An ASCD Study Guide for Teaching Students to Communicate Mathematically

This Study Guide is designed to deepen your understanding of Teaching Students to Communicate Mathematically, an ASCD book written by Laney Sammons.

You can use the study guide before or after you have read the book, or as you finish each chapter. The study questions provided are not meant to cover all aspects of the book, but, rather, to address specific ideas that might warrant further reflection.

Most of the questions contained in this study guide are ones you can think about on your own, but you might consider pairing with a colleague or forming a study group with others who have read, or are reading, Teaching Students to Communicate Mathematically.

Chapter 1. The Essentials of Mathematical Communication

Reflect on your elementary, middle, and high school math classes. To what extent were students expected to communicate their mathematical thinking? How did these expectations affect your mathematical learning?

Based on your professional experience, what do you think are the three most important reasons for teaching students how to clearly express mathematical ideas in a variety of modes? Explain your thinking.

What are the greatest challenges teachers face as they begin to teach mathematical communication skills and encourage greater student engagement in the expression of their mathematical thinking?

What aspects of your classroom environment support students' mathematical communication? In what ways can you make your classroom more conducive to the expression of mathematical ideas in multiple modes?

Chapter 2. Effective Mathematical Conversations

Consider the three language processes identified by Zwiers and Crawford (2011)—listening, speaking, and negotiating meaning. For which of these do you think students need the greatest amount of instruction? Why?

How does participation in constructive mathematical conversations bolster and extend students' mathematical understanding?

Observe and listen as your students engage in a mathematical conversation. What do you notice? What do they do well? How can you help them improve their conversational skills?

In which instructional format—whole-class lessons, small-group lessons, independent small-group work, cooperative learning groups, math workshop, math conferences—do the most productive math conversations in your class occur? How can you encourage these conversations in other formats?

What role can student self-assessment play in teaching students how to more effectively participate in meaningful math conversations?

Chapter 3. Teaching Students to Engage in Mathematical Conversations

Why do you think that teachers often find it difficult to release much of the responsibility for math conversations to their students?

How do you think your students define the word listen? How can you help students expand their conceptions of the word so that they become participatory listeners?

Working with a colleague, choose a challenging math problem to solve and have your colleague do the same. After finding the solutions, take turns explaining your problem- solving process and justifying your solution. As you listen to your colleague's explanation, what listening comprehension strategies are you using to help you understand your colleague's thinking? How can you teach your students the value of using these strategies when listening to others?

During mathematical conversations among students in a class, what do you think is the most difficult responsibility of the teacher? Why?

Chapter 4. Writing About Math

Author Flannery O'Connor wrote, "I write because I don't know what I think until I read what I say." How do you think that applies to students' mathematical writing?

In what ways can students' engagement in mathematical reading enhance their writing skills?

From your students' points of view, what are the criteria for quality mathematical writing in your class? How well does that align with your criteria for quality mathematical writing by students? If students' criteria and your criteria are well aligned, what led to the alignment? If not, what can you do to ensure that they become more closely aligned?

Chapter 5. Teaching Students to Write About Mathematics

Reflect on your experience teaching writing. If you teach in a self-contained classroom or have previously taught language arts/writing, how can you apply the literacy instructional strategies you used to teach students to write about math? If you can't, which of the instructional techniques suggested in this chapter could you implement in your classroom to improve the mathematical writing of your students?

By employing the instructional modes of showing, sharing, and supporting, educators can teach students to write more effectively about math. Select a type of mathematical writing you want your students to use. Plan and teach lessons that focus on that type of writing for each of these three modes based on suggestions from this chapter.

Why is it important for students to be able to share their mathematical writing with others? Do your students have opportunities to share their written work? If so, in what ways is it shared? If not, what ideas from this chapter might you use so that students' writing is shared?

How do you currently support the development of the mathematical vocabulary knowledge of your students? What additional instructional strategies might you implement to promote the development of their mathematical vocabulary knowledge?

What kinds of math vocabulary resources do your students use? Are there other resources that you may decide to make available to them?

How do you think students can be encouraged most effectively to monitor their own understanding and use of the mathematical vocabulary that is important and relevant to the math content with which they are working?

How do you identify the essential mathematical vocabulary that your students should know and be able to use as they communicate mathematically?

Chapter 7. Mathematical Representations

Reflect on the value of visualization in understanding and applying mathematical concepts. In light of this value, why is the development of students' proficiency with representations such an important part of mathematics instruction?

Explain why you think that Van de Walle and colleagues (2010) state that when students have more ways to think about a mathematical idea, "the better chance they will correctly form and integrate it into a rich web of concepts" (p. 27).

Choose a math concept that you teach. How can that concept be represented in each of the four kinds of mathematical representations—concrete, graphic, abstract, and real- world? What are the limitations of each representation? Do you think that all math concepts can be represented in all four ways? Why or why not?

In the traditional mode of math instruction in which the teacher tells students what they will learn and then exactly how to do it, students often struggle to create their own representations of their mathematical ideas in multiple ways. Why do you think this is the case?

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