How much is enough?

Recently two books about math education crossed my path. The first is The Math Myth and Other STEM Delusions by Andrew Hacker and the other is A Mathematician’s Lament by Paul Lockhart. Although quite different in their perspective, each author questions the current math education being offered by traditional schools.

The Math Myth challenges the standard high school math sequence and Hacker questions the value of any math beyond Algebra I. He makes some interesting points about math being elevated as a subject simply because it is easily measured through standardized testing and how its used as a proxy for overall intelligence. He argues that few professions have any need for advanced algebra, trigonometry, or calculus and that requiring these subjects for college entrance acts as a defacto gate-keeping mechanism that primarily hurts poor and minority students who have less access to tutoring and math-rich environments. The author essentially asks: Why should someone be denied the opportunity to study for a career in graphic design or a job as a vet tech simply because they haven’t mastered the binomial theorem and other obscure math principles that they will never use in their personal or professional life? I found myself agreeing with some of Hacker’s points but I object to the idea that K-12 education is solely about practicality and that mathematics does not help one learn how to think.

A Mathematician’s Lament is also severely critical of the current state of math education, but Lockhart takes a different and more startling view – math is more similar to fine arts, he argues, and should be treated as we do drawing, painting, and music. These artistic disciplines definitely require technical skills and knowledge to do well, but unlike mathematics there’s also an emphasis on performance, creativity, and joy. He makes an analogy that how most students learn math now would be equivalent to teaching painting with a  “paint by numbers” program that only requires students to match colors to predetermined blocks on a canvas. In Lockhart’s world, math education would center around discovery, originality, abstraction, and beauty. He abhors the idea of making math more practical and relevant: “In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide — a relief from daily life, an anodyne to the practical workaday world.” He makes a strong argument for the kind of interesting puzzles and pondering that I see excites my students.

I see merit in both of these arguments, and one way to reconcile both viewpoints, that I strongly argue for, is a greater emphasis on discrete mathematics in our school system. Pushing every student into a math sequence that leads to calculus is inappropriate and unnecessary. Topics like combinatorics, number theory, logic, and graph theory are very approachable to students of varying ability, teach mathematical reasoning skills, and are just plain fun. So many of these topics can be framed as puzzles with elegant solutions which elevates mathematics into something more than tedious calculations. For example, my 10 year-old son and I are working through a book on group theory (the study of symmetry) and we just created some really cool diagrams of the group formed when certain rules are applied to switching art on 3 walls. There are no numbers involved, but its much closer to what real mathematicians do than adding up columns of sums.

From a practical standpoint discrete math is foundational to the study of computer science, and its no less “rigorous” (whatever that means) than calculus. I would also love to see a statistics course added to the high school sequence, especially one that emphasizes interpreting statistics, data visualization, and graphic design. Students going into any science related field, including social sciences like political science, psychology, and sociology, would benefit enormously from this kind of background and in today’s data driven world, making sense of data and newspaper graphics is part of being an informed citizen.

I don’t hold out hope that mathematics teaching in schools is going to change any time soon, but whenever I hear criticism of Common Core and a call for “back to basics” in math education, I inwardly cringe. I understand the frustration, but unfortunately there is no turning back. The math taught to our parents – routine memorizing of algorithms and focus on arithmetic computation has no place in a 21st century education. I welcome discussions, like those started by Hacker and Lockhart, that challenge the status quo, even if its not something I wholly agree with.