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 the *Common Core State Standards for Mathematics
(CCSSM)*,* *are that
students should learn mathematics—

- for its own sake because it is a
beautiful and amazing human accomplishment; and
- to be prepared for college and
future careers, especially in science, technology, engineering, and mathematics
(STEM) fields.

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
providing *all* 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—

- learn about and appreciate
diversity in human thinking and accomplishments throughout history and around
the world;
- see the role of mathematics in
their daily lives, their community practices, and their cultural backgrounds;
and
- understand, analyze, critique,
and take action regarding important social and political issues in our world,
especially issues of injustice.

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.