Earlier this week, I wrote about the history of progressive math education, the culture wars it has inspired over the past hundred years, and the controversy over the California Math Framework. Today, I want to start with a much broader question: What do we really know about how to teach math to children?
The answer is not all that much—and what little we do know is highly contested. An American math education usually proceeds in a linear fashion, with the idea that one subject prepares you for the next. Take, for example, the typical path through mathematics for a relatively advanced student. They will start with basic arithmetic, learn multiplication and division, and graduate to fractions. Then they’ll go into algebra, then geometry, then Algebra II/trigonometry, before tackling calculus. There may be small variations to this sequence, but that’s more or less how most kids learn math in the U.S.
But are we sure that these math subjects should really go in this order? And are we sure that these are the only steps that should be included? There are arguments, for example, that say that children should engage in play-based exploration of concepts of calculus in preschool and kindergarten before they start learning to add and subtract, because proper guidance through pattern-recognition activities like Legos and origami will place arithmetic into the correct context and make it feel less tedious.
A much less radical example can be found at a school district in Escondido, California, that recently altered the traditional math procession by placing all its freshmen and sophomores in “Math I” and then “Math II.” When they reach their junior year, those students go through a “decision tree” where they answer questions like “Do you know what type of career you want to have?” and “Is your career in a STEM field?” Students who answer yes, and say they want to ultimately take calculus, are put in a math class that includes precalculus; if not, they are placed in statistics-based courses. The idea is to make math education better for all students, even those who might not want to pursue careers in STEM, though some in the district have also acknowledged concerns that the system might reinforce inequality, with the statistics track being considered the “pathway for students of color.”
The Escondido experiment highlights a lot of the more entrenched questions in math education. Does kicking an equity issue down the road really solve it? How should we address disparate outcomes in achievement while also accepting that most students won’t go on to do college-level math? And why is there an assumption that statistics, with all its potential applications and iterations, should be seen as the remedial route while calculus gets reserved for the more accomplished students?
Beyond the question of tracking, there are debates about whether PEMDAS, the acronym many of us learned about the order of operations in a math problem, is actually the right way to do things; whether the traditional pedagogical structure, in which a teacher tells you
