Mrs. Jackson’s Grade 6 class has been working on a fractions, rates, and ratios unit. Yesterday she gave the class a quiz to assess her students’ understanding. After reviewing the results, she wants more detail about her students’ thinking in order...
Thinking aloud helps your students learn how to reason by focusing on their thinking (see UDL Checkpoint 9.3: Develop self-assessment and reflection). Most students are not used to answering questions that require more than a single-word or short-phrase response. Many don’t know how to talk about mathematics or explain their thinking. These strategies provide a strong starting point for differentiating instruction.
Best Practices with Technology
Step 1: Provide Clear Explanations
-
Explain to your students that you're as interested in how they get their answer as you are in whether the answer is correct (see UDL Checkpoint 6.2: Support planning and strategy development). Tell them that you will help them work on “thinking aloud” and explaining their reasoning.
-
When you demonstrate solving problems, model the process of thinking aloud 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 (see UDL Checkpoint 3.2: Highlight patterns, critical features, big ideas, and relationships).
- Ask guiding questions to help your students focus on their reasoning, not just the solution, even when their answer is correct. Ask students to explain why they chose a process or how they made a calculation, emphasizing that the decision process is a core part of mathematical reasoning. When you highlight the process as part of thinking aloud, you help your students to flex and strengthen their reasoning skills.
Examples of guiding questions
- Why did you choose that number/operation?
- How did you find that number?
- Can you explain how you got that answer?
- Who did it differently? How?
- You said _________________. Can you tell us more about what you were thinking then?
View evidence behind this recommendation
IES Recommendations
Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.
Evidence:
Strong
Interventions should include instruction on solving word problems that is based on common underlying structures
Evidence:
Strong
Teach number and operations using a developmental progression.
Evidence:
Moderate
Step 2: Give Students Strategies and Models
- Give your students a series of prompts—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.
Prompts for the thinking aloud process
- I know that...
- I'm trying to figure out...
- One thing I can try is...
- I want to try ... because ...
-
Have students use models and diagrams to support their thinking and take notes as they go along. These visual supports can help students figure out if their thinking is faulty. The supports also provide you with a way of helping students to pinpoint where and how they have made an error in their thinking. Students can employ technology to improve their visualizations and note taking.
- Ask students to explain their reasoning often. Prompt students to share their thinking when they get correct answers—they can get the correct answer, but for wrong reasons—as well as when they get incorrect answers. All students can benefit from hearing peers’ sound, on-target reasoning, and all students can learn from peers’ explanations when reasoning goes awry.
View evidence behind this recommendation
IES Recommendations
Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas.
Evidence:
Moderate
Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward.
Evidence:
Moderate
Source: IES Practice Guide: Developing Effective Fractions Instruction for Kindergarten Through 8th Grade
Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.
Evidence:
Strong
Help students understand why procedures for computations with fractions make sense.
Evidence:
Moderate
Source: IES Practice Guide: Developing Effective Fractions Instruction for Kindergarten Through 8th Grade
Step 3: Provide Ongoing Formative Assessment
-
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 (e.g., 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 the students a chance to hear others before sharing their thinking.
-
Thinking aloud can help your students learn how to develop a plan to solve a problem (see UDL Checkpoint 6.2: Support planning and strategy development). Have students describe and justify a plan they would use to solve a problem. Then, ask them to implement the plan as they think aloud about why it is effective, where they need to make changes, and why.
- Consider each student’s needs and learning styles when you decide on the actions you will take to move students closer to the learning goals. Whatever actions you take, give students time to ask you questions, share their thinking, and respond to the feedback you provide.
Moving students closer to learning goals
- For some students, it might work best for you to provide feedback individually.
- Other students might benefit from you sharing feedback with them as a group.
- Some or all of your students might need you to review part of the lesson.
View evidence behind this recommendation
IES Recommendations
Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review
Evidence:
Strong
Discover Lessons in Action:
Thinking Aloud: Number Crunching
Resource Type: Lesson in Action
Mrs. Jefferson’s 5th grade class can be reluctant to describe aloud the steps they follow to find an answer. In this lesson, students will begin practicing the thinking aloud strategy and learn the mathematical language necessary to communicate...
Watch Our Quick View Technology Videos:
Quick View: Virtual Manipulatives
(Get More Info)
Resource Type: Quick View
In the past, most classrooms only had physical manipulatives. Today, more classrooms have improved access to computers and the Internet. As a result, virtual manipulatives are becoming more common. These can be useful tools for students and can help...
Review the Research:
A synthesis of empirical research on teaching mathematics to low-achieving students
Resource Type: Research
This meta-analysis synthesizes the research on the effects of interventions designed to improve mathematics achievement of students considered low achieving or at risk for failure. It examined the effects of experimental studies that used five...
Developing effective fractions instruction for kindergarten through 8th grade: A practice guide
Resource Type: Research
This practice guide presents five recommendations to help educators improve students? understanding of fractions. It features strategies to develop young children?s understanding of early fraction concepts and ways to help older children understand...
Direct instruction in math word problems: Students with learning disabilities
Resource Type: Research
The study investigated the effectiveness of strategy teaching and sequencing practice problems when teaching students with learning disabilities (LD) how to solve word problems. Students were randomly assigned to one of three intervention groups: 1...
Effectiveness of reading and mathematics software products: Findings from two student cohorts—Executive Summary (NCEE 2009-4042)
Resource Type: Research
A 2003 design effort by ED working with educational technology and research experts recommended focusing the study on software products used to support reading and math instruction. The study team set up a competitive process and worked with ED to...
Effects of mathematical word problem solving by students at risk or with mild disabilities
Resource Type: Research
The purpose of this study is two-fold. First, the researchers sought to assess the effectiveness of two instructional strategies, an explicit schema-based strategy and a traditional basal strategy, on one-step addition and subtraction word problems...
Effects of reciprocal peer tutoring on mathematics and school adjusttment: A component analysis
Resource Type: Research
This study investigated the differential impact of the structured peer tutoring and group reward components within a reciprocal peer-tutoring (RPT) intervention to enhance mathematics performance for students at risk for failure. Participating...
Effects of self-explanation as a metacognitive strategy for solving mathematical word programs
Resource Type: Research
The study examined the effects of a metacognitive strategy (i.e., self-explanation) on elementary school students’ ability to solve word problems. Students were assigned to one of three conditions: (1) self-explanation, (2) self-learning, and (3)...
Explicit instruction in mathematics problem solving
Resource Type: Research
This study examined the effectiveness of the explicit translation strategy method that explicitly teaches fourth-graders to translate word story problems into mathematical equation form. The study also explored the impact of providing students with...
Research on Math Practices
Resource Type: Bibliography
The PowerUp WHAT WORKS Team at the Center for Technology Implementation, has conducted extensive reviews of the literature on mathematics teaching and learning. View our bibliography for a collection of references on evidence-based math practices.
Strategy training and attributional feedback with learning disabled students
Resource Type: Research
The study explored strategies of verbalization and effort-attributional feedback on student self- efficacy and skills. Grounded in the hypothesis that verbalization enhances learning outcomes, the researchers explored the differential impact of this...