Mathematics is the Music of Reason
by Allison Gaines Pell
Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion— not because it makes no sense to you, but because you gave it sense and you still don’t understand what your creation is up to; to have a breakthrough idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it. Remove this from mathematics and you can have all the conferences you like; it won’t matter. Operate all you want, doctors: your patient is already dead. - Paul Lockhart, the Mathematician’s Lament
What if math could be, as this quote suggests, thought of as an intellectually engaged, artistic pursuit, with the “basic skills” as a necessary but not sufficient aspect of the curriculum? What if math can be the place where collaboration, persistence, mistake-celebration, growth mindset, perspective taking and creativity come from the shadowy margin to the center?
I spent a week this summer with a group of nine of Blue School’s fine educators taking an online class with Jo Boaler, a researcher and professor at Stanford University. She discussed and shared research on mindset, mistakes and perseverance in mathematics, and moved through a series of applications for teaching math (or maths as she calls it) that are purposeful, research-based, creative, pragmatic and effective.
Along the way, within our group, we talked about our own math education, about the types of classrooms we want and have, and about you, our families, and how to share the inspiration and learning we have gained over these years. We also wanted you to be assured: all of the changes we are seeing in mathematics teaching through the introduction of Common Core and the development of shared best practices, which often look very unlike the ways we all were taught, mirror the best thinking about the brain, learning, and our approach to education. We want to find ways for you to experience this, which as we know, is the only way to learn it.
A few key take-aways:
Mistakes are the most important work we can do to grow our brains: When we make a mistake, synapses in our brain fire and help our brains to grow. This can happen with small and big mistakes, and obviously can be applied to many disciplines and of course, to life!
Students should own the cognitive demand of their work: There is a “didactic contract” that pervades many of our classrooms. This unspoken contract reflects a dynamic in which teachers, wanting to support students, give so much support as to empty the learning from the task. Teaching math by elevating thinking, through talking about, visualizing, debating and exploring numbers, allows for the focus to be on the cognition. We have to believe and ensure that thinking is at the center.
Stop the cultural acceptance of talk about ‘hating' math and about designating who is a 'math person.' We all send terrible, fixed messages about math because of our own possibly negative experiences with it, and because somehow this has become acceptable in our society. We all need to always bring curiosity, creativity, and love to math, not because it will just help students, but because MATH DESERVES OUR DEEP ADMIRATION AND LOVE!
A “growth mindset" is very important: As has been widely researched, praise that is offered around specific work done (“You worked really hard on that problem” or “What an important idea you’ve had!”) nurtures a growth mindset, critically important for learning and life. A fixed mindset, created by many messages such as groups who are thought to be naturally “better” at math or feedback such as “you are so smart!”
Conceptual mathematics and problem-based learning is equated with both higher test scores and more challenging, professional jobs. In a study completed in England of two schools with a Problem-Based Learning (PBL) approach vs a traditional memorization and didactic approach over three years saw dramatic differences in test scores for the PBL school, and in a longitudinal study of the same students, saw dramatic differences in their job and career choices and abilities. When interviewed about why a student thought she did well on the exam, she said “I just go into them thinking I can do them; I just work it out from my own knowledge until I get there.”
This also comes to an important question about the purpose and orientation of education. In one section of the course, we watched a video of interviews with freshman at Stanford University, presumably young people who graduated at the top of their classes, and whose academic and social achievements are many. In many cases, these students spoke about their lack of intellectual engagement in school, how they never understood that learning could be about collaboration, thinking, engagement, and interest.
So, let’s bring our love, curiosity, and celebration of mistakes, achievements, struggle, and mathematics to our work here at school and with children.
Here are some great resources for your perusal:
Daring to Stumble on the Road to Discovery, by Peter Sims
YouCubed - a week of inspirational math to do together!
You Cubed Parent Resources and Articles
Jo Boaler’s Online Course - for FREE!
Advice for Parents from Jo Boaler
Upcoming Parent Math Workshops
- December 7, 2016
- February 8, 2017
- March 22, 2017
Notes from Meredith and Esther's first Math Workshop. (Wednesday, October 5, 2016)