James Hiebert

A Knowledge Base for the Teaching Profession: What Would It Look Like and How Can We Get One?:

To improve classroom teaching in a steady, lasting way, the teaching profession needs a knowledge base that grows and improves. In spite of the continuing efforts of researchers, archived research knowledge has had little effect on the improvement of practice in the average classroom. We explore the possibility of building a useful knowledge base for teaching by beginning with practitioners’ knowledge. We outline key features of this knowledge and identify the requirements for this knowledge to be transformed into a professional knowledge base for teaching. By reviewing educational history, we offer an incomplete explanation for why the United States has no countrywide system that meets these requirements. We conclude by wondering if U.S. researchers and teachers can make different choices in the future to enable a system for building and sustaining a professional knowledge base for teaching.

Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics

We argue that reform in curriculum and instruction should be based on allowing students to problematize the subject. Rather than mastering skills and applying them, students should be engaged in resolving problems. In mathematics, this principle fits under the umbrella of problem solving, but our interpretation is different from many problem-solving approaches. We first note that the history of problem solving in the curriculum has been infused with a distinction between acquiring knowledge and applying it. We then propose our alternative principle by building on John Dewey’s idea of “reflective inquiry,” argue that such an approach would facilitate students’ understanding, and compare our proposal with other views on the role of problem solving in the curriculum. We close by considering several common dichotomies that take on a different meaning from this perspective

Instructional Tasks, Classroom Discourse, and Students’ Learning in Second-Grade Arithmetic

To investigate relationships between teaching and learning mathematics, the six second-grade classrooms in one school were observed regularly during the 12 weeks of instruction on place value and multidigit addition and subtraction. Two classrooms implemented an alternative to the more conventional textbook approach. The alternative approach emphasized constructing relationships between place value and computation strategies rather than practicing prescribed procedures. Students were assessed at the beginning and the end of the year on place value understanding, routine computation, and novel computation. Students in the alternative classrooms, compared with their more traditionally taught peers, received fewer problems and spent more time with each problem, were asked more questions requesting them to describe and explain alternative strategies, talked more using longer responses, and showed higher levels of performance or gained more by the end of the year on most types of items. The results suggest that relationships between teaching and learning are a function of the instructional environment; different relationships emerged in the alternative classrooms than those that have been reported for more traditional classrooms.

Relationships between research and the NCTM standards

The current debates about the future of mathematics education often lead to confusion about the role that research should play in settling disputes. On the one hand, researchers are called upon to resolve issues that really are about values and priorities, and, on the other hand, research is ignored when empirical evidence is essential. When research is appropriately solicited, expectations often overestimate, or underestimate, what research can provide. In this article, by distinguishing between values and research problems and by calibrating appropriate expectations for research, I address the role that research can and should play in shaping standards. Research contributions to the current debates are illustrated with brief summaries of some findings that are relevant to the standards set by the NCTM.

Preparing Teachers to Learn from Teaching

The authors propose a framework for teacher preparation programs that aims to help prospective teachers learn how to teach from studying teaching. The framework is motivated by their interest in defining a set of competencies that provide a deliberate, systematic path to becoming an effective teacher over time. The framework is composed of four skills, rooted in the daily activity of teaching, that when deployed deliberately and systematically, constitute a process of creating and testing hypotheses about cause-effect relationships between teaching and learning during classroom lessons. In spite of the challenges of acquiring these skills, the authors argue that the framework outlines a more realistic and more promising set of beginning teacher competencies than those of traditional programs designed to produce graduates with expert teaching strategies.

Using Video Surveys to Compare Classrooms and Teaching Across Cultures: Examples and Lessons From the TIMSS Video Studies

Examining the extent, nature, and scope of peer group influence on academic outcomes is an important direction for future research to enrich our understanding of adolescent motivation, engagement, and achievement. Conceptual and methodological issues involved in studying peer groups are discussed. Existing research that addresses the influence of peer groups on academic outcomes is reviewed. Processes of how peer groups socialize achievement beliefs and behaviors are considered. Promising directions for future research are discussed.

Children's Conceptual Structures for Multidigit Numbers and Methods of Multidigit Addition and Subtraction.

Researchers from 4 projects with a problem-solving approach to teaching and learning multidigit number concepts and operations describe (a) a common framework of conceptual structures children construct for multidigit numbers and (b) categories of methods children devise for multidigit addition and subtraction. For each of the quantitative conceptual structures for 2-digit numbers, a somewhat different triad of relations is established between the number words, written 2digit marks, and quantities. The conceptions are unitary, decade and ones, sequence-tens and ones, separate-tens and ones, and integrated sequence-separate conceptions. Conceptual supports used within each of the 4 projects are described and linked to multidigit addition and subtraction methods used by project children. Typical errors that may arise with each method are identified. We identify as crucial across all projects sustained opportunities for children to (a) construct triad conceptual structures that relate ten-structured quantities to number words and written 2-digit numerals and (b) use these triads in solving multidigit addition and subtraction situations.

Mathematics Teaching in the United States Today (and Tomorrow): Results From the TIMSS 1999 Video Study:

The Third International Mathematics and Science Study (TIMSS) 1999 Video Study examined eighth-grade mathematics teaching in the United States and six higher-achieving countries. A range of teaching systems were found across higher-achieving countries that balanced attention to challenging content, procedural skill, and conceptual understanding in different ways. The United States displayed a unique system of teaching, not because of any particular feature but because of a constellation of features that reinforced attention to lower-level mathematics skills. The authors argue that these results are relevant for policy (mathematics) debates in the United States because they provide a current account of what actually is happening inside U.S. classrooms and because they demonstrate that current debates often pose overly simple choices. The authors suggest ways to learn from examining teaching systems that are not alien to U.S. teachers but that balance a skill emphasis with attention to challenging mathematics and conceptual development.

LEARNING TO LEARN TO TEACH: AN "EXPERIMENT" MODEL FOR TEACHING AND TEACHER PREPARATION IN MATHEMATICS

This paper describes a model for generating and accumulating knowledge for both teaching and teacher education. The model is applied first to prepare prospective teachers to learn to teach mathematics when they enter the classroom. The concept of treating lessons as experiments is used to explicate the intentional, rigorous, and systematic process of learning to teach through studying ones ownpractice. The concept of planning teaching experiences so that others can learn from ones experience is used to put into practice the notion of contributing to a shared professional knowledge base for teaching mathematics. The same model is then applied to the work of improving teacher preparation programs in mathematics. Parallels are drawn between the concepts emphasized for prospective teachers and those that are employed by instructors who study and improve teacher preparation experiences. In this way, parallels also are seen in the processes used to generate an accumulating knowledge base for teaching and for teacher education.

Teaching, Rather Than Teachers, As a Path Toward Improving Classroom Instruction

For several historical and cultural reasons, the United States has long pursued a strategy of improving teaching by improving teachers. The rarely questioned logic underlying this choice says that by improving the right characteristics of teachers, they will teach more effectively. The authors expose the assumptions on which this logic is built, propose an alternative approach to improving teaching that engages teachers (and researchers) directly in the work of improving teaching, present some indirect evidence to support this approach, and examine the cultural traditions and beliefs that have kept the conventional approach in place for so long.