Conference Material

The Stages of Change

The Creation of Change

It is convenient to distinguish two calibers of change. If you are thinking of using a new book in place of an old one, then the kind of change you are thinking of doing requires only that you, and perhaps a couple of others, make a decision and go with it. But even this caliber of change requires that you be able to answer a number of questions: Why is the change needed? What are the specific problems we are trying to overcome? What makes the new approach better? Is there anything I must do that I haven't done before? How much must teachers be retrained to teach this course? Will the students act differently?

The second caliber of change is more substantial. It can be distinguished in various ways from the first caliber. Would the change persist if you left your school district? Can the change be so noticeable by someone who receives your students that they must change what they do? This constitutes substantial change. To get substantial change, you must build each year on changes made in the previous year; otherwise even large efforts in one year go to waste.

What are some substantial changes? Beginning at grade 4, I would like to see mathematics taught by teachers who feel a responsibility to teach mathematics, and likewise for science. If music can have a specialized teacher, why not mathematics, which is surely at least as important. A school organized the way we envision would have specialized teachers in science and perhaps also in social studies, as well as mathematics. Time for these disciplines would be guaranteed by the schedule, and the ability of teachers to maintain subject matter expertise and attend professional meetings would be possible because they would not be pulled by every discipline. The elementary school teacher of today has an impossible job; no one can keep up with knowledge and teaching trends in all the disciplines. Let's realize this and change the position.

The best students should take algebra in 7th grade and virtually all students should have the equivalent of a year of algebra by 8th grade. Average to above average students going through the first four years of the secondary curriculum would complete geometry and advanced algebra by the end of their sophomore year even iuf they were not advanced placement students.

Here's one for science. Biology, chemistry, and physics should not be taught as independent subjects.

These three ideas require major changes in the ways in which schools deliver instruction to children. In particular, a single teacher cannot implement any one of them without help from other teachers and the school administration. As a result, they represent some of the more difficult ideas to implement. To accomplish this caliber of change, I believe five steps are required.

The first difficulty in implementing change is that there are always some people who do not believe change is needed. Thus the first step in implementing change has to be recognition. You must convince people that there is a problem, and if you want major change, you must convince people that there is a major problem, and that your change has a chance to help alleviate the problem.

Let us first understand what we consider to be the problems: Huge numbers of students leave school mathematically and scientifically ill-prepared for the activities they will undertake. They often terminate their study of mathematics and science too soon, not realizing the importance these subjects have in later schooling and in the marketplace. They do not know enough probability or statistics or applications of mathematics even to be an enlightened citizen. They are not acquainted enough with the current technology to be comfortable with its use in business or in engineering or the sciences. They are not acquainted with the mathematics used on jobs or the science needed by an educated consumer. They do not get enough experience with problems and questions that require some thought before answering, and they do not develop the skills necessary to learn mathematics or science on their own.

If we want any evidence of how bad the situation is in mathematics, simply take a look at the catalog of any two-year college. It is dominated by high school courses, and not necessarily the upper level courses. You will see many arithmetic and elementary algebra courses. I was told by a major college publisher that the number of intermediate algebra books sold each year at the college level in the U.S. exceeds the number of second-year algebra books sold at the high school level. The problem is there, and it is so large that it almost seems senseless to tackle it. But we must. Mathematics is too important for so large a segment of our population not to be versed in it.

No one wants to be alone in trying to solve a problem. Perhaps the most common thing told to us by schoolpeople is, "If we make this major change, what will we do with students who come into the school district from outside?" Think about this question. It assumes districts are alike, which they aren't. Students who come in from other school districts always have to adapt. Students who change from one teacher to the teacher next door have to adapt, often greatly. In switching districts, students may have read a story last year that they will see this year; they may have studied South America last year and find they will study it again. The answer to this question is: every school district has to accommodate students new to it, regardless of its curriculum. Do we refrain to teach our children reading because some new students who come into the district cannot read as well as ours do? Do we refrain from offering algebra in the 8th grade simply because there are some who are not ready for algebra? No–we take pains to get them reading and get them more ready for algebra.

Another answer to the question of what to do with students who are new to the district is to point to the number of organizations that are supporting the kinds of changes you want. Display the reports from inside the subject community but also make certain that you have reports that are from outside the mathematics or science community. Otherwise you will be viewed as simply arguing for your own interests. It is important to support the improvements desired by others; mathematics may be in bad shape, but I think science is in worse shape than mathematics and social studies seems not far behind. One study about ten years ago found that a greater percentage of students in Europe could estimate the population of the United States as about 250 million than could those from the United States. How bad must it get before we get specialized teachers in the elementary school?

