A r c h i v e d  I n f o r m a t i o n

SENATOR GLENN: What does research tell us? Deborah Ball is a professor of mathematics education and teacher ed at the University of Michigan, which, Brit, beat Ohio State, I guess, we don't admit that this year. She is currently co-director of a longitudinal study designed to improve instruction and learning in mathematics in high poverty elementary schools, and is also directing a study focusing on the practice of elementary mathematics teaching.

Deborah will build on Nanette's presentation with a synopsis of relevant research results. Deborah, thank you.

DR. BALL: Thank you very much. Is this mike fine now?

[See Slide 1] The Commission?s charge, our charge as commissioners, is to make recommendations for the improvement of mathematics and science teaching. One premise of our work, particularly what we're working on at this meeting, is that we can't make recommendations for the improvement of teaching without understanding better the phenomenon we're seeking to improve.

Nanette?s presentation offered us the opportunity to consider the practice of teaching and what the work looks like up close. And her response near the end saying, what we were doing was different than what Jim Stigler helped us do last time. She took us inside seven minutes, I mean seven minutes out of 180 days, seven minutes of class time to look more closely at some aspects of the work. And I think one thing that she illuminated was a glimpse of the multiple considerations that teachers must weigh, the factors with which they must contend. She helped us to see, we said over and over again, that teaching is much more complex than some of the cultural images that we hold. A lot of teaching is invisible to the familiar eye. We think we know teaching and so, therefore, we think we know what it takes to do it. We take a lot for granted. And one crucial aspect of our own work is that efforts or recommendations to improve teaching that ignore some of those more intricate aspects of the work are unlikely to make a difference. Indeed, in this country we have a long history of efforts to impact teaching and learning that have essentially failed to go past the classroom door.

So this meeting is actually a very important one for us. We need to challenge ourselves to resist the temptation to talk outside of the work, and to spend some time thinking carefully about what are these interactions that go on inside of classrooms in mathematics and science teaching, and what does our understanding of those help us to come to when we think about what the recommendations need to be.

To do that, I would like to begin with a basic diagram that Nanette had up in the background of many of her slides that looked like this. [See Slide 2] Sometimes people think about teaching or about instruction as what teachers do to students or with curriculum material. And the purpose of this diagram, which some of my colleagues and I and other people as well sometimes use to offer a simple schematic of what teaching and learning entail, offers a somewhat different way of thinking about it. It makes plain that what happens in any classroom is a product of a set of dynamic set of relationships among teachers, students, and content. And this goes for any kind of teaching. This model would be a descriptive diagram for lecture teaching. It would be a descriptive model for what Javier referred to earlier as cooperative learning. It's not implying that students and teachers are talking equally in this diagram, it simply says that the dynamic among them is what produces opportunity to learn in the classroom.

[See Slide 4] Take the problem you saw on the videotape for example. This one, I think we've seen as much of that as we probably want to for today. But one thing you can think about in relation to the diagram is that what happened in that particular class ensued from the way this particular math problem was interpreted by this teacher and those students. The way that she used it with her students, the things her students said, what she made of that, what she gave space for, what she didn't give space for, what her students did with each other's work, how the teacher used and interpreted what students brought up, what she cut off, and so on.

We could just as easily imagine this same problem taught in another third grade class, and I think we should do that for a moment just to remind ourselves that the purpose of looking at a tape is not to suggest there's a single way to do this but, instead, to understand that this dynamic set of relations that I'm talking about is what produces differences across lessons.

[See Slide 5] So imagine, for example, that another teacher uses this problem. And what he decides to do is to focus on the how many more aspect of this question. In our group, which was the content group, we discussed that in learning subtraction, somebody else mentioned it as well, "take away" tends to be the dominant model. We use words like "take away" when we refer to subtraction, and when students encounter problems that ask how many more, they often find this difficult.

So imagine that a teacher sees this problem, and sees it as an opportunity to work directly on that phrase, and to think about how to teach his students that when you see the phrase "how many more" it's a key to you that you should subtract. And he might tell the students this, and explain that, and then he might show them how to set up a subtraction problem like this, [See Slide 6] and then he might carefully review the steps of the borrowing procedure, or the regrouping procedure. We could see that the children in the other class had also learned that procedure, but another teacher might use this problem to directly focus on this procedure. [See Slide 7] He might explain how the steps work carefully, going through it, showing, as several people explained earlier, that you regroup the three tens so that you now have one ten and two ones, which permits you to subtract the six. [See Slide 8] It's crucial for students to understand that two tens and 12 ones is still the same amount as 32.

There's a lot to understand here if you want to teach it carefully, and a teacher might use this problem to do that, and he might then, after going through this example, assign other problems, giving them a chance to practice.

