Growth Mindset Maths is a Must

Well, I don"t care what Alfie Kohn says, and I do usually agree with him, but I think  Mindset Theory is the best thing I've added to my teaching repertoire since I discovered John Dewey's ideas of Inspired Vision and Executive Means back in 1969.

I've now introduced it in both my undergraduate and graduate math courses and the results have been great. This is especially true in my undergraduate math class where we've been exploring teaching everyone's seemingly least favorite maths topic, fractions. For some reason, my students nearly always seem to enter this topic with very little relational understanding of fraction concepts or fraction sense. It's as if they've slogged through endless hours of learning nothing but how to add, subtract, multiply, and maybe divide, using archaic, instrumental strategies such as "you can't add apples and oranges", or " invert and multiply"or "cross multiply" to name but a few.

They seem to have one revelation after another when they realize the power of the ONE or referent when when working with fractions. The idea that you can count like fractions the same as you can count anything else and the remarkable patterns fractions make like these two 1/2 2/3 3/4 4/5 5/6 6/7 7/8 8/9 9/10 and 2/1 3/2 4/3 5/4 6/5 7/6 8/7 9/8 10/9. Each forms a pattern approach ONE but never getting there.

Frequently, during class-time, we refer back to the Mindset class we had near the beginning of the course and they all remember Carol Dweck's maxim of "yet".  This idea seems to work well with the Learning Communities in the class where each member of the community bears a responsibility for making sure that every one in their group of 4 or 5 students is developing an understanding of the topic, fraction concepts and skills in this case,

The more I try to develop my Mindset language the more I see the students responding in a positive way. I feel like I am even more "on their side" so to speak than I thought I was before. My job is clearly to help them all succeed in developing the relational understanding of maths  required of being an elementary school teacher. 

Math and a Student's Mindset

I can't think of any better application that Carol Dweck's mindset theory than to the study of mathematics. For years so many students learning math have developed, and subsequently suffered from, the fixed mindset embodied in the statements "I can't do math" or "I'm no good at math". Remarkably, it's a phrase that is repeated so often that it is now quite an acceptable excuse for not being able to do a simple math exercise computation of problem solve. It's even reached the point where it's almost worn as a badge of h9onor by some people because it distinguishes them from the "less cool" people who actually like math and are good at it.

The reason for this is  most likely the way we have taught maths in the past as a dry, sterile subject with little relevance to life, other than balancing a check book, and with little aesthetic value. A situation that has to change if mathematics is to captivate students' interest and imagination.

For several years I have been advocating for the study of fractals in the elementary school math curriculum and it seems I have an ally in the Common Core Math Standards, at least in the Math Practice Standards section. Math practice standards 7 and 8 both suggest that students need to search for pattern in order to make sense of the world of maths. Talking of fractals I took my son Adnrew to see the movie Frozen last Sunday and there in one of the songs about the ice castle wwas the word "fractal" as she described the patterns the ice made. The study of pattern in fractals could do a lot to help students develop a growth mindset in math class.

And here is a neat website worth watching that focuses on the idea of Growth Mindset Maths. 



  


 
 

How To Learn Math

For the past week I've been auditing the on-line course by Jo Boaler of Stanford University. The course, How to Learn Math raises so many wonderful  issues about how we need to develop a more user friendly and conceptually-based  way of teaching math; how math needs to be seen as a creative activity and how we need to get away from the idea  that math is a closed set of procedures to be memorized. Now while these are things I have been advocating for for almost my entire professional life there is something in the course that is having a radical influence  on the way I see my role as a teacher of teachers of elementary school math.

This is the idea of fixed versus growth mindset. developed by Dr. Carol Dweck as described in her book Mindset.   This is clearly an  incredibly important issue for helping children become better at math especially those students who, because of our current system of  testing, have pretty much given up on ever achieving anything mathematically. To be told you are a mathematical failure at age 6 and have no hope of changing that is the world of the fixed mindset indeed.

But there's another application of this incredible idea which is to apply it to parents in terms of their attitudes toward math education. Over the years I have engaged in may discussions, arguments and  even confrontations, some even in public forums, with parents who truly believe that the math they learned by rote in school 30 years ago "was good enough for them so it should be good enough for their children". Sadly, the proponent of the fixed mindset are frequently successful businessmen who point to their success as the reason for maintaining the"no pain, no gain" approach to learning mathematics.

If we are to bring about the evolution of math education to a truly conceptual approach we have to do much to bring about a cultural shift in thinking about mathematics education, a task made more difficult by the disaster of the "new math' activities of the early 1970s in the last century. Perhaps the only way to succeed is to show that the methods advocated by Jo Boaler and the rest of us really do improve scores on tests.