Wednesday, October 29, 2014

Visualise, Verbalise, Verify

This year I've been learning more and more about the importance of Spatial Reasoning in Math. I've learned that Spatial Reasoning is multifaceted and that you can be very good in one area and not so good in another. For example, the one thing that I love to do more than anything else is hiking. Now when I first started hiking and reading maps, I relied solely on man-made features such as paths and cairns and trig points. I knew that the contours on a map represented height but couldn't look at these to see what the hills looked like. Then one day in the hills, something funny happened: I looked at the 2-D map
and in my mind's eye could clearly see the shape of the hills in 3-D:

As a hiker, this is very powerful and now I must say (blowing my own trumpet) that I am pretty awesome at reading maps.
Yet I still have to think very carefully about 'left' and 'right'!
So at a session run last week by Ontario's Ministry of Education, I came across some great advice to help improve Spatial Reasoning:
Visualise, Verbalise, Verify
For example, consider the views of an object as shown below:

Visualising gets a student exercising her mind's eye to try to build a mental image about what the structure might look like. Ideally this should be done individually.
Verbalising gets students describing what they have just visualised; it forces the students to reason, to use spatial and positional language, to communicate with words and gestures. Sometimes the students will agree, sometimes they won't (and this is more fun!)
Verifying is when we allow students to create the structure to check if they are right. In the past, I have jumped straight to this stage but now I realise the importance of the getting students to visualise and verbalise. What is nice about problems such as this is that once a student has proven that their solution is correct, we can ask: "Is there another solution?" For example:

Spatial Reasoning is malleable. I am convinced that if we can get our students to visualise, verbalise and verify, then their Spatial Reasoning will improve dramatically and this will have a knock-on effect on the Math understanding.

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