Today, my students are learning how to use the simplest of equations for the first time in this class. Their task is to solve mathematical problems involving motion. I have introduced the equations, and they have done several practice problems in class while I walk around and check their progress. After putting solutions on the board, I hand out the first homework problem set. It consists of six problems that are identical to the type they have just been practicing.

“Take a look at these problems. They are similar enough to the ones you just did that most of you should be able to complete them at home on your own. However, it’s likely that some of you will get stumped at some point or another, so I have included “Helpful Hints” on the back of this sheet. Take a quick look.”

They turn the sheets over, and I add, “But not for too long”, with a laugh, and they turn them back to the front.

“If you get stuck trying to set up the problem, the helpful hints will show you how to get started. They list the factors you have been given and the unknown that you are trying to find. Starting the problem is often the hardest part.

“Let’s say you are able to successfully start the problem but then get stuck at the next step, choosing the right equation to use, that is also included as a helpful hint. In other words, helpful hints will give you the beginning and the middle of every problem. They won’t tell you how to solve the problem and get the right answer - that’s your job. The idea is that no matter where you got stuck, with these helpful hints you should be able to make it to the end of the problem on your own.

Alicia asks what I’m sure a number of students are thinking. “Why won’t people just cheat and use the helpful hints right away?”

“The idea behind the helpful hints is that you will only use them if you can’t proceed on your own. Some of you may think that looking at the helpful hints at all is “cheating”, but I don’t see it that way. If you need help and use the hints, they are allowing you to get over a hurdle and be able to complete problems. Surely that is better than just giving up and leaving the page blank.”

“As for people who just turn the sheet over and use the helpful hints immediately, ask yourself what they are gaining by doing that. Technically speaking, they will complete the homework, but they will end up not having practiced the problem on their own. They won’t have learned anything. Besides, it’s not that much more work to actually *do* the problem than it is to copy the helpful hints and then finish it on your own. If all you are doing is copying, you really won’t be able to participate in going over the homework with your study group, and it certainly won’t help you when you have to solve the same kind of problem on a test. In other words, you’ve chosen to turn an opportunity to learn into busywork that doesn’t serve any purpose.

“The idea of cheating implies that you are doing the homework for *me*, when in fact the homework is an essential part of *your* learning process. It isn’t for me at all.

“Tomorrow, when you come in, you’ll get into random study groups again, and I’ll stamp in your work if you have completed each problem as far as you can take it. That should be at least as far as the helpful hints go. Then, I’ll hand out answer keys to every study group. Every time you do homework, I do the same homework and create an answer key. That way, you can compare your work to mine. If there’s any difference between thetwo, your study group will help explain it.

“When you turn your work in, it is excellent if it is complete and correct. It will, in fact, look just like my homework. If your problems don’t look just like mine, write them over again in your journal so that you’ll have the practice of finishing them completely and correctly.

“Now, here’s the part that’s different from traditional homework: if you used the helpful hints at all, or if you needed the answer key to make your problem solving look like my problem solving, that is critically important information for you. It tells you that you haven’t learned to do these problems independently yet. That is your goal - to do the entire problem, from start to finish, on your own without any assistance. So if you weren’t able to do that this time, it is your job to choose to do more practice until you are able to do it independently. We’ll talk about how that works tomorrow.”