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The Creative Enterprise of Mathematics Teaching Research: Elements of Methodology and Practice - From Teachers to Teachers

Bronislaw Czarnocha, William Baker, Olen Dias and Vrunda Prabhu, editors
Sense Publishers
Publication Date: 
Number of Pages: 
[Reviewed by
Annie Selden
, on

This majority of this book (29 of 32 chapters, 7 with others) was written by the editors and reports the development of a teaching method, called the TR/NYCity Model. The model was developed over time by combining prior mathematics education theory and research results with the editors’ own teaching observations. The editors refer to themselves as teacher-researchers and are mostly regular faculty from Hostos and Bronx Community Colleges. They developed their model by combining and generalizing action research and design experiment methodology. Basically, they planned and investigated their own teaching over a number of years, informed by the mathematics education research and creativity literatures.

The underlying motivation that ultimately evolved into the TR/MYCity Model seems to have begun with the teacher-researchers’ concerns about their underserved, mainly immigrant, first-generation, remedial, community college students. Perhaps because their students had experienced repeated failures with mathematics, they decided that interactive inquiry-based learning needed to be instituted with an emphasis on a creative learning environment that would “transition students from habits of failure to excellence.”

Much credit for the development of this approach is given by the other editors to Vrunda Prabhu, who passed away during the preparation of this book and to whom it is dedicated. Indeed, Unit 2 reads somewhat like a personal journey of discovery by Vrunda Prabhu on teaching fractions, ratio, and proportion, interspersed with theoretical considerations, such as Vygotksy’s Zone of Proximal Development, Brousseau’s didactical contract, and Koesler’s bisociation theory.

The teaching of other mathematical topics, not necessarily using the TR/NYCity Model, is also included in this volume. For example, Chapter 4.9 is on teaching calculus using a “real world” approach and was written by Hannes Stoppel, a former high school mathematics and physics teacher, now at University of Munster. Why the editors decided to include ideas not clearly embracing their TR/NYCity Model is unclear.

This is a long book (536 pages) divided into five parts, termed units. Perhaps because many of the authors are describing their ideas and implementations of the TR/NYCity Model, parts of the chapters, especially the theoretical background, can seem somewhat repetitive. Despite, the book’s length, I feel that not quite enough practical information is given for readers to implement the authors’ ideas — so this is not a “how to” book. When illustrative examples and classroom dialogs are given, they are rather short. Perhaps because the teachers-researchers are dealing with remedial students, the examples and dialogs often deal with such topics as place value, fractions, proportion, and ratio. Some of the many figures in the book seem like many-faceted, very detailed, complex flow diagrams — indeed, I found some of the print in the “boxes” too small to read without a magnifying glass. It is clear that some of the authors are not native speakers of English as indicated by occasional lapses in the use of the articles “a” and “the”; however, these lapses do not constitute a major distraction.

Even if one does not decide to try to follow the TR/NYCity Model in one’s teaching, there are a number of innovations in this volume that one might want to consider trying. For example, as described in Chapter 3.6, some of the teacher-researchers use concept maps, not only in their research and planning for teaching, but also in class as pictorial, revisable syllabi for students to visualize the flow of the course, as well as scaffolding to plan how students could construct mental schema for important course concepts.

Annie Selden is Adjunct Professor of Mathematics at New Mexico State University and Professor Emerita of Mathematics from Tennessee Technological University. She regularly teaches graduate courses in mathematics and mathematics education. In 2002, she was recipient of the Association for Women in Mathematics 12th Annual Louise Hay Award for Contributions to Mathematics Education. She remains active in mathematics education research and curriculum development. 


Barbara Jaworski



Unit 1: The Main Themes of the Book

1.1  Teaching-Research New York City Model (TR/NY City)

Bronislaw Czarnocha

1.2. Creativity Research and Koestler: An Overview

Bronislaw Czarnocha, Vrunda Prabhu, Olen Dias and William Baker

1.3. Underserved Students and Creativity

William Baker

Unit 2: Creative Learning Environment

2.1. The Didactic Contract, a Handshake and a Compromise: A Teaching-Action-Research Project

Vrunda Prabhu, Bronislaw Czarnocha and Howard Pflanzer

2.2. Focus on Creativity – Literacy – Numeracy

Vrunda Prabhu and James Watson

2.3. The Poznan Theatre Problem

Vrunda Prabhu, Peter Barbatis and Howard Pflanzer

2.4. The Creative Learning Environment

Vrunda Prabhu

2.5. The Reflections of the Teacher-Researcher upon the Creativity Principle

Vrunda Prabhu

2.6. Reflection and Case Study of Creative Learning Environment

Olen Dias

Unit 3: Tools of Teaching-Research

3.1. How to Arrive at a Teaching-Research Question?

Vrunda Prabhu, William Baker and Bronislaw Czarnocha

3.2. How to Approach a Teaching Experiment?

Bronislaw Czarnocha

3.3. Qualitative and Quantitative Analysis

William Baker

3.4. Teaching Research Interviews

Eric Fuchs and Bronislaw Czarnocha

3.5. Use of Concept Maps in Classroom Research

Vrunda Prabhu, Haiyue Jin and Roberto Catanuto

3.6. Pictorial Scaffolding in the Schema Construction of Concepts

Vrunda Prabhu

3.7. Concept Maps: Learning through Assesment

Haiyue Jin

3.8. The Method Learning Routes

Robert Catanuto

3.9. Discovery Method and Teaching-Research

William Baker

Unit 4: Teacher as the Designer of Instruction: TR Design

4.1. Koestler’s Theory as a Foundation for Problem-Solving

William Baker

4.2  Comparative Study of Three Approaches to Teaching Rates

Olen Dias, William Baker and Bronislaw Czarnocha

4.3  Rate and Proportion Teaching Sequence

Olen Dias

4.4  Proportional Reasoning and Percent

William Baker

4.5  Rate Teaching Sequence

Bronislaw Czarnocha

4.6. Two Learning Trajectories

William Baker and Bronislaw Czarnocha

4.7. Learning Trajectory: Rational Numbers Sense to Proportional Reasoning

William Baker

4.8. Learning Trajectory: Linear Equations

Bronislaw Czarnocha

4.9. Calculus: Searching for a “Real World” Approach

Hannes Stoppel

4.10. From Arithmetic to Algebra: A Sequence of Theory-Based Tasks

William Baker and Bronislaw Czarnocha

Unit 5: Teaching Research Communities

5.1. Algebra/English as a Second Language (ESL) Teaching Experiment

Bronislaw Czarnocha

5.2. “Just Tell Us the Formula!” Co-Constructing the Relevance of Education in Freshman Learning Communities

Ted Ingram, Vrunda Prabhu and H. Elizabeth Smith

5.3. Professional Development of Teacher-Researchers (PDTR) in Tamil Nadu, India: Focus on Women in Community-Based Schools of Tamil Nadu

Vrunda Prabhu and Bronislaw Czarnocha

5.4. PDTR: The Development of a Teacher-Researcher: Formulation of a Hypothesis

Bronislaw Czarnocha, Maria Mellone and Roberto Tortora


Bronislaw Czarnocha, William Baker and Olen Dias

About the Contributors