be a mouse; be a robot

Mar 2015
73
7
Los Angeles
I wanted to get feedback about a math teaching idea I use with my students (I'm a private tutor). I tell my students that "sometimes you have to be a mouse, and sometimes you have to be a robot."

A mouse sniffs its way through a maze, searching for cheese. This is like exploring a math problem, brainstorming, or guessing what math technique to try next.

For instance, you are given a problem in which you have to simplify a rational expression. You're not sure what to do next. You might have to guess at something and try it.

A robot follows instructions. It does exactly what it's told, methodically This would be like deciding you are going to factor the top of the fraction. At this point, you need to use the exact steps for factoring. You need to check your work methodically. You may need to recall a list of common errors and check for them.

It seems that mixing up these modes causes problems. For example, at the beginning a student may be afraid to explore. They've been told that math has "right and wrong" answers, and they don't want to be wrong. They may shoot down their ideas before they've even given them a chance. So their concerns about "being right" get in the way of brainstorming.

Then, when it's time to be methodical, they get distracted because they are thinking where the problem leads. The whole time they are factoring, they are wondering if it's the right thing. In other words, their desire to explore and "think outside the box" is distracting them from being methodical.

So I ask them to be clear in any given moment whether they are being a mouse or being a robot.

I've noticed it has another benefit. Whenever I ask a student to switch modes, they pause for a moment and gain a little mindfulness of their process. This slows down and calms their thoughts, and keeps them from rushing forward heedless of mistakes. This little pause doesn't have to come from switching modes -- it could come from anything. I could ask them to pause and switch pen colors, or pause and listen to music. But it's efficient to have it happen automatically as part of mode switching.

I would be interested in feedback from more experienced teachers here. Does this idea seem helpful? Do you do something similar?
 

skipjack

Forum Staff
Dec 2006
21,325
2,392
If unsure what to do, try substituting a much simpler problem (of the same type) that is easy to do. Then consider what methods of tackling that problem exist that might also work for the original problem, and how to check fairly quickly whether they do.
 
  • Like
Reactions: 2 people
Feb 2016
1,849
657
.
I'm not a more experienced teacher.. but the idea seems innocent enough, and probably beneficial. I think the point though, as you have said, is that it causes students to stop and think.

By the way, have you read George Polya's "How to solve it"? If not, I strongly recommend. Lots of useful guidance for both teacher and student. Plus it's a classic.
 

Denis

Math Team
Oct 2011
14,592
1,026
Ottawa Ontario, Canada
If unsure what to do, try substituting a much simpler problem (of the same type) that is easy to do. Then consider what methods of tackling that problem exist that might also work for the original problem, and how to check fairly quickly whether they do.
YA!! That's my favorite method...
 
Mar 2015
73
7
Los Angeles
Yes, I've read "How to Solve It." Lovely book. I first read this book when I was in high school (my father had a copy).

"Solve a simpler problem first" is one of the ideas in that book. So that would be an example of working "as a mouse." Part of what I'm saying in my original post is that students have a hard time committing to either mode, because they want to hover somewhere in-between.

For example, when it came time to brainstorm about choosing a simpler problem, most of my students would probably hesitate to brainstorm for fear of being wrong. They would think that "choosing a simpler problem" is yet another technique that they might screw up, not realizing that it's actually "mouse time."

Once they've made a choice, they need to work "as a robot" in order to find where their choice leads accurately. Sometimes they hesitate to commit to this because they fear they made the wrong choice in the first place.
 

skipjack

Forum Staff
Dec 2006
21,325
2,392
That's why I suggested that the simpler problem is one that is easy to do - easy enough for them to know that they will get it right.