Week 2 - Multisensory Mathematics - Critical Reflection

  “A recursive model is an interesting way to think about using multisensory math learning experiences as resources to think with…use the sensory activities to experiment with imagery and metaphor…These activities can become learning resources that helps learners synthesize multiple sense images to learn, remember and reconstruct these patterns with a deeper understanding.”                    Susan Gerofsky, course materials, Week 2

         The paragraph containing the above quotation was my first big stop in the readings and viewings and it related to many of my other stops, especially in reading the Fernades and Healy (2013) paper. The term “learning resources” was what initially made me stop, think, and process. I appreciate the idea that when we offer students, as what Susan wrote, “a really engaging and well-designed, shared multisensory activity”, students can draw upon these kinds of experiences, as resources, just as they might draw upon physical resources in our classrooms. What I took from the Fernades and Healy (2013) paper in a similar regard was that even if these experiences are drawn upon in imagination, they support learning. For example, one of the participants, Edson, had visual memories of mirrors that he was encouraged to use to support his development of the concept of symmetry. Additionally, the other participant, Lucas, had some assistance in the form of questioning from the researcher and then was able to employ that assistance and his own multimodal representations from previous tasks to tasks moving forward. How students are supported in perceiving and conceiving mathematical concepts gives them tools (multimodal representations) to use in future tasks and enriches their understanding.

I ended up using this idea of drawing upon previous experiences as learning resources to reflect on two experiences with the hexaflexagons this week: when I worked with some grade 1 and 2 students during a morning when I was redeployed and in my own exploration of hexaflexagons.

I landed in an inner city grade 1 and 2 class on Friday morning at the last minute. The day before I had printed several copies of Vi Hart’s hexaflexagon templates to carry in my bag in case I was redeployed and needed something to do with students. After a long play outside to start the day and the cries of “I’m hungry” coming back to the classroom, snack time it was and not enough time before recess to start an art project that was in the plans for the rest of the morning. The assistants and I suggested the students read or draw when snacks were done. One boy, let’s call him Bowie, said, “Instead, can I teach you origami?” and I agreed, as long as he also let me teach him hexaflexagons to help me with my homework. Bowie and I settled in at one of the tables and he taught me how to make a leaping frog.

Another boy, we’ll say Tim, joined us wanting to do origami but was being ignored by Bowie and my hexaflexagon template caught his eye. So while Bowie proceeded to make more origami (and not help me with my homework as agreed), I helped Tim with a hexaflexagon. This was quite difficult, even just to have him fold on the dotted lines and still so after I gently creased them for him. We got it constructed, he coloured the two sides, and I taught him how to flex and open it. I wish Bowie had fulfilled his part of our agreement because I was so interested if the folding would have been as difficult for him. My feeling is that Bowie would have folded it really well. His folding for origami was accurate and the creases were very sharp. In reflection, this is because Bowie has experiences of paper folding to draw upon if he were to make a hexaflexagon. My interpretation of Tim is that he avoids a lot of things that might be hard for him and relies on other people to entertain him. What experiences has he had that he draws upon to tell him to avoid things? Maybe his hexaflexagon experience will now be something he uses in the future to inform new learning.

My hexaflexagons from Vi Hart's templates

            I have to admit, my first reaction to knowing I would have to try out hexaflexagons this week was a bit negative. Jen and Jen did hexaflexagons for the Virtual Math Fair last year and I was in their room. I tried making a hexaflexagon both during our practice session and during one of their math fair sessions and was unsuccessful (now I know I was really over complicating the initial folding to make the triangles). I gave up and have not tried again since. However, I reset myself after my first reaction to it this week, used Vi Hart’s template, and got it! So, I asked myself, not only can great multisensory experiences affect future learning, but negative ones can also come into play. I alluded to this above in relation to Tim and after considering him in this way, I realized that I had initially been blocked by seeing all my failed hexaflexagons in my imagination. I sucked it up and got my hexaflexagon made and then made the sturdier one. Now I can make them without the template out of any size scrap strip of paper. I saw a video online for a hexa-hexa-flexagon I’d like to try, too (If I try it, I’ll edit my post and add it in!). How do we make sure that our students store their experiences with multisensory mathematics activities positively, so they are learning resources, not road blocks?

 

(I didn’t explore the bagel cutting myself, as cool as it looks, because, although I had some bagels in my freezer, they were pre-sliced ones!  No Flex Mex either – no tortillas and no need to consume any this week so I didn’t make the purchase. My imagination went to a Flexi-Crepe though – with Nutella or other such yumminess!)

 

Questions to Ponder

As in my last paragraph, how do we make sure that our students store their experiences with multisensory mathematics activities positively, so they are learning resources, not road blocks?

The snacks were fun to work with, but I resist using food in classrooms for a multitude of reasons. What other engaging materials that might stimulate the senses could be used for data analysis or geometric explorations? How might you use them?

In regard to the paper I read, what expectation is there on researchers to seek advice from experts in the impairment they are addressing to be sure their methods do not skew their results? For example, Fernades and Healy (2013) were surprised that both students approached examining figures in a symmetrical action – both hands moving on each side of the figure in a mirrored way. However, this didn’t surprise me as it is what I have observed people with visual impairment to do. How do they tease out what is a pre-learned strategy from what is developed through the tasks of the study?

References

Fernandes, S. & Healy, L. (2013). Multimodality and mathematical meaning-making: Blind stduents' interactions with symmetry. RIPEM, 3(1), 36-55.