Chapter 6 - Summary

Summary

Cases discussions have a multitude of possible uses in professional development. Depending on the content of the case and the focus of the discussion, this type of activity can address all the teacher learning needs we identified in Chapter 1. The extreme flexibility in using cases is one of its greatest strengths as a professional development tool. At the same time, because cases can vary so much, it is more difficult to evaluate their effectiveness without context-specific information.

Suggested follow-up resources

If you are interested in learning more about how to use cases for a variety of professional development goals, we recommend the following resources, in addition to the Developing Mathematics Ideas (DMI) materials already mentioned in Chapter 5:

Barnett, C., Goldenstein, D., and Jackson, B. (Eds.) (1994b). Fractions, decimals, ratios, and percents: Hard to teach and hard to learn? (casebook and facilitator’s guide) Portsmouth, NH: Heinemann.

This set of 29 teacher-written cases illustrates recurring dilemmas and problems in teaching and learning fractions, decimals, ratios and percents. The editors primarily intend these cases for mathematics teachers in grades 4 – 8; however, we find them to be beneficial for teachers from kindergarten through grade 12. The facilitator’s guide identifies the central mathematical and pedagogical issues addressed by each case, offers suggestions for facilitating the discussions, and identifies some of the common misconceptions that can emerge during the discussions.

Stein, M. K., Smith, M. S., Henningsen, M. A., and Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York: Teachers College Press.

This book, intended for teacher educators and teachers, is more than a set of cases. The authors introduce their mathematical task framework and describe the typical pedagogical patterns teachers use in implementing tasks, uncovered as the result of their research of middle school mathematics classrooms. The explicit description of the task framework and the pedagogical patterns helps teachers become aware of the cognitive demands of a mathematical task and of the issues involved in maintaining the cognitive level of a task. The cases, inspired by real classroom experiences, provide opportunities for teachers to practice identifying the cognitive demands of a particular mathematical task, to see firsthand how pedagogical practices impact the task, and to grapple with the issues raised by the example. Each case includes a section in which the featured teacher discusses her class and a section describing her implementation. In addition, each case is accompanied by a set of discussion questions and notes to support the case discussion.

Harvard Mathematics Case Development Project (in press). Cases in secondary mathematics classrooms. New York: Teachers College Press.

This book includes several cases at each level of high school mathematics (i.e., Pre-Algebra and Algebra, geometry, Algebra II and Trigonometry, Probability and Statistics, Pre-Calculus and Calculus). Before presenting the cases, the authors outline in detail their theoretical framework for constructing them. They examine the mathematical, pedagogical, student assessment and contextual issues they believe teachers need in order to promote learning at high levels. The book also includes a guide for case facilitators and for participants in case discussions, and it lists the major mathematical and pedagogical issues raised by each case. Each case is supplemented by notes for the facilitator that include a prediscussion activity, tips for teaching the case, suggested discussion questions, possible extensions and annotated references for further reading on either the mathematics content or the pedagogy.

Miller, B., and Kantrov, I. (1998). Casebook on school reform. Portsmouth, NH: Heinemann.

This book includes six ready-to-use cases that describe teachers’ reform efforts in mathematics or science. The introduction of the book provides a rationale for using cases, an explanation of why and how the cases were developed and some suggestions for how to use them. The cases, developed to highlight issues raised when educators engage in school reform, are intended to stimulate thinking and discussions from multiple perspectives. Each case is accompanied by a facilitator’s guide that suggests ways to elicit discussion about the “big ideas” underlying the case.




	Summary Cases discussions have a multitude of possible uses in professional development. Depending on the content of the case and the focus of the discussion, this type of activity can address all the teacher learning needs we identified in Chapter 1. The extreme flexibility in using cases is one of its greatest strengths as a professional development tool. At the same time, because cases can vary so much, it is more difficult to evaluate their effectiveness without context-specific information. Suggested follow-up resources If you are interested in learning more about how to use cases for a variety of professional development goals, we recommend the following resources, in addition to the Developing Mathematics Ideas (DMI) materials already mentioned in Chapter 5: Barnett, C., Goldenstein, D., and Jackson, B. (Eds.) (1994b). Fractions, decimals, ratios, and percents: Hard to teach and hard to learn? (casebook and facilitator’s guide) Portsmouth, NH: Heinemann. This set of 29 teacher-written cases illustrates recurring dilemmas and problems in teaching and learning fractions, decimals, ratios and percents. The editors primarily intend these cases for mathematics teachers in grades 4 – 8; however, we find them to be beneficial for teachers from kindergarten through grade 12. The facilitator’s guide identifies the central mathematical and pedagogical issues addressed by each case, offers suggestions for facilitating the discussions, and identifies some of the common misconceptions that can emerge during the discussions. Stein, M. K., Smith, M. S., Henningsen, M. A., and Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York: Teachers College Press. This book, intended for teacher educators and teachers, is more than a set of cases. The authors introduce their mathematical task framework and describe the typical pedagogical patterns teachers use in implementing tasks, uncovered as the result of their research of middle school mathematics classrooms. The explicit description of the task framework and the pedagogical patterns helps teachers become aware of the cognitive demands of a mathematical task and of the issues involved in maintaining the cognitive level of a task. The cases, inspired by real classroom experiences, provide opportunities for teachers to practice identifying the cognitive demands of a particular mathematical task, to see firsthand how pedagogical practices impact the task, and to grapple with the issues raised by the example. Each case includes a section in which the featured teacher discusses her class and a section describing her implementation. In addition, each case is accompanied by a set of discussion questions and notes to support the case discussion. Harvard Mathematics Case Development Project (in press). Cases in secondary mathematics classrooms. New York: Teachers College Press. This book includes several cases at each level of high school mathematics (i.e., Pre-Algebra and Algebra, geometry, Algebra II and Trigonometry, Probability and Statistics, Pre-Calculus and Calculus). Before presenting the cases, the authors outline in detail their theoretical framework for constructing them. They examine the mathematical, pedagogical, student assessment and contextual issues they believe teachers need in order to promote learning at high levels. The book also includes a guide for case facilitators and for participants in case discussions, and it lists the major mathematical and pedagogical issues raised by each case. Each case is supplemented by notes for the facilitator that include a prediscussion activity, tips for teaching the case, suggested discussion questions, possible extensions and annotated references for further reading on either the mathematics content or the pedagogy. Miller, B., and Kantrov, I. (1998). Casebook on school reform. Portsmouth, NH: Heinemann. This book includes six ready-to-use cases that describe teachers’ reform efforts in mathematics or science. The introduction of the book provides a rationale for using cases, an explanation of why and how the cases were developed and some suggestions for how to use them. The cases, developed to highlight issues raised when educators engage in school reform, are intended to stimulate thinking and discussions from multiple perspectives. Each case is accompanied by a facilitator’s guide that suggests ways to elicit discussion about the “big ideas” underlying the case.