I have been thinking a lot about growth mindset lately (really, what teacher is not.) But I have really been trying to come up with positive, constructive ways to model and use it in the classroom as a way to change the learners beliefs.
One way I came up with using it is to have some statements that I can use consistently when learners are struggling in class. My personal challenge when dealing with the fixed mindset is what to say, how to constructively come back with something that will start impacting beliefs. As a teacher, we hear it, but how do we respond? It has to be consistent or we lose their focus. These cannot just be quotes on the wall, but statements delivered with conviction face to face to have an impact.
So, here are some statements I hope to use in my classroom. I am going to print them out and post them where I can see them every day in the morning and before every class to remind myself to use them until I don’t need the list any more.
|Learner Says or is Doing:||Teacher (ME!) says:|
|Learner is struggling with material||“If it was easy, I would not waste your time with it”|
|Learner whips through problem, too easy||“I apologize for wasting your time, I will find something more appropriate for you.”|
|“This is too hard.”||“What strategies have we discussed that could help you get started?”|
|“This is too hard.”||“It is difficult now, but so was adding in elementary school. You overcame that with effort and you will overcome this with effort.”|
|“I am not good at this.”||“The more you practice the math, the better at it you will become.”|
|“This is easy.”||“I am glad you understand this, can you develop a more complex idea with it that challenges you?”|
|“This is as good as I can do.”||“You can always improve, as long as you give it some more effort. What other strategy have you not used yet?”|
|“I made a mistake, I can’t do this.”||“Mistakes are how we learn. If it was easy, you wouldn’t be learning anything new.”|
|“This is good enough.”||“Is this your best work to show your learning?”|
|“I didn’t get it on the first try, so I won’t.”||“So your plan A didn’t work out. Good thing there are 25 more letters. Start on plan B.”|
|“You are just too hard on us. We can’t do it.”||“I’m giving you this assignment because I have very high expectations and I know that you can reach them.”|
The goal here is to have a bank of statements that reinforce growth mindset that are easy to memorize, adopt, use and believe in so that every day I am consistently changing the dialogue in the classroom. I have found that it is easy to get sideswiped by a comment and not have a positive response handy. My goal is to fix that.
Any suggestions? Additions? Changes?
Some resources for Growth Mindset I will also use come from:
http://mathmamawrites.blogspot.com/2010/07/day-one-of-class-beliefs-about-math.html Sue is an amazing writer and teacher. Her take on this is invaluable
http://mathhombre.blogspot.com/2010/07/growth-model.html Just download John Golden’s Implict Theory of Mathematics Learning worksheet now and give it out the first week of school. I am, and you will be glad you did it too.
http://practicalsavvy.com/2012/01/31/inspiring-quotes-demonstrating-the-growth-mindset/ These are great quotes, but quotes around the room won’t cut it. It has to come from my mouth, every day.
This post is really for a friend of mine who is very much math aware and capable, but does not teach math. He has twin sons who are absolutely amazeballs smart, and through talking with him one day I espoused my approach to algebra. He was intrigued and wanted more info. This is my attempt at more info. I figured that others may find value in it, so I am publically posting it for all to see (and read, hopefully.) Please rip it to shreds if you feel I am in error or made a mistake. I want to do better, and I can’t if I am doing something wrong.
So let me begin with where this came from. At the NCTM Las Vegas regional conference in 2013 I was introduced by an elementary teacher to what she called 13 Rules that Expire.
There are some definite Algebra concepts on here like number 2) Use keywords to solve word problems and number 3) you can’t take a bigger number from a smaller number or what really kills me is number 8) multiply everything inside the parenthesis by the number outside the parenthesis.
Yea, right. Try that with f(x)=2x+5.
And from there we have Nix the Tricks. A more rigorous treatment of the stupid things we as math teachers do to mess up learners in the guise of teaching them to get an answer instead of understand the mathematics.
So I sat back and tried to come up with some rules that did not expire. Some essential rules that always work, that always build understanding and not destroy it. I ended up with 3.
1. When solving an equation, you can do absolutely anything you want, as long as you do it to all terms of the equation.
2. When working with expressions, you can only change it by adding or subtracting 0 (by using additive inverses), or when solving equations, you create zeros by adding or subtracting 0 (by using additive inverses).
3. When working with expressions, you can only change it by multiplying by 1 (in any form), or when solving equations, you create 1 by using the inverse functions/operations.
That’s it. When I am teaching math, I stress the idea of creating a zero or using a zero. When demanding written explanations, I demand they say that 5+-5=0 in their explanation. So, a nice short example.
Find the function that is the inverse of y = 1/3x – 4
Work Why did I do what I did?
x = 1/3y – 4 Because the first step in finding the inverse is switching the x & y
+ 4 +4 Add 4 to both sides because –4 + 4 = 0 (additive inverses = identity)
x + 4 = 1/3y result
3(x+4) = 3(1/3)y Mult by 3 because 3(1/3) = 1, (multiplicative inverses = identity)
3(x+4) = y finished, but should check it by …….
So there is an example of the work I require. I want them to be using the language of inverses and identity. Why does the square and the square root cancel each other? Because the exponent of 1/2 (the square root) and the exponent of 2 (the square) when multiplied equals 1, the identity.
Along with this, there are some forbidden words and phrases in my classroom. One is above, “Cancel”. I do not allow my learners to use it. At all. Ever.
Why? Because I have seen all of the following described by the word: -5 + 5 cancels to make 0. 3/3 cancels to make 1. Log10^4 cancels to make 4, sqrt(5^2) cancels to make 5 and on and on and on.
If those all “cancel” then that word means nothing, and it does not mean anything at all. It is just a word used to hid the mathematical knowledge of inverses and identities.
Another phrase that I will not allow is the common answer to the question, “Why did we add 4 in the first step above?” They typical answer I get is, “Because we want the y by itself.”
Huh? That is not why we added 4. We could do anything we want in the world. We could have added 6, or subtracted 3, or taken both left and right side and made them exponents with a base of 7.5. We added 4 because –4 + 4 = 0. That zero is important. I also write it down. I think most teachers do not. Or they draw a line through the –4 and 4. What does that line mean? I tell them it means a 1, and did we make a one? No, we made a zero.
It takes some time to unlearn the bad habits, but this is a Nix the Tricks kind of endeavor. In the end, I think I am helping the learners understand math better and more deeply. At least, I hope I am. Only time will tell.
My friend over at Cheesemonkey Wonders posted a list of Growth Mindset Quotes on her blog, and it made me realize that I do something similar. Every single day of the year, I put a different quote on my board. They all deal with academics, success, fighting to learn or achieve, or something similar.
I started doing this three years ago, and I did it for myself at first. I just thought I would inject a little thoughtfulness and philosophy into my math class and started collecting quotes to do so. That document is now 26 pages long with nothing but quotes I have saved.
One day, I was lazy or in a hurry and did not put up a new quote. One of my learners actually came back out of my room, stood in front of me and said, “That quote is the same as yesterday’s. You need to fix that.” At that point I realized my learners were reading them, and did actually care about the quotes I was putting up.
Since then, my learners have told me they enjoy them, they find them inspirational, and one learner actually told me she saw my quotes on facebook because another learner liked it, photographed it and posted it.
Little things matter. Sometimes, they matter more than big things. With that in mind, here are some of my favorite quotes from my 26 pages. I will put it below the fold, because this may be a little long.