First, second, and third graders (n=33) were observed in classrooms during a three-year study of the development of private speech and its relationship to behavioral accompaniment to task, attention, and task performance. Findings agreed with Vygotskian predictions that private speech promotes effective task-related behavior. (SH)

Described is an activity that uses the techniques of integral calculus to determine the volume of a bundt cake. The cake is used as an example of a solid of revolution. Included are the procedures and assumptions used by students to solve this problem. (KR)

Presented is a calculation for the probability of a athletic event. Assumptions, computations, and questions to be considered in the solution of this problem are discussed. (CW)

The purpose of this study was to compare the achievement for the operations of multiplication and division on whole numbers of elementary grade students who were taught functional diagnostic strategies with a randomly selected group who were not taught the informal diagnostic strategies. Included are the methodology, results, and discussion. (KR)

A trend at U.S. colleges and universities in teaching first-year science courses is discussed. An approach in the classroom and lab in which students engage in science through observation and hypothesis is emphasized. Hands-on science, experiential science, and constructing science through cooperative learning are discussed. (KR)

A study was arranged in a pre/postexperimental/control design, in which fifth graders in the experimental group viewed 30 half-hour telecasts of "Square One TV." Results indicated significant gains for the treatment group both in diversity of problem-solving capabilities and in measures of completeness and sophistication of mathematical…

A review of studies of mentoring for new college faculty suggests practical guidelines for maximizing the mentoring experience. Recommendations include "cataloging" (of past, current, and planned activities); group mentoring; and application of a theory stressing involvement, regimen, solving the right problem, and social networking. (DB)

A novel approach is examined for using developmental sequence data for deciding between Universal Grammar-based and problem solving models of adult nonnative grammatical development. Results support the Universal Grammar-based model of nonnative language acquisition. (19 references) (Author/LB)

Number sequences are useful complements to traditional drill and practice. Described is an activity in which the basic rule, add the tens digit to five times the ones digit, is used to generate a sequence of numbers. The dialogue between teacher and student discussing characteristics of emerging patterns is given. (MDH)

Presented are the solutions generated by a fifth grade class to the problem of finding the sum of the number of blocks in a pyramid with a bottom layer containing seven blocks. Three methods were recorded: a levels method, a columns method, and a vertical slice method. (MDH)

Describes a study whose purpose was to develop and validate a set of belief scales for measuring secondary school and college students' beliefs about mathematics as a subject, how mathematics is learned, and mathematical problem solving. Provides an example of the "Indiana Mathematics Belief Scales." (MDH)

Describes a classroom experience in which the teacher experiments with integrating mathematics history into a calculus class by presenting a historical problem taken from L'Hopital to be solved by the students. Extracts the role that history can play in teaching mathematics from the experience. (MDH)

Context-dependent item sets, containing a subset of test items related to a passage or stimulus, are discussed. A brief review of methods for developing item sets reveals their potential for measuring high-level thinking. Theories and technologies for scoring item sets remain largely experimental. Research needs are discussed. (SLD)

This article recommends a holistic approach to student problems in mathematics. Teachers need to be aware of all paradigms (e.g., developmental, behaviorist, psychoanalytic) explaining causes of problems in mathematics. Examples of misunderstandings resulting from insufficient knowledge, insufficient mathematical vocabulary, and overgeneralization…

To be effective in the current rapidly changing environment, individuals need more than a knowledge base. They also need information literacy which includes techniques for exploring new information, synthesizing it, and using it in practical ways. Undergraduate education should focus on such resource-based learning directed at problem solving.…