So although these were both third grade classes, and although the same problem was used in both, what students do and have opportunities to learn differs between these two different lessons. These differences arise as a function of the teacher's interpretation of the problem and its opportunities for his or her students. The students work on it, the teacher's use of and response to their students work. [See Slide 3] So think about this diagram that I showed you a moment ago, this one, think of this diagram as more than a device, in fact, it will be a device for organizing my presentation this afternoon. But think of it also as a kind of finding also from research on teaching. That is, that opportunities to learn and instruction are a product of the interactions among these elements.

So I'm going to use this diagram to organize my presentation of a small set of recurrent findings from research on teaching, from studies of teaching and learning. I think that the schematic offers us a way to organize some of what is known from research on teaching. Consider that each of the points I'm going to make, which are going to rotate around this instructional triangle, consider them as contributing to understanding more about these interactions, and how they play out to affect the quality of mathematics and science instruction.

I will return to this at the end because understanding the set of relationships, I would argue, is key to thinking about strategies for improving instruction.

Let me make a few short remarks about the nature of what I'm about to say in this presentation this afternoon. First, I can't possibly present in 45 minutes, no matter how fast I talk, a comprehensive account of such research. Instead, what I have done is selected a set of findings that seemed to me to have particular import for our work as a Commission.

Second, and I think we're going to continue to struggle with this, much research on teaching and learning has, in fact, been generic. Other research has been specific to mathematics and science. But I drew from both in an effort to assemble material that bears on the work of this commission and, in particular, bears on efforts to improve instruction in mathematics and science teaching.

Third, the body of research from which I drew is highly varied. It includes international and U.S. studies, it includes qualitative and quantitative work. It includes recent work, and it includes enduring findings from studies from the sort of birth of research on teaching, which was not all that long ago, but was as much as 30 years ago.

Finally, and I would caution you about this, although the findings that I'm going to report or talk about may sound, in fact, rather obvious to you, and not at all surprising, in other words they may seem to you to be things that anyone who has been paying attention to teaching would know, consider the fact that for many of the things I'm going to talk about few policy initiatives in this country take these particular aspects of teaching and learning into account in their efforts to improve instruction. I'll return to that throughout my talk because, although some of these findings may appear to you to be obvious, it's important to realize how rarely they're used in planning strategies for the improvement of teaching.

So I'm going to begin on one side of this triangle, I'm a novice at PowerPoint. [See Slide 9] I'm going to start on the side that has to do with teachers and content. And by content what I mean is both the subject matter of mathematics and science, as well as the curriculum materials used to teach it.

How teachers interact with content

So the first question I'm going to address in presenting a small set of findings from research is what's known about how teachers interact with content that bears on instruction.

[See Slide 10] So the first one that may seem obvious to you, but is worth mentioning, is that teaching in the U.S. relies substantially on commercial textbooks. Most science and mathematics teachers use textbooks as the basis for instruction. They use them as the guide for what to teach and for the student exercises in math and activities and informational material in science. Many school districts mandate the use of a particular text in mathematics and science, and some allow teachers to choose.

What is meant by "textbooks" is more than meets the eye as well. Curriculum materials in the United States, as many have noted, are voluminous, including extra materials, teachers? manuals, supplementary stuff, tools, equipment, counting materials, and so on. And we actually know little about what teachers actually have access to, what they use beyond the basic student text.

However, some early research on teachers' use of teacher?s guide revealed that mathematics teachers often use the teacher's guides principally as an answer key, despite the extensive suggestions for teaching that were included in the teacher's guide. But, in fact, little work has been done about the ways in which teachers make use of these voluminous materials provided by curriculum developers. And this is an important point.

[See Slide 11] At the same time that teaching in mathematics and science in this country is heavily based on textbooks, a second finding is in some paradoxical relationship with that, which is that teachers make significant choices as they use textbooks. They exercise considerable autonomy in how they actually use the textbook. They omit or reorder lessons, they change the suggested materials, they alter explanations, activities, and examples. They modify problems to make them more appropriate for their own students, easier or harder. They change the order of sections, of units, and supplement with other activities. Thus, textbooks both do and don?t provide considerable structure for instruction in this country.

[See Slide 12] Third, teachers' understandings math and science shape their use of textbooks. So do their beliefs about the nature of these subjects and how students learn them.

Let me give you a couple of examples. As teachers modify a math problem to make it appropriate for their students, a quintessential activity of teaching, how they understand the mathematics shapes what they do with that problem. They may improve it or they may, in fact, distort it. Teachers' sense for mathematical or scientific reasoning affects how they make use of a problem in class, how they conduct discussions of textbook activities, how they treat student answers. As they run into difficulty with a science activity, what they know about the topic affects how they deal with it. Teachers who don't have experience with scientific inquiry will deal with an experiment in their textbook differently than will teachers who have considerable sense for such scientific practice.

