Sunday, March 2, 2014

My Daughter the Map Maker [Spatial Reasoning]

I'm thinking about spatial reasoning: what it is, how its developed, and how it interacts with math learning. Also, why it is not spoken of much in my Twitter feed which happens to be a veritable goldmine of priceless thinking and information related to math education.

Yesterday, my 8yo and I went to the KidsCommons, a children's museum in Columbus, IN well known for it's larger-than-life toilet which resides inside an otherwise kid-scaled house. You climb in, there's a flushing sound, and then there's a slide to the bottom floor of the house.

This morning my kid woke up and immediately started describing all the little hidden passages inside that three-storied play house the adults can't really access. Then she said: "I'm going to draw you a map!"

So she did and, when finished, talked me through what she had drawn. Observing all this I was reminded, yet again, that she has been expressing her ideas through maps for as long as I can remember.

Drawing and reading maps is a key spatial reasoning skill.

This one is from our house to Grandma's house in Ohio, drawn one morning when she was newly six:

Half a year later, she was still drawing lots of maps.  In this one she mapped out a set of sequential instructions for sewing a dress:

We've made and played games with maps (this one is about capturing territory for our kitty clans):

There was her "map of angles"

And the time that she and her friends found a real x-marks-the-spot treasure map (on birch bark, no less) at the Farmers Market and spent 30 minutes investigating where that X was in real life. They found it.

Here's just one more map, where I wrote
"She used the new graph paper I had printed out for our graphing game and as she drew she described to me how each color, line and picture symbolized a landmark along our [walking] route downtown.  She even threw in a fractal tree to represent the campus woods."

Later on in that post (written over 1 1/2 years ago) I write:
"She seems really drawn to visual representation as a way to communicate to others what she knows, especially math concepts.  Over the last year she has shown me what she thinks and understands through spontaneous, unprompted creation of charts, maps, and diagrams; often these are private ruminations that I happen to unearth while tidying up after bedtime.  I view these self-initiated efforts to symbolize and quantify (in a way that makes sense to her) as a kind of bridge between the experience and her eventual use of standard mathematical notation and representation.
This is a particularly important to thing to re-read as it has led me to a very interesting realization: I have always assumed spatial concepts as being part of mathematics. But, maybe they're not?

There's lots of information out there about tests for determining spatial reasoning skills, many of them very specifically about rotating 2D and 3D shapes in one's mind. It also appears, based on some cursory reading, that one can improve one's spatial reasoning skills using activities that are similar to these tests.  

But there seems to be precious little documentation related to the intentional pedagogy of and reasoning around the development of spatial skills.  

Does the development of spatial reasoning and math reasoning interact? If so, how do we gracefully fold spatial skills into the daily mathematical lives of our students?  I have a feeling doing so could be very fun, as well as beneficial.

In a sense, these map artifacts from my daughter's life over the past 2+ years have become a treasure map of sorts for me as I try to figure this out. I always love company on my journeys -- if you have any insights, personal experiences, or aha! moments about what it looks and sounds like to include spatial reasoning in the classroom in an intentional way, please do get in touch.


  1. Your walk through memory lane might include the chapter you authored in (the soon-to-be-published book) Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers, titled Mapping the Familiar. I love that chapter.

  2. Very interesting, good job and thanks for sharing such a good blog.


Thanks for reading. I would love to hear your thoughts and comments!


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