Teaching Math in the Post-Covid World

Among math-related memes, the image of Mr. Incredible leaning over his son yelling “math is math!” is particularly memorable for many thanks to its pungent relatability. As high school mathematicians, Mr. Incredible’s passionate outburst might compel us to remember our parents communicating similar sentiments when we asked them for help with math as children; or, it might even remind us of our own moments of confusion and frustration today, when math teachers encourage us to use new methods to solve otherwise familiar problems. In any case, it’s clear: math isn’t just math, especially within educational contexts. Process matters, and the way we learn, arrive at, and procure new knowledge in mathematics reflects — and reinforces — broader educational aims. 

Math pedagogy — how and why the subject is taught — has been in the process of transformation in the United States. The last few decades have witnessed a general trend away from teaching models consisting almost entirely of lectures to those that prioritize collaboration and student-led exploration. The nature of problems, too, has changed. Where older questions might have required a student to demonstrate a skill directly (multiply x and y, take the derivative of f(x), etc), newer ones typically add a layer of complexity by requiring a student to apply said skills — whether that comes in the form of word problems, projects, or conceptual questions. However varied these newer approaches may be, much of the impetus behind them is to create math classrooms in which understanding is valued over simply getting the correct answers, a shift that educators hope will impart in students a capacity for problem-solving, critical thinking, creativity, and, most of all, a genuine curiosity about mathematics. 

The espousal of these ideals in math classrooms at Bush is clear. The very structure of our math classrooms — desks arranged in student-centered islands as opposed to teacher-centered rows — allows prospective families to infer the fact that Bush math students rarely endure class-long lectures. Rather, their classes are more often a mixture of collaborative exploration into new topics (through guided worksheets or other math resources like Desmos), individual and group practice, and project work, in addition to more traditional lectures. 

Yet, at the same time that educators have been thus tinkering with math pedagogy, Covid and the fallout of the pandemic have severely stunted math learning for students across the country. A report from the Center on Reinventing Public Education, for instance, indicates that, nationally, only 56 percent of fourth graders were performing at grade level in spring of 2023, compared to 69 percent in 2019. Echoing this pattern, a study from Brookings found that standardized test scores across grades 3-8 dropped significantly between 2019 and 2021, and, even more troublingly, that in that same time frame, the gap in such test scores between low-poverty and high-poverty elementary schools grew by 20 percent. 

Bush has experienced a degree of stagnation in math following the pandemic, an issue that the math department continues to address. This year especially, while student capability increases as the reverberation of the pandemic wane, the department has increased course load and rigor in an attempt to return to pre-Covid instruction. Importantly, it has endeavored to do so while remaining true to its tenets of progressive math education. Thus far, changes have been met with mixed reviews. Regardless of the sentiments, students across all math levels report a faster pace of learning, higher complexity of material, increased difficulty of tests, and, more generally, an elevated set of expectations as to what it looks like to excel in a math classroom. 

To better understand Bush’s math philosophy and the impacts of Covid on it, The Rambler interviewed Academic Dean Christine Miller and upper school math teacher Tom Bergeron. Both Christine and Tom say the overall diminishment in content mastery has been more temperate than might otherwise be expected. Christine adds, however, that Covid created larger disparities within student groups: “The kids who loved school found it as their salvation, and the kids who already didn’t like school then had a reason to not engage." Echoing this, Tom feels that the most profound slippage has not been a great decrease in content understanding, but rather that “student skills have been diminished,” like listening, note-taking, collaboration, and other traits vital in the classroom. 

Despite this, Christine finds that, today, Bush math is in a position to achieve increased fidelity to the curriculum that existed prior to the pandemic. Not only do students in the upper school exhibit a greater potential for learning today, she says, but Bush’s middle school arm of the math department has also reported that its 8th grade algebra class is currently covering more content than it has in the previous three years. 

The challenge now faced by the department is in striking the appropriate balance between how math is taught and how much content is delivered. To elucidate the issue, Christine makes a distinction between “part-to-whole” and “whole-to-part” approaches, where the former (and more traditional approach) involves directly instructing (lecturing) students in a set of skills that eventually build to a larger concept, and where the latter (and more progressive approach) involves the teacher first introducing a general concept and then guiding students through a series of problems, activities, and projects that build those necessary skills while simultaneously reinforcing the larger concept or idea. Each approach comes with its own strengths and weaknesses. The part-to-whole approach is inherently more efficient, but it carries the risk of never endowing students with a larger conceptual understanding of a topic. Conversely, the whole-to-part method ensures that, in a student’s mind, the skills necessarily lead to the concept, but this kind of instruction can fall short if the initial concept is simply too large to be understood on its own. Neither approach is singularly the solution, but rather a mix of the two is. As you increase the time spent on exploratory activities and projects, you sacrifice the volume of content that can be delivered to the student. Conversely, as you increase the time spent doing direct instruction, you sacrifice the valuable student skills and traits gained from the whole-to-part method: problem-solving, critical thinking, passion, and excitement. 

Ultimately, there is no right answer, and the proper balance for any institution rests in the why of learning math. Tom hopes that through high school math, students are primed in the style of discovery and confident in their ability to figure things out for themselves: “I want you to go off to college and not have to have your teacher tell you everything. I want you to be able to conceptually get into a topic and figure things out. That’s what a mathematician is,” he says. In this sense, then, math isn’t just something your teacher taught you, but rather a vehicle for lifelong cognitive skills that apply to all different kinds of disciplines. 

Moving forward, Christine says that the math department will continue to be receptive to feedback in search of the right balance in the classroom — and it’s likely that high school math departments across the country will likewise go through this same process of weighing the pros and cons of different teaching styles in search of said balance, especially in light of the Covid slippage. 

In such a rapidly transforming world as today, imparting in students the capacity for abstract, critical thinking through mathematics is a positive aim, and balancing that with the necessity of acquainting them with a broad wealth of mathematical skills will ensure that the process of learning math continues to have the same edifying effects that educators have so long preached that it should.