Generalizing or making claims that extend beyond particular situations is a central mathematical practice and a focus of classroom mathematics instruction. This study examines how aspects of generality are produced through the situated activities of a group of middle school mathematics students working on an 8-week population-modeling project. The…

Students sometimes have difficulty in mathematics because they solve problems mechanically, without understanding the ideas represented by their equations. This brief note provides mathematics instructors with ideas for rectifying this fundamental flaw in students' paradigm of problem solving. (Contains 1 footnote.)

Educational reform centres on changing teacher behaviour, as it is teachers who filter through the curriculum to learners. Educational reform could therefore be viewed as reforming or changing teacher behaviour. This article investigates some of the factors influencing teachers' behaviour namely knowledge, attitude and views and beliefs. The…

Twenty-two papers and discussions presented at the 1979 annual meeting of the American Statistical Association are reproduced. Papers dealing with student evaluation of instruction include "An Analysis of Student Evaluation of Instruction and Relationships Among Salary, Chairman's Ratings, and Student Ratings of Faculty," by Alvin C. Rencher;…

Criticizes the current method of formalization in Italian schools and the use of tools of the mathematical method. Proposes a general three-stage formalization method which can used for physical quantities, the particular significance of certain quantities, and the description and interpretation of phenomena. (TW)

This paper applies a theory of growth in academic achievement to the study of the effects of ability grouping on reading achievement. The theory sees students' ability and effort determining how they utilize opportunities for learning provided by instruction. (Author/JAZ)

Children in grades four and five had instruction on fractions with a continuous manipulative aid to help transfer their knowledge to tasks with a discrete manipulative aid. Results suggest that discrete-embodiment tasks are more difficult than continuous-embodiment tasks. (MNS)

Discusses the surprising result that the expected number of marbles of one color drawn from a set of marbles of two colors after two draws without replacement is the same as the expected number of that color marble after two draws with replacement. Presents mathematical models to help explain this phenomenon. (MDH)

Discusses a pedagogical approach to calculus based on the question: What kinds of problems should students be able to solve? Includes a discussion of types of problems and curriculum threads for such a course. Describes a projects-based calculus with examples of projects and classroom activities. (Author/MDH)

The importance of algebra instruction has increased in the United States in the past few years. Thus, in most states, middle school students are required to take Algebra 1. Middle school students with math difficulties in inclusion algebra settings may require a different instructional approach. The purpose of this research was to compare student…

An individualized project is introduced to accompany a differential equations course with different modules ranging from standard to advanced levels with "Matlab" scripts. (Contains 1 figure.)

Progress is reported on four research tasks. An experiment tested the effectiveness of a computer-based phonology instructional system for second-language learning. In research on models of human-computer interactions, experiments were performed demonstrating that the provision of certain incentives to the users of a time-sharing system can have…

The problem of structuring sequences of instructional stimuli such that learning is optimized is modelled as a sequential decision problem with an imbedded mathematical model of learning providing a criterion function. Three types of optimization methods for such a representation are investigated for the specific case of paired-associate learning…

Abstracts of 36 research reports are provided. The reports were prepared by investigators for presentation at the 55th annual meeting of the National Council of Teachers of Mathematics. A broad range of topics related to mathematics education is covered. Nine reports deal with problem solving, eight are concerned with instructional methods, five…

Discusses how all applications of mathematics have a unifying theme, namely, that of mathematical modeling. Three examples of models in science and technology are briefly described. These are suggested as suitable project work in the classroom, which involve collaborative work between science and mathematics. Advantages and benefits of modeling…