A symposium hosted by the Center for Science, Mathematics, and Engineering Education

 
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

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. Teacher-proof 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 then-existing 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 up-front. 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 medium-sized 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 materials-based 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 curriculum-based 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 in-service 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 in-service opportunities. The latter takes the curriculum as one of the tools to help teachers re-think 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 in-service 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 aligned--curriculum, 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 sound-bite 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.

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