March 14, 2006

The problem with word problems 2

For the purpose of this post, we could divide word problems to three different categories:
1) routine word problems
2) non-routine word problems
3) algebra word problems

Actually you could divide algebra word problems to routine and non-routine as well, but I want to now talk about word problems kids encounter in school before algebra - in grades 1-8 usually.

J.D. Fisher suggested in the comments section of my previous post on word problems that kids are encouraged to think linearly, step-by-step. Then, when the word problems they encounter don't anymore follow any step-by-step recipe, they are lost. You might want to go back and read that.

Don't typical math book lessons kind of follow this recipe:

LESSON X
---------------------
Explanation and examples.
Numerical exercises.
A few word problems.


In other words, the word problems are usually in the end of the lesson. (That might make solving them a rush.)

Then, have you ever noticed... If the lesson is about topic X, then the word problems are about the topic X too!

For example, if the topic in the lesson is long division, then the word problems found in the lesson are extremely likely to be solved by long division.

And, typically the word problems only have two numbers in them. So, even if you didn't understand a word in the word problem, you might be able to do it. Just try: let's say that the following made-up problem is found within a long division lesson. Can you solve it?
La tienda tiene 870 sabanas en 9 colores diferentes. Hay la misma cantidad en cada color. Cuantos sabanas de cada color tiene la tienda?

My thought is that over the years, when kids are exposed to such lessons over and over again, they kind of figure it out that it's mentally less demanding just not even read the problem too carefully. Why bother? Just take the two numbers and divide (or multiply, or add, or subtract) them and that's it.

I'm not saying that such word problems are not needed in the end of division lessons. I'm sure they have their place. But too much of those simple 'routine' problems can be a problem... I feel kids then "learn" a rule: "Word problems found in math books are solved by some routine or rule that you find in the beginning of the corresponding lesson."

It might teach their minds to be lazy and not willing to tackle non-routine problems.

Maybe it would help to give students a bunch of short routine word problems, and NOT ask them to find answer. Instead, ask them to tell what operation(s) are needed to find the answer.

Maybe it would help to have separate lessons with mixed word problems, including some non-routine, and devote some time to them.

I'm curious to hear your thoughts on this.

And lastly, visit some (most are free) word problem resources if you need more than what is in your math book.
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