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A Focus on Addition and Subtraction: Bringing Mathematics Education Research to the Classroom

reviewed by Julie Sliva Spitzer - July 19, 2021

coverTitle: A Focus on Addition and Subtraction: Bringing Mathematics Education Research to the Classroom
Author(s): Caroline B. Ebby, Elizabeth T. Hubert, & Rachel M. Broadhead
Publisher: Routledge, New York
ISBN: 0367462885, Pages: 238, Year: 2020
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A Focus on Addition and Subtraction: Bringing Mathematics Education Research to the Classroom is the fourth book in the series of books “A Focus on...” written by Caroline B. Ebby, Elizabeth T. Hubert, and Rachel M. Broadhead. In this book, the authors describe their research with the Ongoing Assessment Project (OGAP) and focus on their findings for how the OGAP Addition, Subtraction, and Base Ten Number Progressions may be used to support students’ becoming mathematically proficient.  

The OGAP project has developed learning progressions which are a carefully researched and sequenced set of building blocks which, when used in conjunction with instructional strategies, support students’ development of a solid mathematical knowledge base. They enable teachers to identify where their students are in their learning of mathematics and translate their work into meaningful descriptions of their mathematical progress. These progressions provide teachers with the knowledge and tools to explain a student’s thinking so that they can modify their teaching, select appropriate instructional strategies, and improve student learning. The OGAP Progressions are described by the authors as “an intentional, content-focused formative assessment system, where learning progressions are used to analyze evidence in student work and inform mathematics instruction” (p. 29). Formative assessment, which is an ongoing cyclical process, is an integral part of this. The three aspects of this approach begin with teachers first obtaining evidence of students learning about a learning goal. The student work is analyzed and then teachers make instructional decisions based on this work. A collection sheet is provided so that teachers may record students’ work and look for and compare trends. The authors provide excellent reflection questions which may be used to assist teachers in making the next instructional decision, such as “What are developing understandings in the student work that can be built upon?”; “What issues or concerns are evidenced in the student work?”; and “What are potential next instructional steps for the whole class, small groups or individuals?”.

This book guides classroom and preservice teachers through the learning progressions for additive reasoning, which the authors believe is at the core of mathematical reasoning and provides a necessary foundation for multiplicative reasoning and mathematical reasoning in grades K–8. Throughout the book, the authors discuss the progression of teaching these foundational mathematics concepts in grades K–3, using authentic student work. These artifacts are supported by detailed explanations of the mathematics the student is understanding and/or might not be understanding based on their written work. Additionally, there is an in depth description of the progression of strategies and the connections between the strategies, which are crucial to moving students forward in their understanding of mathematics. As the teachers understand these progressions, they can more easily help their students, who all learn at different paces and acquire skills and concepts at different times and in various ways, develop conceptual understandings of the content.

In conjunction with the research presented in the book, the OGAP Additive Reasoning Framework is a tool based on mathematics education research on how students make sense of the skills and demonstrate fluency with concepts related to number and base-ten understanding, addition, and subtraction at the earliest grade levels. The book provides access to a site where the framework may be downloaded. The eResource provides a copy of the OGAP Additive Framework and the OGAP Number Line Continuum. This Framework contains three progressions for base-ten number, addition, and subtraction which are tailored to the needs of classroom teachers so that they may effectively examine and select instructional materials, respond to an array of individual student needs, and move all of their students forward in these critical building blocks to become “additive reasoners.” Lastly, the resource expands on the importance of fluency with basic addition facts. In line with other concepts in the book, there is a description of an approach to automaticity that builds on fluency and conceptual understanding supported by evidence of student work and the Common Core State Standards for Math.

At the end of each chapter, the authors pose questions on topics discussed throughout the chapter. These questions can further support the teacher and their reflections of essential understandings which are highlighted throughout the book. Additionally, instructional links are included to support teachers as they relate concepts from each chapter to their own instructional materials and programs. The eResource also provides an answer key to these Looking Back questions.

The author’s research and development of the OGAP program and framework provide a very detailed step-by-step pathway to guide teachers in their students’ learning of crucial early mathematics. This book encompasses strategies for mathematics content from counting to base-ten understandings. It provides an exceptionally “grain-size” view of the approaches students may take to learn mathematics. The extensive use of authentic work provides an insight into student thinking that allows teachers to peer through the eyes and experience of a child when learning these early skills. These artifacts, coupled with the tools the authors provide via the OGAP Additive Framework, the questions at the end of each chapter, and the links to instruction bring to life the experience of teaching young students the critical skills of additive reasoning as well as conceptual understandings of addition, subtraction, and base ten. With these tools, the teachers are able to effectively select instructional strategies to move their students forward.

Both classroom and preservice teachers can benefit immensely from the research and experience compiled in this book as they support their students on their journey to becoming mathematically proficient.

Cite This Article as: Teachers College Record, Date Published: July 19, 2021
https://www.tcrecord.org ID Number: 23794, Date Accessed: 7/27/2021 12:56:48 AM

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About the Author
  • Julie Sliva Spitzer
    San Jose State University
    E-mail Author
    JULIE SLIVA SPITZER, Ph.D., is a mathematics educator at San Jose State University whose research interests focus on the teaching and learning of mathematics for special needs learners. Her current work involves preparing undergraduate students to teach mathematics and providing professional development for K-12 teachers.
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