Analogies and Algebra

Analogies

In the course I attended recently, we spent a fair bit of time on discussing Analogies as a teaching-learning strategy.  There is probably not one person who has never used this strategy before, particularly if you ascribe to the thinking that we learn by connections.  Hence, the initial omission.

However, I’ve learned today how good this strategy really is. Hence, the special mention.

Analogies and Algebra

Undoubtedly, the abstract nature of Algebra – it’s very power – is the reason people are generally averse to it. Having overcome the obstacle of why we use x (variables or pronumerals) to begin with, I thought the next problem was balancing equations. My observations proved otherwise. Balancing equations was not an issue (drilled as they were that whatever you do to one side, you do to the other to keep them balanced).  Rather, the problem really was why we needed to isolate x in the first place, to find its value. Pretty obvious, I thought.

The analogy I used today involved the use of a bowl with chocolates and crackers. The question was how many chocolates were in the bowl.  I showed them the bowl. They could see hints of chocolate hidden by a mound of crackers. A quick discussion ensued. Soon enough they realised that the best way was to remove the crackers so the chocolates can be seen. Light-bulb moment. It was wonderful.

For the record, I’ve actually extended this activity to involve revision of the distributive property of multiplication (I had 2 bowls with equal number of chocolates and crackers), substitution of pronumerals (to work out total quantities) and simplification of equations. As soon as I rewarded one insightful comment with chocolate, I got a whole class motivated to contribute to the class discussion, rather Pavlovian. Not enough chocolates for everyone, but I obviously chose the right brand of crackers – everyone had some!

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3 thoughts on “Analogies and Algebra

  1. Shawn Urban says:

    I get students who are stuck on variables to close their eyes and picture themselves looking out a window with a thick spruce tree blocking the middle of it. To either side of the spruce is blue sky and white ground. Kids are on either side. Some are ducked behind white walls; others are leaning over them.

    The questions: What is happening behind the spruce (exactly; we flesh out details, such as trajectory)? What clues tell us this (again in detail)? Can we actually see what is happening behind the spruce (married to the realization that we are interpreting from context)?

    So, of course, my spruce are your crackers, and my “snowball” is your chocolate. Your analogy sounds more delicious!

    Shawn

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