Friday, February 17, 2012

Worried Problems - Whirred Problems!

Word problems! the one thing guaranteed to turn just about every student off mathematics. Remember the one about two trains approaching each other?  And then there are the remarkably insane strategies that are used to help children solve simple word problems like the one in the image to the left. There are some amazingly daft suggestions in this strategy such as find the "key words" as if they would really give you a magic way to solve the problem.

"Do the math" is equally ridiculous. Why is "math" limited to the word "compute". Isn't the whole thing math?

Several years ago Thomas Carpenter came up with the idea that all simple addition/subtraction "problems" could be identified as involving part-part-whole, combining, separating or comparing. He

also identified another set of concepts related to multiplication and division; things such as the equal groups, area and the multiplicative comparison concepts. The main task in solving a quantitative problem is to work out what is happening in the problem in the context of one, or more, of these concepts and what is being asked. Once this is done, the solution is easily found by using one of the four operations using one's head, paper and pencil or a calculator.

To show the significance of understanding this, consider these non-problems;

1. If it rains for 3 hours on Monday how much will it rain for the next 4 days?
2. If it takes ½ an hour for 3 friends to walk home how long will it take 5 friends?
3. If 2 students have 5 pet gerbils how many gerbils does each students have?
4. If 2 girls have 3 brothers how many brothers do 4 girls have?
5. If the temperature is 62F today what will it be for the next 3 days?
6. If one train is traveling at 35 mph (clearly an AMTRAC train)
and another similar train is going at 45mph what time will they pass each other?
7. If 2 squares have 8 sides how many sides do 3 triangles have?
8. If it’s 60F in Vermont and 72F in Maine what is the temperature in
New Hampshire?
9. If you eat 2 slices of your birthday cake today and ½ of what’s left
tomorrow how much will you eat the next day?
10. I 140 students are going on a field trip and a school bus will hold 60
students how many school buses will you need?

You could get some really interesting answers by using the "Attacking Word Problem" strategy. e.g. (Each student would have 2½  gerbils)