Books for Teachers
This page lists books that help teachers integrate conceptual depth into their mathematics instruction. Most of the books support teachers' work with all students. Many of them contain ideas for building differentiation into whole-group instruction. Some of the books are targeted specifically to meeting needs of advanced students. These books are for teachers' learning. If you are looking for classroom materials, please see the Classroom Resources page.
5 Practices for Orchestrating Productive Mathematics Discussions, by Margaret S. Smith, and Mary Kay Stein. National Council of Teachers of Mathematics, 2011.
Creating productive discussion in the mathematics classroom is at the heart of effective instruction. This book draws on the latest research in how students learn math to offer a clear five-step approach: anticipating, monitoring, selecting, sequencing, and connecting. The authors describe the five steps and bring them to life with examples of classroom conversation around specific tasks carefully designed to elicit deep thinking. They analyze each conversation and draw helpful conclusions. Near the end, they provide tools that guide teachers through the lesson planning process.
Adding It Up: Helping Children Learn Mathematics, by the National Research Council. National Academy Press, 2001.
This book was instrumental in bringing together research on the mathematical learning of P–8 students and providing research-based recommendations for curriculum, instruction, and teacher training. It defined the concept of mathematical proficiency as consisting of the interdependent and mutually supporting strands of conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. The authors also provide detailed examples and recommendations for developing number and operation concepts in the early grades.
Good Questions: Great Ways to Differentiate Mathematics, by Marian Small. Teachers College Press and NCTM, 2009.
Marian Small offers two key strategies for differentiating math instruction: open questions and parallel tasks. These strategies enable teachers to design tasks and create classroom conversations that challenge talented students while meeting the needs of typical and struggling learners at the same time. She provides a large number of examples of these tasks organized by "big ideas" that connect concepts. She also offers questions for conversation and teaching tips to support implementation.
Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 4–10, by Cathy Humphries and Ruth Parker. Stenhouse, 2015.
This book offers support for integrating Number Talks into the classroom for older students, including those in high school! See the Number Talks book (below) for a general description of the purpose and structure of Number Talks.
Number Talks: Helping Children Build Mental Math and Computation Strategies, by Sherry Parrish, 2014
Number Talks are an excellent vehicle for beginning to build students' thinking into your math instruction. They take about 5 to 15 minutes per day and give you and your students an opportunity to learn to think and communicate mathematically. They naturally meet the needs of talented and other students by enabling them to approach computational tasks at their own level of reasoning. The early part of this book sets the stage by providing clear guidelines and advice for implementing number talks into your daily instructional routine. Most of the book is dedicated to providing a wealth of specific examples of number talks with detailed discussions of typical strategies used by students. The problems are organized according the type of strategies they typically elicit and are correlated with Common Core content standards. The book comes with a significant collection of video clips of actual classroom instruction.
The Peak in the Middle: Developing Mathematically Talented Students in the Middle Grades, edited by Mark Saul, Susan Assouline, and Linda Jensen Sheffiield. National Council of Teachers of Mathematics, National Association for Gifted Children, National Middle School Association, 2010.
A variety of experts in the field have contributed articles to this book that integrates our best understandings in the fields of math education, gifted education, and meeting the needs of young adolescent learners. You will find valuable insights in the areas of identification, acceleration, grouping, program development, curriculum, equity, teacher preparation, and extracurricular opportunities.
Principles to Actions: Ensuring Mathematical Success for All. National Council of Teachers of Mathematics, 2014.
The National Council of Teachers of Mathematics has been at the forefront of standards-based instruction for decades. Over this time, they have developed standards that have informed and clarified our understanding of curriculum content, instructional processes, assessment, and teacher professionalism. The Common Core Standards for Mathematics were strongly informed by this work. This book outlines the principles and the actions that all of us must take to make these standards a reality.
The Teaching Gap, by James W. Stiegler and James Hiebert. Free Press, 1999.
The authors describe what we have learned from a video study that was part of the TIMSS (Third Internations Mathematics and Science Study), a cross-cultural investigation of mathematics instruction and learning. A couple of their key insights are that teaching is the key component in improving students' learning and that teaching mathematics is a cultural activity. The cultural nature of teaching explains why it is so challenging to make changes even when we know more about how students learn than ever before. The authors emphasize that it is not a question of teachers' competence, but of teaching strategies. This book provides specific examples of classroom practice in different countries and introduces the concept of "lesson study" as a template for moving forward.
Using the Common Core State Standards for Mathematics with Gifted and Advanced Learners, edited by Susan K. Johnsen, Ph.D., and Linda J. Sheffield, Ph.D.
Prufrock Press, 2013.
As the title suggests, this book offers guidance for teachers, schools, and districts in using the Common Core State Standards for Mathematics (CCSSM) as a starting point for differentiating content and instruction for gifted and advanced students. Specific examples of tasks for typical learners and advanced learners are set side-by-side for a number of the content standards at a variety of grade levels. There are chapters that address the research base for the authors' work, differentiating assessments, talent trajectories, alignment between Common Core standards and Gifted Education standards as well as between Math Standards and ELA standards, and collaboration between various education professionals and other stakeholders.
A Teacher's Guide to Using the Common Core State Standards With Mathematically Gifted and Advanced Learners, by Susan K. Johnsen, Ph.D., Gail, R. Ryser, Ph.D., and Susan G. Assouline, Ph.D. Prufrock Press, 2014.
This book complements the 2013 book with the similar title (above). In this case, the focus is on teachers and classroom practice. It contains many examples of differentiated learning experiences and includes specific guidance and tools in the areas of assessment, adapting learning progressions, and classroom management strategies.
Please contact me if you have suggestions for other excellent books that support teachers in integrating depth into math instruction, especially for advanced learners. I would like to include them on this page!