When you put this finding, this third one, together with the recurrent and unfortunate finding that many American teachers lack deep and flexible understandings of core content in mathematics and science, it becomes clearer that curriculum materials alone do not and cannot determine what students have opportunities to learn. In fact, a good question is how much one might want textbooks to shape the enacted curriculum in math and science. On one hand, common textbooks could provide a common ground for all students. On the other hand, good teaching depends on teachers being responsive to their students and adapting instruction accordingly.

The question of what to recommend about curriculum materials and their use is an important question and one with many angles, not a simple question.

How students interact with content

[See Slide 13] I?ll shift now to a different side of the triangle, the one between students and content. And I'll, again, go through a short set of recurrent findings.

[See Slide 14] First, students develop and bring to school scientific ideas from everyday experience. They bring a host of well-established ideas to instruction. Their experience in the world has led them to develop theories about how things work. Some of these ideas, in fact, provide a useful foundation on which instruction can build. While others are in tension with scientific explanations, and may, in fact, be quite resilient and persistent.

For example, one of my favorite lines of research trace the ways in which young students understood how plants make food. They derived their ideas about this from watering plants at home, and from feeding plants with fertilizer. And they quite reasonably come to think of plant fertilizer as food for plants, and don't have a sense about photosynthesis as the process by which plants make their own food so to speak.

Since this notion of food is not intuitive from their everyday human experience with food, they may not easily exchange their ideas for scientific ones. And, in fact, considerable research in this area suggest that these ideas about food for plants and photosynthesis are quite resistant to even what might appear to be quite good instruction.

Other topics in science reveal similar theories that can be counterintuitive. For example, how we see how light works or how gravity works.

[See Slide 15] There's a parallel finding in mathematics, which is that some mathematical topics are surprisingly and persistently difficult for students to learn, and these don't necessarily meet the eye as obvious. In fact, I think Nanette made a point with us, trying to get us to go back in time to understand how it is that this procedure for subtraction that we're all perfectly skillful at using is, in fact, a very difficult procedure for young students to learn. I remember when I was first teaching and explaining very carefully the meaning of the procedure, and going through it and giving my students practice with it, and having them exhibit the fact that they could do several of these on Friday correctly, and on Monday again have forgotten how to do it, and again be subtracting up. It's just not an easy procedure, and there are other topics like this. Integers, for example, and operations with integers. What are negative numbers, how do we operate sensibly with them? Rational numbers, fractions, decimal numbers, percents, ratios, and connections among those and operations with them. The notion of variable, concepts of function, definitions and proof, all turn out to present some persistent challenges for students? learning.

These two sets of findings in science and in math make plain how much learners? knowledge shapes what they bring to instruction and what they make of it. Although these may seem common place to you, lots of mathematics and science instruction all levels proceeds with little design for addressing in special ways the sorts of ideas that students develop that are, in fact, at odds with mathematical and scientific understandings. We persist in believing that if we say it again, or say it louder, that somehow students will give up ideas that they've developed. And, in fact, one of the basic challenges for teaching is how to take account of some of these more resilient ideas that students develop and find ways to work with them to change their minds.

[See Slide 16] A more generic, and probably the most banal thing I'm going to say this afternoon, but still worth saying I decided, is that the time engaged in worthwhile academic tasks makes a differences for learning. You can laugh about this but, in fact, this is one of the earliest findings from research on teaching. And what it suggests is that the amount of time that students spend engaged in worthwhile tasks has a significant impact on what they learn.

This is a complicated finding because it's dependent on the quality of the task. Time spent obviously on poor academic tasks or on work that's too easy or too hard does not have these sorts of effects. But there's not agreement on what too easy or too hard is. It depends a lot on your conception of what there is to be learned. Some research on teaching suggested that appropriate work given to students was work that was easy enough that they could proceed without getting stuck at all. However, there are views of mathematics that would suggest that becoming stuck, working your way through that stuckness, is a critical part of learning to be mathematically proficient. So, generic research on teaching that suggested that activities should be within reach of students without any further assistance could, in fact, be at odds with good mathematics teaching.

As I said, this may seem the most banal of all possible research findings. Who needs research for this. But the reason I think it's important to bring this up is because, in fact, when you put this together with the finding that mathematics and science are not taught every day, at least in our elementary schools, and that time allocated to these two subjects in this country is often much lower than it is in other countries, and that, in fact, both subjects suffer from a lack of academic time.

One simple improvement we might consider is that time is one of the highest predictors of student learning, and that we should think carefully about the way in which time is spent in elementary classrooms, and middle school classrooms.

[See Slide 17] Finally, a finding that's really somewhat different than any of the other three up here, is that mathematics and science learning depends on integrating abstract and concrete models. Sometimes learning starts with concrete and moves to the abstract, which is, I think, a commonplace assumption that people make, things we often hear people say. But sometimes it's the other way around. Sometimes, for example, first graders come to school already reading two digit numbers competently and having no idea what they mean.

