Introduction
The NSF Strategy
MACOS Materials
Lessons Learned
J. Myron Atkin
Rodger W. Bybee
George DeBoer
Peter Dow
Marye Anne Fox
John Goodlad
Jeremy Kilpatrick
(Glenda T. Lappan)
Thomas T. Liao
F. James Rutherford
Introduction
The NSF Strategy
MACOS Materials
Lessons Learned
J. Myron Atkin
Rodger W. Bybee
George DeBoer
Peter Dow
Marye Anne Fox
John Goodlad
Jeremy Kilpatrick
(Glenda T. Lappan)
Thomas T. Liao
F. James Rutherford
Introduction
The NSF Strategy
MACOS Materials
Lessons Learned
J. Myron Atkin
Rodger W. Bybee
George DeBoer
Peter Dow
Marye Anne Fox
John Goodlad
Jeremy Kilpatrick
(Glenda T. Lappan)
Thomas T. Liao
F. James Rutherford
  Lessons from the Sputnik Era in Mathematics Education (continued)
Glenda T. Lappan, Michigan State University What have we learned from the Sputnik era?
As a person who has both experienced the “new” math effort and
who has been deeply involved in efforts over the past 30 years to
improve mathematics teaching and learning, I have pondered this
question many times. The following is a list of things that I think we
have learned, or at least the Sputnik era has pushed us toward, and a
bit of elaboration on each.
Teachers are key to improving mathematics education.
Teacherproof curriculum is a myth. The curriculum projects of
the 1950s and 60s seemed to send mixed messages on the role of
the teacher in reform. Some projects took a very firm stand that
teachers could not implement the curriculum without training from the
project developers. (The University of Illinois project under the
direction of Max Beberman was one of these.) Other projects
concentrated on the content and took a less explicit stand on
instruction. This left the teacher with two dilemmas¾how do I teach
this stuff, and what do I do when I do not know the mathematics I
am being asked to teach? In the current NSF curriculum
development projects, there has been a great deal more attention to
creating materials from which teachers as well as students can learn.
The level of innovation of new curriculum materials has to be
reachable by average caring teachers. In the throes of a great
excitement about creating innovative curricula, developers in the
Sputnik era created materials that were, in some instances, a
considerable change from thenexisting programs and expectations.
This created enormous problems for teachers and for schools. In
today’s NSF curriculum projects, developers have faced this
problem of change upfront. The projects have continued to ask the
questions, “How do students learn mathematics?” and, “What size
step can curriculum materials take from existing practice so that a
large percentage of schools will be able to reach from their current
programs to the new materials?” As a result, the set of recent NSF
projects at any grade span are arrayed along a continuum from a
mediumsized stretch to a fairly large stretch from current practice. In
addition, they pay a great deal of attention to what cognitive scientists
have to say about student learning.
Curricula have an implicit or explicit stance on instructional
practice. To be effective, curricula must give teachers help in
understanding the mathematics content, suggest supportive
instructional practices, and provide assessments that helps
teachers make instructional decisions. The new NSF curriculum
projects have produced materials that have considerably more help
for teachers than earlier projects. Many of the project developers
have written materials that have the spirit of having a conversation
with teachers about what has happened in trial classrooms, about the
underlying mathematics, about what the mathematical potential of the
activities is, and what an instructional model that would support the
learning might look like. This attention to a supportive instructional
model is much more explicit and is a part of the philosophies that
support the new materials development.
Professional development that is curriculum materialsbased
has a greater chance of success in helping teachers improve
their practice. There will be some who do not agree with me on
this. However, I have become convinced that professional
development that is not tied to the implementation of specific
materials is not as effective as those efforts that are. In the Sputnik
era there was a great deal of effort aimed at increasing teachers
knowledge of mathematics. As I claimed earlier, this certainly
benefited mathematics education. However, teachers who took
mathematics courses in the ‘60s still were faced with the daunting
task of figuring out how to implement specific new curricula in their
classrooms. Not knowing the philosophy and the vision of instruction
that would support that curricula that was in the heads of the
developers, led to some ineffective implementations of materials. In
my own work, I have experimented with teacher enhancement that is
tied to materials and that which is not. I am not claiming that the latter
does not help teachers; my claim is that curriculumbased teacher
enhancement adds value to the experience for teachers. Being able to
provide teachers with a safe, supportive opportunity to try out
instructional ideas from the inservice seems to help teachers examine
their own beliefs about mathematics and what students should know
and be able to do, as well as what it means for a student to know
something.
The infrastructure of leadership in mathematics and science
education must be adequate to the job of supporting reform.
