The Process Standards
According to the NCTM, their process standards ”highlight the mathematical processes that students draw on to acquire and use their [mathematical] content knowledge.” The process standards are Problem Solving, Reasoning and Proof, Communication, Connections, and Representation. I wrote about them here.
Students require opportunities to engage with these mathematics processes to develop proficiency in mathematics. Aside from brief exposure to problem solving for the odd word problem they may have encountered, most students have not needed to consider these processes.
To increase awareness of the NCTM process standards, in whole and in part, I plan to post about one of the five standards over the next few days. Today’s NCTM process standard consists of Connections.
NB: While the Common Core State Standards for Mathematics (CCSSM) includes a set of eight mathematical processes, they originated in the NCTM process standards as well as the Five Strands of Mathematical Proficiency published by the National Research Council (NRC). I will write about the CCSSM mathematical practices later.
In Principles and Standards for School Mathematics, the NCTM states: “When students can connect mathematical ideas, their understanding is deeper and more lasting. They can see mathematical connections in the rich interplay among mathematical topics, in contexts that relate mathematics to other subjects, and in their own interests and experience. Through instruction that emphasizes the interrelatedness of mathematical ideas, students not only learn mathematics, they also learn about the utility of mathematics.”
It is essential that students have opportunities to make connections within mathematics as well as between mathematics and their experiences in the world. These opportunities should start in kindergarten and continue through high school. At times, teachers should make the connections explicitly, while at other times, they should guide students to “discover” the connections. From middle school through high school, concepts such as ratio need to be connected to slope to rates of change starting with constant functions through linear functions and beyond to non-linear functions such as rational expressions, exponential expressions, and etcetera.
The key elements for the NCTM connections process standard follow. Students should engage with each of these in all of their mathematics courses.
- recognize and use connections among mathematical ideas;
- understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
- recognize and apply mathematics in contexts outside of mathematics.
To help administrators, colleagues, parents, and students better understand the NCTM process standards, I created a single slide summarizing the key points for each process standard. The slide for Connections follows.