Lately I've been thinking a lot about homework. Do we give students too much homework? It's obvious that the natural inclination on the students' part is to complain that we do, and from some angles they have a lot of support. On the other hand, both common sense and experience tell us that kids need to practice the skills they learn at school for more than the 45 minutes alloted per subject.

Those two seemingly opposing statements are not diametrically aligned, though, and I think the answer lies somewhere in the creative space between them. My idealistic side says that kids should be motivated by inspiring parents and by interesting teachers to challenge themselves and expand their mental horizon, and then be given as much a homework burden as they are willing to bear.

After all, isn't this the attitude we want to instill in them for their lives as adults? Do we want them to be workhorses, sacrificing human interaction for another degree or project completed? Or to be well-rounded individuals that have learned to judge the value of things, and balance their time between improving themselves and helping others?

Today I read an essay that touches indirectly on this topic and inspired me to finally write this post. One resource that I've found very inspiring in my teaching this year is the On Course Newsletter, an e-mail newsletter promoting a workshop series that always has an article teaching a strategy or two for helping your students achieve greater success. It's actually directed at high-school and college level instructors, generally in the humanities, but it's still applicable to some extent to middle school math. This issue's "Feature Strategy" talks about giving writing students a sample called a metacognative reflection essay, which is an essay with flow-of-consciousness thought process from the author embedded in it with square brackets.

The idea of the metacognative reflection essay is to encourage students to think critically about what they write by showing them the thought process of a writer as he composes an essay. This process resonates with me as a person who writes recreationally. Critical thought is the difference between a well-written essay that communicates effectively, and a page of obfuscated drivel of hardly any value to reader or writer. When writing a post, I have to consider word choice, sentence structure, literary devices, and the flow of ideas that leads, most of the time, to new insight into the topic at hand.

So how is this of use to a middle-school math teacher? Well, I also want my students to think critically and reflectively when they work on a math problem. The idea is not that they can look at

and find the value(s) of x, but that they see the question and think critically about how to add and multiply positive and negative numbers, about what it means for a variable to have a coefficient in front of it, and how an inequality means that x can take on any of a range of values.

Does assigning large amounts of homework encourage students to think critically? The answer, I think, is no.

Instead, I think, the way is to stress in class the value of thinking through a problem and then trusting (or verifying through work shown, or not shown) the student to spend the time reflect critically on limited number of problems. This sort of reflection will hopefull lead the student to self-motivated exploration and actually seeking out more homework for themselves. Believe me, it can happen!

(Though you end up fighting against ingrown training, and also a sort of "tragedy of the commons" where teachers vie for students' "mind time.")