Children's difficulties remembering correct algorithms for operations with fractions are traced to difficulties in the instructional sequence. Many teachers "teach mistakes" by failing to provide sufficient referents for their pupils. (MP)

An unusual alternative starting point for instruction in a beginning calculus course that focuses on Fixed Point Iteration (FPI) is presented. (MP)

Three differences between the mathematics training of students from Spanish-speaking countries and that typical for pupils in the United States are discussed. (MP)

The role of the computer in coordinating the activities surrounding five modes of mathematics instruction is discussed. The modes are: computer-assisted instruction, computer-managed instruction, computer-based simulations, algorithmic exercise solving, and computer-aided problem solving. (MP)

Research on the cognitive processes used by physicians during patient care (template matching, deductive logic starting with multiple hypotheses, and algorithmic logic) is examined for its applicability to optometrists and the problem-solving strategies used by optometric students in the classroom or clinic. (Author/MSE)

A model is presented for item responses when different subjects use different strategies, but only responses--not choice of strategy--can be observed. Substantive theory is used to differentiate the likelihoods of response vectors under a fixed set of strategies, and response probabilities are modeled via item parameters for each strategy. (TJH)

Presents a framework for studying the effects of the Maturation Hypothesis on the problem of language learning, parametrically conceived, and offers a method for finding all existing maturational solutions for any parametric hypothesis space and any learning algorithm that differs from Gibson and Wexler's Triggering Learning Algorithm. (27…

This study investigated students' conceptual and procedural understanding of calculus within the context of an engineering mechanics course. Four traditional calculus students were compared with three students from one of the calculus reform projects, Calculus & Mathematica. Task-based interviews were conducted with each participant throughout…

The purpose of this investigation was to identify and describe the differences in the methods used by experts (university chemistry professors) and nonscience major introductory chemistry students, enrolled in a course at the university level, to solve paired algorithmic and conceptual problems. Of the 180 students involved, the problem-solving…

This review of the literature and annotated bibliography summarizes the available research relating to teaching programming to high school students. It is noted that, while the process of programming a computer could be broken down into five steps--problem definition, algorithm design, code writing, debugging, and documentation--current research…

Intended to be used in conjunction with a traditional curriculum, this book demonstrates the use of the computer, especially the on-line, interactive type of computer, to solve a variety of problems studied in secondary school mathematics. Each chapter presents several problems, and each problem introduces one or two concepts that must be…

An introduction to the theory of algorithms reviews the theoretical issues of teaching algorithms, the logical and psychological problems of devising algorithms of identification, and the selection of efficient algorithms; and then relates all of these to the classroom teaching process. It also descirbes some major research on the effectiveness of…

Comprehension of a problem or task that is generated in the real world rather than presented as a well-defined problem-statement of the kind encountered in textbooks or psychological laboratories was related to the ability of recognizing, selecting and formulating problems. The process of acquiring and utilizing this ability was conceptualized…

This series of four text-workbooks was designed for tenth grade mathematics students who have exhibited lack of problem-solving skills. Electric desk calculators are to be used with the text. In the first five chapters of the series, students learn how to use the machine while reviewing basic operations with whole numbers, decimals, fractions, and…

Ten nursery school children who knew how to count but were unacquainted with arithmetic were taught a simple algorithm for solving single-digit addition problems and were then given extended practice. The reaction time on the final block of extended practice suggested that subjects had invented a more efficient procedure to replace the original…