We continue our review of possible ways to spark off a Maths topic (it is recommended to read the previous post: How to spark off a Maths topic ? – Part 1: concept processors).
Today, we are talking about the second category of sparks: memory reinforcers.
The idea of memory reinforcers is to spark off a topic with something that engages beyond the intellect in order to reinforce memory. What you choose may not seem logical, but that is beside the point if you reach your goal of memory reinforcing.
As memory champion Josua Foer explains: ‘We remember when we are able to take a piece of information and experience it. We remember when we pay attention. We remember when we are engaged’.
A memory reinforcer can be…
Example n°1: …an image that students will remember
Example n°2: … an unusual way to emphasize the main point:
For example, when explaining how to add fractions, I use a sequence of capital letters, each on a separate Powerpoint slide: E – N – O – R – M – O – U – S… ‘That makes ENORMOUS, OK ? Today’s main point is: ENORMOUS. It is so enormous that I want you to write it in your exercise books in capital letters: NEVER ADD OR SUBTRACT FRACTIONS BEFORE THEY HAVE THE SAME DENOMINATOR !’.
Of course, that spark does not dispense from explaining the rationale of having to work with same denominators. This is explained during the lesson, but at least the rule is remembered even by students who are not completely clear about the mathematical rationale.
Proceeding this way is often disregarded by ‘fanatics of understanding’, who claim that students should only memorize what they understand. In an ideal and rational world, they are right. But the world we live in, and particularly the world of teenagers, is neither ideal nor rational. So it is sometimes best for students to memorize the main point and understand it later through further practice.
Example n°3: … a far-fetched and excruciating repetition
One of the virtues of memory reinforcers is that they can work on repetition and unexpexted logic. In fact, the more excruciatingly repetitive and illogical they seem at first, the better.
To get students to memorize the main point about equivalent fractions, I have used the following 7 pictures, which I show to students one by one on a slideshow with questions and answers in between.
On showing Picture 1, the dialogue goes this way: what do you see ? do you notice anything ? etc. Then you show Picture 2 and ask the same questions, which usually prompt more or else the same answers (how else…?). Then Picture 3 etc. until it gets really irritating, because it’s always the same … Then, after the last picture comes an excruciating illogical conclusion: with equivalent fractions, it’s exactly the same: many fractions are equivalent because they have the same value, but only one fraction is in its simplest terms.
That conclusion is so far-fetched and perplexing that students will usually remember it forever (particularly boys, for some reason).
The beauty of it is that, because it is so illogical, it creates a logical void in the class, which has the effect of arousing curiosity: some students will want to know what ‘simplest terms’ means, or why ‘only one’, etc. whereas they might not have been so interested if you had presented a mathematical proof right away.