Communicating Work In Math


In a previous article, I discussed giving gifted students an actual reason to show their work beyond the nebulous claim that “someday you’ll need to show work because the problems will be so long!”

Steps Help Communication

Many wrote in to add that showing work is important as a way of communicating and offering proof to an audience. But, whether we realize it or not, the only audience many students are performing for is a test scanner.

So, teachers, let’s put our money where our mouths are and give them a chance to experience that showing steps is vital to communication. And give them this chance daily!

Use Homework

As soon as math starts, table groups whip their homework problems out and compare answers. I walk around and check to see that the work (which is typically eight to ten problems) was completed and listen for patterns in their discussion.

Some Common Statements

  • “Wait! How’d you get that?”
  • “Oh, I see what I did.”
  • “Let’s see why we’re different.”

For the most part, students confirm that they got the same answer. Often, someone will have something different, and this lets the group compare work to see where the difference came from.

But inevitably, someone has a different answer but has shown no steps. This leads to a teacher’s paradise, in which students get annoyed at each other for not showing steps (Yes! Math peer pressure!), which leads to the student reworking the problem to prove his solution to his peers.

Then, if you’re really lucky, that student was right the whole time and now has helped his group understand the problem. Or else, the rest of the group gets to point out how skipping the steps caused him to make a mistake.

Either way, everyone is experiencing the importance of showing work as a tool for communication, and you don’t have to be a nag.

Increase The Drama

Now it helps that I have a pretty motivated group of kids who, for the most part, really care about getting this stuff right.

If motivation is a problem, I’ve had students present homework problems to the class (steps required!) after this discussion time, earning some token for their group. This ramps up the drama a bit, since everyone has a chance of representing the group.

I use raffle tickets as a prize. When a presenter makes an error or skips a step, I stop him, give him a chance to catch the error, but, if he doesn’t see it, I call another group up and double the potential prize! This leads to some serious excitement.

Now, you have to know your kids and be prepared to work around those who have math anxiety. This should be a time to reward success, not continuously punish those who are known to be struggling. Be strategic in calling up certain students. Give them a chance to shine when you know they’ve got it.

Improving Interactions

Another problem might be group interactions, so you’ve gotta get that seating chart just right. Don’t put the bossy brainiac next to the shy, struggling math student. Instead, use those caring, nurturing students to provide a safer environment for a student in need. I’ve seen this make a world of difference for some students.

If you’ve got a super genius who is doing this math in their sleep and messing the group interactions up, goodness gracious test them out and give them something interesting to do!

Also, if kids are having trouble “discussing” and not “arguing,” create a scaffold of appropriate ways to communicate:

Rude Polite
Wrong! Can you show me how you got that?
You don’t get this? It’s so easy! Here, let me help you understand this.
Johnny is wrong! I disagree with Johnny because…

This time is an amazing informal assessment on kids’ progress, since you’re free to walk the room and check in on who is floundering and who is nailing it.

If you absolutely need a written assessment, you can give a quickie quiz and collect it after these discussions.

More Hints

  • Limit time. This should take three to five minutes.
  • This means math homework is short (but you already know not to give gifted kids repetitive practice, right?).
  • Intervene quickly when you hear inappropriate interactions.
  • Take notes on examples of great discussion and share them out.
  • In the end, work any problems that caused mass confusion.

Photo by ttarasiuk