Josh earned $1,962 over the summer. Hilary earned $129 more than Josh during the summer. How much money did Hilary earn over the summer?When I taught middle school math in the 80s and 90s, this was the type of word "problem" that filled the curriculum my district used. Furthermore, the "problem" was typically at the end of a worksheet entitled Adding with Two Addends that was filled with 12 other addition exercises. Even back then I knew that these were not true problems for my 8th-graders, and that if I gave them a reading assessment they would have no idea who Josh and Hilary were and what they did over the summer. They had simply added the two numbers. And who could blame them?
It was during this time that I began to explore the idea of subtle shifts. At that point, I did not have the time nor the expertise to develop a whole new curriculum. Instead, I decided to rewrite these exercises in order to make them problematic for my learners. How? I received my inspiration from the Charlie Brown cartoons.
I replaced every syllable in the story with "wu" - as if the teacher in the cartoon were reading it aloud. It removed the real-world context but forced the 8th-graders to rely on their number sense. They had to decide which operation (addition, subtraction, multiplication, or division) made the most sense and why. Here are a few for you to try:
Wawa wa four wa wawawa. Wa wawawa wa wa wa 150 wa. Wa wa wa wa Wawa wa?
Wawa wawa $519 wa wa wawawa, Wawa wa $267 wa. Wa wa wa wawa wa wawa wa wa wa wawawa?
Wa Wa Wawa, wa wa 936 wa wa Wawa Wawa wa 1,443 wa wa Wawawa. Wa wa wawa wa wa wa Wawawa?
Wa wawa wa wa wa eight- wawawa wawawawa wa wa wawa 232 wawawa?Unlike Peppermint Patty in the clip, my learners were much more engaged in these stories. Maybe it was the novelty of them. I suspect, however, that it had to do with the fact that they were more challenging, and therefore more interesting, than the originals. And the 8th-graders were usually fairly successful predicting the operation required in the original story.
Nearly 30 years later, I still use these Charlie Brown Word Problems with the preservice and inservice teachers that I work with. They help to represent the difference between exercises and problems. And they demonstrate how subtle shifts can enhance learners' mathematical experiences.
There's sociolinguistic research on math registers, like those of story problems, and how understanding (or not) these registers--particularly the vocabulary involved, are the basis for students' success or failure in math. I don't have the references handy, but if you're interested, I'll get them for you.ReplyDelete
Interesting idea and one I hope to get to try one day. I do want to share a couple of posts by way of extending this conversation:ReplyDelete
- Problem vs Exercises - challenging learners, in the spirit of Vygotsky
- Polya, GGSC and Algebra - helping decode word problems with the help of the class hero: Polya
Through teacher assisting I've seen how much students dread the story problems always placed at the end of each assignment. Shouldn't these be the fun problems? Not if they have no emotional attachment to the story! By giving the students humor, learners could attach an emotion with the problem. Great idea Dave!ReplyDelete