Maths; The Way It Should Be

Last night marked the last class of probably the best group of graduate students I have ever had the pleasure of working with. The course, Math and Diversity, focused on teaching maths to children with diverse needs including ELL, Special education, poverty, maths disabilities such as dyscalculia, and working with mathematically talented students. The course focused on developing the students' relational understanding of math as well as a growth mindset. Here's a sample journal from Bria, one of the students in the class that is pretty typical of how all the students in the course saw their growth as math teachers this semester.

 "I am so glad that I took this class. My mathematics confidence has skyrocketed as a result of this semester. I used to be told that I was good at math, but I didn’t believe it because I was grouped with people who were notably good at math and did not compare to them. I was one of the weaker links in Mathletes, for example, and I felt that I struggled in my college calculus class. I know that I will never be as strong in math as many others, at least as long as it is not my academic or professional focus. But what I am learning is that I am better at mental calculations and quick consolidation of numerical information than many other people I come across in my everyday life. I was able to comprehend and work with new concepts presented in this class fairly quickly, and enjoyed being able to experiment with my new knowledge. By gaining conceptual understandings of things I had learned procedurally growing up, I am able to approach new math problems that come to me in life more thoughtfully, and I understand those thought processes. My new hobby is doing mental calculations of various operations and then analyzing exactly how I came to my answer. Feeling in control of math is a fairly new feeling, and I love it. It makes me more confident in my mathematics skills, and makes me more comfortable when I find myself out of control of math.

In the past I have not been able to be comfortable with accepting that something was challenging for me; I would admit defeat at the first sign of struggle. I understand that this is a common ailment of the person who has spent their childhood floating through academic requirements and being told that they are smart. But through the education I am receiving in the graduate program at Saint Michael’s, I am finally learning to practice what I preach. I am learning that finding something challenging does not put a blemish on my intelligence, and asking for help does not signify weakness or make the person asked think I am less intelligent than they are. I believe these things wholeheartedly when they come out of my mouth as a teacher, but I continue to struggle with it personally because I always prided myself on being “smart” growing up and worried that people would find me less so if I asked for help. But during the second half of this course, when a concept or problem presented in class was challenging I began to actually feel alright about admitting it and getting help from a neighbor, rather than chastising myself for not understanding something as quickly as my classmates. I think that the confidence I built from taking this class has allowed me to get over any math-related anxiety I used to feel, such that I now know I am “good at math.” I understand that people were not lying when they told me this in the past. With this newfound knowledge, I am comfortable with struggling. Finding math concepts that are difficult for me are not something to avoid, but something to tackle head-on. It’s fun now, and I have this class to thank for it."

Another student in the course felt that, as a child,  she was "a conceptual person trapped in a procedural world". I will miss teaching this course. 

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.