### 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.

Anonymous said…
I totally agree with the idea of giving the kids word problems for the simple reason of figuring out which function to use. This was suggested to me by a secretary! I've used it with wonderful results for my daughter. We use Saxon math but I don't make her do all of the problems...I choose several of their word probs to make her think instead of figure and she does well with them. I say, "Try it, you just may like it!"
This happens in many disciplines, it's not unique to math. My son loves workbooks and I often cringe when I see him following a pattern and barely even reading the problems. On the one hand, I am happy he is smart enough to see the pattern, but on the other hand, I do need to step in and mix things up for him to be sure he understands the "how."
Anonymous said…
Yeah, we also had problems with word problems. Specially with other complex ones, the students doesnt know how to think, they just memorize. The goal of learning is to figure out how to solve it not to find the correct "template" for the problem.

Try this software, it helped my cousines.
http://www.ikodeko.com/worksheetmaker/wsm.php
Dana said…
OK, here's an interesting concept. My little math program occasionally introduces the concept with a word problem. My first grader figured out a multiplication problem from a word problem the other day having never been taught multiplication and not knowing what "times" or "multiply" even means. We give her "real life" math problems in the form of story problems and let her go about figuring them out. She uses fingers, blocks, hash marks...whatever she can to figure out the problem. We talk a lot about what she did to solve the problem, why she chose that method and whether her answer makes sense.
Algebra word problems -- My daughter is preparing for the ACT test (3 weeks away). I thought she was an average-to-good problem-solver, but the type of problems they have on the practice tests routinely stump us.

I've found good explanations online for the following problem, but my question is, "How can we improve in our ability to set up problems like this independently?" Once we see the answer, we get it. We can do algebra--but writing the equations are the problem.

This is one type that stumps us:
If Sally can paint a house in 4 hours and Bobby can paint the same house in 6 hours, how many hours would it take for them to paint it together? I know how to do this now, but ask me in 2 months and I probably won't remember how to write the equation again.

What's wrong with me? hehe...