Suggestions for Engaging in Productive Dialogue on the Future of Instruction in Mathematics

Position Statement of the National Council of Supervisors of Mathematics


Changing school mathematics programs is a challenging task that often engenders strong feelings, tensions, and controversies. Many individuals, groups, and organizations have a vested interest in these changes and are actively engaged in the current discussions on the most appropriate approaches to school mathematics. Positions as diverse as "Back to the Basics" and "Vast changes in the world require vast changes in the mathematics classroom" charge the debate conflict and confusion Positions harden as each side believes that they have the best interests of young people at heart. The shared purpose of this discussion is the identification and implementation of a mathematics curriculum that prepares each student for productive citizenship in the 21st Century.

NCSM acknowledges and appreciates that all participants in these discussions are sincere and well-meaning. Parents and caregivers legitimately ask whether we are experimenting on their children, and whether the changes might limit their children's opportunities. School administrators at all levels have legitimate concerns about defending changes in mathematics programs and how to serve as instructional leaders of reforms they do not fully understand. Teachers on the front lines have legitimate questions about how far to move, how fast to move, and what's real and what's a fad. Mathematicians and professors of mathematics have equally legitimate fears that reform will result in inadequate preparation of future undergraduates and graduate students. Business leaders have deep concern about the mathematical competence of the present and future workforce.

Given the magnitude of the reform being proposed and the seriousness of these diverse stakeholders, it is essential that debate among the affected constituencies be conducted in a calm, focused, and professional setting. A setting will permit a full discussion of all points of view in a positive, results-oriented environment. A context that fosters consensus and compromise for each school, district, community, and state in which the debate occurs.


Like a mathematical proof or an axiomatic system, this debate should begin with a "accepted facts." These "accepted facts" are statements that we believe that nearly all concerned parties can accept. NCSM suggests the following fundamental givens:

  1. We all seek broad mathematical literacy and mathematical power for all students;
  2. The world has significantly changed in the last generation in terms of societal needs and technological realities.


But givens are not immutable. They are open to interpretation and lead to important questions that NCSM believes must be asked in the discussion. NCSM suggests that every community examine the following fundamental questions:

  1. Which of the old "basics" need to be updated or replaced?
  2. Do the new "basics" require all of the old "basics" or do emerging future needs change the focus of "what is basic?"
  3. How has new information on how children learn change the "mathematics learning environment?"
  4. Do new tools open the doors to new ways of learning?
  5. Has technology changed the expectations of "what is basic" or "how to use the basics?"
  6. Do new approaches to assessment open new ways to measuring what has been learned?


When asking difficult questions it is imperative that the ultimate goal of the activity must be kept in view. NCSM believes that the identification of the appropriate curriculum for a community is most assuredly not found in a simplistic "one size fits all" or an "all or nothing" package. Certainly there are topics and techniques that have been part of our school traditions that will serve well in the future. Just as certainly, new knowledge on how children learn mathematics, new technologies, new techniques, and new learning strategies offer potential for appropriate inclusion in our curriculum. NCSM affirms the conviction that our students will be best served if the emerging curriculum is a "Balancing the Best." The goal, in every community, should be to balance the best of the past with the best of the emerging content, methods, strategies, and technology.


NCSM counsels all stakeholders in the dialogue to:

  1. focus on the students' future, not the adult world's past;
  2. acknowledge that change does not require condemning the past, but rather learning from it;
  3. conduct deliberations in an atmosphere that encourages active listening, careful analysis, and mutual respect;
  4. consider, without prejudgment, all points of view on the future of mathematics instruction;
  5. identify the curriculum and delivery systems that are best suited to the needs and resources of its community;
  6. recognize that the accumulated knowledge of the successful approaches to mathematics instruction of the past should be important components of any future curriculum;
  7. acknowledge that the pace of change in our society is rapid. Appropriately, the tools, knowledge, and skills required for productive citizenship are also changing and will be vital to the emerging curriculum;
  8. accept that all stakeholders in the discussion are seeking to identify a common curriculum that will best serve our children and our society.


  1. The identification of the critical skills and abilities that are best learned in a mathematics environment.
  2. The search for the most appropriate methods, settings, strategies, and technologies that will aid all students in achieving these mathematical skills and abilities.
  3. Planning for the implementation of a wide variety of ways to assess student achievement of this blended curriculum.

(Note for draft- order and items need proper ordering)
NCSM recommends that the emerging curriculum in each community should include:

  1. appropriate emphasis on the development of mental arithmetic skills;
  2. appropriate use of paper and pencil computational skills;
  3. appropriate investigations in the use of algebraic, geometric, quantitative reasoning;
  4. appropriate use of computers, calculators, interactive multi-media, as well as other emerging technologies;
  5. appropriate individual and group learning strategies;
  6. appropriate contextual background for students in areas such as use of manipulatives and other concrete learning aids, and simulations;
  7. appropriate integration of writing and other linguistic activities;
  8. appropriate connections to other disciplines and areas of student interest;
  9. appropriate experiences in problem solving, exploration, and creative activity;
  10. appropriate emphasis on estimation, accuracy, and the reasonableness of results;
  11. appropriate experience in reading, and interpreting graphs, tables, and charts;
  12. appropriate use of varied assessment tools and methods which match the instructional program;
  13. appropriate mathematical content and rigor to foster advanced study in science and technology.


NCSM encourages and eagerly engages in the future dialogue. NCSM believes that:

  1. the NCTM Standards provide an excellent resource in this dialogue and offer insightful guidance for resolution of many of the critical issues that must be addressed in each community;
  2. each community should ensure that a mathematics specialist be actively involved in the dialogue. The mathematics specialist can serve as a research resource and a conduit to materials, approaches and perspectives. If a specialist is not on staff, NCSM can aid in identifying local leaders with the appropriate background needed to engage constructively in the dialogue.


This position paper represents an attempt of the National Council of Supervisors of Mathematics to communicate its position on change in mathematics instruction. NCSM encourages the dialogue and suggests that it be conducted in an atmosphere that respects and considers all points of view. The NCSM position underscores the fundamental belief of this organization that any effective mathematics curriculum will, in fact, represent a balancing of the best of our past successes with the best of an emerging present. A curriculum molded with this broad-based perspective will best provide our children with a sound foundation to face the future with the ability to use mathematics as a vital tool in their life-long quest to learn.

You are encouraged to make and distribute copies of this paper.

Position Statement of the National Council of Supervisors of Mathematics. Released Fall 1998.
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