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 each day for the next five days. Today’s NCTM process standard consists of Communications.
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: “Students who have opportunities, encouragement, and support for speaking, writing, reading, and listening in mathematics classes reap dual benefits: they communicate to learn mathematics, and they learn to communicate mathematically.”
It is essential that students have theses opportunities starting in kindergarten and proceeding through high school. Not only must students understand the mathematics they learn, they must be able to explain it to others clearly. These others include their teacher(s), classmates, and in some cases, parents.
The key elements for the NCTM communications process standard follow. Students should engage with each of these in all of their mathematics courses.
- Organize and consolidate their mathematical thinking through communication
- Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
- Analyze and evaluate the mathematical thinking and strategies of others;
- Use the language of mathematics to express mathematical ideas precisely.
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 Communications follows.
Feel free to use this slide, and others I created, to explain the importance of this NCTM process standard.