Week 1 Activity Reflections

In his TED Talk, Antonsen relays that to really understand something we must be able to appreciate it from multiple perspectives. This reminds me of Diamond Paper from Jo Boaler (Mathematical Mindsets, YouCubed) where your concept goes in the center, say 4/3, and then you represent that with words, pictures, symbols, and a real-life situation. However, like Dr. Gerofsky states in our week’s introduction, it still requires students “to ‘just think’ their way into understanding new mathematical ideas, while sitting statically and silently in a chair.” What this activity lacks after watching Antonsen is bodily ways of knowing and imagination. I loved that Antonsen says we can make up the language to represent the mathematical patterns we see. It feels like permission to explore and create in a math world that can feel full of strict rules. I wonder if Diamond Paper could be adapted to include these aspects better - maybe four quadrants is not enough…? Maybe a class breaks into small groups that each create a new perspective to share out? I am excited to open this level of imagination up to students and see what they can come up with. 

 

Both Antonsen and Nathan connect perspective and experience to creating metaphors and analogies to deepen understanding. In a reality where students are looking for an instant answer, I will be looking for opportunities to develop this cognitive skill. 

I grew up on the water and have never known what a fathom is, only that it is about six feet. I found the traditional measurements fascinating. Noticing that there were no volume measurements to calibrate on the list, my daughter Ella (10) and I tried this out while baking some homemade granola bars :)  

   

My palm divot holds ½ tbs                 Ella’s palm divot holds 1 tsp

My hand scoop holds ¼ cup                Ella’s hand scoop holds ⅛ cup

My two hands hold ½ cup                Ella’s two hands hold ⅓ cup

I have always respected those who cook by feel. They just know how much to add here and there, no measuring tools or recipe needed. Muscle memory built by experience over time. There is something very grounding about not needing formal tools to measure. It can just be us and our body - no rules, formality, or external tools required. Next cooking by feel goal: gain the muscle memory needed to estimate the amount of spaghetti noodles needed when cooking for my family. I always seem to be way over or under!   

  

References: 

Antonsen, R. (2016, December 13). Math is the hidden secret to understanding the world [Video]. TED. YouTube. https://www.youtube.com/watch?v=ZQElzjCsl9o

Boaler, J. (2015). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. Jossey-Bass.

YouCubed. (n.d.). YouCubed: Inspire ALL students with open, creative mindset mathematics. Stanford Graduate School of Education. https://www.youcubed.org/