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. 

First Week of Classes at St. Mike's

Another week, another semester and another year. The first week of a new semester is always a time filled with mixed emotions. The excitement of meeting new students, as well as graduated undergraduates returning as graduate students, is mixed with the nervousness of of the unknown. Even after forty years of doing this the first half hour of a new class is a nerve wracking experience that I hope never goes away. I always tell my students that every new class of students they meet whether they be kindergartners or graduate students should be met this way.

One of the things I always try to identify at the beginning of a new semester are those students for whom maths is a chore; those students who dislike or even hate math; those students who misguidedly say they are no good at math. Recent research, especially in the area of Carol Dweck's Mindset Theory   suggests that the way we feel about ourselves in relation to maths directly affects our ability to learn maths. Very often, this negative self concept is something engendered by the actions of an uncaring or thoughtless teacher or a bad experience many years ago. Very often it is not a person's fault that they think they are no good at maths and there is absolutely no reason in the world that any adult can continue to not understand maths. 

One of the things I always try to do in the first class is to give students examples of how exciting and interesting it is to teach maths to young children One of the stories I always tell is of a kindergartner I once met several years ago who was convinced that 6 subtract 6 was five. Nothing we could say would convince him otherwise, so finally we asked him to show us with his fingers. He put up five fingers on his left had, pointed to each one with his right index finger and counted them out loud; "1,2,3,4,5". He then put up his thumb on his right hand and said "6", touching it with his nose. He then said, while removing his right thumb,  "OK, now I take away 6 and I've got 5 left".

According to the cognitive level of development of his numeracy skills he was absolutely right of course. He was in that halfway place of moving from the nominal or naming use of number to the cardinal or counting use of number; something we all go through in our early years. He was fine with 5 because that's an easy one, a handful, but was still working on the other single digit numbers such as 6.  

Learning about how children lean maths is the best thing in the world. I have also decided to use "maths" instead of "math" all the time. "Mathematics" is a plural; so too should be the abbreviation.