Remediation, Acceleration, and Enrichment

Students will inevitably arrive at your school with less than the appropriate level of mathematics. To help these students reach their goals, it’s important to be flexible about placement and to think creatively about remediating and accelerating their learning.  

For middle and high schools, schools should provide students with every chance to get to calculus: it’s true that colleges do favor it. This applies especially to students from historically marginalized communities, who may need extra encouragement to study in STEM fields. Parents should understand that algebra lays the foundation for high school calculus—and that high school mathematics lays the foundation for success in college—and also that accelerated learning holds some risks. If catchup is needed, you might guide students to take both geometry and algebra in the same academic year—or give them the option of taking geometry over the summer. For some schools, it is the norm to send students to third-party programs for the remediation of math skills. 

A condensed learning experience does not usually promote the same depth of understanding. Here again, conversations can be used to assess understanding: it is important to understand whether students have truly advanced in their understanding, or if they are merely mimicking higher level procedures.  

For students who are already well prepared to reach calculus, the question is acceleration and enrichment. Admission officers may be excited to enroll precocious math students, but sometimes their school lacks the program to help these students reach their higher-level mathematical goals. Many 9–12 independent schools offer college-level courses beyond calculus, and some have agreements with nearby colleges that allow students to take advanced classes. But if your school does not have a plan to accommodate accelerated students, it’s critical to communicate with admissions in order toto avoid under-serving students and disappointing parents. 

A Note about Social Emotional Development 

One side-effect of acceleration is that younger students may find themselves in courses with much older students, and socialization may be difficult. Often parents see the prestige of having their child in a higher-level math, but fail todo consider the need for growth in communication, collaboration, and risk-taking skills.  Accelerating a student too quickly could hinder their self-confidence, self-efficacy, and growth mindset (Bi, Buontempo, &, DiSalvo, 2022). In these cases, schools can find ways to enrich math programs with a variety of in-depth enrichment experiences such as mathematics competitions, explorations of other areas of mathematics like Set or Number Theory, or activities that focus on coding skills. By offering alternative enrichment opportunities and STEM-based clubs, schools also send the message that depth and variety of programming is valued and prioritized in the education being delivered. 

The Race to Calculus 

When I was in high school, the only students who took calculus were those who clearly excelled in math and enjoyed studying it—but today, most independent school students will take calculus. I even know of some schools that have added calculus as a graduation requirement.  

The reasoning and motivation behind why students take calculus has changed. In a survey of Rutgers students, 80% of respondents who took calculus said they took calculus in high school because “it looks good on a college application.” (Ahluwalia & Rosenstein, 2014). Calculus is used as a gatekeeper and seen as proof of rigor in a student’s academic preparation: it’s a line in the sand that somehow “proves” an applicant can work successfully in college. 

Proof of what?

This “proof” is not as indisputable as some passionate parents might believe. Key findings of a 2022 JustEquations report clarify the importance of calculus. “Apart from a select number of STEM-focused institutions, like the California Institute of Technology, the Massachusetts Institute of Technology and Harvey Mudd College, calculus is not a requirement for college” (Bauld, 2023). High school calculus doesn’t guarantee advanced math standing in college—and some universities weigh other advanced math courses equally to calculus. Yet, parents who seek every advantage in the college process often push their students to take calculus, with or without a college counselor’s support. A report from the Charles A. Dana Center, a well-respected educational think-tank, said that high schools currently offer a “narrow pathway toward calculus …[that] fails to serve most students” but nevertheless “sends a clear signal to high schools, parents, and students that such courses are the norm and most prized.” (Dana Center, 2020).  

This lack of alternative pathways in high school math is an unfortunate reality. Schools should offer multiple pathways to, and levels of, calculus which can be included on a transcript.  And some students —especially those for whom STEM fields are unlikely pursuits— should be offered a larger variety of math coursework including logic, data analysis, statistics, data science and coding. It is easy to imagine how this same thinking might be applied in other academic disciplines as well: students should be offered more options that match their strengths and depth of understanding, instead of simply being “tracked” to pursue a common transcript that doesn’t serve them best.