Building Consensus Around Foundational Mathematics

Policy decisions about mathematics education need to be rooted in the purposes of teaching math. The reason math plays a central role in the K–12 curriculum and shows up in most college graduation requirements is not to ensure that every student will become a mathematician or enter math-intensive fields. It’s to develop mathematical reasoning skills that students need to understand their world and make good decisions in their professions and as consumers and citizens. 

Students can build on those skills in a variety of ways, depending on their interests and aspirations. Some will go on to become mathematicians or STEM professionals, but the majority—roughly three-quarters—will not. Thus, the design and delivery of math education needs to support more than one possible student trajectory—as does any evaluation of its effectiveness. 

My last blog explored the range of viewpoints about math-related policies, including California’s draft math framework. I highlighted two groups to exemplify the spectrum of valid concerns: 

• University STEM faculty rightly worried about preparing more students—particularly students from historically excluded groups—to enter their disciplines; and 
• K–12 math teachers understandably troubled by the large numbers of students who are turned off by traditional math courses and searching for new content and pedagogy to make math more inviting and engaging. 

I challenged the assumption that the two groups’ priorities are dichotomous. Increasingly, even mathematics faculty who want students to be prepared for STEM fields recognize that making math classes more meaningful and relevant—without watering down the content—can actually enhance students’ ability to acquire those skills in deeper ways. “We need to move away from boring kids to death and then using that as a filter for who goes into STEM,” notes Kate Stevenson of California State University, Northridge, who has worked with the Los Angeles Unified School District to introduce a new course for juniors and seniors.  

Finding strategies to engage and inspire students is simply good teaching. Doing so needn’t be a recipe for removing rigor from mathematics (though we should be rigorous about defining rigor). Such strategies may be especially important for historically marginalized students. As Stevenson and others have noted, students who haven’t traditionally felt supported by the education system are likely to have less tolerance for challenging but tedious courses where the relevance or payoff isn’t apparent. 

But ensuring that the needs of all students are addressed may require clarity around foundational math. What are the core skills needed by all students, regardless of whether they’ll ultimately pursue a STEM field? The answers do not always align with course titles. 

Six years ago, for example, California State University faculty wrestled with how to define foundational quantitative reasoning. To determine the threshold for incoming students to “guarantee the mathematical skills necessary for non–algebra-intensive majors, quantitative reasoning skills for life, and a very narrow set of skills and knowledge … necessary for a liberal arts education,” a task force co-chaired by Stevenson weighed numerous pieces of evidence, including: 

• An analysis of skills historically prioritized in CSU’s own placement exam for entering students. 
• Research studies, reports from mathematics and statistics professional associations, and expectations for various STEM and non-STEM professions (especially nursing, teaching, law enforcement, and business).

The placement exam analysis revealed “a decreased emphasis on second-year algebra and an increased focus on deeper mastery of the skills developed in Algebra I and Geometry.” To be prepared for statistics, the task force said, students should be able to “evaluate algebraic expressions in order to calculate numerical summary statistics, test statistics, confidence intervals, z-scores, and regression coefficients in statistics.” 

Learning financial models, they noted, “requires the skills found in Algebra 1 or Integrated Math 1.” Students should also be able to “evaluate algebraic expressions, compute compound interest or … solve a linear equation in one variable,” but those in non–algebra-intensive fields needn’t be able to solve for time in a compound interest formula using logarithms, they added.

Importantly, the report did not change CSU’s admissions requirements—the system still required students to complete Algebra 2 in high school. Rather, it pointed to the proficiency level students needed to demonstrate to be successful in the system. 

An earlier report, by the National Center for Education and the Economy, examined the skills needed for first-year community college students and had a similar finding: Outside of STEM majors, most students do not need the content of second-year algebra. 

“A substantial part of the high school mathematics we teach is mathematics that most students do not need, some of what is needed in the first year of community college is not taught in our schools, and the mathematics that is most needed by our community college students is actually elementary and middle school mathematics that is not learned well enough by many to enable them to succeed in community college,” the authors observed.

More recently, in 2018, a report on high school math by the National Council of Teachers of Mathematics said, “Teachers find it difficult to teach at the desired level of rigor, given the sheer amount of content that standards expect them to teach and their students to learn.” To focus the curriculum, the report proposed a set of “essential concepts” including number, algebra, functions, statistics and probability, and geometry and measurement, while eliminating some “obsolete legacy content,” particularly from Algebra II. Two to three years learning these concepts were to be followed by deeper exploration in specific areas of mathematics in the last year or two of high school. 

These efforts all prioritize a solid foundation in first-year algebra, an increased role for statistics, and—to varying degrees—a decreased emphasis on second-year algebra. Yet, exactly what Algebra II content to prioritize is a source of considerable disagreement, for several reasons: 

1. Not all students will use Algebra II topics in their future educational or career pursuits, yet some Algebra II content is important for students going on to take Calculus. This matters because some newly designed math courses assume an Algebra II prerequisite, while others do not. (In California, the vast majority of students taking these courses take Algebra II first.) 
2. It is reasonable to ask whether sophomore or junior year is too early for students to choose a non-Calculus path by skipping Algebra II. Despite the opportunity to engage students in statistics and other relevant math, there are concerns about closing doors to certain majors, particularly at research universities. There is, however, general agreement that transparency around skipping Algebra II is important 
3. College faculty do not have a common understanding of where Algebra I leaves off and Algebra II begins and ends, not to mention the actual skills that most students acquire in those courses.  
4. There is little knowledge about how well newly developed math courses or sequences prepare students for education and careers. New options need further study. 

Regardless of what Algebra II content they most value, the educators I’ve connected with share a common goal: ensuring that math education opens, rather than closes off, educational opportunities for more students. They just don’t agree on how to achieve that—something I hope to explore in a future blog post.