Welcome to my blog, a way to present ideas, reflections, and observations with the school community and beyond. I blog on a regular basis, commenting on a thought-provoking experience, a significant development in education, and news of student and teacher work here at Catlin Gabel. My goal is to make you think, provoke a reaction, elicit diverse points of view, and affirm your faith in our school's mission. I hope you'll share with me and other readers any reactions you may have to my posts.
The Math Phenomenon
Catlin Gabel students take math seriously – and do well. While standardized measures are inherently flawed, outcomes here are impressive. Our students scored in the top quartile on the SAT and ACT math sections compared to students in 38 independent schools in last year’s nationwide INDEX benchmark report. The average BC Calculus score for students over the past 5 years is 4.87 (out of 5), and Catlin Gabel graduates universally report they are well prepared and ready for high-level mathematics in college.
But here, as with every school in which I have taught or led, mathematics is the academic subject that draws the most attention. Responses on our bi-annual community survey and an informal check-in with division heads show that we receive more questions about math than any other subject. Why is that? Is math so much more important than science or English that it deserves an inordinate amount of student focus, parent conference time, and curriculum revision? In talking with colleagues and parents about this, various reasons come to mind:
- Math has a right/wrong clarity (although that may not necessarily indicate understanding)
- Math teaching methods have changed since most parents were in school
- Math is based on repeating patterns; mastering each skill or concept affects future success
- Students are prone to adopt a fixed mindset about math more than in other subjects
- Every standardized test students take includes substantial math sections
- Math is often a “tracked” subject, and placement is visible and valued (like varsity sports)
- The most selective colleges implicitly promote the importance of completing calculus
- Math is related to important fields such as computing, coding, engineering, and science
- Parents project their own math experience and anxiety on to children
There are other reasons, of course, but these may be enough to illustrate why math curriculum and pedagogy is subject to so much discussion and analysis. In recent years, we have invested innumerable hours into examination and improvement of the math program, in a proactive effort to design a curriculum built for the future. Our goal is to ensure mastery of essential skills and concepts, while fostering a growth mindset and helping students to reach their potential as mathematical thinkers. Led by Courtney Nelson, Kenny Nguyen, and Shannon Rush, our math teachers have revised the PS-12 curriculum considerably since 2014. Reflecting the best thinking of experts such as Cathy Fosnot of the University of Connecticut and Jo Boaler of the Stanford Graduate School of Education, and frameworks such as First Steps, Stepping Stones, and Big Ideas that connect the PS-5 and 6-12 curriculum, our math learning objectives are more closely aligned and self-reinforcing than ever.
Perhaps the biggest challenge facing math instruction, here and in all schools, is the tension among readiness, mastery, and content coverage. Do we keep pushing students into the next concept, even if they haven’t mastered the previous one? Or do we focus on mastery and introduce next topics when students are ready for them? This creates a more solid foundation but may mean that students don’t “get as far” in the math sequence as families or colleges would hope. Grade-level benchmarks, ongoing formative and summative assessments, and teacher team conversations help us to address this fundamental tension in a dynamic way.
What we are learning, and we hope the community understands, is that there is no perfect math curriculum, and that methods need to evolve and be as diverse as the students we serve. In keeping with our mission to teach the whole child, we are not seeking to develop math automatons, but to help every child believe they can learn and enjoy math. We want to avoid a disproportionate emphasis on math content and rote application of algorithms and ensure that we also are teaching applied problem-solving, conceptual understanding, and creative math thinking. Advanced math should not just be for those who can finish the problem fastest; it also should be for math thinkers who generate creative solutions and ask complex questions. Statistics classes should be for every student interested in mathematical thinking and application, not just for students who don’t take calculus. Achievement in math should not be measured primarily by content recall on tests; it also should be measured by a student’s ability to transfer what they know to novel questions or problems.
I applaud our math teachers for their ongoing efforts to assess and improve the curriculum and support all students. They are exploring new ways to assess and report on mastery of math skills and concepts, increasing math support services across divisions, and aligning objectives across the grades while making individual decisions about how to best serve their specific classes and students.
Are we there yet? No. There is more work to do to realize our vision for the math experience of students at Catlin Gabel School. Informed by data, designed in collaboration, and reflecting modern math thinking in and beyond our school, we will continue to improve our program. The good news is that this is not your parents’ math curriculum; and our students are better for it.
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