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Wednesday, December 15, 2010

How do you assess "Explaining"?

The Math dept. spent some of our time today, during our "snow day", writing student friendly outcomes for our Math 20-1 course. One of the things we immediately noticed is that MANY of the outcomes ask students to "explain" Mathematical processes.

I experimented with having students videotape explanations of factoring quadratic equations. This worked OK. However, was a bit time consuming.

We discussed having students answer "explain" outcomes on the summative exam. But, I pointed out that we want to know BEFORE the summative assessment if they can explain or not.

Any suggestions of how else we can get students to explain a mathematical process?

Also, I developed a rubric to assess the explanation of the factoring of a quadratic equation. The rubric seems to work well. I gave the students the rubric after I watched their videos BUT they did not get to re-watch their video to compare it to the rubric. This is a downfall.

I DO NOT feel we need to assign a grade to the explain outcomes. I feel that the rubric is more beneficial. However, we have to document the assessment. I guess we can keep a copy of the rubric in our "Marks book" and record the level they achieved on the rubric in the "Mark book" then we have evidence to show parents.

Any feedback on this would be appreciated.


  1. Tough to tackle. Do you include written comments with your marks? Could you use words to quantify their ability to explain their processes? (eg. When asked to explain her mathematical process, Susie is able to do so clearly and logically - or - When asked to explain his mathematical process, Timmy has difficulty articulating what he has done, despite his process being logical.)

  2. It takes a while for teachers to learn to assess 'explain', too. Teachers often choose the verb 'explain' as a substitute for 'understand', which is now deprecated because it is unobservable. Peer-assessed explanation tasks require skills of understanding the audience's cognition and sentiment, on top of topic knowledge. To remove ambiguity, it might be better for outcomes to say 'teach' (if that is what is meant) or 'recognise [specific] fallacies' or 'construct a mathematical argument' or 'correctly identify the steps used in a mathematical example'.

    This all begs the curriculum question of how long it will be before we start rewarding, teaching and assessing C21st methods of mathematical work including use of Maple/Mathematica etc.