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Making Sense of Mathematics for Teaching the Small Group

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When done right, small-group instruction is a powerful tool for facilitating student understanding in K-5 mathematics. Throughout the book, best practices for small-group math instruction are addressed in detail, from planning tasks that encourage deep understanding to asking effective questions to engaging learners in meaningful conversations. Readers will learn how teaching mathematics in small groups allows you to differentiate instruction for both remediation and enrichment. The included small-group instruction videos demonstrate the suggested strategies in a real-classroom setting, giving readers the opportunity to see best practice in action.

Develop math-specific instruction strategies for teaching small groups in elementary school:

  • Explore the benefits of small-group math activities and how these activities are unique compared to large-group instruction.
  • Discover the teacher's and students' roles in small-group instruction and how teachers can help students develop the skills to fulfill their role.
  • Learn how to apply the general tasks, questions, and evidence (TQE) process to small-group instruction in order to enhance student learning and improve your knowledge of teaching mathematics.
  • View examples of small-group instruction, which provide both math intervention and math enrichment activities for different students.

Contents:
Acknowledgments
Table of Contents
About the Authors
Introduction
Chapter 1: Best Practices in Small-Group Instruction
Chapter 2: The TQE Process in Small-Group Instruction
Chapter 3: Discourse in Small-Group Instruction
Chapter 4: How to Tie It All Together
References
Index

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Chapter 1

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CHAPTER 1

Best Practices in Small-Group Instruction

Most of the elementary educators we have worked with view small-group instruction as an essential part of their mathematics block. Why? What are the benefits of small-group instruction that make it a priority in the school day? Typically, teachers consider it essential because they believe that they can fill gaps in student learning and meet students’ individual needs during this time. However, based on a wealth of research on effective mathematics education, we can assume that small-group instruction that is focused solely on correcting errors in procedural computations rarely serves its intended purpose (NCTM, 2014).

In this chapter, we explore best practices and effective strategies for working with small groups, and we discuss how teachers can use the time as a powerful means to advance and deepen mathematical understanding for each and every learner, including those who have met the initial learning goal. We begin by analyzing a video that depicts several best practices for small-group mathematics instruction in the classroom, allowing you to consider the lesson’s learning goal, the roles of the teacher and students, and the tools the teacher uses to support learning. Throughout the chapter we will discuss the teacher’s role, effective teaching strategies, the students’ roles, and how the teacher can help students negotiate those roles. We conclude by discussing management of the pulled small group.

 

Chapter 2

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CHAPTER 2

The TQE Process in Small-Group Instruction

Teachers should determine their use of pulled small groups based on the students’ needs to achieve a specific learning goal. Too often, teachers use small-group instruction merely because of the expectation that they use it in every lesson. We strongly caution against this practice. However, when its use is warranted, like with all classroom instruction, effective small-group instruction begins in the planning stage.

In this chapter, we present a model for planning and implementing small-group instruction: the TQE process. We discuss how this model can help teachers prepare tasks, utilize questions, and elicit evidence of student learning in small groups. We then present a planning tool to help teachers utilize the TQE process in their own classrooms.

The TQE Process

The TQE process, previously described in Making Sense of Mathematics for Teaching Grades K–2 (Dixon,

Nolan, Adams, Brooks, & Howse, 2016) and Making Sense of Mathematics for Teaching Grades 3–5

 

Chapter 3

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CHAPTER 3

Discourse in Small-Group Instruction

We have explored best practices in small-group instruction and discussed how to use the TQE process to plan for pulled-small-group time. However, you may still be wondering how to support the level of discourse observed in the videos you have watched thus far. In this chapter, we will answer the following questions: How do you support students to engage in productive discussions related to the learning goal? What are reasonable expectations for student contributions in small-group instruction? Let’s begin this discussion by viewing an example of small-group discourse. We will then present five strategies for establishing effective discourse in the small group and discuss effective teaching practices that facilitate discourse.

Discourse During Small-Group Instruction

Before reading further, watch the small-group video of kindergarten students engaging in the lesson

Count and Compare Cubes. Use the questions provided in figure 3.1 to guide your thinking.

 

Appendix A

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APPENDIX A

Sample Lesson Plan for Grades K–2 Using

TQE Process Lesson-Planning Tool

Figure A.1 is a sample lesson plan for the task in figure 1.2 (page 8). The lesson plan was created using

Dixon et al.’s (2016) TQE process lesson-planning tool.

TQE Process Lesson-Planning Tool

Learning Goal

Students will connect the concept of adding three-digit numbers with regrouping to a standard algorithm.

What are your considerations for grouping students? Is it appropriate to use small-group instruction to meet this learning goal?

Students struggle with understanding the “why” behind the traditional algorithm for addition. In this lesson, students will be asked to link the concept of regrouping using base ten blocks to the traditional algorithm. Moderately heterogeneous grouping sets up an environment for mathematical discourse, in which students will be encouraged to use place value language to explain the algorithm to one another. Students who can follow the steps of the traditional algorithm may struggle to understand the connection to the base ten blocks. Students who struggle with the steps of the algorithm may be able to explain the connection. The small-group setting allows growth opportunities for both sets of students. The small-group setting will also provide an avenue for holding each student accountable for participating in the conversation as they develop conceptual understanding.

 

Appendix B

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APPENDIX B

Sample Lesson Plan for Grades 3–5 Using

TQE Process Lesson-Planning Tool

Figure B.1 is a sample lesson plan for the task in the video on page 59. The lesson plan was created using

Dixon et al.’s (2016) TQE process lesson-planning tool.

TQE Process Lesson-Planning Tool

Learning Goal

Students will make sense of adding fractions with unlike denominators.

What are your considerations for grouping students? Is it appropriate to use small-group instruction to meet this learning goal?

Since the purpose of the lesson is for students to develop conceptual understanding of adding fractions with unlike denominators, moderately heterogeneous grouping will enable students to learn from one another’s thinking.

Small-group instruction will allow the teacher to collect evidence regarding each student’s understanding and ask individualized questions to build upon students’ current knowledge of fraction concepts.

Task

This high-cognitive-demand task links to the learning goal and allows students to engage in

 

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