Building a list of robust student engagement strategies is essential for all teachers. When students are engaged in the classroom, they remain focused and on task. Good classroom management and effective teaching and learning result from student engagement. The table below illustrates several student engagement strategies for the mathematics classroom.

# Student Engagement Strategy

**Description:** Students partner to make appointments for discussions or work (a good grouping strategy).

**Math Example:** Students are given a page with a clock printed on it. They use the clock to set appointments with other students to discuss math problems.

**Description:** Each group posts sample work on the wall, and the leader for that group stands near the work while the rest of the group circulates around the room, looking at all the samples.

**Math Example:** Each group is given a poster board and ask to work on a math problem. When all groups have finished their work, each poster is affixed to the classroom walls. Each leader stays close to the poster created by his or her group and explains the work, while the other students walk around the room looking at other groups’ work.

**Description:** Students act out a scenario, individually or with a team.

**Math Example:** Students work in teams to act out word problems while others try to solve the problems.

**Description:** One partner has a picture of information that the other student does not have. Sitting back to back or using a visual barrier, students communicate to complete the task.

**Math Example:** Working in pairs, each student communicates a different problem to the other student, who has to try to solve the problem from the information provided by the first student. The students sit with a barrier between them during the activity.

**Description:** Sharing their individual ideas, the group comes to a consensus and reveals that consensus to the entire class.

**Math Example:** Each member of the group shares an answer to a given problem, the steps used, and so forth. When the group comes to a consensus, they reveal it to the entire class.

**Description:** Assign half the class to be explorers and half to be settlers. Explorers seek a settler to discuss a question. Students may exchange roles and repeat the process.

**Math Example:** Half of the students are designated as explorers who have a math term or problem. The other students are designated as settlers who have the definitions or answers. Explorers seek the settler with the correct answers and discuss the information.

**Description: **Students are given cards and must find the person who matches their card. One person has a card with a rule, and the other has an example of that rule. This is a great strategy for practicing inductive/deductive reasoning. It also works well for grouping students randomly and developing problem-solving skills.

**Math Example:** Two types of cards are prepared: one with a problem and the other with the rule pertaining to that problem. Students circulate throughout the room to match the cards that are connected or related to the rule. Once all members of the group have been found, group members articulate the rule and how the group is connected.

**Description: **Each student is given a card that matches another student’s card in some way.

**Math Example:**

Example Cards:

Rectangle

Prime Number: 37

Problem 9+7

Solution 16

Polynomial with degree 3

4x³ – 3x² + 5x – 7

**Description: **Assign each corner of the room a category related to a topic. Students write which category they are most interested in, giving reasons, and then form groups in those corners.

**Math Example: **The corners of the room are numbered 2, 3, 4, and 5. Students are divided into four groups, and each group is sent to a corner. The teacher then poses a problem whose answer is a multiple of 2, 3, 4, or 5. Students in a corner that is a factor of that number will move to a different corner. If the teacher calls out 6, students in the corners labeled 2 and 3 will move. The activity ends with a prime-number answer, and students return to their seats.

**Description: **Students stand or sit in two concentric circles, creating partners who face one another. The teacher poses a question to the class, and one partner responds. At a signal, the inner circle or outer circle rotates, and the conversation continues.

**Math Example: **Students share information to solve problems. The teacher (or student) prepares question cards for each student. The inner-circle students ask a question from their card, the outer-circle students answer, and then these partners discuss the problem before switching roles. Once both students have asked and answered a question, the inner circle rotates clockwise to a new partner.

**Description: **A group of students is assigned a portion of text; these students then teach that portion to the remainder of the class.

**Math Example: **“Factoring Jigsaw” is a game in which each student becomes an expert on a different concept or procedure in the factoring process and then teaches that concept to other students.

**Description: **A cognitive graphic organizer sets the stage for learning. The teacher asks students to identify what they already Know, what they Want to know, and what they need to do to Learn the skill or concept.

