What does it mean to be “smart” at math?

Traditionally, one who is fast at math is good at math or smart at math.  If it comes easily that is considered a good thing.  I recently visited several schools that are communicating a different message about math.  I also attended the Creating Balance in an Unjust World Conference at one of the high schools. Burton and Mission high schools in San Francisco graciously welcomed us into their classrooms to observe and reflect on the learning that was going on. Their district math departments are using an idea called Complex Instruction .  As has been the case with all my visits so far, I saw nothing wild and crazy; nothing that couldn’t be implemented with any student in a rural Vermont school with an economically diverse population.  The most important thing I noticed was that students weren’t talking about right answers. It was unclear to me who was “fast” at math and who was struggling.  Since I am trained in special education, it is my general tendency to search for the struggling student but just as I thought I might have found one, that student would make an astute observation or ask an insightful question and I would question myself.  It became clear that these teachers communicated that it doesn’t matter who is fast and I will certainly be working on my bad habit of looking for the weak links.

Creativity

So if math isn’t about right answers and speed, what is it about? Looking in from the outside into these classrooms, it seemed to be about a creative process.  Teachers shared that they spend their planning time developing tasks that force students to look at common math skills from a different perspective which in turn forces students to think about the concept rather than focus on memorizing procedures.  Once such task required students to draw a picture of various fractions.  This went fairly smoothly until 3/2.  At that point, students started to talk about the fractions as ideas rather than think about the numbers.  This was a pre-calculus course and the teachers had identified that ratios were a weakness conceptually so these tasks were created to strengthen upcoming work with trigonometric identities.

Relationships

Math was also about collaboration, communication and relationships.  The interconnectedness between people, ideas, events, phenomenon, and in general, anything relevant to the students’ lives was the focus of planning math lessons and thinking about math skills.  At the conference, the first example of “social justice math” was in regards to payday loans presented by Joel Walsh from UCS Hybrid school.  In order to learn about logarithms and exponential equations through an investigation of payday loan providers.  They explored how these business practices exploit low-income and minority populations in their own communities.  We actually called a local payday loan business and questioned them to gather information right there during the conference. Ken Collins from Charlotte Latin School explored the question of how we can use math to in voting to help reflect the “will of the people”? Finally, the last example came from a Vanson Nguyen, a community college teacher who used various forms of data to encourage students to solve real world social problems or consider social questions.  In one example, students collected a variety of data related to their school population.  They chose the most compelling data, which is itself a math skill, and then they collected and compiled more data to propose a solution.  In the second example, his students considered a popular music group.  They looked for social themes presented by the teacher and compiled the data about how many times these themes came up in an album.  Using this information, they formulated an argument about whether or not these bands were positively or negatively impacting the social issue.  In both these examples, the mathematical concepts for the course were explored through the problems presented.  When this instructor fielded questions about rigor he and I had similar thoughts.  The focus is on engagement because when students are engaged they can learn the math. People who argue that it isn’t rigorous aren’t thinking mathematically about it.  If a disengaged student requires 3 months to learn how to solve equations because of their disengagement and lack of purpose, this is highly inefficient.  A student who spends a month exploring a fascinating idea and only a couple of weeks learning how to solve equations in that context has learned the skill in half the time and doesn’t hate math either.

Math is everywhere

When I left these classrooms as well as began to process the examples shared at the conference, I began to see math everywhere.  All sorts of data started popping up in my head that I had never considered before.  Questions about how Uber software worked; the math behind the best stance to get a bulls eye in darts.  The math related to these questions began to scream in neon signage all over my brain.  I started looking for math everywhere.  We should be looking for math everywhere as we develop math curriculum in order to engage students, make math more personal for students and at the very least make sure students don’t hate math.  I understand the importance of fluency in completing math procedures but what if math isn’t about procedures?

Many thanks to Taica Hsu and Hossein Koch from Mission High School and Mr. Pablo, Mr. Yamamoto, and Mr. Popalisky for allowing us to observe their classrooms.