Conference Material

The Stages of Change

EXAMPLE 2: THE STANDARDS

I am certain that many of you are ahead of me, and are already thinking of the Standards. Now let us go through the stages that appeared with new math and see their counterparts in the Standards.

Stage 1. Work by the pioneers

The NCTM Standards are essentially not a curriculum, but a set of policy documents. Thus we have to look at earlier policy documents, too, to see the pioneers. These pioneers are also the pioneers of today's science standards, because the NCTM Standards directly influenced the National Research Council to come up with science standards. The first of the reports that presaged the standards era was the report of the National Advisory Commission on Mathematics Education in 1975. Its leader, Shirley Hill, who had been at Stanford during the time of SMSG, realized that policy makers and people outside of mathematics education needed to be aware of changes.

The work of the pioneers began in the 1960s. I had a little hand in it in the 1970s, with a project developing algebra through applications. Alan Hoffer headed some projects at Oregon in geometry and at the middle school level. These and other projects were based on the belief that mathematics was broader than just theory and skill.

Adapting a National Institute of Education report on basic skills, in 1977 the National Council of Supervisors of Mathematics, under the leadership of Ross Taylor, presented its list of ten basic skill areas. In contrast, NCTM was not an early pioneer. Shell-shocked by the lack of lasting support for the new math, NCTM was willing in the 1970s to stay out of the policy arena. Its first emergence into this arena, with Shirley Hill as its president, was with a brief pamphlet, An Agenda for Action, in 1980, that emphasized problem solving as the center of school mathematics.

Stage 2. Proselytizing of and by the apostles

It is very difficult to make major change if school administrators do not want to change. So these reports from mathematics education organizations recommending change did not create major change. The overall climate for change began to appear primarily because of the appearance in 1983 of A Nation at Risk and reports from both the College Board and the Conference Board of the Mathematical Sciences on how mathematics needed to be changed.

Consequently, when we began UCSMP with the help of the Amoco Foundation in 1983, the same year as A Nation at Risk, we knew that we might play some of the role that UICSM had played with the new math in the 1950s. Thus we might be called pioneers, and if so, then 1983 for the Standards is like 1951 for the new math, in that in both years a major curriculum project that had the essence of the new movement began, and 1989, the appearance six years later of the Standards as a catalyst to really get the movement going, is like the appearance of Sputnik in 1957, six years after UICSM began.

Stage 3. Use by those disenchanted with the old

No mathematics curriculum projects in the early 1980s were supported by the government, so there were many disenchanted mathematics teachers and supervisors in our nation's schools. We had very little trouble obtaining sites for our project tests, and indeed, we found very little opposition to our work by any of the disenchanted. Our materials were used in project form by many schools before we ever were associated with a publisher. In fact, when we put our curriculum out for bidding, and five publishers bid, two of those publishers in their bids gave sales expectations for the first year of commercial sales of the books that were far less than the number of copies we were selling from our University offices.

Stage 4. Acceptance by the establishment

By 1985, the leadership of NCTM became committed to change, for it is then that the development of the Standards was set in motion. When in October of 1987, the draft Curriculum and Evaluation Standards appeared, they constituted endorsement of a new movement in mathematics education almost precisely along the content lines that had been in the NCSM basic skills report 10 years earlier, and with the technology and applications thrusts that had been in more recent reports.

5. Joining by the piggybackers

The influence of NCTM's Standards has far exceeded any expectations that NCTM had. Virtually everyone had to join the movement. Of course, since NCTM itself was now leading the movement, it is to be expected that its journals, yearbooks, and other publications would fall in line. But, through the efforts of the Mathematical Sciences Education Board, so too did the National PTA, the Mathematical Association of America, and many other organizations. Furthermore, in a development that certainly should be viewed as astounding, all of the other subject matter areas began to develop their own Standards.

It is well-known and I have already mentioned that during the time of new math, there were similar developments in science curricula. Not as well known today is that there was a new social studies, that English and language arts teaching also underwent major changes, and that foreign language instruction was overhauled. So the changing of all subjects at once is not new, but in the sense of having "standards", it is absolutely clear that other organizations piggybacked NCTM.

But the biggest piggybackers have been within the mathematics education community — individuals and school districts who are linking everything they want to do as being recommended by the Standards, regardless of whether there is support for the idea there. Both the Curriculum and Evaluation Standards and the Professional Teaching Standards go out of their way to point out many times how there is more than one way to reach the goals that they are setting, but we see many school districts asserting that the Standards force a particular interpretation. For example, the Standards say almost nothing about interdisciplinary curricula, or about constructivism, or about removing tracking, but people who favor those ideas will refer to the Standards as supporting them, and vice versa.

This kind of piggybacking among mathematics educators has the same dangers as the "standards" movements outside our subject. No one has ever claimed that the Standards would be a panacea. There will always be problems. If everything we do is justified by reference to the Standards, all our problems will also be attached to them.

6. Forcing of the enchanted

When the Standards first appeared, not everyone was disenchanted. In this movement, with change being dictated more and more by national reports and state regulations and testing, the classroom teacher has felt powerless. Thus, though when one looks through NCTM publications and conferences there seems to be almost no opposition, when one gets to the classroom level one sees many teachers who are not convinced that they need to change and are frustrated by their inability to be heard.

We know where we will have the most problems with UCSMP curricula; it is in places where the supervisor has more or less dictated the use of our materials without due process of the teachers, and where for whatever reason there has only been minimal opportunities for teachers to be retrained, to voice their concerns and fears, and to talk with one another in a constructive away about the changes that need to be made. I continue to be dumbfounded by school district administrators who expect their teachers to change without making adequate provision for retraining in that change.