There are myths about change.

1. The most common, when one changes curriculum, is that standardized test scores will plunge. At the elementary level people are worried about the effects of calculators on the computation tests. At the secondary level, its the SATs and ACTs.

Our general evidence with students using the UCSMP curriculum is that, for the most part, the standardized tests are our friends. Students who are a year ahead will perform a year ahead. The evidence from our evaluations, ranging from kindergarten through algebra, is that this improvement is possible. In many states, the top scoring schools use our curriculum. We know it works. But these kinds of substantial improvements can only occur with the second caliber of change. Changes one year must be stepping stones to accomplish changes the next.

To explode this myth, you must test. You must be honest. You will be required to give tests that are biased against new curricula, that are too narrow, or that focus just on paper-and-pencil computation. This is a fact of life which cannot be avoided. But you must also test on the new things you are trying to accomplish. If you implement calculators, you must test children with them. If you teach some physics at 7th grade, you must test 7th grade children on physics.

We have had a quandary in evaluating some parts of the project. If you have truly made significant change, you may find it hard to find a comparison group to determine the magnitude of the change. For instance, suppose you adopt the ideas of our secondary curriculum, and many more students are now taking geometry in 9th grade than did before. You would like to know how much more a student knows now than that same student would have known in your previous setup. You can't compare that student with a 10th grade geometry student because he or she is only a 9th grader. To compare that student with the other 9th graders is very difficult, because if you put a lot of geometry on the test, then the comparison students will become quickly discouraged. The UCSMP students know so much more at that same age that no test designed to show how much more is able to be given to other students.

Some districts have tried to solve this problem by comparing UCSMP students to the only such high-performing students they know, the ones in their gifted programs. We view that as wrong. We are not trying to make all students gifted. We are simply trying to give average students the sort of mathematics education they deserve. One cannot expect average students to possess the same inherent desire, ability, and often the home backgrounds that characterize many gifted students. You must have comparison studies with matched cohorts.

There are other reasons for testing on the new. It forces teachers to teach the new. And it makes it possible to build each year on the expectations of the previous year.

2. A second myth is that you either have it or you don't at math, and the purpose of math instruction is to find out who has it. For science, the myth is that there are math-science types, and if you are not one of those types not only can't you learn the stuff, but you shouldn't. And the culture perpetuates the stupid notion that the people of those types are nerds, and those that aren't nerds are exceptions to a rule.

How do we destroy this myth, so common in our culture? I proceed by analogy. Reading was once thought to be accessible only to the god-gifted, the aristocracy. Unless we see something in Arabic or Chinese or Thai, we tend to forget that letters are symbols. Anyone who can learn to read can learn to decode the symbols of mathematics. But we don't teach children or adults to read by giving them lists of words without any context. We teach them with stories and information in context. We know that almost everyone can learn to be literate that way. Now let's get them to be numerate. Giving them lists of multiplications to do won't do it; we need context in mathematics as much as we need it in reading.

For science, the myth can be dispelled in the following way. You can think of better examples than I can, but here is a start. A farmer has to know either zoology or botany, and no one thinks of farmers as nerds. Chemistry is used by anyone who looks at skin lotions or makes beer — beauticians and brewmeisters are not usually considered nerds. And physics is used by anyone who shoots bows and arrows, moves heavy objects, even anyone who drives a car.

3. The panacea myth. There are myths the other way. Some people think we have all the answers. Some people think you will cure all their problems. I have had numerous people come up to me and ask something like "We have been thinking about implementing some of the ideas you propose. What do we do with a student who does not keep up with the others?" Or "We have an incompetent teacher. What do we do with that teacher?" I have two responses. First is that we cannot solve all the problems of the world of education. There will be students who aren't successful even with the extraordinary materials we have created. There will be teachers who are poor teachers, even after they have been to ten in-service meetings with you in charge. We are not a panacea; we are only attempting to be a better means to a higher end. My second response is more practical: What do you do now with students who do not keep up? What do you do now with that incompetent teacher? Do not expect your current solutions to become obsolete. My third response for that incompetent teacher or poor student is: If the teacher is incompetent now, things will not become worse with our new stuff. Worry about the teachers who are great at the old stuff. Similarly, do not be so quick to change the students who were terrific.

4. A fourth myth is that there is no hope, a belief that nothing can be really be done to change the current situation. The teacher or administrator reads about what is done in Japan and says, "Their society is different. We can't do that here."

