By Victor Mateas, posted September 1, 2016 –

In my article “Debunking Myths about the Standards for Mathematical Practice,” I describe five common myths about the mathematical practices (SMP) described in the Common Core and offer some suggestions about aligning instruction to the SMP. Perhaps the most thought-provoking myth discussed in the article is . . .

Myth 3: The mathematics task alone determines which mathematical practices students will use. 

I proceed to debunk this myth with the following statements:

“Although it is common to tag tasks to particular content standards or topics, an essential part in developing standards-based lessons, doing so for the SMP is a little more challenging. The SMP and the Standards for Mathematical Content both set expectations for students; however, the two sets of standards are different in what they ask of students. For the most part, the Standards for Mathematical Content determine the topic and the SMP describe the mathematical thinking. Therefore, evidence of the mathematical practices lies in a student’s thinking and approach, not in the text of the task a student is given. Tasks can, however, set up opportunities for students to engage in certain mathematical practices, depending on what the problem is asking students to do. Linking possible mathematical practices to a task is helpful for planning, while acknowledging that the roles of the student and teacher in the enactment of the task can alter which, if any, of the mathematical practices will be ultimately used.” (page 96)

In the article, I provide three samples of student work for the same rich mathematics task (see fig. 2 on page 95) to illustrate this point. Although the students are faced with the same problem, their mathematical thinking is drastically different. The first two students engage in mathematical practices, yet different ones are employed, given each individual’s unique approach. The third student, however, displays none of the mathematical practices. This student does show the potential for SMP 1 and SMP 3, but only with the right prompting by a teacher. 

Debunking this myth is particularly revealing about the nature of the SMP and provides two important insights. The first is that the focus of the SMP really is on what the student is thinking and how he or she is reasoning through a problem. Sure, some tasks might offer certain affordances or constraints regarding mathematical practices, but a task cannot guarantee the use of any particular mathematical practice. 

The second insight relates to the role of the teacher. Given that tasks yield different (or no) applications of the mathematical practices by students, the work that teachers do in leveraging the opportunities that tasks provide becomes increasingly important. This work is done through planning and instruction that (1) anticipates student thinking at the task level, (2) focuses on a subset of relevant mathematical practices, and (3) encourages that subset through various instructional methods.

I invite you to comment below on other myths about the SMP that you have seen or challenges that you have experienced regarding planning/instruction for the SMP. I hope we can all learn together through this dialogue. Thank you for sharing!

  Note: This article will be the subject of a Twitter chat on Wednesday, September 21, 2016. Join us at #MTMSchat.

Victor Mateas, vmateas@fenwayhs.org, is a teacher in the Boston Public Schools, a doctoral student at Boston University, and a research associate at Education Development Center (EDC). His interests include mathematical practices, curriculum, and the use of mathematics in high school science.