My Math Forum  

Go Back   My Math Forum > Math Forums > Math

Math General Math Forum - For general math related discussion and news


Thanks Tree2Thanks
  • 2 Post By skipjack
Reply
 
LinkBack Thread Tools Display Modes
September 17th, 2018, 01:45 AM   #1
Member
 
Joined: Mar 2015
From: Los Angeles

Posts: 73
Thanks: 7

be a mouse; be a robot

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?
mike1127 is offline  
 
September 17th, 2018, 02:38 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 19,713
Thanks: 1806

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.
Thanks from Denis and mike1127
skipjack is offline  
September 17th, 2018, 02:53 AM   #3
Senior Member
 
Joined: Feb 2016
From: Australia

Posts: 1,717
Thanks: 597

Math Focus: Yet to find out.
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.
Joppy is offline  
September 17th, 2018, 04:53 AM   #4
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 13,302
Thanks: 935

Quote:
Originally Posted by skipjack View Post
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...
Denis is offline  
September 17th, 2018, 02:10 PM   #5
Member
 
Joined: Mar 2015
From: Los Angeles

Posts: 73
Thanks: 7

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.
mike1127 is offline  
September 18th, 2018, 01:12 AM   #6
Global Moderator
 
Joined: Dec 2006

Posts: 19,713
Thanks: 1806

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.
skipjack is offline  
Reply

  My Math Forum > Math Forums > Math

Tags
mouse, robot



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Robot neck trig njc Trigonometry 9 February 17th, 2014 08:13 AM
Cat chases mouse hawser Calculus 7 December 20th, 2008 05:43 AM
Is this damn mouse now trapped??? pauliewalnuts Calculus 0 May 11th, 2008 01:46 AM





Copyright © 2018 My Math Forum. All rights reserved.