School News

Got Problems? We have a curriculum for that: Fayerweather’s journey to a problem-based math curriculum

From Michael Bowler, Assistant Head of School
I bet most of us adults have some pretty strong memories (and maybe even emotions) about our math education growing up. Mine, thankfully, were mostly positive. I remember I had the ability to compute fast, and I loved the satisfaction of getting the “right answer.” My teachers noticed these qualities in me, and I remember knowing they (and my peers) thought I was “smart” and “strong” as a math student. In some ways, these positive messages and my quest to solve things correctly propelled me to success; I was a straight “A” student, and I had the opportunity to take Calculus in high school (which was not as commonplace as it is now). As I ventured off to college, I thought that maybe I would even be a math major. 
But as I look back on my math experience now, from an educator’s lens, I notice how I was conditioned to be a risk-averse, surface-level mathematician. 

By the time I made it to college, I had internalized being “smart” and “good at math” so much that I often avoided math challenges and difficult problems because they seemed to directly challenge my self-identity. What if I couldn’t solve this problem? What would people think of me now? What would I think about my own “ability” and “talent” as a mathematician? I often chose to take the easier path in math class and stayed in my comfort zone as a result. And when the going got tough in college, I abandoned my thoughts of being a math major and charted a different course. I had never learned the mindset of what it meant to truly problem solve and tackle new challenges, to struggle through a developing mathematical idea. 

I remember my first college-level math class quite well. My professor had a reputation as a “quirky” mathematician, one who would smear chalk all over his own face while contemplating a good mathematical problem. The chalk smearing certainly struck me as different, but the real difference was how focused the class was on the conceptual understanding of mathematics. The discussions dove deeply into the concepts and thinking/theory behind the different ways we “found the right answer.” I felt like a fish out of water. I just wanted the professor to tell me how to solve it, to give me the right algorithm, to point me toward how to get the “right answer.” I now realize, my conceptual understanding was weak because of how I was taught and conditioned in school. I didn’t quite internalize that at the time, but instead insisted I just wasn’t as “smart” at math as I thought. I struggled through the class but managed to earn a “B,” but I would never take another math class again. 

I started this piece by sharing my own story and journey with mathematics, because I feel like it highlights why I am so excited about Illustrative Mathematics, the new math curriculum we are implementing here at Fayerweather. Last year, with the assistance of Dr. Polina Sabinin, Associate Professor of Mathematics at Bridgewater State University, we conducted a formal math review that had us examining our own, as well as new math curricula. But also, just as importantly, this review had us really thinking about math teaching and learning here at Fayerweather. When that process concluded, we decided to adopt Illustrative Mathematics. We will have opportunities to share more with you about this curriculum, but for now, let me highlight why I wish I had a math program like Illustrative Math when I was this age. Our selection of Illustrative Mathematics came down to several key reasons:
  • It is a Problem-Based Curriculum that fits with our beliefs around math teaching and learning and our progressive approach to education in general. You can read more about its design principles here. I want to highlight just a few important points related to those design principles:
    • All Students are Capable Learners of Mathematics- 
      • Developed with an equity lens at its heart, IM (Illustrative Mathematics) believes that, “Mathematics ability is a function of opportunity, experience, and effort– not innate intelligence. Mathematics teaching and learning cultivate mathematics abilities. All students are capable of participating and achieving in mathematics, and all deserve support to achieve at the highest level.”
      • I could have benefited greatly from this lesson early in my math education!
    • Learning Mathematics by Doing Mathematics
      • “Students learn mathematics as a result of solving problems. Mathematical ideas are the outcomes of the problem-solving experience rather than the elements that must be taught before problem-solving” (Hiebert et al., 1996). 
      • A problem-based instructional framework supports teachers in structuring lessons so students are the ones doing the problem-solving to learn the mathematics. We believe in this approach at Fayerweather in our other subjects, and it was great to find a math program to match.
    • A Problem-Based Approach
      • William McCallum, University Distinguished Professor of Mathematics at the University of Arizona and one of the creators of Illustrative Mathematics, spoke about how this approach is not just about aligning with a philosophy but that it is research-based. He notes- “The National Academies publication How People Learn shows that student learning is more robust if students first have a chance to grapple with a problem before hearing explicit instruction on it. Both components, and the order in which they happen, are important.”
      • That is why Illustrative Math flips the traditional math pyramid of learning and starts with students exploring and problem-solving (see Figures 1.1 and 1.2 below). In this way, students start by building their own conceptual understanding of mathematics before progressing to the algorithm. 
      • I wonder how much more satisfaction I would have found as a math learner if I were used to solving and tackling unfamiliar problems, not to mention the conceptual understanding I would have built. Perhaps my math education would have taken a different turn!
  • Continuity/Alignment: IM is one of the few K-8 curricula. It allows us to keep our pedagogical approach consistent across grades, use common language and ensure stronger learning progressions. The need for stronger alignment across grades was a noticing of the math review committee.
  • Extremely Well Reviewed: ED Reports, which does independent reviews of math curricula, has Illustrative Math’s K-8 program earning its highest marks (categories of Focus and Coherence, Rigor and Mathematical Practices, and Usability).
  • Created by a non-profit organization of mathematicians and math educators, not a publishing company with a focus on equity and representation in the curricula as a core goal

I am excited to talk more about Illustrative Math here at Fayerweather at our parent education event over Zoom on Wednesday, October 26th from 6:30-8:00 pm, where I will be joined by Jennifer Hawkins, a certified Illustrative Math trainer who has worked on developing the curriculum itself and is helping our faculty implement it in their classrooms this year. We also hope to host a “Math Morning” in March to invite parents in to see some of the math learning in action and try it out themselves. Like any new practice, we are learning and growing as a staff as we take on something new, but the possibilities for math learning at Fayerweather are exciting!

Michael Bowler 
Assistant Head of School

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Fayerweather Street School | 765 Concord Avenue, Cambridge, MA 02138 | 617-876-4746
Fayerweather is a private PreK, kindergarten, elementary and middle school. We engage each child’s intellect.