Report from the Task Force on the NCTM Standards

January 27, 1997

Questions from NCTM

In November Mary Lindquist, chair of the NCTM Commission on the Future of the Standards, asked our task force to react to some statements of the content Standards as they are now phrased. Specifically, we were asked to respond to three questions.

  1. Your view of mathematics. Consider the nature of mathematics -- its content, processes, and procedures -- that you feel is important for students from pre-kindergarten through grade 12. Do the current statements of the Standards adequately communicate your view of the discipline?

  2. Consistency and growth. Do the statements of the current curriculum Standards convey a sense of consistency and growth in content themes as the student moves across the grade levels? (Content themes would include, for example, ideas of measurement, number sense, and algebraic and geometric thinking.)

  3. Expected understanding of content. Do the statements of the content Standards adequately reflect the mathematical understanding expected of a student graduating in the 21st-century? Do they reflect the needs of students who are planning post-secondary study in a mathematics-related discipline?

    We were also asked the following question.

  4. Blending the three sets of Standards. The NCTM project to reissue a Standards document in the year 2000 intends to meld together the dimension of content, teaching, and assessment. What suggestions could you make as to the most effective ways of blending these ideas?
You will find below our task force's first report to NCTM. You will see that, while we didn't respond to the first three questions in an orderly fashion, all the issues and more were addressed. We didn't respond to the fourth question. I think that this question came too early in the process. You will also find a response from Mary Lindquist.

First Report of the Task Force

The first meeting of the MAA President's Task Force on the NCTM Standards was held on January 9, 1997. In advance I provided the members of the task force with copies of your letter of 19 November 1996, seeking response to four questions, and the "bare-bones" listing of the Standards. The initial discussion ranged over many topics and, in the time available, we were not able to prepare direct responses to your four questions. Following the meeting, two Task Force members who had been unable to attend in person contributed to the discussion by email. Several themes emerged during these interchanges among Task Force members.

Positive Comments about the Standards

  1. The members of the Task Force applaud the NCTM for its courage in formulating a set of standards for school mathematics. This has resulted in getting the entire mathematical community to think about and to discuss basic mathematical issues. Moreover, important educational issues are now routinely brought to the public's attention in the press through many articles on mathematics and mathematics education.

  2. Equally noteworthy is the fact that the Standards seek to address the mathematical needs of all students, not just those requiring background for college courses in mathematics and science. In addition, in formulating the Standards the NCTM addressed the oft-expressed wish of industry and client departments that mathematics instruction be broadened to better help students develop their abilities to recognize and formulate quantitative problems and to apply mathematical formalism to actual situations.

  3. The current proliferation of talks, workshops, books, and articles spawned by the Standards has stimulated teachers to spend more time thinking and talking about mathematical ideas and exploring ways of communicating them more effectively.

Reservations and Concerns about the Standards

  1. A difficulty that faces us all is that the Standards are being interpreted in a multitude of ways. Even though teachers are enthusiastic and excited about having some coherent vision for school mathematics, bringing that vision to life in classrooms is a difficult task. There is, as yet, little consistency in classroom interpretations of a coherent vision for school mathematics, and this is an issue the NCTM needs to address as it revisits the Standards.

  2. There is concern that one of the assets of the Standards is also a liability, since the focus on "mathematics for all" appears to neglect the needs of "some." One Task Force member expressed the hope that the Standards would not lead to "lowest common denominator" education. While the Standards do present a vision of school mathematics for all students, members of the Task Force frequently returned to discussing what skills are needed by students, when those skills are important, and how the skills differ by audience. The Standards frame a set of expectations that stretch the current mathematical preparation for general students moving through the system, but fall somewhat short of providing challenging expectations for those who will become major users of mathematics in their choice of career. In brief, there is a call for the Standards to address more specifically the range of skills and understandings needed by different populations of students. We must avoid having an "algebra experience" be comparable to a student having a "French experience" by going to a local bakery and eating a croissant.