I remember when my daughter was learning to use a microwave, and she could type in quite easily 45 seconds on the microwave. She would go to the microwave and type 45 and say 45, and then one day I saw her in the kitchen, and she typed 405. I thought, what is this, this hotdog is definitely going to get really scorched. But what I recognized in a very interesting way is that what looked like regression or some very peculiar sort of error was, in fact, progress. Because it was at that moment where Sarah had suddenly realized that 45 is 40 and 5, not 4-5. So, in fact, years before she understood that, she could write 45 and read 45.

So examples like this permeate student learning, cases where they develop abstract formula or symbolic knowledge before they develop concrete understandings. So the notion that it goes in one direction or another is actually not what research has shown. But what is crucial is the capacity to link among them. And this is a place where instruction has often been the weakest. How does one actually map across representations. How can concrete materials and mathematics be used effectively together with symbolic and other forms. This is essentially mathematical as well as cognitive. And mathematics, as Nanette said several times, mapping multiple representations, inspecting the ways in which they're similar or different, is an essential mathematical activity. It turns out also to be core for learning.

Again, this may seem altogether so obvious as not to be worth saying, but much instruction continues to proceed without engaging students in any concrete experience, on one hand, on the other hand, we've also come through a period, probably still are in such a period, where excessive faith in concrete materials has led us to ignore the challenges entailed in helping students make good use of concrete experience to move in the direction of both abstract and concrete understanding. So that's this side of the triangle.

How teachers and students interact

We'll move to the last side, the teacher student side. [See Slide 18] Here the findings that I?ll report really emphasize the fact that the arrows in this diagram are bidirectional. I haven't said much about that so far, but if you think back many things I've been mentioning go both ways. I've talked about students understanding of the content and I've also talked, for example, how the content does and does not yield to student learning. But on the teacher-student side, it's really crucial to understand that some of the most important findings about teaching and learning have to do with the bidirectional nature of this relationship.

The first one, therefore, that I report is that students shape instruction. [See Slide 19] They shape instruction in some in fundamental ways. And this is a finding that may surprise people, or not exactly surprise them, but one which we consider only rarely. Certainly few efforts at improving math or science instruction reflect a serious awareness of what this means for teachers or for classrooms.

One way in which students shape instruction from some bodies of research has been referred to as bargaining. Students when confronted with difficult work, ask teachers for help, complain about the level of demand, and as teachers respond in various ways to these pleas for help and these complaints, researchers have been able to trace real changes in the nature of the academic tasks which students are doing. The intellectual challenge of the work is degraded or reduced, sometimes to the point that the work is substantially different from that which was first assigned. Students' resistance, complaints, pleas, all work to affect whether and how they engage with what sort of academic task. A task isn't the task that's simply given at the beginning of a period, it's what students make of it, and some of this work on bargaining illustrates quite profoundly how what appears to be intellectually challenging work can be reduced into something very different.

Another way in which students shape instruction lies in teachers' fundamental dependence on students. Teachers cannot make students learn. If teachers hold a discussion, for example, and no one answers questions or volunteers ideas, no discussion can occur. If students don't do the work that teachers create for them or assign, or don't engage in it as the teacher intends, then the intended lesson cannot happen. This can be attributable to motivation, or tailoring instruction, or to other factors, but this finding is robust whatever the explanation that students affect instruction.

And a third way in which that students affect instruction that didn't come up very much in our discussion of the video is that they learn from one another. They're shaped by their peers' attitudes and ideas for better and for worse. One very interesting thing that Jim Stigler has been reporting is something that fits with this notion of culturally different views of teaching and learning, and that is that in Japanese classrooms the notion that a few children up at an overhead performing an explanation or talking is, in fact, an opportunity for all students to learn. That students learn to create these presentations to their peers, that other students in the class see listening as a critical part of learning, as a critical part of the work to do in classrooms, is a very different idea than permeates many American classrooms where, if the teacher is not talking, students assume it's not for them, nothing they have to pay attention to. And the notion that we could take the fact that students attend to one another and turn it into a productive source of learning is a provocative and important derivation of this particular finding.

[See Slide 20] A second finding in this category is a very old one and a robust one, which is that teachers' expectations shape what students learn. Teachers who hold and convey high expectations of their students learning get much better results than those who don't. This is an important finding also cross-culturally for there is some research that suggests that Americans think of mathematical ability as inborn or innate in some way, whereas in Japan mathematics learning is thought to be mainly a product of diligent and concerted effort.

[See Slide 21] Third, teaching depends on teachers' capacity to understand their students? understanding. Some of you exercised that a little bit in watching the video, trying to figure out what did Bernadette know, what did Ronya mean, what did those different students think or what were they learning. This capacity to understand what students understand is affected by teachers' own content knowledge as well as their knowledge of students.

