Week 5

This week’s article was titled “What Mathematics Education Can Learn from Art: The Assumptions, Values, and Vision of Mathematics Education” by Leslie Dietiker (2015).  

Traditional math classrooms are “monotonous”, “flat-lined” and “dry as dust”, at least that’s what the author of this article is claiming.  Even with the advancements in technology and countless studies investigating how students best learn mathematical concepts, little has changed in the last few decades.  Students still spend the majority of their time listening to the “expert” at the front of the room followed by replicating what they’ve been told through endless practice problems.  Textbooks and curriculum are designed to be unemotional, sequential, and efficient.

STOP - I paused here to consider my current and past classroom practices, the technology that I use, and the issue of textbooks.  I have to admit, that this year I’ve fallen back into old habits of lecturing from the front of the room, and then handing out worksheets with similar problems.  While I use manipulatives extensively, I don’t really use any other technology to support my lessons.  Just a couple of years ago I was more inclined to try new things and I was using Peter Liljedahl’s methodologies quite heavily.  After reflecting on this change, I think I went back to old habits as a coping mechanism to help me deal with how stressful my current students are in terms of their behaviour and academic ability.  Approximately ⅓ of my students are diagnosed with FASD and ASD.  They do better with the predictability of a more structured, traditional classroom, and are better able to regulate their emotions and behaviours.  As for textbooks, my school stopped purchasing textbooks over 10 years ago because the students couldn’t read them or take care of them responsibly and it was just too costly to continue to replace them.  I realized that I haven’t actually opened a textbook in so long that I’m no longer able to comment on how effective/ineffective they are.

So how might educators shake up the conventional math curriculum and invite the imagining of rich new mathematical stories?  

Dietiker proposes that making use of sensory experiences, engaging imaginations, risk-taking, and movement within the math classroom enhance the learning experiences of students.  They are more likely to feel a sense of wonder, pride, and joy when learning.  While there are many ways of bringing these types of activities into the classroom, Dietiker believes that making use of stories provides a natural avenue for incorporating all of the above.

These stories could be in the form of historical origins of math problems, narratives, or mathematical (similar to a rich task, or 3 Act task).  The best stories are the ones that draw students into the setting with interesting characters and unexpected plot twists.  These stories compel students to investigate alternate endings, take risks, and ask questions.

STOP - I’ve used stories a few different times within my math classroom, and while I enjoyed them, I’m not sure my students would say the same.  Perhaps I didn’t choose the right stories, or I failed to help students connect the math concepts with the story.  Either way, it didn’t seem to work for me and I moved on to trying other strategies.  

Have you tried using stories in your math classroom?  In what context have you used, or could see yourself using, stories to engage students in their math learning?

Activity - Sorry there's no pictures! I tried to get my kids to take pictures, but they were laughing so hard at my attempts that none of them turned out.

After watching both videos, I ended up choosing to try Sarah Chase’s dancing combinatorics to try.  This surprised me, as I am not a dancer. I was quite intimidated by the idea of creating my own movements, so I started by copying her example of 2 and 3 with just my arms.  As I predicted, I struggled for a long time to get my arms to move simultaneously within the pattern.  I tried using her idea to connect the movements to my emotions but that actually felt harder because then I was concentrating on moving my arms and speaking at the same time.  While I’m not sure if I could confidently demonstrate this activity to my class, I could still invite students to try this activity.  

I could see this activity working well with a lesson on finding the lowest common multiple.  Even though my students are in grade 8/9, they still struggle with this concept.  Partly because they are not great at their multiplication facts, which makes it difficult for them to find common multiples.  

Issue - Students struggle to find the lowest common multiple through knowledge of their multiplication facts

Guiding Question - How can dancing combinatorics be used to support students understanding of lowest common multiples?

Integrated Embodied learning - students create sequences for pairs of numbers using whole body movements as a means of investigating how many times the sequence needs to run in order to cycle back around to the first movement

Possible Extensions - Students use their knowledge of dancing combinatorics to explore greatest common factor.