Summary
Metaphors are often associated with flowery, figurative language and do not routinely find their way into mathematics courses. In this lesson, we create space for students to form arguments and better understand mathematically abstract concepts when they are provided opportunities to connect them to their personal experiences. This lesson can be implemented in nearly every subject and within multiple grade levels since it involves broadly connecting mathematics concepts to personal experiences and ideas.
Essential Question(s)
How do mathematical concepts connect to or represent parts of your life?
Snapshot
Engage
Students will use Window Notes to organize their thinking about a mathematical concept.
Explore
Students will explore how they can use a mathematical concept to metaphorically represent an aspect of their life.
Explain
Students will share their metaphors with other students.
Extend
Students will be asked to create visual representations of their metaphors as a way of integrating art into mathematics
Evaluate
Students will reflect on the process using the What? So What? Now What? strategy.
Materials
Paper
Colored pencils/markers
Scissors (optional)
Word processor
Engage
Using the Window Notes strategy, ask students to take out a blank sheet of paper, divide it into four quadrants, and label the quadrants Facts, My Procedure, Diagrams, and Feelings.
Depending on the content you are covering in your class, these categories might need to be changed. The goal, though, is for students to think about the facts involved in describing the mathematical concept, the procedures that could be involved in using the mathematical concept, what diagrams, graphs, or equations illustrate the concept, and how they are feeling about the concept.
Give students approximately 10 minutes to think through each of the four areas.
Explore
Ask students to think of how the mathematical concept they described above using Window Notes relates to an aspect of their life or to their life as a whole. For example, the concept could provide a way of explaining how they feel when the are going through a difficult time, or the concept could illustrate an aspect of their identity. Give them ample time to think and to brainstorm.
Instruct students that they will have 30 minutes to begin crafting a metaphor for their life or an aspect of it. Students are free to write using pen and paper or a word processor. The time can be adjusted as you see fit. This can even be given as a homework assignment to allow longer processing time.
Below are some sentence stems to help students begin writing:
This concept reminds me of...
An important event in my life was...
This concept makes me feel...
I am...
People describe me as...
This relates to (the mathematical concept) because....
The shape of the graph is similar to...
The equation represents...
Explain
After students have written their metaphor, ask them to sit in groups of three.
Allow each person in the group to take turns sharing their metaphors, giving the other group members time to respond.
This process should take about 15 minutes, allowing about 5 minutes for each student.
Extend
After students have written and shared their metaphors, they can now extend their learning by creating a visual representation.
This process can potentially be quite open-ended. Students can draw, color, fold paper, make an online slide show, or use any other medium.
Give students about 30 minutes to create a visual representation for their metaphor and let them know that the products will be displayed in the classroom.
After students have written, shared, and created a visual for their metaphor, have students attach their metaphor to their visual representation. Collect their assignments to display in the classroom.
Evaluate
Ask students to reflect on their day's work using the What? So What? Now What? strategy.
What? What did you do today?
So What? What did you find meaningful in today's assignment? About yourself? About others?
Now What? How does understanding others' perspectives impact our classroom community?
Resources
K20 Center (n.d.) What? So what? Now what?. Strategies. Retrieved from https://learn.k20center.ou.edu/strategy/b30762a7557ba0b391f207f4c6002113
K20 Center (n.d.) Window notes. Strategies. Retrieved from https://learn.k20center.ou.edu/strategy/fc74060730ea745c8c4f356aa2015ac0
Wells, C. (2018). Metamathematics: Three approaches to reflective writing in math classrooms. Manuscript submitted for publication.