This paper discusses the experience of a preservice secondary mathematics teacher during lesson study. Although the preservice teacher was a strong undergraduate mathematics student, she used compensation "moves" to deflect attention away from her insecurities about her conceptual understanding of secondary mathematics. She feared being labeled as…

In this article, we describe preservice elementary teachers' reactions to Liping Ma's (1999) book, "Knowing and Teaching Elementary Mathematics" (KTEM), from five universities. Ma's discussion of solely teaching elementary mathematics procedurally and its consequences awakens the preservice teachers' memories of learning elementary mathematics.…

This study investigates how well 381 prospective elementary, early childhood, and special education majors solved four arithmetic problems that required using the order of operations. Self-reported data show these students to be relatively able mathematically and confident in their ability, with no substantial dislike of mathematics. The…

Develops a division algorithm in terms of familiar manipulations of concrete objects and presents it with a series of questions for diagnosis of students' understanding of the algorithm in terms of the concrete model utilized. Also offers general guidelines for using concrete illustrations to explain algorithms and other mathematical principles.…

Discusses a strategy for teaching degrees of freedom (in conjunction with sampling theory). The strategy, used successfully with students who have completed no more than beginning secondary school algebra, involves drawing items from a pool of five in a hat while explaining sample means and variances. (DH)

Suggests activities which provide students with opportunities to give meanings to symbols and to find reasons for doing computations. Includes investigations with a pendulum, circular running track, salary increases, and container volume. Indicates that teachers should place less emphasis on drill and manipulation to give meaning to abstract…

Describes three studies in which students (N=515; N=60; N=135) were asked to indicate appropriate operations and numbers used in solving open mathematical sentences. Analysis of data and interviews suggest two error patterns: "finding a solution" and "inverse operation." Indicates that "finding a solution" strategy…

Use of calculators for teaching percent to first-year general mathematics students is explained by addressing such areas as sequence of lessons, teaching/learning problems, calculator errors, and recommended instructional strategies. Teaching concepts independent of calculator usage, not using special percentage keys, and initiating estimation as…

Presented are several consequences of Ceva's theorem which deal with ratios of segments formed when a parallel to one of the sides is drawn through the point of concurrency. The proofs of these theorems are included and are of varying degrees of difficulty. (KR)

Discusses the need for curricular and instructional integration of science and mathematics. Describes some reports supporting integration and some curriculum projects that include integration. (YP)

Describes activities for developing mathematical and science process skills using the labels on food packages. Provides objectives, rationale, lesson outlines, procedures, worksheets, evaluation, teacher notes, extensions, and student worksheets for the activities. (YP)

Problem solving by example is an intermediate step toward mastering problem-solving heuristics. Discussed are problem-solving processes by using two problem examples. Emphasized are heuristics cataloging in a problem-solving log, and approaches to solutions, not the solutions themselves. (YP)

Reports that those who were taught proportions exhibit more of a tendency to transfer than those who were not. Investigates the relationship of previous learning and problem-solving abilities to the learning of proportionality in facilitating transfer. Shows the magnitude of effects of task assignment on transfer. (YP)

Presents a lesson to compute differences of positive and negative numbers using historical events of science. Describes the skills, concepts, objectives, rationale, outline, procedure, evaluation, and extensions of the lesson. Provides a list of events in the history of science. (YP)

Presents an activity for upper elementary students called "Soil Structure and Ground Water." Provides procedures, materials, key concepts, background, and extensions. (YP)