Rethinking Algebra II
By David Bressoud @dbressoud
David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College and Director of the Conference Board of the Mathematical Sciences
Amir Asghari has just posted a piece by me on "Learning to Teach." It is under Teaching Ideas at https://maths4maryams.org/mathed/. He has also translated it into Farsi.
In 2016, Andrew Hacker published his attack on Algebra II in The Math Myth and Other STEM Delusions. I responded in a review that appeared in the AMS Notices that fall. As I said in the opening paragraph of that review,
While there is much to dislike about Andrew Hacker’s book, it is too easy, especially for the audience of these Notices, to dismiss it and ignore the underlying issues. This book and similar attacks on the role of algebra arise from real structural problems within mathematics education. (Bressoud, 2016, p. 1181)
It is not just that Algebra II is too often poorly taught, as a collection of techniques to be memorized for solving problems that have no meaning for the students. Ideally, Algebra II should be a place students dig into and refine their expertise in the practice standards espoused by the Common Core:
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Especially in under-resourced schools and with at-risk students, the focus instead is on getting them through the tests. It is difficult to emphasize these practices when teachers are struggling to “cover” the long list of topics in this course. This is especially unfortunate when many typical Algebra II topics and procedures will never be seen or used again.
This gets to the crux of the problem with Algebra II. Students who will continue along the path toward calculus, especially those heading into STEM fields, will not only need familiarity with all of the topics in the class, they need a high degree of facility in their use. Those who are not headed toward calculus would benefit more from other mathematics.
One solution is to separate the students who are being prepared for a mathematically intensive career from those whose pathways are headed in a different direction, making Algebra II optional. But this runs counter to the attitude toward higher education in the United States, that no student should be blocked from most opportunities in higher education. As Mark Green has said,
You have a danger of people being limited throughout their lives by what math they got early on—or didn’t. There’s a lot of stuff that uses Algebra 2, and students who don’t take it may be unaware that they are limiting their options later on. On the other hand, it’s much better to have someone who genuinely understands modeling and quantitative reasoning and has a feeling for statistics than someone who took an Algebra 2 class but is totally bewildered by it. (as quoted in Burdman, 2015, p. 20)
What we need is an alternative version of Algebra II that more accurately addresses the needs of the students who are not headed toward calculus without closing off the possibility of eventually returning to this path. We also need higher education admission and placement policies that allow for such an alternative. As decades of experience have shown, the solution to getting students back onto a path toward calculus is not met by providing post-secondary remedial work that repeats the courses they missed but this time faster and louder. A few students manage to survive this gauntlet, but very few.
The most promising avenue toward solving the problem of Algebra II comes from a growing movement of people developing “pathways programs” for the last years of high school mathematics. A common feature is an alternative that emphasizes modeling, data, and statistics. This is not tracking. The alternatives are, or should be, equally rigorous routes through mathematics that more accurately meet the needs of the students who take them while providing all students with a basis that allows for options for future directions. Phil Daro and Harold Asturias have recently published an important report with the Just Equations project, Branching Out: Designing Math Pathways for Equity. It describes the rationale for these pathways, especially as an equity issue, and looks at several ongoing efforts to create solutions. In particular, it describes the pathways programs developed by the Oregon Department of Education, the Escondido Unified School District, and the San Francisco Unified School District.
The Dana Center at the University of Texas, Austin is also creating a pathways program, their Launch Years project. They are currently working with three states—Washington, Texas, and Georgia—with pilot projects in multiple districts in each. Several important aspects of their work include:
Involvement of the mathematical community within the state systems of higher education as well as business and industry as early and integral participants of the planning process
Recognition of the need to address teacher capacity, quality, supply, and diversity to ensure that schools and districts are equipped to support the planned changes
Attention to the content and structure of the new pathways so that all options are seen as rigorous preparation for further study in the mathematical sciences
These are intended to confront directly the biggest dangers such a project faces: unwillingness by K-12 systems to modernize, lack of buy-in by higher education or the general population, lack of an adequately prepared teacher corps, and the degeneration of the alternate pathways into second-best options that effectively recreate the tracking we seek to avoid.
No one claims that this will be easy or that our first attempts will completely succeed. But it is important that we do this, involving all stakeholders, and that we keep working on it until we get it right.
References
Bressoud, D.M. (2016). Review of The Math Myth and Other STEM Delusions. AMS Notices 63(10):1181–1183. https://www.ams.org/journals/notices/201610/rnoti-p1181.pdf
Burdman, P. (2015). Degrees of Freedom: Diversifying Math Requirements for College Readiness and Graduation, Report 1 of a 3-part series from Policy Analysis for California Education. https://edpolicyinca.org/sites/default/files/PACE%201%2008-2015.pdf
Daro, P. and Asturias, H. (2019). Branching Out: Designing Math Pathways for Equity. Berkeley, CA: Just Equations. https://justequations.org/wp-content/uploads/Just-Equations-2019-Report-Branching-Out-Digital.pdf
Hacker, A. (2016). The Math Myth and Other STEM Delusions. New York, NY: The New Press.
Download the list of all past Launchings columns, dating back to 2005, with links to each column.