Fostering a New Generation of Confident Mathematical Thinkers

As a teacher, teacher leader, and instructional coach, Matt McLeod brings over 15 years of experience in student and adult learning and teaching strategies. Matt works to improve teachers’ content knowledge and hone their instructional strategies to help develop their students into true mathematicians. He is highly experienced in designing and providing professional development to teachers and district leaders in mathematical content, curriculum, and pedagogical best practices. Much of his work focuses on the Common Core State Standards for Mathematics, including the Implementing the Mathematical Practice Standards website and the Mathematical Practices Institute. In this post, he reflects on his work as part of a team that is studying the impact of providing professional development and resources to teachers who are using EDC's CME Project Algebra 1 curriculum for the first time.

For many years, when people asked “What do you do?” my response often brought a gasp followed by “I could never do that” or “You must have the patience of a saint” or something along those lines. I teach middle school mathematics. Or at least, I used to.  It is not a world-changing revelation to say that teaching is a very special profession. In my transition from working with students to working with teachers, I found that even among teachers, the desire and calling to be a math teacher was regarded as even more unusual. Many teachers are intimidated at the prospect of teaching math. Being my curious self, I wondered why. Through very informal research over several years, I have discovered a few causes:

  • The way these teachers were taught during their school years
  • The way teacher preparation programs emphasize (or minimize) the importance of a teacher’s fluency with mathematical thinking
  • Our perception of incoming students’ ability (or supposed lack thereof) and willingness to do mathematics
  • Our curricular materials

There are some seemingly “easy” fixes—curricular materials, for example—to this situation, but no one fix by itself will be a cure. A combination of approaches could, however, have a very significant impact.

Prior to joining EDC, I was part of a team that worked with many teachers over the course of 4 years in a large urban district. My role was to support the teachers in their classrooms as they taught EDC’s CME Project Algebra 1 to Grade 8 students. The CME Project curriculum was written with a focus on Mathematical Habits of Mind—specialized ways of approaching mathematical problems and thinking about mathematical concepts that resemble the ways employed by mathematicians—and presents the material in a way that is significantly different from what most teachers have experienced. The Habits of Mind used in the writing of the CME Project are very closely connected (some would say influenced) the Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSS-M). Anecdotally, we collected a great deal of evidence that the use of this curriculum influenced teachers’ own mathematical understanding and their instructional methods even outside of Algebra class. Largely out of this work, our three-year, Institute of Education Sciences (IES)-funded Learning and Teaching Algebra (LTA) study was born.

In the LTA study, we are working with teachers who are using CME Project Algebra 1 for the first time. We provide teachers with professional development related to the curriculum, as well as some print resources that we designed to ease implementation issues. Because of the intensive focus on Habits of Mind in the curriculum, the professional development also works to improve teachers’ understanding of the Habits of Mind/SMP which in turn, we hope, influences their use of these Habits in their own mathematical approaches and their teaching. Our findings are preliminary—we are now in Year 2 of the study—but we seem to be seeing some positive effects from LTA’s multi-pronged approach.

To date, we have gathered qualitative data from teachers to measure their use of the Habits of Mind/SMP in their approach to mathematics, as well as their teaching. Much of this is done through formal and informal interviews with teachers. We are also using an assessment given at the beginning and the end of the year to measure teachers’ use of Habits of Mind. While these findings are, again, preliminary, we are hearing from teachers that through their use of CME Project and their participation in the professional development, they know and can do algebra in a new way. They are able to make connections among topics and now have a better understanding of the derivation and the underlying mathematics in the algorithms they have used for many years. This improved fluency in algebra enables them to better understand a student’s novel approach to a problem in a way that allows them to either validate the process or redirect the student. Many teachers have also told us that the Habits of Mind have “bled over” to their instruction in other classes which, they report, has improved student achievement in those classes as well.

We recognize that improving teacher understanding of mathematics and providing excellent curricular materials is not a novel or groundbreaking approach to raising student achievement in mathematics. Yet we have found that the idea of focusing both of these instructional supports on the Habits of Mind is largely new to most teachers and districts. By bringing these Habits of Mind and the SMP to the forefront of teaching mathematics, we are hopeful that our students will become mathematical thinkers who feel confident in their ability to approach new problems and topics and who are on their way to being the next generation of innovators and leaders.