June 2024
Ted Coe and Catherine A. Roberts
Catherine: After seven years as the executive director at the American Mathematical Society and a short stint at the Consortium for Mathematics and Its Applications, I am now getting back into collegiate teaching. As an applied mathematician keenly interested in mathematics education, I want to reacquaint myself with the broader education landscape. There are lots of voices clamoring to be heard. I thought it might be helpful to hear from an expert on what is going on in secondary math education, so I invited Ted Coe to address a few of my questions. First, I’ll ask Ted to introduce himself.
Ted: Thank you for the invitation, Catherine. Throughout my career I’ve had the opportunity to serve in many roles across different sectors – it’s been an adventure! I’ve been a high school mathematics teacher, a community college professor and chair, an assistant dean, the mathematics director at Achieve (a DC-based independent, nonpartisan, nonprofit education reform organization), and I’m currently the VP of Academic Advocacy for Mathematics at NWEA. I also have the privilege of serving as the treasurer of the Conference Board of the Mathematical Sciences and I support the work of Charles A. Dana Center on the Launch Years project to improve transitions between high school and college.
These days, I am often involved in working with state teams to examine and rethink the mathematics students encounter in the transition space from high school to college. We bring together representatives from all education sectors to try to figure out how we can better meet our students’ needs. It’s wonderful yet challenging work.
Catherine: Thanks, and welcome! Perhaps we could start with the work going on in various U.S. states regarding high school math pathways? What is this? And what do you think faculty in higher education ought to be paying attention to?
Ted: Sure! One of the most exciting things is an attempt to better align secondary mathematical experiences to students’ future careers. It’s typically not an easy discussion. There is a desire at all levels to connect students to mathematics that is engaging and relevant, yet there is also a healthy concern that modifications to high school programs may leave students unprepared as they transition to postsecondary endeavors. Will they be ready for the demands of college classes? When should students be allowed to choose which classes they take? What happens if students change their minds after they have started down a specific pathway?
Many colleges and universities used to require that all students satisfy a math requirement that was generally some version of College Algebra. However, a shift that has happened in many higher education institutions is the recognition that College Algebra is not necessarily seen as the best default math requirement. There are better options that better match mathematics requirements to student programs and interests and serve as more appropriate terminal math course experiences.
Catherine: It seems to me that this shift has been going on for decades!
Ted: Yes, precisely. This has been a change that has taken place over many years, and there have been some wonderful curricular examples over the years that connected content with context in meaningful ways. The 2015 CBMS Survey, for example, highlighted how 58% of two-year colleges had implemented some forms of math pathways. I can only imagine that number has grown significantly since then. But the tricky issue now is to consider how these evolving changes in higher education create issues and opportunities for high school. If college students no longer need College Algebra, we need to have conversations about how much algebra every student needs to see in high school. What algebra should all students experience before digging into the algebra that is more specialized for students heading to Calculus? What different mathematics might make better use of that time? These conversations get messy, as you can imagine. CBMS helped pull state teams together a few years ago. The Launch Years work of the Dana Center continues to provide support to states as they navigate these waters. Some states have made a lot of progress, although many are still in the early stages. Each state, though, is heading in a different-ish direction, so at some point the field needs to get together and find points of consensus.
Catherine: Back in the early 1990s during the calculus reform movement, I remember when I was searching for a faculty position that my potential future colleagues would ask me which calculus textbook I preferred. I viewed that question as a way to determine if I would fit in as a “traditionalist” or a “reformist”. Now, it seems like controversies are swirling around what our gen ed math courses ought to be – and where College Algebra lives in light of statistics, data science, math modeling, and other approaches to quantitative thinking and learning. And that this is really boiling at the interface between high schools and colleges.
Ted: I find the conversations I’m involved with to be less about College Algebra or not, and more about determining what options should students have. I remember those calculus reform years as well, as it was when I was starting out as a high school teacher, but I’d say the work on pathways is less about polarization and taking sides than it is about how to navigate the mess of issues that arise when systems try to work together. There are challenges that arise when high schools want to make changes to curriculum. Their students go to many different higher education institutions, and so there are mixed signals on what matters. Some colleges recognize different courses, while others do not. When higher education institutions don’t agree, it can cause challenges for high schools.
Calculus surely doesn’t have a lock on rigor in mathematics, but it is still unclear on the high school side to say when some other non-calculus pathway course is or is not rigorous. With the support of higher education faculty, we can answer these questions. Ohio did a pretty remarkable thing on this issue when they brought together representatives from K-12 and higher education to create an Ohio definition of rigor. Ideally, we need state teams made up of members across the education sectors working together to clarify what makes for a respectable and valuable math experience.
Much of the work in states comes back to the role of Algebra 2. It’s tempting to think of that course in terms of our own historical experiences, but it’s always eye-opening when those who do not teach the course examine the course standards and textbooks. It’s important that we focus more on actual content than course names. Washington State is doing some creative work rethinking Algebra 2, which will be interesting to watch. It is in a pilot phase right now.
Readers might take just a moment to reflect on the general notion of college readiness. What did it mean to be college ready in 2010? What will it mean to be college ready in 2030? If those two are different, do you know if your state has made progress in bridging the gap? Everyone who cares about mathematics education, all the different segments, need to work more intently and directly with each other.
Catherine: Something that has fascinated me is seeing such a transformation in the ways we teach and learn. I remember thinking as a college math professor, I ought to be aware of the evidence-based research that could make my teaching more effective. Can you say a little bit about this?
Ted: While many may be looking for some silver bullet, a one-size-fits-all perfect pedagogy, there are too many factors to ever be able to say one thing will always work best. Teaching is both a science and an art, after all. Some pedagogies are better in some situations than others. That said, the learning sciences (in math education and other areas) have helped us to understand the importance of things we might overlook. I like to remember the claim in the national academies’ How People Learn II that “Quite literally, it is neurobiologically impossible to think deeply about or remember information about which one has had no emotion because the healthy brain does not waste energy processing information that does not matter to the individual.” In the higher education space, we know that active learning is effective [see CBMS statement]. NCTM’s Effective Mathematics Teaching Practices apply to all levels of teaching. There’s one noteworthy shift happening in K-12 focused on Peter Liljedahl’s “Building Thinking Classrooms” At CBMS we are preparing to issue a call for the National Academies to create a Grades 9-14 math framework to address issues around content, pedagogy, and technology. It’s an exciting time.
Catherine: Well, clearly there is a lot for me to be paying attention to, Ted. I really appreciate this primer on the secondary school math education landscape. What is your wish for anyone reading this column?
Ted: There’s a lot going on out there, and it’s messy, complicated work. After all, it isn’t easy to change things that are deeply entrenched across different systems. I hope our readers keep an open mind, regularly talk to people outside of their regular circles, and surface the wide areas of agreement that exist. I also hope they check out the work that is happening (or has happened) in their states, look for ways to get involved, and always keep the best interests of students at the forefront.
Catherine: Thank you so much, Ted. We all really appreciate your time and insights!