Option C: Stylianidou, A., & Nardi, E. (2019). Tactile construction of mathematical meaning: Benefits for visually impaired and sighted pupils. In Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 343–350). International Group for the Psychology of Mathematics Education.
This paper uses a sociocultural theoretical framework to create a tactile perception activity. Both visually impaired (VI) students and sighted students are invited to participate in the activity to investigate whether tactile perception can benefit math learning. Observations of 29 audio- or video-recorded mathematics lessons and interviews with teachers and support educators are analyzed.
In the activity, all sighted students need to close their eyes and determine the difference between the following two shapes: Shape X and Circle. All the shapes were constructed on the same white A4 paper and distributed to each student. Zak (sighted student) indicated that there is a straight line segment on Shape X, but he couldn’t identify a straight line segment clearly with his eyes. He then described this experience as “the hidden facts on the shapes”. Luke (VI student) identified the difference between Shape X and a circle that he said the circle can roll more, but Shape X cannot. As can be seen, other students focused on the actual characteristics of the shape, while Luke used “embodied imagination” on what the shape can do.
STOP 1: “The latter [universal design] denotes the design of environments, services and tools that can be used by every person, to the biggest extent possible, without the necessity for adaptation or specialised design.”
This is my first time thinking about the difference between reasonable accommodation and universal design. Reasonable accommodation ensures people with disabilities can be supported by modification and adjustments to achieve an equal basis with others, while universal design focuses on creating an environment and way that inclusively covers the needs of all people. This paper starts from the idea of using tactile perception to teach visually impaired (VI) students to transfer the strategies to a border picture that can benefit all the students. I really support this idea that teaching is never an isolated thing that a good teaching design should be beneficial to all the students.
STOP 2: “It would make the VI pupil feel that he is no more the only child in class who accesses mathematics differently from his peers. It would increase the sighted pupils’ familiarity with a sense which is mostly associated with VI pupils and often under-used by sighted pupils.”
This is an excellent example of “universal design” that benefits both VI and sighted students. People use different senses to experience math. Most sighted students can easily trap their thinking into views (i.e. the visible parts of math; a written equation, etc.). I have to say sight is probably the number one sense that many students use in a math class. Reflecting on the book Data Feminism that we read in our previous course, many students may assume numbers and data are something written on a piece of paper, but they never feel the actual power of numbers and data that exist in their everyday lives. Seeing something doesn’t mean you are experiencing it.
STOP 3: Furthermore, being aware of the characteristics of vision and touch – vision is wholistic and touch is gradual, allowing the exploration of an object from its individual parts to its whole.
I like the idea of exploring the characteristics of the object gradually from individual parts to the whole. I have to say, in our current time, most students are attracted to phones, videos and social media, so that one’s vision dominates most of the thinking. It is really important to discover different senses that humans can use to connect with the world. Sometimes seeing is far away, but touching is close and tangible (I would argue that, for example, you may watch some travel videos online that show a lot of amazing places, but this is completely different from you actually going to that place and experiencing everything around you).
Question:
1. What other senses can we apply to math teaching (i.e. listening, smelling, etc.)?
2. How can we create an inclusive environment where all students are welcome to explore mathematics in different ways?
Sunny,
ReplyDeleteYour point that seeing does not necessarily equal experiencing really made me pause, and I strongly agree with it. Even with simple math problems, watching a teacher demonstrate a solution on the board is very different from students working through the problem themselves. This reminds me of my experience making a hexaflexagon this week. While the steps in the video looked straightforward, it actually took me several attempts before I successfully made one. That hands-on struggle helped me understand the structure much more deeply than observation alone.
I also agree that sight is often the dominant sense used in mathematics learning, as it is in many subjects. However, depending on the concept, there are meaningful ways to engage other senses as well. For example, students could close their eyes and listen to a basketball bouncing, then explore questions such as the time between bounces, how many bounces occur before the ball stops, or how long the entire sequence lasts. Activities like this invite listening, movement, and timing into mathematical thinking.
Furthermore, I think creating an inclusive math learning environment where all students feel welcome requires intentional planning and ongoing input from students themselves. Listening to students’ feedback and understanding their needs allows teachers to design experiences that support multiple ways of engaging with mathematics. In this way, inclusivity becomes an ongoing practice rather than a one-size-fits-all approach.
I am also curious to hear about other multi-sensory math activities others have tried, and how students responded to them.
Hi Sukie, the basketball activity is so brilliant! I can't express how much I like this idea. I remember I did something similar in my physics class --- video record the bouncing ball's motion and analyze it, but I've never thought about letting students record the sound of it to determine how many bounces happened, and how long each interval! It is indeed a great example of using ears to experience math.
Delete“Seeing something doesn’t mean you are experiencing it.” Your quote really resonated with me as well. Similarly to Sukie, I had so much trouble this week trying to figure out the Hexaflexagons – despite its deceivingly simple presentation - as well as decode Kepler’s descriptions of geometry. I enjoyed the struggle. Thinking about the level at which I was able to engage with the material, I only understood it once I had my hands on it AND it worked – sometimes, it was a surprise when it (the hexaflexagon) worked and I was equally puzzled by my success. So even putting my hands on it didn’t guarantee my understanding of it.
ReplyDeleteTo try and answer your question: What other senses can we apply to math teaching (i.e. listening, smelling, etc.)?
There has to be meaningful ways of engaging the senses beyond vision. The idea of using disability as a jumping point for innovation really stuck with me. Trying to stick with some basics, I imagine we could represent rational numbers with flavour combinations of fruits and vegetables, meats and cheeses. Perhaps pouring interesting liquid ratios of various juices/pops for potentially delicious drink combinations might make an interesting lesson!
I wonder if lighting up scented candles in various ratios would also provide a meaningful and interesting lesson.
At the end of the day, I think this is a fantastic suggestion to put towards your students. Each of us has strengths, preferences and experiences that could lend itself to connections with the current curricular topic. For them to draw upon their experiences and apply the concepts in their personal contexts, then report out could be a really powerful way to gain a repertoire of ideas, benefitting both the student and the teacher.
Thanks for the thoughts!
Hi Oliver, thanks for sharing your experience of making the hexaflexagon! Like Sukie said above, viewing the demonstration and doing the problem by ourselves can be really different. That's why, as teachers, we need to think carefully on if our students are really supported by the demonstration and instructions, or are there other ways to help students learn things better?
DeleteGreat discussion, everyone! I really like your multisensory math suggestions -- listening to basketball bounces, mixing ratios of juices and tasting them, noticing that vision can be from afar but touch is close-up and immediate... Very very interesting.
ReplyDelete