a pre-service teacher, it could
mean that certain courses focus on in-depth opportunities for selected categories, leaving
other categories for other methods courses.
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When considering statistically significant correlations (at p = .01 or below)
between course hours and individual MTEd Instrument categories, we see that one
statistically significant strong negative relationship appears between mathematical tasks
and course hours within the full data set. Again, this result could be interpreted that when
course hours increase, the level for mathematical tasks activities decreases, and vice
versa. A plausible interpretation could be that this category could have been the focus on
another method course or experience.
Limitations of the study
There are some limitations in the study that will be addressed. First, the sample
may not have been fully representative of all mathematics methods courses in a program,
at a university or in the country, and may not have been vigorous enough to generalize
the result. Hence, a larger sample size may have been needed, given the methodology
adopted to reach data saturation. Second, the instrument may need further development
both in category content and design to obtain deeper and richer data for generalization of
results. It may be argued that the categories are not fully representative of the field. While
this may be true, the preliminary contributions of this work and this instrument are viewed
by us as still noteworthy.
The MTEd Instrument used a rating scale that was limited to level one through
level four, which may have caused a compression of trends due to its small range.
Alternatively, it could be argued that a different or a larger ranged grading scale may be
appropriate. We recognize the limitations that the MTEd Instrument weighted all the
categories equally when it could be argued that some of the eleven categories are more
deferentially important to mathematics teacher education in different contexts. In future
research, it would be important to use MTEd categories together with categories arising
from more recent studies. Furthermore, the study does not consider how the syllabus is
implemented in the classroom or the implications for pre-service teachers’ learning and
their subsequent practices in their own classrooms. We agree with Hora and Ferrare
(2013) that firsthand observations of classroom practice and activities, the achieved and
tested curriculum (Burkhardt et al., 1990) or classroom curriculum (Deng, 2011) would
capture multiple dimensions of what is learned in mathematics methods courses and how
this learning comes to life in practice.
These limitations should not diminish the importance of this preliminary work,
given the important first message that a syllabus provides to a student about a discipline
and their learning.
Suggestions for further research
Further research that validates the instrument would be important extensions of
this work. For instance, the strong evidence of technology applied across the dataset,
may demonstrate that technology is an excellent indicator of overall score on the MTEd
Instrument. Hence, this measure could be used in place of an elaborate rubric to quickly
evaluate the extent to which a pre-service teacher mathematics education program
reflects current research. The MTEd instrument could also be very useful for instructors
to evaluate intentionally if what is proposed to be optimal for learning in the research is
reflected in their curricular plans and goals. The MTEd has established a way for teacher
educators to self-evaluate what is included in their syllabi. Moreover, the more correlated
categories in both data sets–technology and assessment–could be further studied to
consider what they entail.
On the other hand, three categories–mathematical tasks, affect, and content
knowledge–on the MTEd Instrument did not have any correlation with the overall score
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of the syllabi. The most surprising result is related to content knowledge. There is
extensive research available on content knowledge and its importance in teacher
development (e.g., Ball, 2000; Ball et al., 2005; Ball & Grevholm, 2008; Blömeke, 2014;
NCTM, 2012; Tatto, 2013; Wang & Tang, 2013). So, it is surprising that no correlation
exists between content knowledge and overall score. This raises a lot of research
questions that would need further research, which would in turn replicate the present
study.
It would also be of great interest to explore variation in teacher practices
considering pre-service teachers who participated in courses that exhibited low,
moderate, and high evidence of research, such as theory and practice connections, policy
and politics of mathematics teaching within their course syllabi.
Finally, certain categories reflected on the syllabus may not result in implemented
curriculum (Burkhardt et al., 1990) in the classroom; and, conversely, those categories
not listed in the syllabi may nevertheless have been implemented. Further research would
be useful to explore implemented curriculum in mathematics teacher education programs.
Conclusions
This study examined paper syllabi from six countries to analyze the intended
learning experiences and the course effectiveness in mathematics education courses of
pre-service teachers. Although pre-service teachers take a variety of courses, the focus of
this research was limited to mathematics education courses.
This research found that recommendations in research related to the mathematics
education of pre-service teachers were moderately represented in the course syllabi
analyzed (according to the MTEd Instrument). Technology and assessment were the only
two categories that proved to be correlated in both datasets, elementary and secondary
syllabi differed on content, where elementary syllabi were shown to have a higher overall
level. Moreover, in terms of representation on the syllabus, equity and technology had
the greatest amount of variance, followed by three categories—theory, policy, and
content— that showed low variance with mathematical tasks; whereas affect categories
had the lowest representation on the syllabi.
Lastly course hours are not related to overall score, which suggests that more
course hours may not necessarily result in pre-service teachers gaining qualitative
differences in knowledge and understanding about research-informed practice. This study
recommends future research to further examine the relationship between the number of
course hours a mathematics teacher education course offers and the level of knowledge
and understanding that pre-service teachers receive from that course.
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Appendix A: MTEd. Instrument
Low evidence of research
(overall score less than 22)
Moderate evidence of research (overall
score from 22 to 32)
High evidence of research
(overall score more than 32)
Categories Level 1 Level 2 Level 3 Level 4
1.
