Many years ago, this problem appears on a “benchmark” test given to third graders in Philadelphia:
Almost half the third graders (46%) in a group of schools I was supporting chose B. The correct answer, C, was chosen by 31% of the students. I don’t recall being all that surprised, but as I have thought about it over the years, I’ve come to see it as one more piece of evidence that many students do not do “sense-making” when they’re doing math. They look for numbers and guess what operation they’re supposed to do (addition is very popular). I have a theory that if you had asked those same third graders to draw a picture of the story, many more of them would get the problem correct. So the problem above becomes this task:
To informally test this theory, I invite anyone with access to students in grades 2-5 (or older kids if you think they might be good subjects) to run a small experiment for me. I’ve written two sets of questions, one math and one drawing. Each has three questions. The math questions are taken directly from some Grade 3 benchmark tests, but I can see them being used in grades 2-5 for the purposes of this experiment (though you are welcome to use them with whomever you want – it’s an experiment, after all, not hard scientific research).
Since I am interested in how students solve problems when they think they’re supposed to “do math” versus when they might not realize they’re engaging in mathematical thinking, I’d ask that the math questions be given during math instructional time and the drawing questions be given during literacy instructional time, or, barring that, any time that isn’t math, and that the two sets of questions be given a couple of weeks apart.
The attached PDF contains 26 copies of each set of tasks (labled Student A through Student Z), instructions, and a roster sheet so that you can keep track of which student corresponds to which letter. (If you have more than 26 students, be creative.) You can report results through an online survey or send me copies of the completed task sheets (as a scanned PDF, or toss them in an envelope) or both.
Download the files: Fetter Sense-Making Experiment v1 [PDF]
So, wanna play? I hope so!