SMP

MHoM first appeared in the literature as an integral part of the secondary mathematics curriculum in a paper by Cuoco, Goldenberg, and Mark (1996). Recent policy and standards documents have also emphasized the need for students and teachers to develop these habits. In particular, we show notable overlap between mathematical habits of mind and the Common Core State Standards for Mathematics (NGA Center & CCSSO, 2010).

 

The Common Core Standards for Mathematical Practice (SMP) describe critical aspects of mathematical proficiency that have been central to our work on MHoM, and there is considerable overlap in the two. For example, both place importance on seeking and using mathematical structure, uses of precision, and the act of abstracting regularity from repeated actions.

 

In particular, the three mathematical habits defined above are closely related to the following SMP:

  • SMP1: Make sense of problems and persevere in solving them
  • SMP2: Reason abstractly and quantitatively
  • SMP6: Attend to precision
  • SMP7: Look for and make use of structure
  • SMP8: Look for and express regularity in repeated reasoning

But instead of directly studying the SMP, we have parsed them for measurement purposes. For example, the two processes of seeking structure and using structure in SMP7 look different in the actual practice of mathematics, so we are studying them separately. Given the complexity of the habit of seeking mathematical structure, we have also incorporated into it SMP8 and elements of both SMP1 and SMP2. And while our “describing” habit is closely tied to SMP6, we have placed more emphasis on clarity, rather than on precision. We are studying these habits in teachers—and while precision is important habit for teaching, we have learned that clarity is paramount (Matsuura et al., 2013b).

 

Our MHoM definition is an evolving document, which we have continued to revise as we obtained more research data. From our data, we have learned which habits are more prominently used by secondary teachers—both when doing and teaching mathematics. We have also consulted external mathematicians from multiple fields in refining the ways in which we think about and articulate these habits.