NCTM Process Standards for Mathematics

Another assignment in the summer work for my rising AP Calculus AB students is to review a set of six slides I created that overview the process standards for mathematics defined by the National Council of Teachers of Mathematics (NCTM).  The NCTM published the process standards in Principles and Standards for School Mathematics.

Principles and Standards for School Mathematics, published by NCTM in 2000, outlines the essential components of a high-quality school mathematics program.  It calls for and presents a common foundation of mathematics to be learned by all students.  It emphasizes the need for well-prepared and well-supported teachers and administrators.  It acknowledges the importance of a carefully organized system for assessing students’ learning and a program’s effectiveness.  It also underscores the need for all partners— students, teachers, administrators, community leaders, and parents—to contribute to building a high-quality program for all students.

National Council of Teachers of Mathematics, Principles and Standards for School Mathematics, Executive Summary.

I created this task to provide students with the opportunity to consider various mathematics processes as they are used by those proficient in mathematics.  Most students have not considered these processes beyond the act of problem solving, and perhaps reasoning and proof, since traditional instruction rarely makes explicit the additional processes of making connections among and between content standards, using multiple representations to illustrate mathematical relationships, and the act of communication to organize and express mathematical thoughts clearly and effectively.

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.

  • Problem Solving

  • Reasoning and Proof

  • Communication

  • Connections

  • Representations

NCTM Process Standards Task

 Instructions for my students for this task follow.

  • NCTM Process Standards (250-500 words)
    • In your own words, explain each of the NCTM’s process standards for mathematics.
    • How familiar are you with each of the process standards?
    • Which of the process standards have you applied / used in prior math classes?
      • Which of these did you find easiest to use?  Why?
      • Which of these did you find hardest to use?  Why?

Questions for my readers:

Has anyone required their students to consider the NCTM’s process standards for mathematics?  If so, in what ways?  And if so, how did it go?

What are your reactions to this assignment?

About Dave aka Mr. Math Teacher

Independent consultant and junior college adjunct instructor. Former secondary math teacher who taught math intervention, algebra 1, geometry, accelerated algebra 2, precalculus, honors precalculus, AP Calculus AB, and AP Statistics. Prior to teaching, I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.
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9 Responses to NCTM Process Standards for Mathematics

  1. This is a very interesting assignment. It seems a little intensive, but appropriate for students taking AP courses. The assignment will require students to think about what is required of them during the learning process and what is expected of you during the teaching process. I’m interested in hearing about your students’ reactions to this assignment.


  2. J Fun says:

    I am personally very familiar with both the NCTM Process Standards and with the strands of proficiency from the National Research Council. I’m curious if you know of the Standards for Mathematical Practice, the eight K-12 standards written in conjunction with the Common Core State Standards Mathematics Content Standards. These eight statements were derived from the two sources your rising AP Calculus students are exploring this summer, and in my opinion, are the most important part of the CCSS-M standards. Without deliberate attention to the Standards for Mathematical Practice, the transformation in math education intended by the writers of CCSS will not be realized.

    I would bet that alerting your AP students to these ideas will have a positive impact on their math studies this upcoming school year. I am wondering why this was not assigned to your math intervention and Algebra 1 students as well! I believe one of the disservices we do in our approaches to math instruction is to save the higher order thinking for the more advanced students. Personally, I believe that students who struggle the most need to understand these ideas more than students who have already found success in math classes, like your AP students. I believe this, combined with Carol Dweck’s work around “Mindsets” could empower and enhance the learning of all students in mathematics.


    • Thanks for your comment. Yes, I am aware of the CCSSM’s use of both content standards and practice standards. And that the practice standards evolved out of the NCTM and NRC frameworks. I plan to teach my two algebra 1 classes following a CCSSM-based curriculum I helped define this summer.

      I incorporate the NCTM and NRC frameworks in all of my classes. I did not assign it as summer work for those classes since the vast majority are rising freshmen. Also, I do not know who is assigned to me yet in those classes. Rest assured, they will experience mathematical practice standards galore this year!


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  5. Pingback: NCTM Process Standard: Communications | Reflections of a Second-career Math Teacher

  6. Pingback: NCTM Process Standard: Connections | Reflections of a Second-career Math Teacher

  7. Pingback: NCTM Process Standard: Representation | Reflections of a Second-career Math Teacher

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