  3. All members of the Task Force want the revision of the Standards to be more specific, with regard to both skills and expectations for students' intellectual growth from one grade level to the next. Many teachers, both those teaching from "reform" materials and those who continue to use a more traditional approach, would like the Standards to specify what skills are really needed for each level of mathematics.

  4. A number of Task Force members expressed the belief that, in order to grow intellectually, students must have significant intellectual demands placed upon them. Indeed, no discussion of teaching and assessment is complete without a thorough discussion of ways to induce students to work harder. The Standards emphasize the responsibility of our profession to stimulate and "mathematically empower" students, but they do not simultaneously emphasize the necessity of students to work hard and to stretch their attention spans. Students need to be aware that mathematics is not an inborn inherited trait and that everyone finds it difficult at some stage. They need to realize that, to learn an important fundamental subject, everyone must exert effort, perseverance and persistence while being entitled to support and encouragement.

  5. One critical concern of the members of the Task Force is the need for the Standards to more fully address issues of mathematical reasoning, the need for precision in mathematical discourse, and the role of proof. Many members of the Task Force perceived a discrepancy between what the Standards say and how they are being put into practice. There is a feeling that the growing appreciation for the role of experimentation and conjecture in mathematical thinking may have given people the idea that careful reasoning and logical deduction are no longer of much significance. Students need to be consciously aware of when they are exploring topics in mathematics and when they are providing more rigorous arguments. Many mathematicians at the post secondary level are quite concerned about students' lack of ability to think in a logical fashion. This aspect of mathematics should be included throughout the curriculum. However, some members of the Task Force cautioned that we shouldn't be trying to replicate ourselves. There needs to be ongoing and dispassionate discussion on the level of proof and rigor expected in the school curriculum. There is consensus that the Standards at present do not deal adequately with this matter. But these are difficult issues, and we expect to have further serious discussions about them in our Task Force.

  6. Another concern expressed in the Task Force's discussion is maintaining a healthy balance between pure and applied approaches. As the "new math" was viewed by many as being too "pure," some of the efforts to implement the Standards may seem too "applied." On the other hand, there was also the feeling that the Standards' emphasis on "problem formulation" before "problem solving" should be strengthened.

  7. Concern was also expressed about the fact that in each grade level grouping the Standards recommend including more topics and types of activities than the traditional curriculum, thereby risking superficiality. Further, as currently written, the Standards appear inconsistent in recommending decreased coverage of certain traditionally difficult topics (such as formal proof in geometry) while suggesting (for the college-intending) added coverage of other topics, an understanding of which would seem to depend on the omitted material (such as "developing an understanding of an axiomatic system through investigating and comparing various geometries").

  8. Several Task Force members expressed concern that effective use of the Standards appears to demand much more of teachers than the traditional curriculum and questioned whether we are preparing teachers adequately to deal with these new demands. Because of their traditional education, too few active teachers have the tools to use the Standards effectively as a blueprint for instruction. What are the consequences for K-12 students?

  9. Another issue is the public's understanding of the contributions that mathematics makes to our current society. Parents especially should become more aware of the uses of mathematics and the need for their children to have a strong mathematical education to be successful in today's workplace. Addressing the perceived needs of business and industry should also be taken into account. The Task Force expects that NCTM will be asking for response and reaction from these stakeholders as the process of review moves forward.

In summary, this initial meeting of the Task Force provided an opportunity to set the stage for further discussion. Specific items that we wish to call to the attention of the NCTM Commission on the Future of the Standards from our first meeting are:

The Task Force looks forward to continued discussion and interaction with you and the NCTM Commission as this important work evolves.

Kenneth Ross
Department of Mathematics
University of Oregon
Eugene, OR 97403-1222
phone: 541-346-4721
fax: 541-346-0987
web: http://darkwing.uoregon.edu/~ross1/
ross@math.uoregon.edu

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Last modified: Fri Sep 19 12:42:23 1997