Introduction
The article “Mathematical Learning and Gesture” by Susan reports on a research project in mathematics education involving the use of gestures. It highlights the role of body movement, gestures, and vocal sounds during the mathematical learning process.
The paper uses the framework about gestures from McNeill (1992), which identifies two viewpoints when using gestures. The first is called the observer viewpoint (O-VPT), where subjects gesture the action as if they were standing apart from it and observing from a distance. The second is called the character viewpoint (C-VPT), where subjects use gestures as if they were the character themselves rather than observing the character.
Based on this framework, the research team conducted two studies about graphing polynomial functions and categorized the ways students used gestures.
The first study involved 22 students from Grades 8 and 11. Students were asked to use gestures to represent the shapes of five graphs taken from a calculus textbook and mounted on large cards. The study found that students at the same mathematical level showed similar patterns when using gestures to represent polynomial graphs. The“top” students consistently used gestures based on type II (C-VPT), while“average” students were more likely to use gestures based on type I (O-VPT).
The second study was conducted with 25 Grade 8 students paired with Grade 12 students. The research team conducted an extended teaching experiment with the class over six months, using C-VPT gestures as a prelude to a brief lesson on abstract aspects of functions. They also introduced vocal sounds as part of students' multimodal representations of the graphs. At the end of the study, two students showed an exceptionally high rate of retention and reconstitution of knowledge. Many students referred to the movements, gestures, and especially sounds to help them recall what they had learned a year earlier.
In conclusion, gestures, movements, and sounds play an important role and show great potential in promoting mathematical engagement and understanding based on the results of the two studies.
Stops
“All this suggests that there should be a different pedagogical approach in mathematics, one which values and makes space and time for experiences involving modalities like movement, sound, tangible objects, and integrating these resources with conceptual and abstract learning and thinking.” （p27）
“These sounds comprised rising vocal pitch when the slope of the graph was positive, falling pitch when the slope was negative, a “pop” sound at the roots of the function, and a “gasp” at the extrema (maximum and minimum points).“ （p333）
And I found student’s feedbacks from the second study are inspiring:
Reflection
This study is fascinating to me because it's a field I had never deeply considered before. I believe you will feel the same way when you read the sections I picked and realize how powerful gestures can be in contributing to learning outcomes, or even as a pedagogical tool in teaching mathematics. We know that gestures play an important role in mathematical communication and can be part of the language we use in the classroom. However, they are much more powerful than we might have thought.
When reading the first study and seeing how they coded the use of gestures, I initially thought it was just a different method of recording with no significant difference. However, the results show that the use of gestures actually presents different viewpoints of the graph, which is linked to the understanding of the mathematical content. This is a new idea I had never considered before. Moreover, the second study demonstrates that the proper use of body movements, gestures, and vocal sounds can help students construct the C-VPT, significantly aiding in visualizing and remembering abstract concepts when graphing polynomial functions. I particularly liked the sound component and how it was designed to connect to specific math concepts (stop 2), allowing students to notice details they might have missed before.
I hadn't paid much attention to the role of gestures in my teaching; they were more like natural movements without my conscious control. However, the article demonstrated that these movements and sounds can be purposefully modified to engage students and help them gain a comprehensive understanding. The results from both studies have given me a new perspective on using gestures in the classroom. The suggestions from the article are also highly applicable. If you are teaching right now, I think you should try incorporating these techniques into your classroom as soon as possible.
Thanks for your reflection, Lee. I also hadn't really considered how gesture can be used as a teaching tool before; they were more of a sub-conscious action for me as well. I also found it interesting how sound and movement were linked in the graph and it makes me wonder how I might have taught my graphing unit differently than what I did. I did try to incorporate narrative and movement but from an authorial perspective where students were creating a story about a character moving on a coordinate grid, but perhaps it would be more valuable if they engaged in the movement themselves. It might also help some students who are less able to communicate an idea verbally demonstrate their comprehension. This may be especially true for students whose L1 is not the language of instruction.
ReplyDeleteHi, Lee. Thank you for your summary and for sharing your thoughts. Last year, in Susan's lesson, I learned how gestures, music, and even poetry can connect with math. When I first saw how sound and movement were linked in a graph, I was amazed, it felt like it reshaped my understanding of what math is. Now, when I teach, I also encourage my students to use gestures to represent mathematical concepts, especially function graphs. I think they find it both enjoyable. I also remember a fascinating video that Susan shared with us. If you're interested, I'd love to share it with you: https://www.youtube.com/watch?v=ZQElzjCsl9o&t=494s
ReplyDeleteThanks Lee, Nathan and Jialian! We'll do a bit of experimentation with this kind of intentional/ elicited gesture in today's class too (as opposed to unconscious speech-accompanying gesture). Jialian, I love Roger Antonsen's TED talk too! Thanks for sharing the link with everyone.
ReplyDeleteThank you, Lee, for your summary and reflections. Jialian and I had the opportunity to take Susan’s class last year, where we explored how gesture, music, dance, and poetry can be integrated into mathematics education. As Jialian mentioned, these creative elements can play a significant role in teaching and learning math. Although I am not a musician or a dancer, I have experimented with incorporating movement into my lessons. When teaching certain concepts, I encourage students to use their bodies to express their understanding. Simple actions, like using hand gestures to represent mathematical operations or demonstrating geometric shapes with body movements, make learning more interactive and engaging. By adding physical movement to math instruction, students become active participants in their own learning. They are not just passively absorbing information but physically experiencing and internalizing concepts in a meaningful way. Movement can also make abstract ideas more concrete, helping students visualize and remember them better. This approach fosters creativity, deepens understanding, and increases student engagement. Incorporating gestures and movement into teaching is a powerful way to make learning more dynamic and effective, transforming the classroom into a space where students can think, move, and explore math in new ways.
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