Why can’t we just teach them the rule? At what point do we stop this “exploration” and just give them the rule? When I was in school, the teacher just taught us the rule–we didn’t need to understand it.
I’ve talked before about why teaching math as a bunch of rules to memorize is a problem–even if you teach the rules in a really creative way or with a catchy song. If students don’t have any understanding of why rules work, they begin to think of math as this mysterious thing that doesn’t make sense. They mix rules up and constantly need a teacher or answer key to tell them if they picked the right rule. They lose the ability to make sense of things on their own. I often talk with students who can reason about a problem and get the right answer, but get it wrong because they are following a rule that they incorrectly memorized.
I recently read a great article “13 rules that expire” that talks about another problem—the fact that many of the rules we teach kids in elementary school don’t work anymore when students move to middle and high school math. For example, when I taught middle school, my students were often confused about multiplication of fractions. They kept telling me that “multiplication makes numbers bigger.”
I recommend taking the time to read the article. It’s is an important reminder to be precise with language when working with young students. It’s also a good read for middle and high school teachers. It gives some insight into the struggles students face when they try to reconcile the rules they may have learned with new experiences that break those rules.
I’m interested to hear what you think of it.