**Math Example: **Math teachers use KWL as a diagnostic tool to determine student readiness, using pretest questions and a KWL chart.

**Description: **Students line up in a particular order given by the teacher (e.g., alphabetically by first name, by birth date, shortest to tallest, and so on).

**Math Example: **Students line up in order by the number given to them: square root, fraction, decimal, or multiples of a given number. Once in line, they explain how they found their place. This is a good activity for the first day of class.

**Description: **Two students, using one word or phrase, add items to a list.

**Math Example: **Students receive a multi-step or word problem and name the steps needed to solve the problem

**Description: **This is a cooperative learning strategy that holds each student accountable for learning the material. Students are placed in groups, and each person is given a number (from one to the maximum number in each group). The teacher poses a question, and students “put their heads together” to figure out the answer. The teacher calls a specific number to respond as spokesperson for the group. With students working together in a group, this strategy ensures that each member knows the answer to problems or questions asked by the teacher. Because no one knows which number will be called, all team members must be prepared.

**Math Example: **Each group is given a problem to solve. The student whose number is called explains how the group came up with their answer.

**Description: **Using two-sided cards prepared in advance by the teacher, students in pairs quiz each other, trade cards, and then find another partner.

**Math Example: **May be used to help students review math vocabulary, discuss math facts, or improve their mental math skills.

**Description: **A group of students participate in a rigorous, thoughtful dialogue, seeking deeper understanding of complex ideas. Guidelines and language strategies are taught and followed during the seminar.

**Math Example: **The teacher presents a distance-versus-time graph and asks students to describe what is happening. Alternatively, the teacher could present an action with four choices of graphs that depict the action. Students choose one of the graphs and explain and defend their choice.

**Description: **After brainstorming ideas, students circulate among other students, giving one idea and receiving one. Students fold a piece of paper lengthwise to label the left side “Give one” and the right side “Get one.”

**Math Example: **The teacher gives the class a multi-step problem to solve within a specific time limit. On the “Give one” side of the paper, students name all the steps they know before finding a partner. Partner A gives an answer to partner B. If partner B has that answer, both students check it off. If partner B does not have the answer, partner B writes it on the “Get one” side. Students repeat the process with partner B going first. Once both partners have exchanged ideas, they raise their hands, find new partners, and continue until the teacher says to stop.

**Description: **Teams take turns to share their final product.

**Math Example: **Students work in teams on different math problems. Each team solves its assigned problem cooperatively. The team then has the opportunity to explain its answer with the entire class.

**Description: **After the teacher poses a question, students are given time to think about their response. The teacher asks students to pair up in a specific way (e.g., elbow partners) and share their response only with their partner. This strategy helps students practice and refine their response.

**Math Example: **What is the difference between prime numbers and composite numbers?

**Description: **This is a variation of think–pair–share. Students are asked to think about their response, write down their response, pair, and share. This strategy might be used when a more complicated response from students is required.

**Math Example: **Students are given a word problem to solve. First, they are asked to think about what the problem is asking. Then they are asked to write down their idea. Finally, students share their idea with a partner.

**Description: **The teacher poses a prompt that has multiple answers. Students write down as many responses as possible. Then the teacher “whips” around the room, calling on one student at a time. Each student shares one of his or her responses. When called on, students should not repeat a response; they must add something new.

**Math Example:**

What are examples of quadrilaterals?

What are some tools you could use to help solve this problem?

**Description: **After students write their ideas about a topic, each student shares one idea, repeating the statement of the previous student.

**Math Example: **The teacher gives the entire class a problem and then allows time for students to write out the steps to solve the problem. Then each student describes one step in the process.

# Classroom Application

## NCTM: Engagement as a Tool for Equality

View Website# Research

Seeley, Cathy, (2004). * Engagement as a Tool for Equity, NCTM News Bulletin, *November 2004.