"Cognitive Science Meets Pre-Algebra" reports on a recent study of "interleaving homework" in a middle school in Tampa. The idea was to compare the usual approach (homework is on the topic currently under study) with interleaving, which involves homework on a range of old topics. I am not surprised at the results: when students were given a pop cumulative test, they did much, much better on the interleaved topics than on the other ones. This is because giving students a mix of problems forces them to stay alert, instead of turning them into automatons, doing similar problems one after the other with their brain turned off. Amen!
A problem with this approach is that it's a pain in the neck for the teacher: it's far easier to just assign the next block of exercises in the book. Granted, education is not about teacher convenience, but student learning. Still, teacher convenience cannot be ignored if you want to see real change. One version of interleaving which is relatively easy to manage is the combination of approaches I introduced in recent blog posts: lagging homework, separating related topics, cumulative quizzes & for-credit quiz corrections. This has most of the same benefits (students must stay alert, and exposure is extended,) without requiring the teacher to micro-mix the homework.
Another interesting NY Times article is about how Massachusetts managed to improve math results over the past 15 years or so, including some success with algebra for all. A couple of quotes:
None of the topics were novel, but they were consistent in their hands-on approach, inviting students to explore and explain. “Much more hands-on than what we ever used to do,” said Dianne D. Rees, the district’s science director. “Hands-on as much as possible.”
Parents were not offered vouchers for private schools. The state did not close poorly performing schools, eliminate tenure for teachers or add merit pay.Of course, merely because these approaches worked there does not guarantee we'll see them implemented elsewhere...