Examining Mathematics Practice through Classroom Artifacts / Edition 1

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Overview

Examining Mathematics Practice through Classroom Artifacts

Lynn Goldsmith and Nanette Seago

Offering an innovative framework, this book helps teachers learn how to use classroom artifacts to assess students' mathematical thinking and students’ understanding of mathematical content.

Teachers need to be able to diagnose what their students do and don't understand about mathematics. Examining Mathematics Practice through Classroom Artifacts helps teachers become more analytic about their students' thinking by showing them how to use student artifacts to evaluate what is happening in the classroom. Focusing on elementary through middle grades, chapters investigate what classroom artifacts are, how to interpret them and ways to use this data to improve mathematics instruction.

“The book takes a qualitative view of a quantitative subject, which is not easy to do successfully. The discussion on the strengths of using habits of mind as a basis for lesson plan evaluation was very strong. I would use that idea as the basis for PD in my own school district.“

- Julie A. Drewry, K-12 Mathematics Supervisor, Roanoke City Public Schools, Roanoke, VA

"[This book] examined and delineated the thinking that needs to occur to develop mathematically strong instruction and to improve our analysis of students’ thinking. It shifted our attention from errors as merely mistakes, to errors that help us to identify strengths as well as weaknesses. How to interpret student thinking based on artifacts from the classroom, how to identify the mathematical “big ideas” in curriculum, how to ensure the rigor of our lessons, and how students represent their mathematical thinking as well as using errors to develop next steps are the key ideas of this manuscript. All of these topics are critical components of quality instruction.”

- Jane Elizabeth Gillis, Math Cadre, Red Clay Consolidated School District, Wilmington, DE

Lynn Goldsmith began her career as a developmental psychologist, where her major research interests lay in understanding the formal and informal systems that support the development of extreme talent. For the past 20 years, she has worked in the field of mathematics education, investigating factors contributing to successful professional development, the role of curriculum in educational reform, and the emotional aspects of learning. She has co-authored Choosing a Standards-based Mathematics Curriculum (Heinemann, 2000), served as series co-editor of the Guiding Middle-grades Curriculum Decisions series (Heinemann, 2000), and co-authored Nature’s Gambit: Child Prodigies and the Development of Human Potential (Teachers College Press, 1991).

Nanette Seago was the primary author of Learning and Teaching Linear Functions: Videocases for Mathematics Professional Development. She has been working in mathematics professional development for twenty years. Currently, she is working at WestEd as a Principal Investigator for a National Science Foundation project focused on the research and design of videocase materials for middle school teachers–Learning and Teaching Geometry.

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Editorial Reviews

From the Publisher

“The book takes a qualitative view of a quantitative subject, which is not easy to do successfully. The discussion on the strengths of using habits of mind as a basis for lesson plan evaluation was very strong. I would use that idea as the basis for PD in my own school district.“

- Julie A. Drewry, K-12 Mathematics Supervisor, Roanoke City Public Schools, Roanoke, VA

"[This book] examined and delineated the thinking that needs to occur to develop mathematically strong instruction and to improve our analysis of students’ thinking. It shifted our attention from errors as merely mistakes, to errors that help us to identify strengths as well as weaknesses. How to interpret student thinking based on artifacts from the classroom, how to identify the mathematical “big ideas” in curriculum, how to ensure the rigor of our lessons, and how students represent their mathematical thinking as well as using errors to develop next steps are the key ideas of this manuscript. All of these topics are critical components of quality instruction.”

- Jane Elizabeth Gillis, Math Cadre, Red Clay Consolidated School District, Wilmington, DE

Read More Show Less

Product Details

  • ISBN-13: 9780132101288
  • Publisher: Pearson
  • Publication date: 2/23/2012
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 192
  • Product dimensions: 7.30 (w) x 9.10 (h) x 0.50 (d)

Meet the Author

Lynn Goldsmith began her career as a developmental psychologist, where her major research interests lay in understanding the formal and informal systems that support the development of extreme talent. For the past 20 years, she has worked in the field of mathematics education, investigating factors contributing to successful professional development, the role of curriculum in educational reform, and the emotional aspects of learning. She has co-authored Choosing a Standards-based Mathematics Curriculum (Heinemann, 2000), served as series co-editor of the Guiding Middle-grades Curriculum Decisions series (Heinemann, 2000), and co-authored Nature’s Gambit: Child Prodigies and the Development of Human Potential (Teachers College Press, 1991).

Nanette Seago was the primary author of Learning and Teaching Linear Functions: Videocases for Mathematics Professional Development. She has been working in mathematics professional development for twenty years. Currently, she is working at WestEd as a Principal Investigator for a National Science Foundation project focused on the research and design of videocase materials for middle school teachers—Learning and Teaching Geometry.

Read More Show Less

Table of Contents

Preface

Acknowledgments

Chapter 1: Turning to the Evidence

Vignette: Jeffrey Stockdale

What are artifacts and why analyze them?

Learning to see through multiple lenses

Our vision of mathematical learning and teaching

A framework for using artifacts skillfully

Section 1: Attending to thinking

Chapter 2: Describing and Interpreting Classroom Artifacts

Vignette: Lorena and Linda’s solution to the Crossing the River problem

Why focus on evidence?

Using artifacts in your own classroom

Wrapping Up

Additional Exercises: Two Video Interviews

Chapter 3: Seeing the Potential in Student Thinking

Vignette: Toll House Cookies and other “errors”

Why focus on errors?

Using errors to see potential, instead of just deficits, in students’ thinking

General commentary about errors

Working with errors in your own practice

Wrapping up

Section 2: Attending to content

Chapter 4: Keeping an Eye on Rigorous Mathematics

Vignette: Jasmine and Nguyet

Naming and framing mathematical rigor

General Commentary on Using Mathematical Frameworks to Consider Mathematical Rigor

Wrapping Up

Chapter 5: Choosing, Using, and Connecting Mathematical Representations

Vignette: Ms. Ridgeway

General Commentary about Representations

Exercises

Your Own Practice and Work with Representations

Wrapping Up

Additional exercises

Section 3: Putting it All Together in the Classroom

Chapter 6: Putting it All Together

Vignette: Jeffrey Stockdale Part II

Exercises: Integrated Analysis of Whole Lessons

Linking to your own practice

Final thoughts

References

Book Study Guide

Deciding on a Facilitator

Structuring Your Book Study Sessions

Book Study Questions for Each Chapter

Reading Reaction Sheet

Appendices

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