Reflection
No opportunities to
engage in reflection.
Opportunities to
engage in only one
type of reflection.
Opportunities to
engage in only two
types of reflection.
Opportunities to engage
in all three types of
reflection (priori, initeri,
and posteri).
2.
Mathematical
Tasks
No direct
engagement with
mathematical tasks.
Opportunities to
engage only in
either pupil or pre-
service level tasks.
Some opportunities to
engage in both types
of tasks.
Extensive opportunities
to engage in both types
of tasks.
3.
Lesson Study
No lesson planning. Developing lesson
plans individually
or collaboratively
that are not enacted.
[No reflection piece]
Developing lesson
plans individually or
collaboratively that
are presented to the
class.
[No reflection piece]
Developing lesson plans
collaboratively that are
presented to the class
and reflected upon.
4.
Assessment
No opportunities to
engage in
assessment.
Limited
opportunities to
engage in
assessment and
analyze pupil level
mathematization.
Some opportunities to
engage in assessment
and analyze pupil
level
mathematization.
Extensive opportunities
to engage in assessment
and to analyze pupil
level mathematization.
5.
Theory and
Practice
Connections
No opportunities to
engage with
research.
[e.g., only the
textbook – no
references to other
research]
Limited
opportunities to
engage with
research through
course readings and
discussions.
[e.g., attempt made
to introduce students
to research literature
– highly structured
or select]
Some opportunities to
engage with research
through course
readings and
discussions (course is
somewhat grounded
in research and
research is evident in
the course content).
[e.g., when a new
topic is introduced the
students are provided
with links to current
research]
Extensive and
authentic opportunities
to engage in and with
research (course is
grounded in research
and research is evident
in the course content).
[e.g., when a new topic
is introduced the
students are provided
with links to current
research and in addition,
the student has the
opportunity to engage in
their own inquiry or
research]
6.
Policy and
Politics of
Mathematics
Teaching
No evidence of any
exploration of the
political aspects of
mathematics
education.
Limited evidence of
exploration of the
political aspects of
mathematics
education. [e.g.,
Regional
Curriculum
Documents]
Some evidence of
exploration of the
political aspects of
mathematics
education. [e.g.,
Regional Curriculum
Documents - with
some journal-type
readings which further
the discussion about
the role of those
documents]
Extensive evidence of
exploration of the
political aspects of
mathematics education.
[e.g., Regional
Curriculum Documents
- with lots of journal-
type readings which
further the discussion
about the role of those
documents, and the
issues (i.e., high stakes
testing)]
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7.
Equity and
Diversity
No evidence of any
exploration of the
equity and diversity
considerations in
mathematics
education.
Limited evidence of
exploration of the
equity and diversity
considerations in
mathematics
education.
Some evidence of
exploration of the
equity and diversity
considerations in
mathematics
education. [e.g., one
lesson]
Extensive evidence of
exploration of the equity
and diversity
considerations in
mathematics education.
[e.g., a diversity
statement on the syllabi]
8.
Affect
No evidence of
addressing the
implications of
affect on the
teaching of
mathematics.
Evidence of
addressing the
implications of
affect on the
teaching of
mathematics.
Evidence of
addressing and
challenging the
implications of affect
on the teaching of
mathematics.
Evidence of addressing,
challenging, and
potentially changing
the implications of
affect on the teaching of
mathematics.
9.
Content
Knowledge
No evidence of
exploration of
content knowledge
at any level.
Engaging in a
selective
component of
content knowledge
at the level of
instruction of the
students.
Engaging in content
knowledge at the
level of instruction of
the students.
Engaging in broader
ranges of content
knowledge beyond the
level of instruction of
the students.
10.
Pedagogical
Content
Knowledge
No evidence of
pedagogical
discussion.
Examine
pedagogical
strategies. [e.g.,
limited opportunity
for critical analysis]
Examine and develop
pedagogical
strategies. [e.g., some
opportunity for critical
analysis]
Examine, develop, and
analyze pedagogical
strategies. [e.g.,
extensive opportunity
for critical analysis]
11.
Technology
No evidence of
technology
integration.
Didactic methods
of technology
investigation and
implementation.
[e.g., teacher-led
only]
Some evidence of pre-
service teacher
investigation and
implementation of
technology. [e.g., one
lesson]
Extensive evidence of
pre-service teacher
investigation and
implementation of
technology. [e.g., a unit
of study or a technology-
use statement in the
syllabi]
https://ojs.library.ubc.ca/index.php/tci/index
Unsworth, Namukasa, Aryee, Kotsopoulos. Mathematics Education Course Syllabus 51
Transnational Curriculum Inquiry 17 (2) 2021
https://ojs.library.ubc.ca/index.php/tci/index
Notes
1 leslie.anne.unsworth@gmail.com
2 inamukas@uwo.ca
3 karyee@uwo.ca
4 dkotsopo@uwo.ca
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Submitted: January, 10th.
Approved: July, 5th.
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