1. We should pay attention to building spatial reasoning skills in our students. This newly published document from the Ontario Ministry of Education is a gold mine of ideas and conceptual support.
2. We should provide our students with diverse opportunities to experience a math idea in multiple modes and settings. Suzanne Alejandre at The Math Forum and I had a fabulous conversation about this idea in the comments of her post What's in a Touch.
3. The body can have many useful roles in math learning. One of those roles is to act as a "disruption of scale," a phrase I found reading Jasmine Ma's dissertation. Scale disruption generally means that we take familiar math off the page (exploration of polygons or work on a number line, for example) and make it body-scale which has the great potential for helping students build new insights about the math idea in question. I have LOTS of ideas for these kinds of lessons, but I also think that changing the scale of any lesson, even if it's not at body-scale, can have a positive impact on learning.
Not surprisingly, all this thinking and reading and conversing has influenced what's going on at home.
It turns out encouraging new ways to explore space and changing scale can lead to very interesting and inspiring outcomes!
One day I noticed that my kid, never one for block play but with a penchant for map making and for exploring the world with her whole body, started playing with blocks. It was fun to hang out with her and interact within this new realm; I loved listening to her talk through her building -- definitely a new perspective for both of us!
So I got more blocks. And encouraged a generous uncle to buy even more. The most amazing thing was to watch her building from a set of visual directions; amazing because she's not usually one to follow someone else's patterns, preferring to make her own, and also because I was so happy she was having a completely, brand new experience in this realm.
Then there was the day I was walking through a big box store and passed the isle with paper and drawing supplies. All of a sudden I noticed a BIG pad of paper, much larger than her normal canvas. I thought, "I wonder what she'd draw if I got her THAT?"
Well, wonder no more.
Her drawings got BIGGER and the subject matter switched something other than very fine images of cats and girls in dresses. She drew Cahokia Mounds near St. Louis. She "sectioned off" one of the mounds with a GRID, to help her color. Not sure of the logic, but this was the first time I had seen her draw a grid using long lines, instead of drawing out individual cells.
(Only a small aside: Maria Drujkova collects images of children's grid art. She'd be interested to know that the radiating lines of the circular grid, further down, were made section by section. I need to ask Maria more about this phenomenon of kids drawing individual cells vs. when and why they start making grids with intersecting lines.)
I don't think she actually finished the first picture because then she was inspired to draw this:
It's St. Louis and it's FULL of spatial concepts: grids, relative size, relationships (front, back, over, under), some perspective. A bigger pad of paper inspired her to draw a city, y'all. Cities are BIG.
Then some brand new doodling came into view. A circular grid and some intricate star-like structures:
This last image was interesting to me. She took a quarter and traced around it on the big pad to create this design.
What ways can you think of to change the scale or the mode of exploration for a math idea in your children's life? Try something and let me know -- I'd be fascinated to hear what new ideas, expressions and insights might emerge.