Earlier this week, jaycaspiankang wrote about the history of progressive math education and the culture wars it has inspired. Today, he poses a broader question: What do we really know about how to teach math?
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.Read Part I of Jay Caspian Kang’s series on math education. 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 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., 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 afield?” 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, 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?, 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 how to do something and you do it for homework, might be totally backward; and whether the United States, which scores relatively low in math compared with other wealthy nations, isLast month, the Bill and Melinda Gates Foundation announced that it would be spending more thanon improving math education in the U.S. As was the case in the nineteen-nineties math wars, much of the early work will focus on deploying technology, studying how students learn, and addressing racial and economic achievement gaps. According to Bob Hughes, the Gates Foundation’s director of K-12 education, the intention is to help “African American and Latino students and students of all races and backgrounds experiencing poverty,” with an emphasis on transition years, including from eighth to ninth grade, which somehave shown goes a long way in determining whether a student will stick with math in high school and beyond. The Gates Foundation’s math prescriptions are still not set in stone, but Hughes discussed interventions such as cutting costs in order to expand math tutoring for students who have fallen behind their grade level, implementing more digital tools, and developing curricula and classroom materials that will aim to help teachers make math both accessible and challenging. The foundation seems particularly interested in this last part: how different forms of pedagogy and instruction find their way into classrooms. “It’s very hard for quality materials to necessarily buck the trend of incumbent players in the curriculum space,” Hughes said. “So we’re thinking a lot about markets.” The subtext of this project, as I see it, is that math education has become entirely too cluttered with a host of bad or untested ideas. The researchers at the Gates Foundation seem to believe that there’s a way to locate proper techniques, and insure that as many teachers impart them to their students as possible. For them, finding these better methods involves a lot of data, “UX studies,” and “A/B testing,” all of which can be done efficiently and quickly if students are using math-learning technology that will track their progress and proficiency. The Gates Foundation has generally steered clear of politics. Hughes’s tone in our conversation was noncommittal, even when discussing the question of when to teach algebra—something that became controversial in the education world when the authors of the California Mathematics Framework recommended ceasing algebra instruction for middle schoolers. But he did offer a set of “non-negotiables,” which included a need to be “kind and gentle” with students, a focus on grounding solutions in teachers and communities, and, finally, an emphasis on getting the right answer. “Math is unique because there is a right answer, and I think that politicizes it, somehow,” Hughes said. “In other subjects, there may be different answers or you can have a multiplicity of interpretations. Math has a right answer; there are multiple ways to get there, but there is a right answer. We believe it’s important for kids to get to that right answer. And that’s not a universally agreed-upon notion in some quarters.” This stands in opposition to much of the progressive push in math education, which—as Michael Lindaman and
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