Understanding how someone other than yourself thinks is a challenge, and requires a flexibility of knowledge that's not automatically part of any adult's content understanding. It's not part of any mathematician's understanding automatically, it's not automatically part of a physicist?s or other scientist?s understanding. The capacity to be curious about and engaged with the way someone else thinks, particularly someone who is understandings are less developed, less compressed, less mature than your own, it requires a kind of flexibility and capacity to unpack that we only understand in small ways so far.

Being able to figure out what's going on in a student's understanding depends on this capacity to unpack from your own finished understandings of a topic back into the depths of what it looks like as it's developing. This also depends on teachers' knowledge of what are likely student difficulties in a content area. Something that one can actually learn and have in one's mind to anticipate. The fact that I know that borrowing is a difficult topic for second graders would affect the way I could teach that in way that someone who had never encountered second graders before would simply miss. So that's a few things about that side of the triangle.

How the environment affects instruction

Up until now, my comments about this instructional triangle has made it seem as though all instruction occurs in a vacuum, isolated from its surrounding contexts. [See Slide 22] But, just as one thing that research has consistently shown, that the dynamic among teachers, students, and content is central to classroom teaching, another crucial understanding is that the environments in which instruction takes place permeate the classroom. And although this may make sense, few discussions of policy, standards, frameworks, or instructional environments seem to take account of the way in which the external is really internal to instruction.

For now, I'm just going to make a couple of points about this, because I want to end my talk by saying a few things that understanding this dynamic implies for the improvement of teaching.

[See Slide 23] First, environments affect classroom instruction through teachers and students. What I mean by this is that as teachers and students perceive, interpret and respond to features in their environments, these things affect the interactions among them in classrooms. Take, for example, a child who brings home math homework and finds a parent who says, what is this, what are you bringing home, this doesn't look like anything that I brought home when I was in third grade, is going to affect something about the way that child views the work of school, what that child does with the homework, what happens in class the next day. And here I'm not judging one way or the other, I'm illustrating that things that are going on in the community actually do come in through students into the classroom.

Another way in which these "external", so-called "external" factors permeate classroom instruction could be seen in the way that multiple signals and messages about goals and outcomes enter into teachers' minds and work through the multiple sources of curricular guidance with which they must contend in this country. Textbooks, local district guidelines, state frameworks, standardized tests, multiple signals mean that teachers have mixed messages about what it is that they're to teach, and this shows up when they're sitting making lesson plans, when they're figuring what to do in the next month.

What's crucial to understand here is not just that these external forces find their way inside of the classroom, but that, in fact, they're also interpreted differently by different players. Two teachers teaching in the same school with the same principal in the same school district can have entirely different views about the extent to which they're constrained, not constrained, urged to do something, not urged to do something, because people differ in the way that they interpret, perceive, respond to such messages.

So to think of it as purely linear, that is to think of the environment arrow as going only one way would be inaccurate. Research shows persistently that actors: teachers, students, and others in the environment, their interpretations of the environment and or of policies affect how they use them.

I want to stop now by returning to where I began, to the need to understand teaching and learning in order to make sensible recommendations about how to improve it. If we look back at the triangle, I don't know if it's worth going back to it now, I think you're familiar with it, so I won't go back. If you think back about the triangle -- sorry, I told you I wasn't experienced at this. Well, there it is, okay [See Slide 2] and what we know about some of the factors that shape the dynamic in this triangle, it becomes clearer that efforts to improve instruction must target the interactions within the triangle, they must improve the effectiveness of the interactions among teachers, students and content.

What would that mean? My colleague, David Cohen, and I have been working on this question, and what we've come to ask ourselves is, what are problems implied by this diagram with which teachers have to contend and that are, therefore, also central to anybody's work who wants to improve instruction. There're three major factors on which we focus, now I will have to leaf through. You don't want to do the Joshua problem again, do you?

Use of knowledge, incentives for performance, and instructional coordination

I'll start talking while I get there again. Three problems on which we focus we call use of knowledge, incentives for performance, and instructional coordination. And each of these derives from a central challenge of teaching and learning that bears on the probability that students will learn what we actually want them to learn. And I?ll say a little bit about each of them. Let's see if I can this time more patiently get to the right spot.

[See Slide 24] Okay, first, I want to talk about knowledge use. [See Slide 25] Instruction is shaped not just by what teachers know, but how they use the knowledge. Consider the example I gave you at the beginning about two different teachers teaching the same subtraction problem because they thought about mathematics differently, they thought about what there was to learn differently. They used knowledge of students and of mathematics differently to produce a rather different lesson.

Second, knowledge use is also more complex the more ambitious are the aims for instruction. A form of instruction which doesn't require teachers to contend with unexpected student responses or to deal with complex content demands less in terms of knowledge use than a form of instruction that does. But, in any case, there are high demands for using knowledge, using knowledge of students in context, using knowledge of content in context. It's not just what teachers know, although that's critical, it's whether and how they can make use of it in the particular contexts of their work.

