Peer interactions can greatly benefit a student's understanding of mathematical concepts. To facilitate peer collaboration based on differentiated needs, teachers should pair students carefully, model effective ways to interact, provide students with relevant tools, and offer specific advice. Struggling students may find it especially helpful to interact with peers who can provide explanations, clarify a process, and ask and answer questions. This give and take involves listening, speaking, writing, creating visual representations, and using virtual and physical manipulatives.

# Teach with Tech

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.)

Steps:

### 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.

**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.

#### Interventions should include instruction on solving word problems that is based on common underlying structures

#### Teach number and operations using a developmental progression.

Source: **IES Practice Guide**: Teaching Math to Young Children

### 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.

**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.

#### 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.

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.

#### Help students understand why procedures for computations with fractions make sense.

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.

**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

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