Since the TIMSS results were announced last year, we have seen another view. It is to copy the curricula of Japan or Singapore. What is interesting is that we held an international conference this summer at UCSMP and invited people responsible for the curricula in those countries and in China, and they are all moving to copy us! They will all be using more calculators and be trying to accommodate all of their students by increasing the number of real-world applications in their curriculum.

How does one convey the needed optimism, the required confidence, the necessary conviction that things can improve? Look around you. You all must think it can be done. Look at the places in the U.S. that perform as well as any internationally. One is the area in the northern suburbs of Chicago where there is a consortium that gave TIMSS to its students. Expectation is an important variable in education; if we do not have certain expectations for students, they will not achieve them. The parents and the schools in those communities have expectations that start well before kindergarten.

But more than that, tell people what happens if you do not move, if you do not have high expectations. The best way to ensure that something will not be learned is to not teach it.

People must talk. Change of the first caliber does not require much articulation, but change of the second caliber–significant change, multi-year change–requires that administrators and teachers work together. In Illinois, where there are often different elementary and secondary districts in the same community, it can require that two or more districts get together.

Articulation must be both ways, both top-down and bottom-up. It must go from administrators to teachers and back. It must go from elementary schools to high schools and back. Teachers cannot make significant change without administrative support, and administrators cannot make significant change without teacher support. And build bridges to those who do not agree with you. If they are honest and caring, they deserve to be heard.

How does one get such a consensus? One thing is to make improvement your goal–no one can be against that. Do not necessarily work for any single means of improvement. Look around; what are the best materials? What agrees with the goals of your school or school district? To get people to realize that they need more technology in the schools, bring in business people, if necessary. Would the business community like students to be acquainted with computers? Should students be able to use calculators? Of course.

Now that you've set the stage, you have people to work with you, you have a common purpose, and so on, what do you do? Of course, every district is different, but I give you the following suggestions:

The greater the problem that is perceived, the greater the changes that people want to make, but the more quickly people want to make those changes. Yet it seems prudent that great changes should be made carefully and slowly. This is a omnipresent paradox in making significant change.

Small improvements can be made in all grades simultaneously. But big change, by definition, cannot. Suppose you wish to make big change in 2nd grade. If you make significant change in 2nd grade, then 3rd grade should be changed next year. If you change 3rd grade at the same time as 2nd, then the 3rd grade students don't have the background needed. You guarantee yourself that this year will be tough, and then next year you have to change third grade again. So it seems more efficient to change one year at a time. It's also easier to inservice one grade of teacher than all grades.

Despite all planning, significant change seldom occurs without some difficulties. There are people who don't understand the changes and unwittingly do things to make the change more difficult, there are more sorts of practices that are based on current norms than realized, and so on–and of course there are the people who were against change from the beginning and look upon everyday problems as having been caused by the new practices.

It is important to plan ahead. We have found that, at all levels, teachers do not get enough opportunities to talk about what they do. The initiation of a new practice can be a catalyst to do something that should be done all the time: namely, to get teachers talking with each other about what they teach and how it is going. Frank discussions, chaired by a supervisor or someone designated to have that responsibility, are often better inservices than anyone brought in from the outside.

One benefit of such internal meetings is that decisions can be made so as to anticipate what will happen the next year and correct for anything that may not be going as you would like.

I have mentioned this before. But I mention it again. You have new objectives and you must test on them to force teachers to teach the material and show that students can learn it. But — and this is most important — You must not make your goal of testing to show that your way is better, but whether your way is better. That is the only way to keep your credibility in the long run.

Of all things that need to be planned in advance, perhaps the most important is a safety valve. Few if any programs are successful with all students. If a student does not succeed or a teacher does not work out, there needs to be a place for that person. If a new curriculum seems not to have worked in a particular topic area, there must be a plan for what to do the following year. This is still another reason for doing things one year at a time.

A safety valve is not often applied. But it is a wise and important thing to have. You need not have the practice spelled out, but always recognize that there is a possibility that things will not occur as you thought.

However, a caution should be stated here. Do not apply safety valves too early. We have had teachers teach from our pilot materials and supplement as early as Chapter 2 with material that they would have found later in the year, but we didn't want to put so early. You must give your ideas a chance, but give the teachers enough inservice so that they realize what they must do and also realize that there will be opportunity for corrections if things do not work.

And what is the safety valve for this talk? What is the mechanism for being able to clarify things that were not clear, for being able to change things that were said wrong, for being able to add things that were missing? It is the discussion part of this session.