Monday, August 2, 2010

Math without numbers

A friend of mine said he was looking at his daughter's college math textbook, and there were very few numbers in it. How can you have math without numbers! he exclaimed. I was sympathizing until he went on to say "it was all word problems."

Now that's another story. I like word problems, or story problems as some people call them. I've written thousands of them. Sorry kids, the buck stops with Janice Raymond (she started Excel Math) and me. And despite what my friend said, there are numbers in story problems.

Here are some common FAQs on story problems.

Q1. Do you write story problems deliberately to torment us?

A1. No. In fact I often simplify what has a useful problem for years, just because people sometimes don't solve them as easily nowadays.

When I simplify problems, that doesn't mean the calculations get easier. It means I pay close attention to the presentation of the problem on the page. As a life-long editor and typesetter, I think a nicer presentation makes a difference in comprehension.

Q2. What do you mean? Can you give me an example of "presentation simplification"?

A2. Sure.

Stan had \$31.42 to spend on
school supplies, so he bought 4
76¢ pens with black ink and 3
books that cost \$4.87 apiece. How
much money does he have left?

Stan had \$31.42 to spend on supplies.
He bought 4 pens that cost 76¢ each.
He bought 3 books that cost \$4.87 each.
How much money does he have left?

The second presentation has a separate clause on each line. The order of presentation is the same on each line, starting with the buying, then the quantity of items and the amount per item. The math is the same. The reading is easier. Some of the extraneous information is left out.

If you like to suffer while you solve story problems, maybe this is too soft for you.

Q3. Where do you get your ideas for story problems?

A3. From real life. From you - once in awhile we talk to parents and kids to get new ideas for story problems. We have either done these things ourselves, or know someone who did, or we wish we could do them. I don’t like to write stories about talking animals and stuff like that.

Q4. What other factors make you change a story problem?

A4. Changes in society. We are taking out all the candy, cookies, cakes and sodas from our books, even though candy and cookies are a convenient individual unit that kids are interested in baking (addition), eating (subtraction) and even sometimes in sharing (division).

We took out trikes and put in scooters. We took out skates and put in skateboards. We're adding various activities and items that are relevant to kids today - always mindful that we don't mention brand names or commercial products.

Q5. Do you have word counts or readability for different grade levels?

A5. Yes and no. We use a larger font on lower grades, which restricts the words that will fit, and that limits how much we can write. We have limited space on the page and so we tend to use nouns with just a few letters.

If you think we discriminate against Ascension who raises artichokes, you're right. We would  prefer Anna grows beets.

My sister Kathy is a big wheel in reading education. She says write good stuff and kids will figure out how to read it. Write bad stuff and they won’t bother to try. We don’t do a formal readability analysis on each story, but we do change and clarify stories in response to comments from our users.

Q6. Will you send me an answer key so my mom can help me study?

A6. No. I didn't just fall off the turnip truck   razor scooter   hybrid bicycle, you know! Solve the problem yourself and confirm it with the Checkanswer.

(Turnip, in the summer time, at Excel Math)