Many teachers are quite satisfied with the status quo, even enchanted with it. We like to believe that we have convinced these teachers to convert to our beliefs. But we are in a position where teachers find it difficult to disagree publicly with us. There are many stories of conversions of such people, but let us not ignore the unconverted who are waiting for the Standards or their supervisor to go away. In every school district, instead of a conversion of those who were satisfied with what they were doing, we get a forcing of the enchanted to do something they do not want to do.

I must say, in this regard, and I hope that my NSF hosts will not boot me out of here immediately, that what seems to be a requirement in many places — that state systemic initiatives and urban systemic initiatives and local systemic initiatives use NSF-created materials is dangerous particularly for this reason.

Stage 7. Oversimplification and overapplication of the change

We also are seeing oversimplification of the changes. In UCSMP materials, we tell teachers not to explain everything before students get a chance to read it for themselves. You would think that mathematics teachers would understand the difference between "not everything" and "nothing", but in many places we hear of teachers who sit back and view their roles as facilitators to mean never to explain.

The oversimplification also is represented in some of the NSF materials, in which the complexity of mathematics content and learning is replaced by simplistic notions such as: everything should be developed through problem situations; or, there should be no work on paper and pencil skills in isolation; or, all evaluation should be holistic. You can identify other aspects, I'm sure.

In UCSMP, we developed the SPUR approach to understanding in order to emphasize that we had learned from the past, that mathematics consists of skills, properties, uses, and representations, and a curriculum that is all skill-based, or all property-based, or all application-based is not balanced enough to provide an appropriate mathematics experience for any student.

We also see curricula being applied to all students at the same time, in too zealous a reaction to tracking. Chronological age is not the best way to sort students for learning, as we know from experience with any activity that desires high performance. Music students, gymnasts, other athletes may begin in age groups, but by the time they are at the junior high school level, these age-group distinctions become eroded because the differences in the performance of children, and in their desire to work, make it necessary to separate them out. Chronological age is not as good a predictor of performance in mathematics as is entering knowledge, and we should not ignore this fact in setting policy. This poses a problem for any curriculum that is applied to all students, and it also poses a problem for any Standards document.

Stage 8. Failure of the oversimplified and overapplied theory

We already have seen classrooms and schools where there is a failure of the oversimplified and overapplied theory. This stage is not a healthy one for those of us who believe that the NCTM Standards are, in general, a welcome framework within which to operate. In 1995, when I gave the first version of this talk, I said at this point, "It suggests that a backlash will occur in which a few of the major excesses of the Standards will be highlighted as either unrealistic or too idealistic or downright wrong, just as sets were used in the arguments of new math." This is exactly what is happening. Let me continue what I said four years ago, again word for word.

"When will this happen? New math started having problems in the late 1960s, perhaps ten years after Sputnik, even while new projects were arising that were spawned by it. If the time line for the new math is any guide, the decline in the Standards influence will begin to happen in approximately the year 1999 and the Standards will essentially lose their appeal by 2004."

Stage 9. Test scores that do not bear out people's desires

The eery aspect of this time frame, predicted by translating the new math time line up a generation, is that 2000 is the year when Goals 2000 wanted the U.S. to be number one in math and science in the world. Key test scores will appear around that time. At the rate we are going, we are quite likely not to improve our standing from being near the bottom at 12th grade, because most school districts simply have not changed enough, have not increased their expectations enough of what they expect their students to know. Furthermore, in most places there has been only one adoption since the math and science Standards appeared, and even in those places that have changed quickly, few students have had the opportunity to go through an entire K-8 curriculum in accord with the Standards, let alone an entire K-12 curriculum of this type.

The challenge in mathematics is that a major change is needed in the thinking of educators and it requires time to institute the change. Unless you begin some algebra with all your students in 7th grade and give large numbers of them the equivalent of a year of geometry by the end of 8th grade, you are not up with the rest of the world. We have seen a few schools and school districts do this, but they could not do this without first strengthening their K-6 curriculum so much that they are starting pre-high school mathematics in 6th grade with all students. So it took them 6 years to get their first class of students up to the level they needed to make their 7th and 8th grade world class, and they needed the support of the high school to make certain that this work would not be in vain, and that the high school would recognize the students' work in algebra and geometry and begin large numbers of students with second-year algebra.

The point is that not enough schools are doing this. So when the results come in — probably in the years 2001-2002 — from the testing that will take place in the year 2000, I fear that what happened in 1974 with National Assessment will happen again with the Standards. That is, the Standards will be inappropriately blamed for the lack of improvement of the U.S. on international comparisons by people who do not realize that change takes longer to implemeent than just a few years.

Stage 10. Public perception of the failure of the change

This public perception of the failure of the change would signal the end of the movement.

Stage 11. Fatigue of the establishment

To keep this from happening, we must anticipate what will happen. In this regard, that NCTM has put great energy into its Standards 2000 project is critical to improving what goes on in mathematics education, and I think science education, too. Even if you do not agree with everything in it, it gives the important message: Change takes more time than the movement that got you your funding. Consequently, you must build mechanisms that will outlast you. You must have a consistent plan that you do not have to change much, but it should not be a plan whose foundation is on ideas that surely cycle. It should be flexible enough to ride the waves of the cycles.

This finishes the first part of my talk. Now I would like to look at things from a different perspective, the actual creation of change.