Mathematical Communication

Sunday 15 September 2013

'Tell me a story with a beginning, middle and an end'

This is just a short observation based on a couple of experiences this week. I found myself talking about written communication a number of times this week. I'll use a simple example to get the point across.

So I asked a group of students to find as many shapes as they could with an are of 40cm2. (one of my favoutire questions by the way) and I had a number of issues with their responses. In most cases the issue was related to a shape that was drawn with dimensions given but that I was supposed to assume were squares, rectangles, rhombuses etc. The students had not communicated anything to make that clear or added right angles where it was important to know that lengths were perpendicular. More interesting were the more complex, often compound shapes that were drawn, where some, but not enough, infomation was given and followed by a conclusion that the area was indeed correct.

Later in the week I was working on the 3D uncovered activity and came up against some similar issues. The whole point of this activity is about students extracting 2D planes from 3D constructions and then applying trigonometry. In most cases, it was near impossible to trace a students conclusion back to the question because thay had written little or nothing along the way to help.

I tried to make my point with students with two examples related to writing,

  1. If asked to do a piece of writing, would students write the words in random unsequential places on the page and expect the teacher to just 'know' what order they are supposed to come in?
  2. What use would a book be if you were only offered the first and last chapters?

I know analogies can be dangerous and distracting, but instinctively I suppose I was just observing how there is so much to do to teach people to communicate properly and how that is actually an integral part of strengthening understanding.

I am thinking about a couple of ideas for placing more emphasis on this in the future

  1. Some kind of classroom display that shows examples of good and not so good communication.
  2. An activity that encourages students to examine this for themselves. This would involve getting students to llok for the missing bits of communcation.
  3. Perhaps some peer assessment aimed at getting them to see how difficult it can be to follow each others' work if it is not properly communicated.

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