[See Slide 26] A second issue has to do with what we call incentives for performance. And here, I don't want to talk about incentives in the way that they're typically talked about. I want to think about that triangle particularly. If you think about the dynamic among teachers, students, and content, in particular between teachers and students, and recall the finding that I was reporting about the way in which students shape instruction, teachers expectations shape what students learn, and so on, then one has to consider that the principal way in which teachers can feel successful about their work is if their students learn.

Now, consider what that means. That means that when faced with the possibility of teaching the subtraction problem to your students, what's the incentive to teach in a way that opens up subtraction such that multiple representations are exposed, that different children's understandings are exposed, that the time is taken to actually unpack the meaning of it. There's very little incentive to do that in many ways.

If what you want to do is to be assured that your students have learned something, there's a powerful incentive to help your students to constrain the task in a way such that your students get the right answer. There's nothing more pleasing to those of us who teach than to hear our students do well. Consider what it takes to have the patience and the courage, in a sense, to be willing to consider student errors, to open up discourse in such a way that allows the content to be dealt with in a more intellectually serious way. And here, again, I'm not referring to an approach to instruction, I'm talking about what the incentives are to bear down carefully into the content itself.

So the finding here has to do with the fact that teachers face competing incentives for performance. They, on one hand, want kids to get the right answers and to do well on tests. And they also, perhaps, may want them to engage in complex work that will prepare them better for the 21st Century. But if we're serious about expecting teachers to do that, we need to consider what the incentives would be to take the risk of asking students to do intellectually more challenging work. Students will resist, teachers will feel worried about their capacity to be successful. We'll have to think carefully about what the incentives are to raise the standard of instruction in ways that move beyond very conventional and closed forms of content. It's worth underscoring here that this problem of incentives is only exacerbated when standards are raised, and when accountability is heightened. And simple minded ideas about incentives are not the answer here.

In fact, what often happens is, when students fail, is that teachers find other people, students to blame, or other people to blame about why it's not working. We have to figure out how to get the incentives right for teachers to care about high level instruction.

[See Slide 27] The third finding, and the last one, has to do with what we call instructional coordination. If you think about the American system and the fragmentation that we know about in the policy environment, the same thing is true inside the classroom. You have many students, Javier said many classrooms have 30 to 40 students, this is true, so imagine the problem of coordination between having an instructional goal, having 30 to 40 students who each have somewhat different understandings of the content that you're trying to help them learn, different interpretations of the work. And somehow, as teacher, you're trying to coordinate among your students to move the lesson along. That's a tremendously difficult problem of coordination, and that's just at the level of inside the classroom.

If you move beyond that to consider teachers' efforts to link up with what the next grade teacher expects, or what's happening in a parallel class, to think about coordinating between what they're trying to do and what the test will expect, between what they're trying to do and what the parents and the community are wishing for, the challenges of coordination are immense. And efforts to improve instruction that don't pay attention to the incredible lack of coordination and the threats to coordination that exist in a dynamic as complicated as this one also will fail.

I'm going to close by repeating something I said but didn't support at the beginning of my talk, which is, we have a long history in this country of efforts to improve instruction. And many different people have written about our recurrent failure to impact instruction. We've impacted lots of other things, many kinds of things that we've managed to impact in improving instruction aren't inside the classroom. We've changed from ungraded schools to graded schools, for example. Structural things we've been able to change. We've not been successful at changing the dynamic that's represented in that triangle. And if this Commission is serious about improving mathematics and science teaching, we'll have to find a way to consider carefully that this dynamic set of relationships is much more complicated than putting different people in the classroom or changing the textbook. If you take seriously the set of findings, banal as they may be, you'll understand that this dynamic set of relations is core to the quality of instruction, and that efforts to improve it and recommendations about it have to take that seriously.

SENATOR GLENN: Any questions or comments?

MEMBER: You made reference before that a lot of curriculum is driven by textbooks and sadly that?s true. Sometimes, no matter how good a teacher is, they don?t have a choice. Very often, it?s dictated by what Senator Glenn talked about, the 2000 Boards of Education that are responsive to parents. And parents of kids coming home without textbooks are convinced that kids are not learning anything. And the fact that this is a political issue flies in the face of really good science teaching. All too often they have to use the books.

MEMBER: Is it possible to expand on the piece of research that you looked at where the students bargained? In other words, the teachers that confront the unwilling learner, is there something that you have that might lead us to look at how teachers can address the diverse classroom?

