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Mathematics and Teaching

Michele D. Crockett
Publication Date: 
Number of Pages: 
Reflective Teaching and the Social Conditions of Schooling
[Reviewed by
Teri J. Murphy
, on

I am grateful to have had the opportunity to review this book, because I would otherwise have overlooked it, despite being very interested in its topic. This is because the title is not descriptive of the contents: The book uses case stories and reactions to those stories to explore various dimensions of the relationships among mathematics, schools, and culture.

For each case, the author presents a description of the case (about four pages), a set of reader reactions to the case (about six pages), and suggested questions for leading a discussion about the case. The four cases are as follows.

  1. “Race and Teacher Expectations” centers on an experienced teacher (white, female), a student teacher (white, female), and a third grade student (black, male). The experienced teacher believes that the student is incapable and wants to recommend him for special education. The student teacher believes that the evidence indicates that the student is quite capable, but perhaps bored. She also believes that the experienced teacher's perceptions result from racial bias (and possibly some teacher burn out). At the end of the case, the student teacher wonders whether she should share her observations about the student (which were part of a practicum assignment) with the experienced teacher.
  2. “Mathematics for All?” is set in the context of algebra for all eighth graders. The case raises questions about whether all students are capable of learning algebra, who should have access to algebra (and therefore college-preparatory mathematics), and how teachers might react to increased pressure (with no apparent increase in resources).
  3. “Culture and School Mathematics” confronts the common belief that mathematics is “culturally neutral” and offers the viewpoint that the mathematics we teach in the U.S.A. is very Eurocentric. This case was my favorite of the four because of an example that the author presents in the summary (it originally appeared in Tate, 1994), about a mathematics problem that asks whether purchasing daily bus passes or a weekly bus pass is a better deal. The intended answer is that the daily pass is the better deal, which assumes (the problem does not state any assumptions explicitly) a 5-day work week and riding the bus twice per day (once to work, once home from work). Those (cultural!) assumptions are not the least bit valid for many students.
  4. “Politics and School Mathematics” is set in the context of a district meeting to discuss scores on standardized tests. The case illustrates the confusion and frustration that teachers experience as they try to interpret expectations that result from political infighting and attempts to “balance” the curriculum.

The cases are followed by a section titled “Public Arguments”, chunked into three categories:

  • “A ‘Conservative View’: Mathematics for Global Economic Leadership”
  • “A ‘Liberal View’: Equality of Opportunity and School Mathematics in a Democracy”
  • “A ‘Radical Multiculturalist View’: Mathematics for Developing Critical Dispositions for Social Reconstruction”

The author acknowledges that the descriptions in this section are oversimplified. Nevertheless, the statements appearing in this section exemplify claims that people really do make and I can imagine that this section would lead also to good discussions.

I can imagine using the cases and political arguments presented in Mathematics and Teaching with a number of audiences:

The book series title says, “A Series for Prospective and Practicing Teachers”. I have had a bit of experience with K–12 teacher preparation programs; however, I have had much more experience with the professional development of graduate teaching assistants (TAs). I have used a number of resources in that context. In general, I found that new TAs tended to be skeptical of cases, refusing to believe that such situations occur in real life. I had greater success using cases with experienced instructors.

That said, I can imagine using the cases with pre-service teachers. I would personally find that the most difficult group with whom to use this effectively, because they have such very limited experience with classrooms and politics. Furthermore, I know that many teacher education programs struggle to balance time the spend learning mathematics at a deep level, developing pedagogy and classroom management skills, and discussing social/political issues — I get distressed when I hear about programs that spend no time with books such as this one, but I also get distressed when I hear about programs that spend so much time with books such as this one that they disregard the learning of mathematics or pedagogy.

I can imagine the book being more effective with student teachers, who are immersed in teaching and beginning to confront very difficult situations. This group is also in the process of constructing themselves as professionals, making this group a particularly important focus point. I can also imagine using the cases with experienced teachers. I would expect that this group would provide powerful but perhaps conflicting issues: they would have experiences on which to draw and to which to make connections but they may also be more entrenched in their beliefs about mathematics, teaching, learning, students, and politics.

The book itself includes reactions from parents, grandparents, school board members, administrators, and other professionals associated with K–12 schooling. These audiences are not listed explicitly as intended audiences in the series title, but it seems to me that the author did a very powerful thing by having discussions with such people about the cases and including their comments in the reactions sections. These groups can be influential in decision-making processes and are critical in the support structure for teachers who are trying to be maximally effective for all students. 

Teri J. Murphy is an Associate Professor at Northern Kentucky University. Her research area is undergraduate science, engineering, and mathematics education.


Table of Contents

Series Preface iii

Preface iv

Acknowledgments x

Introduction 1


Introduction to Case 1 12

Case 1: "Race and Teacher Expectations" 13

Reader Reactions to "Race and Teacher Expectations" 19

Reactions to "Race and Teacher Expectation 20

Summary and Additional Questions 34

Introduction to Case 2 35

Case 2: "Mathematics for All?" 36

Reader Reactions to "Mathematics for All?" 42

Reactions to "Mathematics for All?" 43

Summary and Additional Questions 55

Introduction to Case 3 57

Case 3: "Culture and School Mathematics" 59

Reader Reactions to "Culture and School Mathematics" 64

Reactions to "Culture and School Mathematics" 65

Summary and Additional Questions 76

Introduction to Case 4 79

Case 4: "Politics and School Mathematics" 81

Reader Reactions to "Politics and School Mathematics" 87

Reactions to "Politics and School Mathematics" 88

Summary and Additional Questions 104

Reader Reactions to the Four Cases 107

Reactions to the Four Cases 108

Part II. Public Arguments 119

A "Conservative View": Mathematics for Global Economic Leadership 122

Comments and Questions 135

A "Liberal View": Equality of Opportunity and School Mathematics in a Democracy 138

Comments and Questions 147

A "Radical Multiculturalist View": Mathematics for Developing Critical Dispositions for Social Reconstruction 150

Comments and Questions 164

Part III. Concluding Remarks, Some Reflections, and Resources for Further Reflections