One of the things I’m happiest with this year is homework.
What I do: Kids get a piece of paper, every day, with 10-15 problems on it. It’s completely mixed practice, mostly lower-level skills, and never includes new content from that day. My goal is that, if someone just picked up my homework, they would have no idea what unit I’m in or what I taught that day. I often start class by having students check one side of the homework, and give them a chance to ask questions. I check for completion, and put a grade into the gradebook every week — if you do it, you get credit, no questions asked.
Why mixed? Kids need to solve problems without being told how to solve them. If, one day, we’re working with linear equations, they know to find a linear equation to solve the problem. If they see something similar on homework a few weeks later, the retrieval of figuring out what tool to use and applying it helps to cement it in their memory.
Why lower-level skills? The most important thing for me is that kids do a little bit of math outside of class, mixed review of everything they should know, every day. Asking too many hard questions turns kids off, creates math anxiety, and also reduces the quality, because on homework when kids have the least support, they’re most likely to do it wrong. And practice and fluency with lower-level skills is important too — as a wise man once said, all problem-solving and no practice makes Johnny a boy who isn’t very good at math.
Why not include that day’s content? Students can still do the homework if they miss class, or if they were confused in class, or if they were making up a test. The biggest issue for me last year was that the kids who weren’t doing my homework were the kids who most needed to. By making homework more accessible, I still have kids whose homework completion is inconsistent, but those are kids who struggle with organization or time management — most of my lowest-skilled students do my homework consistently.
How long does it take? I’ve polled the class twice, and the median is about 10 minutes per assignment. I usually end class with a short exit ticket, and students start their homework when they finish. This makes a big difference for students who struggle completing homework — getting it started in class makes a huge difference in the likelihood they’ll finish it.
What does the feedback look like? Some days, it doesn’t happen — if I give a quiz, or have another priority for the warm-up. That’s fine. Kids do homework because it’s important to practice, not because everything they do has to be right. When they do check it, I only give them half of the answers. This is just practical — it makes it impossible to just copy the answers real quick at the start of class while I’m not looking. I’m not saying cheating doesn’t happen, but this helps minimize the temptation. I take questions on any homework problem kids would like to see.
How long does it take to create? I write them all myself — I don’t know of any resources that create awesome mixed practice, and I can be deliberate about what questions I put in. It takes about 3 minutes to write an assignment — I find that it’s much easier to write a question or two on 10 different topics than 15 questions on one topic. I try to keep a list of foci for homework for that unit to streamline writing.
What might one look like?
1. Find a cube root.
2. Graph y = 200 – 15x
The function f(x) = 9 + 1.5x models the cost of a pizza with x toppings.
3. What does the 9 mean in this function?
4. What does the 1.5 mean in this function?
5. Write 0.00405 in scientific notation.
6. Find one-third of 180
7. Solve: 1000+250x = 2500
8. Sketch a graph that is not a function
and so on.
Not complicated. Not supposed to take too long. But, kids are practicing skills that, when we spend time diving deep into complex problems in class, are necessary to move beyond procedures and reason about worthwhile mathematics.
The most important thing is that, this year, kids are doing my homework. The quality isn’t perfect, I’m sure some of it is copied on the way to school, and there are plenty of kids I have to nag about it, but the norm is that, in Mr. Kane’s class, you do the homework.
Update: Here’s what one recent homework looked like, after a day on piecewise functions: Link.