Mr. Hapt’s seventh grade class has started a unit on statistics. In the previous lesson, the class discussed collecting data and making observations about the data. In this lesson, they will create survey questions, collect their own data, and make...
Exploring math together - discussing, reading, and writing about concepts - can build your students’ mathematical understanding. However, your students need your help to learn how to use their peers as resources, as well as how to be a useful resource for their peers. The strategies given here provide a strong starting point for differentiating instruction. Consider using digital communication methods such as blogs, emails, and text messages. (See UDL Checkpoint 8.3: Foster collaboration and communication.)
Best Practices with Technology
Step 1: Provide Clear Explanations
- Develop a list of class norms for interaction and post them on the class website or a blog. Elicit input by asking students to identify how they want their classmates to respond to both their correct and incorrect ideas.
- Give your students a structure for tutoring classmates. Provide tools (e.g., a class blog or website) so that students can record, track, and share.
Possible structure for tutoring
- When tutoring a math concept, the tutor could begin by presenting three examples. The tutor and the student could then work together to come up with other examples.
- When tutoring on a procedure, the tutor could have a checklist of steps to share with the student.
- Provide structures for student interactions that allow all students to have a voice. Techniques such as Think-Pair-Share or Turn and Talk ensure that all students have their own time to think about the mathematics and to articulate their thoughts.
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
- Use multiple structures and techniques for feedback and student discussions. This provides options for students who are less comfortable with some techniques. It also encourages students to think about interacting in different circumstances (e.g., one on one, as part of a group, when agreeing, when disagreeing).
Discussion formats
- Fishbowl Discussion: A few students discuss the topic while others listen. If someone who is listening has something to add, or if you choose to have someone else step in, that person replaces one of the students in the discussion group.
- Peer-to-Peer Whole Class: When a student says something, ask the class to respond. Stay neutral (neither verify nor correct students) for as long as possible.
- Paired Verbal Fluency: Each student has a set number of seconds to talk uninterrupted while his or her partner listens. The students then switch, and the listener now does the talking. They switch back for a shorter time to give each other opportunities to respond. Have students complete two or three rounds, taking turns in this way.
- Fishbowl Discussion: A few students discuss the topic while others listen. If someone who is listening has something to add, or if you choose to have someone else step in, that person replaces one of the students in the discussion group.
- Encourage students to help each other by giving clues or hints or asking questions, rather than simply providing answers. Sometimes it is effective for students to present their own ideas rather than assuming that their peers hold the same idea. Students can make use of physical manipulatives or virtual tools to create alternative representations that support their ideas.
- When a student provides a solution and a peer accepts that solution without question, ask the peer if she or he needs any clarification. If not, ask the peer to explain the solution back to the original student.
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
- Listen to students’ conversations with peers. Note whether they ask questions for clarification or prompt a classmate to reconsider a proposed solution. Listen for statements that add to the mathematics conversation. Return to certain conversations to verify that a student has corrected any misunderstandings.
- Remind students (as needed) that you want them to be able to talk about math with each other, and not just with you. If they need a less subtle hint, explicitly direct them to address their peers.
- Consider each student’s needs and learning styles when you decide which actions to take to move students closer to 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:
Interacting with Peers: Talking About Fractions
Resource Type: Lesson in Action
Ms. Moore’s 4th grade class is doing a unit on equivalent fractions and adding fractions with like denominators. In this lesson, students will discuss ways to decompose fractions.
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...
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 parent involvement in isolation or in combination with peer tutoring on student self-concept and mathematics achievement
Resource Type: Research
This study assessed the effects of a home-based, parent involvement (PI) intervention and the combined effects of PI with reciprocal peer tutoring (RPT) on self-concept and mathematics achievement. Participating students were randomly assigned to...
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...
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.