This fact came to mind last week as my classes worked on proportions. Some students referred to something called the "Fish Method." Let's use this proportion:
Start with the number in a fraction with x (in this case, 8). Draw a line from the 8 diagonally up to the 2 (multiply those numbers), curve down to the 3 (divide by that), then diagonally up to the x (your answer equals x). What you've drawn looks kind of like a fish.
To be clear, this isn't a "mistake" I had to fix. Rather, it's a case of students clinging to a method that only works in a limited number of cases. For instance, proportions like these had them flailing.
We had to discuss other methods that had broader scope. This isn't a bad thing—I'm all for discussing multiple methods and their respective limitations. But whenever something like this comes up, I try to tread lightly. I don't want to say that their other teacher was wrong, bad, or not as cool as I am.
There are other situations, though (not like this proportions situation), where that's exactly what I'm thinking. It even happened to me as a student. When I was very young, I was told by a teacher (a student teacher, to be fair) that "it's" always has an apostrophe, whether the contraction or the possessive. Yes, really. It took me a few years to (a) figure out she'd been wrong, and (b) correct my bad habit.
I'm sure it can go the other way, too. A teacher instills all kinds of wonderful things in a student, and another teacher down the line destroys all that work.
Is there a way to avoid it? Maybe not. There will always be human error, whether intentional or not. All I can do is try not to be one of those "bad" teachers, and try to repair damage where I find it.
Have you observed or been affected by cases of teachers working against each other? How did it impact you?
2 comments:
As a mom, I see it all the time, and it's hard to watch your kids struggle to undo the mistakes of poor teaching.
However, what I find most interesting--on slightly different level--is that math is taught so differently now than it used to be. The way I tackle equations isn't the way my kids are learning to. When they get stuck and I try to help them, I get a healthy dose of, "That's not how my teacher said to do it."
Yeesh. Both ways get the same exact result, but I can't truly help them because I don't get this new way, and the teachers count it wrong if they do it the old way.
It's a helpless feeling on my behalf and a source of frustration on theirs.
Any wise words, my Favorite Math Guru of the Universe?
I am going to admit merely looking at those equations had me shuddering in fear. Mostly because we didn't learn until I was well out of college about my dyslexia and by then, well, years of teachers and profs had me convinced I am too stupid to do math.
The paragraph above should say what happens when bad teachers get a hold of a student. It wasn't until I scratched my way into Calculus II that a professor figured out how to help me, and ranted after every class about my prev educators. It was the first math class I passed with a C.
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