**By Mathew Felton, Posted June 23, 2014 – **

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.

**Archived Comments**

Compelling set up. I look forward to the future entries. As for the five reasons for teaching math you list, I feel that the fourth (seeing math all around) does not hold up well as a reason to teach math but may instead be a happy result after the fact. I argue that many people go through life without seeing the math and can use math-based objects and tools regularly without seeing the math behind them, so they do not feel a necessity to learn that underlying math. However, when students get bitten by the math bug, perhaps later they will start to notice more patterns and structure around them and in their culture. Posted by: SamuelO_47017 at 6/24/2014 11:01 AM |

Thanks for the comment Sam! I'm enjoying writing them. I see what you're saying about seeing math all around us as a happy result, but I see it as a reason to learn/teach math too. I agree most people can use a variety of tools in their lives without seeing the math behind it, but that's part of what I want them to learn in school. I want them to see the things they do in a new way. So for me it's not just a happy end result; it's one of the goals I have for teaching math in school! Posted by: MathewF_09852 at 6/24/2014 11:53 AM |

Matt, Thanks for getting this conversation started. I very much look forward to this blog discussion. I fully support your (and others') efforts to broaden the spectrum of reasons and methods to teach mathematics. I would like to raise an issue/tension I have seen at almost every mathematics conference I have attended in the last couple of years. I regularly see mathematics educators praise and emphasize the standards of mathematical practice. However, EVERY teacher I work with says that sounds great, but their classroom goals and expectations all revolve around the content standards. They argue that the curricular materials, assessments, and professional development are all about content, not practices. They are concerned that their administrators/evaluators would not support, or even recognize, practice-focused instruction, putting their jobs at risk. Have you seen something similar? How can we address this tension productively? Thanks again, Rodrigo (say hi to Tucson for me!) Posted by: RodrigoG_17929 at 7/1/2014 11:34 AM |

Hi Rodrigo! I would say we need to be focusing on two things. First, helping teachers see how the practices and the content standards can (and should) go hand in hand. You should never really be teaching just the practices--they need to always be implemented around some content. I guess you could argue that you are teaching just the content standards separately from the practices, but that would likely have to be a very teacher-centered "direct instruction" kind of approach. Moreover, some (many?) of the content standards would be very difficult to really teach without engaging in some of the practices. Here's a standard I grabbed quickly from grade 3: "Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends." It's hard to imagine genuinely teaching problems like that without engaging students in problem solving (SMP1), making arguments (SMP3), and identifying regularity (SMP8), and making use of structure (SMP7). So if teachers aren't seeing how (a) the content can be taught through the practices, and (b) how many of the content standards *require* the practices, then we need to really support them with PD experiences that help them see this. But that's the same challenge we've had going back to NCTM's 1989 Standards--it takes sustained PD for teachers to understand a richer approach to mathematics. Second, I think math ed as a field needs to focus more on outreach to administrators and evaluators, so that they can recognize this as good teaching and understand the research base behind it. Of course all of that is more easily said than done--we've been struggling with developing the infrastructure to provide widespread, high quality PD for decades now. Plus, as the new standardized tests roll out, they will be a big factor in determining what the standards actually mean in practice--and I'm very concern they'll push towards the procedural. Posted by: MathewF_09852 at 7/2/2014 4:50 PM |

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