DR. BALL: It's a very big area. I mean, you're pointing at something that's very crucial, because what's called bargaining has good reason behind it, too. I mean, it has a funny name to it, but when students get work that?s difficult for them, it's reasonable that they might say it's too hard, ask for help, and what the research shows that may have been an unexpected sort of thing to notice is that, what may have started out as a very good piece of academic work turns out to be something much more mundane, or not really what the teacher had in mind. So it's not even just the question of unwilling learners, it's also finding ways to help students get engaged with work that don't necessarily distort or degrade the task, unless that's what you intend. If you intend to make the work easier, fine. But part of this research suggested that academic work declined in intellectual quality without necessarily that having been the intent.

So there are two different things going on here. One has to do with what's sometimes called motivation, and there's quite a lot of work on things about motivating learners, to care about learning and so on, and the other is, how does one manage the subtle work of helping students to become engaged in their academic tasks, keeping an eye on whether what you're helping them do is what you had in mind in the first place or whether you're changing it. Those are somewhat different issues, and I think there is work on both of those that we might try to refer to. But I think taking seriously how much capacity the students have to shape what the lesson or the unit becomes is a critical part of considering all of this.

MEMBER: It's somewhat telling that, I think through TIMSS, and what Jim had talked about, even in his book, is that American children tend to love mathematics and think it's easy, and the Asian children did not like mathematics and found it difficult. And so I'm wondering, in the context of your research with students constantly bargaining, whether there's an answer to embedding in our culture that the standards in a regular classroom need to be higher and that students would look upon it in a kinder manner?

DR. BALL: Well, Paul, if you put what you're saying together, which perhaps other people would agree with you, that is, how can we raise the standards and the willingness of students and teachers to engage in difficult work, if you put that together with what I said at the end about incentives, it's important to understand that there are disincentives to get kids stuck, struggling, parents complain that the work is too hard, kids complain, kids don't do well because the work is hard. The patience required to let kids struggle, all of those things are bound up together. So, in some sense, what you're pointing to, if we were serious about that, we'd have to think more carefully about how you support teachers' efforts to do that, how, in fact, you could expect that you'd find classrooms where kids were struggling with what any adult could say in two sentences, but for kids might take some work.

So all of those thing are wrapped up together, and I think you've got your finger on something that would be important if we understood how to think about it in a larger picture.

MEMBER: I have two observations and some questions. The first is, has this body of research actually been embodied in any kind of longitudinal, one might call, it if not experiments, at least controlled conditions, so that one can see really the long-term effects on student learning? Have we created an environment to bring it all together?

And the second, I think they're related, is, if the Commission were to make recommendations to try to make sure that this research is used in policymaking on implementation, what would be the most effective point for those recommendations to be made, in schools of education, school boards, federal government, where?

DR. BALL: Well, on your second question, all of those, right.

MEMBER: But the most effective.

DR. BALL: Well, we'll have to -- I mean, I think that's a question that my work being what I talked about today doesn't really address yet and is a crucial one for us to talk about as a Commission. Your first question -- I mean, I'm not ducking it, I'm happy to talk more, I just don't think I really talked about that. I do think all of those groups will have to be involved, but simply calling for their involvement won't do anything. I think what your question suggests is, what sorts of roles could different constituencies and stakeholders and institutions play, and that is an important question.

But your first question, when you asked has there been longitudinal work, which work were you referring to now?

MEMBER: The bringing together this whole body of observations to which you have alluded. Have we seen them put in practice in a way that one can see the effects of bringing them altogether, or do they come from really isolated observations in different environments.

DR. BALL: That's a very interesting question. If I understand your question correctly, and I might not so I'll answer it quickly in case I'm misunderstanding you. These findings that I assembled actually come from rather disparate areas, disparate fields, and one might argue that teaching itself, as I was trying to assemble it for us, hasn't been looked at with all of those angles. Research on student learning hasn't always been looked at instructionally. Research on curriculum hasn't always been looked at from the point of view of teaching. And part of what I was trying to do by putting it in the triangle was to say to us, if we're going to talk about the improvement of teaching, we probably need to think about these things together. I wasn't yet saying what we should recommend, but that we'd better think about them together or I'm not sanguine that our recommendations will do much.

So perhaps the things I'm saying is something pretty simple, and again rather banal, if you want to improve instruction, you've got to make recommendations that are about instruction, and instruction, what I'm arguing, is this set of relationships. So the recommendations that are only about one element aren't very likely to make much impact.

MEMBER: That answered it.

DR. BALL: Does that answer it?

MEMBER: Yes, thanks.

DR. BALL: Okay.

MEMBER: May I just quickly follow on that. I mean, are you saying that we would be wasting our time to look around the country for best practice schools that are built up from these studies that we should replicate around the country?

DR. BALL: Oh, no, I wasn't saying that. That would be more a question, have there been practice sites where people try to assemble these things. I think that there are, and I think that that would be useful to look. Again what the sorts of data are on those, we'd have to learn something. But I think there are a lot of efforts to put together some assemblage of these things. But even then some of the efforts to create model schools or hold school reforms haven't always assembled all these parts of the system. They've targeted one element or another. For example, some whole school reforms target professional community, and get teachers working together professionally. That doesn't necessarily affect curriculum. It might.

