What’s the point of homework?

The school year is slowly beginning, and my students are starting to bring in their homework. It seems like the ideal time to remind everyone what homework’s purpose is in this life.

For those not familiar with me, I work in a K-12 learning center. I spend a lot of my time with the advanced math students, many of whom bring in their homework either for me to check over or to explain.

I know what you’re thinking. They’re teenagers. They probably didn’t pay attention in class and that’s why they don’t understand. In some cases, that’s true and the student admits it, but we’ve had a startling trend over the past couple of years (as the integrated math program has invaded the younger grades, coincidentally) where math teachers are assigning middle school and high school students homework for the skill they’re studying the next day. In a frightening number of cases, the teacher then fails to either check the homework or teach the skill.

Naturally, I have some very frustrated kids who just want to understand how to do the math being shoved on them.

The point of homework is not to replace instruction. That’s not what the school district is paying for. That’s not what parents want. Amazingly, that’s not what students want, either. Sure, you have the slackers, but eventually even the slackers want to be able to pass the class and not fail the next one.

The point of homework is to give students an opportunity to practice the skill you taught them. It’s a chance to make sure they understand it before you give them a harder skill built upon this skill. It’s a chance to make sure you taught the skill to them in a way the majority of the class understands.

If you’re expecting your students to teach themselves, perhaps it’s time you reconsidered your career choice, if only for the sake of the students.

The struggles of scaffolding

Last year when I started working on Dead Bunny, I realized very quickly that part of why my students struggle with new math concepts is because they often have to learn not just the new concept but a skill they probably should have been taught earlier.

In some cases, a teacher just failed to introduce the earlier skill at all. In others, it’s been a curriculum issue. At any rate, the poor student needs to understand something new to learn the new skill you’re teaching them, which introduces a small overload.

When I noticed that there were skills I was perpetually teaching my students so they could work through a new skill, I grabbed a stack of index cards, wrote the skill at the top, and all the skills the student probably needed to know before successfully being able to learn the current one. Then, I attempted to sequence the cards based on this list of prerequisite skills.

It was an eye-opening experience. I’m pretty sure I’ve blogged about the need to re-order fraction skills (an experiment that met with mixed results in my learning center due to less than ideal conditions), but there are other skills that could benefit from being presented in a different sequence.

For example, I’ve found that if I approach the number line as an example of the x-axis with students just starting with integers or early algebraic reasoning skills, they’re less likely to confuse the x-axis and y-axis when they start learning about coordinate geometry.

Another example (and one I’d love to hear more about how it aids later learning) showed up when I was catching up on my “to read” links the other day. Denise over at Let’s Play Math uses the distributive property to help students better understand their nines facts in multiplication. My high schoolers struggle with the distributive property, so this is pretty interesting to me.

What’s funny is that reading about Denise’s use of the distributive property came right on the heels of a discussion at work about whether it was reasonable or necessary for a second grader to understand the concepts behind the associative and commutative properties as well as their proper names. But if we encourage that understanding in our younger students, would I have fewer high schoolers struggling with the same skills at a more advanced level?

Again, it’s a question of how to best scaffold these skills to really help students not only learn, but retain these skills through their math education and beyond.

Dead Bunny on YouTube

Sorry I’ve been away, everyone. Work has been just a little crazy. Actually, it’s been a lot crazy. On top of that, my computer had problems and had to go away for a long time…with all of my current proijects on it, including Dead Bunny’s book. The computer’s back now, and I have a number of things to learn and work on to catch up those lost months.

While I was on a borrowed computer, though, I did manage to step outside my comfort zone and make some things for you. One of the things I’ve always wanted to have for this site is a series of videos teaching various bits of math. I’m pleased to announce the first five are completed, and available on YouTube.

Please forgive the quality. I’ve never done anything like this before, so it’s been a real learning experience. And as you can see by looking at them, I still have more to learn. So, please forgive the audio and video quality as you enjoy the videos.

Dead Bunny’s Guide to Algebra on YouTube