Two phenomena related to the quality of student responses in regard to items used in a testing situation are involved in the construction of a pupil response model. The underlying phenomenon which defines the individual's cognitive limits is termed the hypothetical cognitive structure (HCS). The second phenomenon, which is a function of not only…

Strategies used by 150 children as they solved addition and subtraction verbal problems were studied over a period of one-and-a-half years. Number size and presence of manipulative materials were variables manipulated in individual interviews given at three separate intervals. Two addition and four subtraction tasks were used. Processes changed…

A mathematics unit for sixth-grade classes was developed in which each of eight activities contains a challenge conveyed in the form of a story. Each activity requires students to manipulate concrete materials such as ceramic tiles, marked string, wooden cubes, and square paper. The mathematical content consists of concepts such as area,…

This study examined the effects of number of illustrative examples and number of practice problems given on seventh graders' achievement in a unit on probability. Four treatment groups were used, one for each combination of two levels of number of examples and two levels of number of practice problems. Prior to treatment students were pretested on…

Since the mid-1960s a new approach has dominated American research in the area of mathematics education -- information-processing theory. The author examines several examples of research in this new tradition and sketches the general features of an emerging information-processing psychology of teaching. Information-processing studies that employ…

This study examines the extent to which modeling facilitates transformational problem solving in mathematics for children in kindergarten and first grade. Subjects were 20 children selected from each level. They responded to two problems for each of four problem types (counting on, story problems, quantitative comparisons, and ordination) under…

This document begins with a discussion of the author's approach to instruction in a mathematics laboratory. This discussion includes an enumeration of types of desirable or necessary equipment and advice on the management of a laboratory. The author examines issues related to achievement and readiness for more traditional school experiences in…

The purpose of this study was the construction of a theoretical model for analyzing mathematical problem solving. A list of general problem-solving abilities was generated through a literature search. This list was narrowed to eight basic abilities pertinent to mathematics problem solving. Each of these was operationally defined and exemplified in…

Designed for the student who has completed the geometry series in the Quinmester Program, this guidebook on minimum course content provides an investigation of challenging mathematical activities which are not usually developed in other mathematics courses. The content includes brainteasers, puzzles, and game theory. Overall course objectives are…

Expanded abstracts and critical analyses are given for each of 14 research articles. Four articles involve variables affecting student achievement and attitudes; two each on teaching abstract concepts to young children, problem solving, conservation in young children, and children's understanding of logic and mathematical relations; one on…

Five activity lessons are proposed to present applications of probability and to exhibit its use in conjunction with statistics as a major decision-making and problem-solving tool. (MP)

A problem from number theory is used to illustrate the use of the computer and programable calculators in solving problems. Programs are included. (MP)

The possibilities that magazines have to offer in the teaching of mathematics with consumer-related problems are discussed. (JT)

Instructional techniques are given for the use of calculators in (1) finding prime numbers, (2) solving trigonometric equations, and (3) solving polynomial equations. (CP)

A variety of calculator activities is described for developing problem solving skills without getting involved in tedious computations. (JT)