Ralph T. Putnam

Teacher Learning: Implications of New Views of Cognition

Current educational reform efforts in the United States are setting forth ambitious goals for schools, teachers, and students (e.g., National Council of Teachers of Mathematics, 1989; National Education Goals Panel, 1991; National Research Council, 1993). Schools and teachers are to help students develop rich understandings of important content, think critically, construct and solve problems, synthesize information, invent, create, express themselves proficiently, and leave school prepared to be responsible citizens and lifelong learners. Reformers hold forth visions of teaching and learning in which teachers and student engage in rich discourse about important ideas and participate in problem solving activities grounded in meaningful contexts (e.g., American Association for the Advancement of Science, 1989; National Council of Teachers of Mathematics, 1989, 1991). These visions of teaching and learning depart significantly from much of the educational practice that currently typifies American classrooms — practice that is based on views of teaching as presenting and explaining content and learning as the rehearsal and retention of presented information and skills.

Structuring and Adjusting Content for Students: A Study of Live and Simulated Tutoring of Addition

This study examined how six experienced teachers acquired information about students’ knowledge and used that information to adjust their instruction while tutoring. Each teacher tutored five simulated students and one live student in the algorithm for whole number addition. A diagnostic/remedial perspective in which the teacher forms a detailed model of the individual student’s knowledge and misconceptions was assumed in the early stages of the study, but did not describe adequately the tutoring of the teachers. Diagnosis was not their primary goal. Rather, each teacher appeared to move through a curriculum script—a loosely ordered but well defined set of skills and concepts students were expected to learn, along with the activities and strategies for teaching this material.

The Skill of Learning From Classroom Lessons

A student trying to learn from classroom instruction is confronted with a complex task. The successful student must determine what actions are expected by the teacher and must grasp the intended content of the lesson, connecting and integrating that content with prior knowledge. This paper presents a model of the skills a student needs to have to make sense of a mathematics lesson taught by a good teacher. The model of the learner contains a variety of cognitive competencies: an action system, a lesson parser, an information gatherer, a knowledge generator, and an evaluator. A description of how the model functions during a 2-day lesson sequence provides an empirical example.

Chapter 2: Alternative Perspectives on Knowing Mathematics in Elementary Schools

From all sides are coming calls for changes in the amount and quality of mathematics instruction in American schools (National Commission on Excellence in Education, 1983; National Council of Teachers of Mathematics, 1980; National Research Council, 1989). Critics of current practice posit that the mathematical achievement and understanding of U.S. students lag behind that of their peers in other industrialized countries (McKnight et al., 1987; National Commission on Excellence in Education, 1983; National Science Board Commission on Pre-College Education in Mathematics Science and Technology, 1983). Mathematics educators and researchers argue that current mathematics instruction in elementary and secondary schools focuses too much on efficient computation and not enough on mathematical understanding, problem solving, and reasoning. Leaders in business and industry are claiming that public education must change to teach to the new kinds of mathematical skills and problem-solving abilities that will be important for the worker of the future (see, e.g., Bernstein, 1988). Accompanying these criticisms of current practice are calls for reform, for making lasting and fundamental

Using Research on Learning from Text to Inform Online Discussion

Drawing on research literature on online discussion and on reading and learning from the text, we argue that research on learning from text has much to offer but has been largely absent in informing the design and study of online learning environments. We propose several key issues to be considered in research and development of online discussion, and a framework for examining the goals and features of online discussions. We then report on an exploratory study of an online discussion environment informed by this framework.