Application of Gerofsky's (2011) article on graphing and gestures
Reading C: Gerofsky (2011) “Seeing the graph and being the graph”
Activity: “Function Charades”
Introduction: After reading Gerofsky’s (2011) article, I designed the game “Function Charades'' based on the activities conducted in her research on graphs and gestures. I explored this game with a Grade 6 class, and intentionally re-named it “Function Charades” instead of “Graph Charades” to move away from known math connotations. They were told the game was a combination of "Taboo" and "Charades". During the game, observations were made on how the students moved, the words they chose to use, and how they progressed from observing each other’s technique round to round.
Students: There were a total of 17 students in this section, participation to play or observe the game was optional. 14 opted to join in. Students had a variety of mathematical experiences, though most in this section are quite confident and comfortable with each other. The students have some prior knowledge of graphing, coordinate systems, the x-axis and y-axis from previous grades, and Science 6, but have not officially been taught the Cartesian plane, quadrants, or functions. Though the students were aware that it was a math game, they were encouraged to not think about it as a math game. Their objective was to simply convey enough information either verbally (Speaker) or physically (Actor) to one student (Drawer/Guesser) who would then draw the image as close as possible.
Materials: The Drawer/Guesser was provided a whiteboard that had grid lines and a whiteboard pen. The Function Charades PowerPoint was shown on the Loft screen.
Observations: 2 rounds were played. Round 1 – Drawer/Guesser (T), Actors (O, J) and Speakers (D, A). Round 2 - Drawer/Guesser (L), Actor (G), Speaker (C).
Other Observations:
Students did not realize the images were graphs, completely forgot they were doing math!
Students were really engaged and enjoyed the game, and wanted to continue playing.
Great demonstration of learning techniques and prompts from each other, noted that symbols helped with the visualization.
Video 1: O's first volunteer to act out the graph in Round 1
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Conclusion + Links
This would be a fun activity to trial with students in Math 9 and 10 who have a stronger knowledge of functions and coordinate systems. The students were given more ‘strict’ parameters than Gerofsky’s study but modifications could be made in future observations. Because there was no risk, the Grade 6 students were quite enthusiastic to be guinea pigs for this activity.
This activity linked well to Antonsen's (2015) TED talk emphasizing the need for students to find patterns, "represent patterns with language" (even if they need to make it up), make assumptions, and try new things. This activity got the students to play around with assumptions and trial techniques to determine which were successful and which perhaps were not. They had to use their imagination to think creatively to meet the objectives of the game and empathize because it was a lot harder to think on the spot than it looked, especially when others were not understanding the language or actions used.
Your post is informative, and I appreciate the way you explored embodiment in various ways. Your own experience of using fingers to reference the inches and your husband's use of tugboat as a reference to measure the distance was a brilliant way of quickly estimating distance.
ReplyDeleteI liked how you applied your students' knowledge of graphing and coordinate systems to "Function Charades" using embodied actions. From the images and video you shared, it is evident that your students used "body-based resources to make meaning and to connect new ideas and representations to prior (graph) experiences" (Natha 2021, p.4).
I also think the key here is that you created the classroom environment where your students had a chance to explore and discover the way to represent the graph. Sometimes, my precal 11 Students have difficulty connecting the transformation of quadratic functions. So, students use their hands to describe parent parabola and taking steps for transformation helped them visualize. We used Parabola dance that is similar to this one https://www.youtube.com/watch?v=eKoSLrQhN70. Being fully embodied in a graph fosters engagement more profoundly than merely viewing the graph.
Hi Pushpa, thank you for your encouraging words! I think for so many of our students, incorporating multiple sensory inputs can expand their learning. We often see this done in other class, like plays and skits to learn language and literature, experiments in science, but how often do we integrate practices like these into our math classrooms? Sometimes I forget that activities do not always need to result in 'acquisition or knowledge', it can be simply as you quoted 'make meaning and connect new ideas'. It's just a different for of representation for students to deepen their understanding.
ReplyDeleteThank you for sharing about Nathan's perspectives, I think it is an article I'd like to go back and read!
Beautiful, Christina! What a great game and super interesting observations of your students' ways of communicating and relating to graphs through this activity. I would love to learn more about this, and to try it out with other classes!
ReplyDeleteI was also very taken with your stories about body measurement: you and your friends' measurement of heels :), your thoughts about students taking ownership of design and measurement with their own bodies, and your observations of your husband and colleagues' very interesting ways of measuring with boat lengths and other marine referents. So much to think about here -- lovely.
Pushpa, thanks for your comments, and I hope that Grace will join in when she feels better.
such ɑ cool way to incorporate "embodied mathematics" and graphing!! Cynthia taught us ɑ game once and I tried it out in my practicum classroom (during an observation!) you may have heard of it: S K U N K. But, it was ɑ really neat way for students to get engaged and learn about probability (I think.) I had ɑ few students who had such ɑ difficult time making the decision to stick with their choices -the point being that I agree, students enjoy the non-risk factor that is involved with learning and games!
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