# Thinking Aloud in Mathematics

By: Judy Zorfass, Tracy Gray, and PowerUp WHAT WORKS

## Introduction

When students verbalize what they know, it helps them to reflect upon and clarify the problem they are trying to solve, and to focus on solving it one step at a time. "Thinking aloud" requires students to talk through the details of the problem, the decisions they have made as they try to solve the problem, and the reasoning behind those decisions. Struggling students, in particular, can benefit from slowing down and articulating the problem-solving process, because it gives them time to focus on the key parts of the problem. This helps them to more fully comprehend the problem before they try to solve it. The graphic lists what students should be thinking and talking about as they delve into problems.

Thinking aloud helps students, especially those who struggle with mathematics, to clarify their ideas, identify what they do and do not understand, and learn from others when they hear how their peers think about and approach the problem. It also helps the teacher to monitor students' progress as part of the formative assessment process.

## Using Evidence-Based Practice

Teachers can help their students to organize information and find and use patterns by adopting three categories of evidence-based practices: provide clear explanations, give students strategies and models, and provide ongoing formative assessment. The chart below provides a concrete teaching strategy for each of these categories.

Evidence-Based Practice Strategy

When you demonstrate problem solving, model the thinking aloud process by explicitly stating what it means to explain your reasoning. Include all the decisions you make, even the very small ones (e.g., which numbers to work with and what operations to use). Employ technology to support note taking and create visualizations of the big ideas as you work to give students a clearer understanding of your thinking process.

Give your students a series of prompts—e.g., questions or sentence starters—to guide them through the process of thinking aloud. Make sure you include questions that require them to justify their decisions, such as:

• I know that…
• I'm trying to figure out…
• One thing I can try is…
• I want to try … because …

When a student engages in thinking aloud, invite a peer to listen and comment on the content while you concentrate on the student's use of the strategy (i.e., check to make sure the student shows an understanding of why those steps were needed). With struggling students, a small group activity might work better because it will give students a chance to hear others before sharing their thinking.

## Technology Resources

Teachers and students can use online and offline tools that allow students to practice this "thinking aloud" strategy. They can create problems with natural stopping points, experiment, consider, and then decide their next steps. This chart shows a variety of tools that you could use in your classroom.

Audio recording a student's thinking aloud (using a recording device on a computer, tablet, or smart phone) allows the student, the teacher, and the student's peers to review the thinking process so that revisions and edits can be made. Teachers can also consider posting podcasts on their class website to show how different students thought about the problem and tried to solve it. Making comparisons allows students to understand how their peers think.

Virtual manipulatives also have a role to play in helping students. This short video, "Virtual Manipulatives" provides background information manipulatives and explains how they can be integrated into instruction. Imagine students manipulating problems and trying out solutions that might work. These virtual manipulatives offer students varied practice in thinking aloud for each new iteration.

## In the Classroom

When school started last week, Mrs. Jefferson devoted some time to figuring out where her fifth-grade students were in terms of their mathematical understanding. She found out that they know their addition and subtraction facts, and that most of them remember their multiplication facts. As she expected, however, the students are reluctant to describe aloud the steps they follow to find an answer. When she asks them to explain the steps they follow in their work, her students say they don't know or they just look at her, clearly unsure what to say.

To ensure that her students are college and career ready, she is focusing on the following Common Core State Standards:

• CCSS.Math.5.OA.3
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.
• CCSS.Math.MP2
Reason abstractly and quantitatively.

She is planning a lesson with a specific objective: Students will begin practicing thinking aloud so that they can effectively employ this strategy as they move forward and learn the mathematical language necessary to communicate their thinking.

Mrs. Jefferson will take advantage of her interactive whiteboard (as well as students' individual whiteboards) to communicate visually with the class and to allow the class to communicate visually with her. She will use a classroom response system to collect anonymous feedback from her students. A colleague recently told her about a particularly effective applet, Whole Number Cruncher, which can provide numerical patterns.

She has found that formative assessment truly helps her strengthen her teaching. She will observe her students as they use the thinking aloud strategy, particularly when they use Whole Number Cruncher. She will elicit comments from students about the learning task and will read students' critiques of the strategy.

Her lesson plan is divided into three sections—launch, learning task, and closure—and is outlined below.