By David Bressoud @dbressoud

Equity. What does it mean in the context of mathematics instruction? No one argues that all students have the same opportunities to learn. Nevertheless, there is a widespread belief, common among mathematicians as well as the population at large, that there is nothing wrong with what we teach or how we teach it. If students do not learn mathematics, then the fault lies with them. This myth is exploded in an important report from Pamela Burdman of the Just Equations project of the Opportunity Institute, The Mathematics of Opportunity: Rethinking the Role of Math in Educational Equity.

The report is structured around three sections. The opening describes the critical role that mathematics plays within the educational progression and the expectation of failure it too often engenders. In and of itself, failure is neutral. Every successful mathematician has failed more often than succeeded. Those who are successful know how to work with failure. But that is not the message of most mathematics instruction. As Burdman writes, “The way mathematics is typically taught and tested, as well as the very requirements students are expected to meet, appear designed to winnow students out, effectively surrendering to the notion that only a few students are ‘math worthy’.” An expectation of failure can be devastating. This is illustrated in the sidebar case of Javier Cabral for whom a bad experience with Algebra I in 7th grade set him up for repeated failures in algebra, blocking his route to a college degree. Burdman quotes Jo Boaler, “Mathematics, more than any other subject, has the power to crush students’ spirits.” (Boaler, 2016, p. x)

The second section of this report lays out three key problem areas. The first describes common misconceptions: that math ability is innate and some people are just not good at math, that there is only one way to correctly solve any math problem with no room left for creativity or expression, and that speed and accuracy are what really matter when doing mathematics. The expectation that there are some students who will never succeed in mathematics is damaging when the student believes it of him- or herself. It can destroy generations of students when a teacher, school, or district embraces it. Mathematicians know the falsity of the second claim. Mathematics does impose structure and rules, but such frameworks can promote creativity. We see this in music, and the strong connection between mathematical and musical ability should not be surprising. The last misconception is particularly pernicious because it is what we test, but it is not what we value once the course has ended and our students need to use their mathematical knowledge.

The second problem revolves around existing inequities, including poorly resourced schools, differential access to strong curricula and good teaching, income inequality, and the nature of the educational support from peers, family, and community. These inequities foster an environment where the common misconceptions flourish.

The third problem area lies in how we use mathematics as a marker of pedigree. As Dan Teague pointed out in the workshop on “The Role of Calculus in the Transition from High School to College Mathematics,” (see my June 2016 column for more on this workshop), a student who wants to go to Duke to study French literature knows that he or she needs to take and do well in AP Calculus. See also my September 2017 column, “Mathematics as Peacock Feathers.”  Across the spectrum, we find that—whenever college students are forced to back up and retake a course they thought they had successfully navigated in high school—the result is tremendous harm to self-esteem and motivation to continue.

In the final section of the report, Burdman lays out four areas where work is needed if we are to advance equity. The first is content. We need to seriously rethink what mathematics students really need. Traditionally, we have either directed students into dead end courses or pushed them along the pathway to calculus until they fall off the tracks. This has been directly responsible for the strong reaction from Hacker and others, arguing that we should abolish any requirement for Algebra II (see Bressoud, 2016). These critics are wrong, but what is taught and how it is packaged requires very serious rethinking.

The second area for work lies in how we teach. This is such a huge subject, one on which I have written often, that I will simply point to it.

The third is assessment. Speed and accuracy have roles to play. But if those are all we really care about, then we do our students a serious disservice. Each year, I have put less emphasis on timed tests, more on assignments and projects. They are hard to assess, especially in situations where large numbers of students must be tested. But the AP Calculus exams, written for 450,000 students, do a much better job of this than many math departments (see Tallman et al, 2016). The fact that this task is difficult does not mean we should abandon hope.

And, finally, there are the readiness structures and support. These encompass high school graduation requirements, college demands, and placement procedures. Both Algebra I in eighth grade and Algebra II as a prerequisite for graduation have proven problematic. Algebra is a collection of tools, marvelously refined in the late sixteenth through early seventeenth centuries to replace hundreds of ad hoc strategies for solving real problems. It is important for students to know how to use these tools, but it is equally important that they are given the opportunity to build and create with them. At the same time, we need to rethink which of these tools are truly essential.

At the college level, I have written about the flaws in many of our expectations and placement programs (see First do No Harm, January 2012). Traditional remediation seldom accomplishes the desired result. There is good news. Pathways programs that direct students toward statistics or quantitative reasoning are gaining wider acceptance. Prerequisites are being replace by co-requisites in a variety of innovative approaches. Universities are re-imagining their support structures for at-risk students.

The need to promote equity is real. This report does a helpful job of laying out the issues and challenges. We are making progress. There is much more to do.

Read Bressoud’s Launchings archive.

References

Boaler, J. (2016). Mathematical mindsets: unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco, CA: Jossey-Bass

Bressoud, D.M. (2016). Book Review of The Math Myth and Other STEM Delusions. Notices of the AMS. 63 (10): 1181–1183. www.ams.org/publications/journals/notices/201610/rnoti-p1181.pdf

Burdman, P. (2018). The Mathematics of opportunity: rethinking the role of math in educational equity. Berkeley, CA: Just Equations justequations.org/resource/the-mathematics-of-opportunity-report/

Tallman, M.A., Carlson, M.P., Bressoud, D.M., and Pearson, J.M. (2016). A Characterization of Calculus I Final Exams in U.S. Colleges and Universities. International Journal of Research in Undergraduate Mathematics Education. 2(1) 105–133.