So the notion of the difficulty of putting these things together into one lens, I think there are examples. But I think what Walter, what Dr. Massey was asking me had to do with was there research that had assembled all these and studied them longitudinally. I think typically not. So, I think, yes, to you and no to Dr. Massey.

MEMBER: Yes. I may be asking almost the same question, but take for example one of your findings, time engaged in worthwhile tasks makes a difference for learning. Do we have a body of knowledge on what are worthwhile tasks? You know, if we don't know what worthwhile tasks are, then the statement --

DR. BALL: No, it's interesting because the early research on teaching was a time on task finding without much regard either for content or for the quality of the content. And more recent work has focused more on quality of task. And, you're absolutely right that what counts as a quality task is something on which there's been less work, partly because it's related to what one counts as worthwhile learning, right? So depending on what your conception is of mathematics and science, and what your goals are for student learning, your conception of what counts as a worthwhile task would differ.

So some worthwhile tasks would be quite constrained and close and focused on a single element of mathematical skill. Another mathematical task might embody both mathematical computation and reasoning about sort of a solutions space. And those are rather different goals. So, the problem with trying to stipulate what counts as a worthwhile task is the fact that it's dependent on what the outcome is that you want for students. If the Commission fixes on that, then you may have an easier time locating work that speaks to that. But as long as that's open, then the nature of tasks will differ.

MEMBER: Question, in your research, when we talk about quality of math or science instruction, we also talk about standards. So, within this research, have you find much written about when separate school districts decide content, maybe at a state level we establish standards, and then from an outside source we purchase an assessment instrument, and whether the quality of our instruction is impacted, or how much by lack of alignment between those three.

DR. BALL: Yes, that's part of what the coordination point at the end was, is that there are these sort of multiple messages that teachers end up contending with. And, as a result, the fact that teachers actually have a fair amount of discretion means that these things vary, and the research -- I was reporting about much more than anything I've done. But in our own research on standards and teachers' interpretations of those, what we see is immense variation; in fact, greater variation in some ways because teachers are contending with these standards, new assessments, new texts, new curricula, and their own knowledge and the fact that they have some discretion means that they make use of those in somewhat different ways, just the opposite, in fact, of what you might expect by instituting standards.

SENATOR GLENN: Time for just a couple more questions, and then Linda is going to go into wrap up.

MEMBER: Is there any research on the teaching for teachers of mathematics and science, especially in grade schools, in the context of the very rapid development of Internet technology particularly many youngsters, they are very skilled on the Internet, and you gave the example about your daughter, Sarah, about the use of the microwave, the timer and so on. How can we introduce this kind of thing more into our instruction?

DR. BALL: I don't know a lot about this, and perhaps there are some members of the Commission or others who can help us with this, but, the advance of the access to the Internet, especially in science instruction has been an interesting new phenomenon, perhaps following some of the same path that manipulatives felt in math, which is, it's there, it's available, people put a high faith in its capacity to be educative. But, like any curriculum material, it depends a great deal on how it's used. And there is some early research now on teachers teaching with the Internet and, again, suggests that, like these other sorts of materials before them, in some cases it's highly educative, and in some cases not at all. It, in itself, is not educative. I mean, that's perhaps one of the big findings: materials by themselves don't teach.

MEMBER: Is there any research that has been done on science curriculum which is not based on textbooks? Is there anything that that tells us if there is such a curriculum?

DR. BALL: I don't think I can answer that as fully as you'd probably like. The main thing I'm aware of there is studies about how teachers make use of those type of curricula, and I think I reported something briefly about teachers' use, for example, of experiments that activity-based science curricula that engaged students more in scientific inquiry will be used differently as a function of how teachers themselves understand the scientific content and the activity. So, again, you have this mediation of the teacher with the curriculum material, so that in studies that would directly trace curriculum material to learning are difficult to do because the interaction is among the students, teachers and curriculum.

EXECUTIVE DIRECTOR: Thank you very much, Deborah.

Luckily we still have many more opportunities to think about the ideas today, and more ideas that will come forward. If I could remind you, Senator Glenn opened the meeting saying that we really had two goals, one was to come out with a set of core premises that were descriptors of high quality teaching in math and science. If the commission is to come out with a set of recommendations that would help ensure that high quality teaching is going on in classrooms across the country, we'd better be sure that we know exactly what that is. The planning group in many, many, many conference calls talked about this notion of core premises, and we began to ask ourselves if we really understood what we meant. So let me, for the moment, we're getting Deborah off and the overhead on, we think, and we thought this might help. And that is looking at some core premises of parenting.

This page last modified March 3, 2000 (sab)