Table of Contents Part 3 Excerpt Chapter Excerpt
This valuable book, which builds on Peter Sullivan and Pat Lilburn’s Good Questions for Math Teaching: Why Ask Them and What to Ask, K–6, includes a wide variety of good questions for classroom use and offers teachers tips on how to create open-ended questions of their own.
Good Questions for Math Teaching: Why Ask Them and What to Ask, Grades 5–8 by Lainie Schuster and Nancy Canavan Anderson, is divided into three sections: the first section addresses the practice of good questioning, followed by how to use the book, and lastly, good questions to use in a mathematics class.
Part One deals with what are good questions, how they are created, and what classroom conditions are necessary to support good answers.
Part Two suggests how to use the book. It is designed to supplement a mathematics curriculum, by using questions as a daily warm-up activity, as homework, or as an assessment. Teaching notes describe the mathematics, possible student misconceptions, extensions, and homework activities.
Part Three addresses good questions to use in the classroom covering the seven strands: number relationships; multiplication and proportional reasoning; fractions, decimals, and percents; geometry; measurement; algebraic thinking; data analysis and probability. Each strand is subdivided into 5–6 and 7–8 grade spans. Appropriate blackline masters are included as well as suggestions for homework.
This book has myriad suggestions and ideas that will be useful for administrators, mathematics coaches, middle and elementary school teachers, and substitutes.
“Questions may be one of the most powerful technologies invented by humans. Even though they require no batteries and need not be plugged into the wall, they are tools which help us make up our minds, solve problems and make decisions.”—McKenzie (1997)
This quotation, which introduces Part One of Good Questions for Math Teaching: Why Ask Them and What to Ask, Grades 5–8, implicitly sets the purpose for this book: to help teachers create and pose good questions that become powerful tools for student learning in the mathematics classroom. The authors follow through on this purpose with clear and practical help throughout Part One: The Practice of Good Questioning, Part Two: How to Use This Book, and particularly in Part 3: Good Questions to Use in Math Class.
Part One guides the reader to know what good questions are, how to create and present them, and the classroom conditions conducive to supporting good answers. Clearly, this part alerts the reader that the questioning strategies to be learned are not of the traditional I-R-E format (teacher Initiates dialogue by asking a question—student gives a Response—teacher Evaluates response) described by Cazden (1988) and others. Quite to the contrary, they are intended to enable genuine inquiry, not rote response, in the mathematics classroom.
Part Two is a two-page guide to using Part Three, which is replete with questions and accompanying explanations. Suggestions for using Part Three include the following: incorporating the questions during instructional time, using them as a daily warm-up activity, assigning them for homework, and using them for assessment purposes.
Part Three constitutes the major portion of this book. It addresses seven strands of mathematical thinking to be developed in grades 5–8: Number relationships; Multiplication and proportional reasoning; Fractions, decimals, and percents; Geometry; Algebraic thinking; Data analysis and probability; and Measurement.
These strands parallel the content standards identified in Principles and Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 2000), with the NCTM standard Number and Operations addressed in the first three strands. Although each strand is subdivided into two grade spans, grades 5-6 and 7-8, no hierarchical or sequential order is intended in each section; questions can be posed individually. The questions presented are designed to supplement the teacher's curriculum and can be used both to initiate and to support inquiry. According to the authors, "Each section can be viewed as an a la carte menu of question choices to help students deepen their understanding of the mathematics they are studying" (pp. 15–16).
Pages 157 through 192 provide blackline masters to accompany tasks included in Part Three. Permission is granted by the publisher for individual teachers who have purchased this book to reproduce masters as needed for use with their own students.
The reference list for the book identifies several Standards-based resources from which the writers adapted many of their questions and also includes several books that address questioning strategies. Surprisingly, the references include only one of the numerous journal articles available to help teachers enhance their questioning in the mathematics classroom.
This book is clearly valuable for the classroom teacher who wishes to promote guided inquiry in her or his mathematics classroom. Its strengths include the following:
I am currently working with two groups in professional development projects that include middle grades teachers. I see this book as very useful and intend to make it available to them, while at the same time reminding them of the following points I consider especially relevant.
Without a doubt, appropriate questioning is essential to guided inquiry. Nonetheless, questions should emanate from and be specific to worthwhile mathematical tasks. Many times these tasks can be embedded in contexts that encourage students to make important connections, e.g., connections to real life or to other ideas within mathematics, to broaden and deepen their understanding of the concept under study. The questions useful in helping achieve this breadth and depth must be carefully designed and sequenced. The a la carte menus of questions provided in this book should be used only as a starting place. Teachers themselves are responsible for designing and sequencing the questions needed to support students in learning important mathematics in deep and connected ways.
Teachers who have had little opportunity to learn to teach mathematics through an inquiry approach will need more help than this book gives to be able to implement the questioning strategies authentically. They may be particularly challenged in scaffolding students with special learning needs. A few good articles are available on this topic, especially in Teaching Children Mathematics and Mathematics Teaching in the Middle School, journals available from NCTM. (Search online at nctm.org if you are an NCTM member, or access through ERIC.)
This complement to Math Solution’s previous publication on questioning strategies, Good Questions for Math Teaching: Why Ask Them and What to Ask, K–6 (Sullivan & Lilburn, 2002) fills a specific and very practical need. It has strong potential for supporting middle school teachers with their questioning as they strive to implement inquiry effectively in their mathematics classrooms.
Cazden, C. B. (1988). Classroom discourse: The language of teaching and learning. Portsmouth, NH: Heinemann.
McKenzie, J. (1997). Telling questions and the search for insight. Retrieved January 1, 2007, from www.questioning.org/Q8/telling.html.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.Sullivan, P., & Lilburn, P. (2002). Good questions for math teaching: Why ask them and what to ask, K–6. Sausalito, CA: Math Solutions.
Good Questions for Math Teaching: Why Ask Them and What to Ask, Grades 5–8, by Lainie Schuster and Nancy Canavan Anderson, is the companion book to the book of the same title for grades [K–6] by Peter Sullivan and Pat Lilburn. Good questions are open-ended and reveal both what students know and what misconceptions they might have. There are three sections in this book. Section one examines types of questions; section two explains how to use the book; three looks at questions to use in the classroom. In this book the questions are arranged into seven strands including topics such as number relationships; multiplication and proportional reasoning; and fractions, decimals and percents. Over thirty blackline masters follow the text.