We are smarter, now, about the nature and depth of teacher
enhancement that is needed to support reform. We have a better
understanding of how long teachers need assistance and about how
long it takes a school community to understand and encourage
change. There are two levels on which one can think about teacher
enhancement around the implementation of curriculum materials. At
one level, there is technical support to get the curriculum in place. At
another level, there is the goal of increasing teachers’ knowledge of
mathematics and science through inservice opportunities. The latter
takes the curriculum as one of the tools to help teachers rethink their
practice. The goal is to help a teacher become a reflective, innovative
teacher who is able to and committed to adapting the curricula being
used to fit his or her particular students. This goal is focused on
teacher learning. The goal of technical support for getting a new
curriculum in place is focused on the curriculum and not so much on
the individual teacher’s growth. In order to provide technical support
to the vast number of teachers in the country, we have to engage
enough teachers in the more intensive inservice opportunities to
move them to the leadership stage where they can then provide
technical support on a local basis.
Public support for the direction of change is critical for
success. Parents have to know how to help their young
children with their mathematics homework and to feel secure.
One lesson learned is that parents care deeply about education and
want the best for their children. We laugh about parents demanding
that their children suffer mathematics in the same way that they did.
But we should be hearing the genuine desire to help their children that
is underneath their words. When parents cannot understand the
problems that their student is being asked to work on at home, they
immediately assume that something is wrong. We have learned from
the painful lessons of the past that we have to find the will and the
energy to help parents understand the goals of new materials and
help them to help their children. The “we know best“ stance will not
work in a time in which information can be sent world wide with the
push of a “send” button. We are learning to be smarter about
communicating with parents, but we have a long way to go.
The way in which basic skills are attended to in innovative
curricula must be clearly spelled out so that parents and
administrators are satisfied that students will not be harmed.
Each project must gather evidence that students are
performing at an acceptable level on basic skills. The tradition
that arithmetic has a place in the curricula because of the need to
develop basic skills for trade and managing one’s affairs is very
strong. Reform is in peril when parents and administrators are not
satisfied that basic skills are a part of reform curricula. The NCTM
Standards documents have been greatly misinterpreted in this area.
By trying to move toward balance among conceptual development,
problem solving, and skill development, the documents open
themselves up to the interpretation that kids do not need to learn their
“facts.” The real message is that estimation and mental arithmetic are
more important than ever! In a technology environment a sense of the
size of a number that is expected as a result of a computation is
essential to monitor the reasonableness of results.
Systems that are alignedcurriculum, teaching, and
assessment have a greater chance of providing success for
students. Changes in any one of these three key aspects of
mathematics education reform without corresponding and supportive
changes in the others surely will lead to a failure to reach the goal of a
powerful mathematics education for all students. The kinds of rich
situations involving mathematics and mathematical thinking that form
the essence of a modern curriculum cannot be taught meaningfully in
classrooms in which tools for doing mathematics, such as computers,
graphics calculators, manipulatives, etc., are not available. Classroom
practice must support communication, reasoning, connecting, and
problem solving as an active part of what is expected of students. On
the other hand, the best teaching strategies in the world cannot make
students mathematically powerful if the mathematics curriculum taught
is not appropriate. If the curriculum is changed and the instructional
strategies are improved to support different, more powerful
mathematical goals, but the assessment program is still geared to low
level facts and skills, then the teachers, students, and parents receive
mixed messages about what is important for students to learn. The
results of such misaligned assessments are inevitably to push
mathematics education back toward the shopkeeper arithmetic
curriculum of the past.
If curriculum and assessment practices are changed, yet the teachers
are given no help in improving instructional strategies and in using
new forms of assessment to foster student learning, then students also
fail to thrive. Current research on educational change in this country
suggests that students in situations where the school and community
have worked consistently over several years to reform their schools
and to provide long term support for teachers in changing curriculum,
instruction, and assessment do better than students in misaligned
situations. This suggests that change such as those envisioned in the
NCTM Standards documents is possible and is powerful for
students. However, tinkering with components of the system rather
than working toward coordinated change is not likely to work, and
may disadvantage students even further.
It takes a very long time for change to become habituated.
Political rhetoric can swamp a long term commitment to a
particular direction of improvement. “Success” is very fragile. A
very few determined persons with a platform from which to speak
can undermine a great deal of effort to help teachers and students
improve the teaching and learning of mathematics and science. This
happened in “new” math and is in danger of happening in the
soundbite world of today with the “new new” math! We have to
take the lessons we have learned to heart and work to make clear
what is to be gained from reform curricula, why it is important that
we continually work to improve mathematics and science programs,
and why a national vision articulated in the form of standards can
guide the work. Reformers themselves must make sure that their
rhetoric in support of reform is reasoned, based on what we know
from best practice and research, and open to continued civil
discourse in which opposing views can be aired and common ground
sought.
