An easy way to change up your routine to make the most of going over homework. Instead of always focusing one problem at a time, these suggestions can help you guide students in looking across problems for big ideas and patterns.
Otten, S., Cirillo, M., & Herbel-Eisenmann, B. (2015). Making the most of going over homework. Mathematics Teaching in the Middle School, 21(2), 98-105.
In U. S. math classrooms, we have a pretty consistent routine for homework review. It goes something like this:
- Step 1: Students come in to class having presumably finished their homework.
- Step 2: The teacher asks which problems they’d like to go over.
- Step 3: Students call out specific problem numbers.
- Step 4: The teacher, or sometimes a student, talks through the correct way to solve those problems.
Some limitations of this routine are that the teacher often does a lot of the work, which amounts to re-teaching rather than new learning opportunities, and this routine focuses on one problem at a time, which can lead students to feel like the emphasis is on procedural execution and they often miss the bigger picture.
So how can we disrupt the routine and get more out of homework review? We’re going to give you two strategies.
First, instead of talking about problems in isolation, you can ask, “What was a key idea across the entire homework assignment?” This can help students reflect on what they did so they can see the forest instead of just the trees, if you will. And if they become aware of the bigger picture as they work, it’s more likely that what they are doing will make sense and they’ll remember it.
If they’re having trouble seeing the big ideas, which is a distinct possibility since they’re still learning this stuff, you can give them some more concrete guidance. Ask them to find two problems that were very similar. For example, if they’re working on multi-step linear equations, they might notice that even though the coefficients and constant terms change, there are patterns in the structure of the equations and in the process for solving them. By comparing problems, it gives you a chance to make these structures explicit, which research shows is a powerful way to help struggling students catch on to things that other students may already be noticing.
Our second suggestion is to have students contrast problems. Ask them to find two problems that are completely different from one another, which might reveal that there were multiple learning goals addressed by the assignment. Or have them find two problems that are somewhat similar but different in one key aspect. For example, with those multi-step equations, students might contrast equations with integer coefficients to those with fractional coefficients. But hopefully they’ll see that the overall goal is the same — making changes while maintaining the equal relationship until you determine x.
Students might also contrast equations that start out in slightly different forms. Realizing that sometimes one form of equation can be turned into another, easier form is a really good problem solving skill, and students can learn not to freak out when a problem looks slightly different than what they’re used to.
Looking across problems for similarities and for differences are two ways to disrupt the homework routine so that you can get your students talking, gather some formative assessment information, and give them new opportunities to see mathematical structure or notice patterns in repeated reasoning.
So be brave, try it out, and let us know how it goes in the comments.
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