Week 5: Wrap up Question #4 Write a letter to a student...

Think of a key concept from Mathematical Mindsets that you want to share with your students.  Write a letter that describes the concept in a way that will have meaning for students.  Share your letters here; we can have the set of letters available to share with students in each of our classes.  (Thank you Sarah Lonberg-Lew for this creative and useful idea!)


Dear __________________,

Did you know that ideas can take up different amounts of space in your brain? When you first learn something new and it is hard and you really struggle with it, it takes up a lot of space in your brain. You need to think hard about how it works and how the ideas connect to other ideas you have learned. But the math that you learned a long time ago and already know really well doesn’t take up much space in your brain at all. You can do things like add 3 + 4 without having to think hard about it even though there was a time when even that was new and difficult for you. That’s because the old familiar ideas have gotten compressed, or squeezed, in to a smaller place in your brain.  They’re still there, but you don’t have to work hard at them. If you keep working hard at the stuff that’s hard for you now, it will also get compressed into a small area of your brain where you can get it easily.

There’s something important you should know about compression, though. Your brain is good at compressing ideas, but it can’t compress rules and methods that you try to memorize. All those rules just take up more and more space in your brain until they get all confused with each other and then math starts to feel really hard and not fun at all. The good news is that if you work hard at understanding ideas instead of memorizing steps, there’s no limit to how much you can learn!

Keep that brain growing!


I really like the way that you were able to compress the concept of compression:) I see this letter as being useful to a variety of students at various stages of their mathematical journey. Some students have the idea that they are horrible in math because they could never remember the rules, while others are stuck on rules and shut down when challenged with working through something that they've never seen before. Your letter is a well written appeal for either fixed mindset.



I was hoping other people might write some too and then we could have a bank of letters that everyone could use :)


Dear Student,

This class that you about to embark on is a math class.  Learn to love your mistakes.  Mistakes are learning blocks for you to learn from.  If your not making mistakes your probably not doing your calculations properly.  Every great inventor made many mistakes before the finished product came about.  These mistakes were all learning tools in making their dream idea come to life.  Every mistake you make, think of it as a learning tool.  Your learning how to do math correctly and this takes time, patience and learning from your mistakes.  Be excited about your mistakes because that means your getting closer to the correct answer and learning through the process.  Laugh at yourself because life is about having fun and enjoying it.  Laugh at me when I make mistakes, because I make them everyday when teaching.  I will laugh with you because life is to short not to laugh at our mistakes.

Your math teacher,

Duane H. Dorion