Doing the math
Five Sonoma Valley school leaders attended the Youcubed Leadership Summit at Stanford this past week. The conference was an invitation-only event for 160 educators from throughout the United States and Canada. The take home message: If students believe they can do math, they will be able to do math!
We are all familiar with the fact that kindergartners think they are great at music and art, and yet within a few short years, many students will say, “oh, I can’t draw,” or “I’m not a good singer.” The same is true for math. Students seem to separate themselves into the math and non-math groups, and sometimes, of course, parents, siblings and teachers can inadvertently reinforce these limited views.
In years gone by, and perhaps even today, it wasn’t “cool” for girls to be too brainy about math or science, compounding a notion shared by some male counterparts. Jo Boaler, a Professor of Math Education at Stanford, is the champion of the “growth mindset,” which promotes the paradigm that every student can learn high level math. The older way, constrained by a “fixed mindset,” suggests you are either good at math, or not, and there’s nothing to be done about it.
Yet Dr. Boaler emphasizes what she sometimes calls inspirational math, which focuses on posing questions rather than finding answers, and brainstorming ways to answer questions rather than simply answering them. Students work in groups, talk excitedly, everyone contributes. Counting on fingers and toes is a way to answer a math question, as is a using a number line. Math intuition, or the “bam moment” when the answer just appears, well, that also counts. Drawing pictures of a math program definitely counts. Using objects such as blocks counts.
The key here is that the wrong answers hold as much information, if not more, than the right ones, because they provide students to explore where the problem solving technique fell short. Was the technique flawed, was there a computational mistake, what happened? All is grist for the mill. Creative thinking is the goal here. Ultimately, effort is praised, not people or right answers.
The old school “plug and chug” works fine for some students, at least through elementary school. But as math becomes more complex, the need for equally complex and creative thinking increases. When we expect students to make a sudden leap from one process to another, without warning, simply because they hit the predetermined level where that is “supposed” to happen, we have created a problem that could have been avoided.
Further, students who learn problem solving for math will be able to apply the same process to other subjects. They will learn to (we hope!) embrace or at least tolerate the struggles they face in school and in life. No longer is the math class the quietest room in the schoolhouse. Instead, students share, collaborate, see what their neighbors are doing, shout out in victory or groan in despair.
So earlier this week in Palo Alto, 160 adults experimented with being students again, overcoming their own math “phobias,” learning that there were other ways to get an answer besides the “right” way. It was fun, it was invigorating, and it was instructive. We worked on math problems that we thought were beyond our abilities, and felt like we perhaps could have gotten that Nobel Prize after all! If a group of grownups could feel this kind of freedom and empowerment, think of what it will mean for our kids!
As we returned to Sonoma, we were planning on next steps to bring this material to our peers, many of whom are already beginning to use these techniques in their classrooms. Next time you check your student’s work and find an error, don’t use a red check mark! Start a conversation, showing curiosity, say, for example, “Huh. That’s funny. I wonder how that happened? Interesting…” You and your child will be off and running toward a growth mindset.
