Shifts in attention. (a) “different roles of the segment ED” when proving Problem 1. (b) Focusing on different types of triangles when proving Yoni’s theorem using Menelaus theorem
26
1.4.
Distinctive characteristics of the three mathematics teacher educators’ communities of practice
30
1.5.
Mathematics teacher educators’ (MTEs’) knowledge in terms of intellectual potential and mathematical challenge
31
3.1.
Adam’s zone configuration during the practicum
60
3.2.
Adam’s zone configuration during his first year of teaching
61
3.3.
Adam’s zone configuration during his second year of teaching
62
3.4.
Three layers of application of zone theory
63
3.5.
Sample pedagogical content knowledge item for primary school teachers
66
3.6.
Sample pedagogical content knowledge item for secondary school teachers
66
4.1.
A church
82
4.2.
The new church
83
6.1.
Exercise A
139
6.2.
Exercise B
140
8.1.
Model for mathematics teacher educators’ (MTEs’) goals and classroom practices for providing prospective teachers with opportunities to develop pedagogical content knowledge
200
9.1.
Conceptual framework
233
10.1.
The five dimensions of powerful classrooms
272
10.2.
A non-linear representation of TRU, representing the interconnections of the five TRU dimensions, with mathematics at the core (from Schoenfeld, 2016, reproduced with permission)
294
11.1.
Probing “defining” and “equating” contructed meanings of the equal sign
316
11.2.
Scaffolding for the task shown in Figure 11.1
317
11.3.
Excerpt of task addressing questions about plus/minus and square root
319
11.4.
Modified complex zeros task for graduate practising teachers (adapted from Usiskin et al., 2003)
Pre- and post-assessment items (from Epperson, 2009)
330
11.7.
Connecting patterns to visual representations (from Epperson, 2010)
333
11.8.
Sample revision of task connecting patterns to visual representations
334
11.9.
Exam question 10 on patterns and visual representations
335
11.10.
Student response receiving full credit on exam question 10
335
13.1.
Ecological systems model (from Bronfenbrenner, 1977)
380
Tables
3.1.
Relationship of Valsiner’s zones to factors influencing mathematics teachers’ use of digital technologies
59
3.2.
Relationship of Valsiner’s zones to influences on mathematics teacher educator (MTE) learning and development
64
8.1.
Mathematics teacher educators’ goals and practices related to providing opportunities to develop prospective teachers’ pedagogical content knowledge (PCK)
204
9.1.
The nine research journals
235
9.2.
Number of articles with respect to methodological approaches used, teacher educators’ specialized subject area, and number of teacher educators studied
237
9.3.
Number of articles in each practice category
238
9.4.
Number of articles with results related to themes of preparation of prospective teachers practice
239
9.5.
Number of articles with results related to themes of professional development for practising teachers practice
245
9.6.
Number of articles with results related to themes of school teaching practice
248
9.7.
Number of articles with results related to themes of research practice
250
9.8.
Number of articles with results related to themes of teacher educators’ education and professional development practice
252
11.1.
Mathematics teacher educator learning themes from Zaslavsky (2008) in graduate (practising) and undergraduate (prospective) courses for the topics of Functions and Equations, Visualising Complex-valued Zeros, and Building Functions
Chapter 8 Conceptualization and Enactment of Pedagogical Content Knowledge by Mathematics Teacher Educators in Prospective Teachers’ Mathematics Content Courses
Chapter 9 Learning to Be Mathematics Teacher Educators
Chapter 11 Mathematics Teacher Educators Learning from Efforts to Facilitate the Learning of Key Mathematics Concepts While Modelling Evidence-Based Teaching Practice
Chapter 12 Mathematics Teaching Development in Higher Education
Chapter 13 Becoming a Mathematics Teacher Educator