Today I taught my daughter how to do her first basic algebra word problems. I decided to do this because she's always coming home with word problems like the following:

Quote
Howie has some bananas. His friend Richie has 4 more bananas than he does. Together, they have 60 bananas. How many bananas does each kid have?

My daughter solved it by subtracting 4 from 60, dividing 56 by 2, and adding 4 to the result. Great. Richie has 32 so Howie must have 28. That's all well and good, but the method breaks down for harder problems:

Quote
Howie has some bananas. His friend Richie has 9 more bananas than he does. Richie's friend Carl has 16 fewer bananas than Richie. Together, they have 65 bananas. How many bananas does each kid have?

Err...well, I can't just subtract something, and I also get a remainder if I divide 65 by 3, so that method gets kind of messy. And of course, it'll get even more complex if I add more people and more fruit. So I taught her how to solve the first problem by using algebra:

  • Howie has x bananas
  • Richie has x+4 bananas
  • Together they have x+x+4 = 60
  • Solve in steps

This was not an easy process for her (see that thread about struggling). But after a while, she became completely focused and the ideas started sinking in. She never focuses like that on the stuff that comes home from school. She was also delighted when she solved a problem by herself. I'm planning to practice this every day for 30 minutes or so, and by the end of this week, she's going to be pretty good at this stuff.

Narrowly-functional approaches that break down outside a small zone really bug me about contemporary mathematics education. Personally, I wonder if these approaches actually send a message that answers should be derived using arithmetic and guesswork. This mindset may make it harder for kids to see that there's a structured way to solve math problems.