Keynote Part I

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The Aim: Improving the Quality of Teaching and Learning

In these conversations of teacher knowledge and in our efforts to remediate the problems we see, it's useful to remind ourselves of the issue we're really trying to address. Sometimes we become distracted about what we're trying to accomplish. The problem we're trying to address is not, in the end, teachers' understanding of content. The problem we are trying to address is the quality of teaching and learning. We are trying to improve what students actually have opportunities to learn in school -- in science, in reading and language arts, in social studies and in mathematics.

What is the actual issue that we are trying to address?

The quality of teaching and learning

Teachers' knowledge of content and their ability to use it in their teaching

In the work that my colleagues and I are doing, we hypothesize, that teachers' knowledge of content, and their ability to use such knowledge in their work - on their feet in their classrooms, with children - is a key factor in the quality of science and mathematics instruction. We suspect teachers' knowledge of content is a key place to intervene if we hope to improve students' learning of content. Typically, however, the remedies tried have not produced the sorts of changes in practice that we'd like to see. Therefore, I'd like to suggest a somewhat different approach to how we might think about the content knowledge - and opportunities to learn it - that teachers need.

Rather than the common approach of starting with an examination of the school curriculum or the discipline to determine the important skills and concepts teachers should know, our research is founded on the premise that we would do better if we started by examining the work of teaching itself. Such an examination could help identify more clearly what teachers have to do when they're teaching mathematics or science, and the ways in which disciplinary reasoning and practice figure in that work. In our work on mathematics teaching we have come to ask: What are the mathematical problems that teachers recurrently face and have to solve? What are the mathematical tasks teachers have to do in the course of their work? Based on answers to such questions, we can begin to analyze the mathematical knowledge and skills, the topics and areas of study, that hold some promise of giving teachers leverage in their work. In science, we might ask, analogously: What are the scientific questions and issues that teachers confront as they teach science? In what ways does the teaching of science require teachers to contend with scientific puzzles, logic, and evidence?

By starting with the work of teaching (instead of the curriculum or the discipline) and trying analyze what is being called upon, we arrive at somewhat different answers about what teachers might need to learn or the knowledge they need to be able to use in their work. It is important to realize that it is not just a list of topics, skills, or orientations to mathematics in which we are interested. Equally important is the need to understand how teachers deploy this knowledge in their work. What are the uses to which they put such knowledge?

Here is how we pursue this:

What is Necessary Mathematics Knowledge for Teaching?

  1. Examine teaching, and identify the mathematical work that teaching entails
  2. Analyze what mathematical knowledge -- topics and skills -- is needed to do that work
  3. Analyze also the qualities of that knowledge -- how it must be understood and known to be serviceable for the work

Consider what we have already seen briefly: One type of mathematical problem solving teachers might have to do recurrently is to confront methods or solutions different from the ones they know, and try to size them up. This is what we did with the three examples of multiplication solutions. When we look closely at what is involved in appraising these three methods, we see something about the quality- the characteristics - of this knowledge. Analyses of these and other typical problems that arise in teaching can enable us to have better answers to the question, "What do teachers need to know about the subjects they teach, and how do they have to use that knowledge?"

This leads to the second part of this keynote in which we are going to spend some time investigating the argument that teaching a subject is embedded with specific disciplinary reasoning and practice. What I will do next is to take you through a way of thinking that will begin to develop this notion a bit. Keep in mind that although I am using examples from mathematics, our discussions over the next couple of weeks will take up science teaching as well.

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