Math Metaphors

  • Math Metaphors

    Grades: 6th to 8th,High School
    Periods: 1
    Author: Toni Amarel and Megan Wickstrom


    Instructional Plan

    This lesson is based on the MTLT article, “Math Metaphors: Windows into Mathematical Experiences” by Toni L. Amarel and Megan H. Wickstrom. In this lesson, students create metaphors to capture and explore their experiences as learners of mathematics with respect to their identity, sense of agency, and emotions.

    Implement during the Orientation Module or the first content module of the course. 


    Provide students with the Math Metaphors Student Handout. Devote some time to discussing and sharing examples of what a metaphor is. If you are teaching online, consider posting the assignment on a discussion board. Depending on your online classroom style and learning needs of students, you may want to provide a video explaining the assignment. It might also be helpful for you to create your own metaphor describing your experience with mathematics to share with students as an additional example and to help build a community. 

    Tip: To encourage interaction among students online, be sure to remind students to subscribe to the discussion board. Consider making a video to explicitly show how to subscribe to a discussion board.

    Explore Gymnastics Math Metaphor

    Students will create their math metaphor slide with narration. This can be written or verbal. Encourage students to incorporate descriptions and relevant photos into their slides. If you are teaching online, students can also use video recording software to narrate their slide. 

    Tip: Consider making a video explaining how to download and use the desktop recording application, such as Loom or Screencastify.

    Class Discussion (in-person)

    Arrange students in either pairs or groups of four. Give each student 3-5 minutes to share their metaphor with one another. Give them the following prompts to reflect on together:

    • What similarities and differences do you notice across metaphors?
    • What did you learn about your own mathematical journey and your classmates' journeys through this task? 

    After students have had time to discuss their metaphors, the teacher can bring the whole class together and invite students to share their responses, as they feel comfortable. 

    Class Discussion Board (online)

    Students will upload their finished presentation to the discussion board and interact with at least two other students. You can provide students with prompts like those above to help focus interactions. 

    At this point, the teacher's goal is to review and analyze each student's metaphor using the Four Domains for Exploring Student Metaphors (identity, agency, emotion, and meta-affect) and monitor student posts in the discussion board to gain insight into each student's relationship with mathematics. This insight is used to inform future interactions with the student and instructional moves.

    Tip: To encourage interaction and build community, consider reminding students through course announcements or email to interact with other student posts. We recommend that the teacher also respond to each student's post with a comment and/or question to encourage engagement.

    Student-Teacher Discussions (Optional, but powerful)

    The teacher will facilitate an initial conversation with each student about their metaphor. If teaching in-person, this could be done with written feedback. The goal of this initial conversation is for the teacher to learn about the student's relationship with math by guiding the student to share why they chose the metaphor and how it reflects their experiences with math. After the discussion, the teacher can see the four Domains for Exploring Student Metaphors to inform analysis of the student's metaphor.

    Behind the scenes, the teacher will leverage the information and insight gained from the student-teacher discussions to guide instruction and future mathematical experiences for students. The teacher can implement strategies that help a student become aware of and regulate emotions, such as asking students to reflect on questions like, “How did you feel across this task?” or “How have your thinking or feelings about math changed?” The teacher can assign competence to a student by highlighting student ideas or contributions to class as a way to bolster a student's identity or give students opportunities to be challenged and creative with mathematics as a way to develop agency.

    Tip: The timing of the student-teacher discussion is left to the professional judgment of the teacher. Some students may need more time than others to feel comfortable sharing their thoughts. 

    Assessments and Extensions

    Extension Options

    Throughout the course, consider having students revisit this assignment to create new math metaphors, particularly after significant experiences in the mathematics classroom, such as after a group project, after an assessment, or at a marking period.

    Consider giving students the prompt: “Find a picture that reflects how you feel about math right now and explain” at different points throughout the course. Ask students to reflect on whether their relationship with math has changed and if so, how and why?” 

    Questions and Reflections

    1. Do I notice any trends in my students' metaphors? What might be the origin(s)? How can I support these trends with my students?
    2. Was I surprised by a student(s) metaphor? What was surprising? Why did it surprise me? 
    3. How can I use the information from my students' metaphors to inform instruction and future interactions with my students? How can I help my students grow as learners of mathematics?

    Objectives and Standards

    The student will reflect and articulate their feelings about learning and doing mathematics.