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.
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.
- 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?
- 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
- 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
We were also asked the following question.
- 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?
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
- 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.
- 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
- 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
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:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
- 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?
- 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.
- Specificity in terms of mathematical skills and understandings needed at
each grade level.
- More emphasis on the fact that school mathematics can
be learned by all with continued effort and perseverence, and does not
require some inborn trait.
- More careful attention to the role of rigor
and logical thinking in the school curriculum.
- Clearer articulation of
what is meant by mathematical thinking, including issues related to problem
solving and problem formulation.
- Better expression of the balance
between "mathematics for all students" and that needed by major users of
The Task Force looks forward to continued discussion and interaction with
you and the NCTM Commission as this important work evolves.
Department of Mathematics
University of Oregon
Eugene, OR 97403-1222
MAA Online is edited by Fernando Q. GouvÍa
Last modified: Fri Sep 19 12:42:23 1997