Education reforms, an unstoppable phenomenon of the elementary and secondary education world, invariably come with strengths and weaknesses. Too often, those strengths are undermined and weaknesses accentuated by cracks in the teaching link of the chain that pulls successful learning.
I saw that link snap too often in my experience as a secondary math teacher and department chair in California and in my many years since researching math teaching and learning.
From the National Council of Teachers of Mathematics (NCTM) reforms that I started my career with more than twenty years ago to the current Common Core State Standards implementation, forging what works has been as tough for education leaders as understanding algebra has been for many students.
The complexities of how to improve student math performance was apparent in a recent New York Times Magazine article by Elizabeth Green that asked “Why Do Americans Stink at Math?” Excerpts from the article appear in her newly released book “How to Build a Better Teacher: How Teaching Works (and How to Teach it to Everyone).” Though disputed by the Brooking Institution’s Tom Loveless, Green argues that teaching methods that tend to focus on memorizing rules rather than understanding concepts is the root cause of the problem – or at least partly explains why more than half of fourth-graders can’t accurately read the temperature on a thermometer. She says that teachers can’t be expected to teach more conceptually unless they have ongoing opportunities to learn and refine new approaches and describes the Japanese lesson study as one way to accomplish this.
I agree that providing the right technical training and support for teachers is essential in the Common Core era, especially for those teachers working with the most disadvantaged students. But there is an elusive tempering element that seems key. We also must understand teachers’ dispositions towards learning and how these dispositions develop. I don’t think we’ve thought about this enough.
In California, I was one of the few teachers in my urban school who fully subscribed to the NCTM curriculum and teaching reforms—perhaps partly because I was young and eager to learn new things. It made sense to me then, and still does today, that students deserved to see math as more than a collection of facts to be memorized and skills to be practiced. Facts and skills are important, but so is knowing why procedures work and learning how to solve challenging problems.
But it is also is true that I found teaching this way to be intellectually stimulating. I had never thought about why many math procedures work until I tried to teach them. Students’ questions helped turn on the light. Mr. Walters, Why do we have to flip one of the fractions when dividing? Can the first fraction be flipped instead of the second one? I found these questions interesting and viewed them as challenging, exciting opportunities to deepen my own understanding and capacity to understand how students learned. Seeing students really understand something was gratifying. It was fun. It is largely why I stayed in the classroom for a decade and continue to do research in math education.
I’m not sure how or when I developed this disposition. But I think having such a disposition is important. It’s one of the first things that stands out when I work with teachers in research settings. I’m reminded of one of the teachers I followed for a year as part of my dissertation work. I first observed her during a summer workshop, which was part of an intensive, yearlong professional development program. She was working on a complicated word problem and became extremely frustrated when she couldn’t articulate her answer. She used the entire break time to meet with the workshop facilitator until she got it straight. She was curious and persistent. She had grit. I followed her and the other 7th grade math teachers in her school for the entire year. She ended up outperforming the other teachers on measures of content knowledge and instructional practice, even though she had taken the fewest number of college math classes. I think she got more out of the professional development program because of her tenacity to understand.
One of my current research projects focuses on understanding and highlighting these traits. The work provides in-depth vignettes of highly regarded high school math teachers who implement different degrees of student-centered and traditional instruction. One of these teachers not only showed a great deal of tenacity and grit as a learner, but she also somehow managed to pass along these traits to her students. In one lesson I observed, when small groups presented their work, the whole class joined in active critique and discussion of the main ideas in the lesson. The students took on much of the intellectual work in the room. They showed persistence in reaching consensus and resolution.
How did these teachers develop these dispositions? Are they mostly innate? If not, how can they be fostered? We are starting to understand much more about what motivates (and deters) students to persist in learning. Work being carried out by the Carnegie Foundation, informed by the research of Dr. Carol Dweck and others, appears quite promising. But also it’s time to press forward with similar questions about teachers. What causes some teachers to delve deeper? What causes them to persist in their own learning? We need to continue to care that teachers deeply understand the content they teach. But why not also care about how they approach learning that content? Their students are exposed to both what they know and how they learn. Studying how teachers develop these traits seems like a logical and important step as we try yet again to reform math education.
Kirk Walters is a Principal Researcher at the American Institutes for Research