Wednesday, November 30, 2005

Word Problems

  1. Probably I've told this story here before, but it's one of my favorites. A few years ago I was at JoAnn (the one on route 35, just south of Red Bank), and there was a woman at the cutting table. She was holding a roll of home-dec fabric and a pattern. The clerk asked her how much fabric she wanted cut. The woman said she didn't know. She was making covers for her dining room chairs, the pattern said that each chair needed 5/8 of a yard of fabric, and she had eight chairs. The clerk didn't know either. They were not wondering whether you could get by with less than five yards of fabric if you arranged the pattern pieces cleverly. No, they had NO IDEA how much fabric she needed.

  2. If I give my gen-ed students a homework assignment where I give them the dimensions of a room (length, width, height), tell them that a gallon of paint covers 400 square feet of wall, direct them to ignore doors/windows, and ask them how much paint you need to cover the room with two coats, many of them will find the VOLUME of the room, divide that by 400, and then multiply by 2. If I further tell them that a gallon of paint costs about $20 and ask them how much this project will cost, they will multiply their very large number of gallons by $20 and report this large number as the cost of painting a room. They will turn this work in without noting that something seems amiss.

  3. I can improve student success on this problem (remember this is a HOMEWORK problem, not a test question) by making one major change: I do not tell them the size of the room (I tell them to use their own room). I do not tell them about the coverage of paint. I do not specify how many coats. I do not quote a price of paint. Much higher success rate.