NCTM’s new Principles to Actions: Ensuring Mathematical Success for All aims to ensure high-quality mathematics education for all students. But what does high-quality mathematics education look like? Another way to come at this question is to ask, “Why do we teach mathematics in school? What do we want students to learn?” The most common responses I see to these questions, especially in policy documents such as Principles to Actions or theCommon Core State Standards for Mathematics (CCSSM), are that students should learn mathematics—
Borrowing from Eric Gutstein, I call these reasons the “classical perspective” on mathematics education. The classical perspective, building on a strong research base about how students learn mathematics with understanding, suggests a particular vision of high-quality mathematics education. This vision generally emphasizes conceptual understanding, problem solving, making connections across representations and mathematical concepts, and engaging in reasoning and argumentation (in other words, engaging students in the Standards for Mathematical Practice). Within the classical perspective, equity is primarily seen as providingall students with access to this vision of high-quality mathematics.
I am a strong supporter of the classical perspective. However, there are other reasons that we might teach mathematics in school, which often receive less attention in major policy discussions. In addition to the goals listed above, I believe that students should study mathematics to—
I call these goals the “equitable-curriculum perspective” on mathematics education. Equity is framed in the classical perspective as providing students with access to well-taught mathematics; in the equitable-curriculum perspective, equity is framed as teaching a form of mathematics that values and integrates issues of diversity and social justice.
Although the Common Core is not perfect (I recommend Usiskin’s excellent analyses here, see sessions 505, and here), I do think the Standards for Mathematical Practice—and especially Standard 4: Model with mathematics—provide an opportunity to integrate these goals into school mathematics (see Koestler, Felton, Bieda, and Otten for more on the practices). However, I am deeply concerned that the Practices will be underemphasized as new standardized tests are implemented and as they play an increasing role in student and teacher evaluation.
In the following weeks, I will unpack the equitable-curriculum perspective and will discuss Complex Instruction (see here and here) as one way to achieve greater access for all students in both the classical and equitable-curriculum perspectives.
What do you think? What other reasons are there for teaching mathematics? Which of the five goals that I described resonates with you? What potential concerns or challenges do you see with these forms of mathematics?
Mathew Felton is an assistant professor of mathematics education in the department of mathematics at the University of Arizona and will be starting in the department of teacher education at Ohio University this fall. He is a coauthor of Connecting the NCTM Process Standards and the CCSSM Practices. His research focuses on supporting current and future teachers in connecting mathematics to real-world contexts and on teachers’ views of issues of equity, diversity, and social justice in mathematics education.