Courtney Humphreys an elementary math coach with the Memphis Teacher Residency program, a faith-based program that trains teachers to work in high-needs urban schools.
As a professor of the elementary math methods course for the Memphis Teacher Residency, I have a number of mantras that I tend to repeat throughout the course. This year, I have found myself repeating over and over this statement: “Kids can think.” It sounds so simple; yet, it is astounding to me the ways that our math classrooms can fail to demonstrate our belief in our students’ ability to think. David Perkins says, “Learning is a consequence of thinking.” I have plenty to learn about teaching math effectively, but this I do know: In order for students to learn math, they must have the opportunity to think about math.
Our school district in Memphis is in the process of adopting the Eureka Math curriculum, and I am excited about the potential the curriculum offers to create opportunities for student thinking in elementary math classrooms. But it is early in the implementation process, and many teachers would attest that the past few months have been equal parts confusing, frustrating, and exhausting. Change takes time, and this curriculum requires a fundamental shift that some teachers have never been asked to make. Some teachers have been expected to adhere to an “I do, we do, you do” framework, where the teacher models a procedure explicitly and students then pick up their pencils and practice applying those steps. Such a formulaic approach to math unfortunately overemphasizes computation and deemphasizes conceptual understanding and problem-solving, key components of mathematical understanding that are abandoned far too often.
I appreciate that the Eureka curriculum emphasizes all three aspects of mathematical understanding and gives students the opportunity to see math (another one of my mantras!) in ways that make sense to them. For example, I don’t remember as a student ever truly understanding what it meant to multiply a fraction by a fraction. I just knew that if I saw “1/2 x 2/3”, I would multiply the numerators and denominators to get my answer. My “answer-getting” required very little thinking; I was simply repeating the steps my teacher had taught me. I believe the Eureka curriculum can foster environments in our classrooms where my former, solely procedural explanation for fraction multiplication will no longer suffice.
I saw the power of representing fractions visually in my elementary math methods course recently. Borrowing from a Teaching Children Mathematics article (“Engaging Students with Multiple Models”) and a 3rd grade Eureka lesson (Module 5, lesson 4), adult learners represented fractions by pouring water into pitchers, walking around a “baseball diamond” taped to the floor, and manipulating fraction strips to locate fractions on a number line. (You’ve never seen adults have so much fun with fractions!) Students’ post-class reflections were profound, with many noting that they had never truly understood what a fraction was until those experiences in class. We do our students a disservice when we don’t give them the opportunity to grapple with the why, to let them notice patterns, represent concepts visually, and different strategies — even if we have to learn those things alongside them.
It can be difficult to teach in a way that most of us were not taught; it causes discomfort and anxiety, but that doesn’t mean it’s not right. I understand that it is uncomfortable and even scary as a teacher to not understand a math concept that we are supposed to teach our students. That fear can drive us to one of two places: it can move us to seek help and to take time to get what we need, or it can move us to a place of denial — where we claim that the curriculum must not be working and that our kids just can’t do it. I am hopeful because I see teachers in Memphis who are choosing to respond to that fear as learners, not as ones who are supposed to have all the answers immediately. As John Cotton Dana said, “Who dares to teach must never cease to learn.” Certainly curriculum alone is not the answer; ultimately, effective teaching is — but I do believe the Eureka curriculum can be part of the solution. I don’t imagine it will be easy, but it’s certainly important and worth it. Because after all, kids in Memphis can think.