Week 5: Developing Mathematics Pedagogies that integrate embodied, multisensory, outdoors and arts-based modalities

This week I really connected with the reading but found myself puzzling over the activity. I chose to do an activity that put me outside of my comfort zone with the 'dancing' aspect and found that it took me a lot longer to complete this time. I've mentioned this in previous weeks but I wouldn't consider myself a really artsy person and find that any sort of body moment where others are watching and I am without explicit instruction is a stretch for me. I grew up figure skating and dancing but was not overly dramatic or comfortable with the 'interpretive' freestyle when there were others around. I chose the movement activity this week in hopes that I would be pushed outside this comfort zone even if my housemate thinks I'm crazy as I do random body movements in the kitchen.  

___________________________________________________________________________________

Reading Reflection

Dietiker, L. (2015). What mathematics education can learn from art: The assumptions, values, and vision of Mathematics Education. Journal of Education, 195(1), 1–10. https://doi.org/10.1177/002205741519500102

While I was reading this week I found that I had a lot of stops where I was putting stars on my notes either because what I was reading stood out to me or connected with me. 

The reading begins with an introduction of how math has been referred to as "dry as dust" "monotonous" or "flat-lined" and how the arts can help to re-inform math experiences. There is an explanation of aesthetic ways of knowing and learning. To challenge current assumptions of math this paper explores how math can be artful and aesthetic. Aesthetic is described as "an individual's response to a mathematical experience" (p. 2) which is said to help mathematicians sense if a result is correct or not. This describes aesthetic to be essential to mathematics whether it is a positive or negative response. Through understanding mathematical aesthetic, the paper discusses using different art to structure aesthetic math. Dietiker uses stories as an example, outlining the various parts of a mathematical story and how it can make math a verbal art. Mathematical stories include characters, setting and plot, much like a regular story. Using stories in math classes can help to 'shake up' the familiarity of traditional math classes. 

The idea of using aesthetic in math was interesting to me, when I first think of aesthetic I think of the way I want things to look and if they look nice then I would consider them aesthetically pleasing. In explaining her experience with math Dietiker (2015) explains a fond interest for math and puzzles growing up which led her to studying math in college and developing a desire to share this with students. This resonated with me as this is largely similar to my experience with math. I used to love doing puzzles with my dad and now as I have spent the last month helping my mom clean out some of his things I found a lot of the puzzles and mind-teasers that we used to do together and am reminded of my love for the puzzle aspect of math. None of my siblings enjoyed these but it was something that my dad and I did together all the time. This was a happy memory that stayed with me as I read and did the activity this week. 

Dietiker (2015) states that math classrooms where students and teachers work is tame and harnessed are something other than mathematical as math is generally untidy; she says that "creating aesthetically-rich mathematical classrooms requires untidying the mathematical experiences of students" (p. 3). 

This stood out to me, mainly because I had not thought of math as tidy or untidy before. When I think of my general math work - in high school or university - I think that my work was generally tidy and "aesthetically pleasing" because I like the neatness of lining up my equal signs and erasing mistakes. When I think of my teaching experience though I love engaging students in math classes where they are able to move around, use different materials and try to come up with a solution to the problem on their own (as we have learned the benefits of this throughout our courses). To me this means embracing mistakes and using these as learning opportunities.

Finally my last connection was to using stories in math. When I was completing my undergrad I was involved in an applied study where I had the opportunity to go into schools and tell students stories. I ended up doing a research project connected to this and explored storytelling and math. I explored different oral stories as well as picture books that tell stories about math concepts. This sparked my desire for including stories in math classes and have used them a few times but find that I often get caught up in needed to get things done and forget about this research and work that I did and how impactful it was. 

Questions

• What do you think it means to untidy the math classroom in your own classroom? 
• Do you use stories in math lessons or is it something you are willing to try? 

_________________________________________________________________________________

Activity 

I chose Sarah Chase's illustration of moving 3 against 2 as the basis for my mini lesson idea. I found myself trying many different combinations of this and becoming confused as I tried to count and move both arms at the same time. While I was doing the movements I was also spending time trying to draw them out to see if my movements were correct with where the arms should line up. I then thought of how students could do this together, having one person do the first number and the other doing the second. I found myself trying to think of how these types of movements could connect to multiplication or division however am still questioning that one. 

Here are some of the ones I tried to draw out, it got a little confusing when I tried to include larger numbers so didn't draw those ones. 

I found that some of them worked with multiplication

 but not all of the movement combinations. 

After moving my arms over and over again I connected this movement to help understanding angles or the unit circle - not directly with what was shown in the video but with the way the arms were used. 

I really struggled with this activity and wanted to give up many times but here is an idea I came up with. 

Unit Circle inspiration

Ideas 

Students will learn about the unit circle on paper and then have a chance to explore it with their arm movements, this will allow them to add a multisensory aspect to the math concept and potentially help them understand or remember it better. 

Guiding Questions 

• How can we understand the unit circle with our bodies? 
• What connection does the unit circle have to angles? 

The Story 

• I am still brainstorming ideas for this part... I can think of stories to go with elementary math concepts but am struggling to come up with one for this. 

Integrating Embodied learning and other learning 

• Students learn about the unit circle and triangles, how to construct the unit circle on paper 
• Imagining that their arms are equal to the radius 1, they can create a larger scale unit circle 
• This can help them to 'memorize' the unit circle with their body being the y-axis and arms stretched out to the sides being the y-axis 
• Using this new tool for understanding the circle students can work together to try and solve math problems that require the unit circle 

Possible extensions

• Ask students to think of what other math concepts they can understand with their body 

Idea for unit circle with body