To investigate the development of function concepts and their relation to mathematical and logical abilities typically acquired during the age period of five to seven years, children were tested on nonnumerical function tasks, numerical tasks, and aspects of logical reasoning. (PCB)

Advantages and disadvantages of the modern definition of function, understanding the concept of function, procedures used in a study of the understandings of ninth graders, and detailed results of the study are discussed. (MNS)

APL was invented specifically as a mathematical teaching tool, and is an excellent vehicle for teaching mathematical concepts using computers. This article illustrates the use of APL in teaching many different topics in mathematics, including logic, set theory, functions, statistics, linear algebra, and matrices. (MNS)

Using calculators (and computers) to develop an understanding and appreciation of statistical ideas is advocated. Manual computation as a prerequisite for developing concepts is negated through several examples. (MNS)

The effects of problem size on judgments of commutativity by 51 moderately and mildly retarded students were investigated. Results indicated that many retarded students who are given computational practice recognize the general principle that addend order does not affect the sum. (Author/DB)

Reviews CATUSPLOT, a mathematics utility aimed at high school algebra through college-level calculus. Basic program capabilities include plotting, tabulating, integrating, and locating of intersections of functions composed of combinations of polynomial, trigonometric, and exponential functions. Rated excellent on all areas examined…

The validation of the developmental Mokken scale for seriation was discussed. It was shown that the observed scale was invariant for different samples from previous research. Stepwise multiple regression analysis revealed that a selection of two seriation tasks on the scale accounted for 76.4 percent of the explained variance. (Author/DWH)

The behavior of one child as she constructed knowledge about fractions over a nine-month period is presented. The intent is to explain behavioral patterns for which certain mental processes, called schemes, seem responsible. (MNS)

On tasks involving assessement of the heights of colored sticks, kindergarten, third-grade, and adult subjects were successful on inferences involving only equalities or only inequalities across various conditions and procedures. A dramatic developmental increase in performance was found on inferences based on the combination of equality and…

Ignored concepts of numbers, notation, and operation with rational numbers are described. It is proposed that these be taught in the time now devoted to paper-and-pencil skills made obsolete by calculators. (MNS)

Three different models with continuous materials, discontinuous materials, and number lines were used to study the operation concept in six investigations on multiplication with fractions with pupils aged 11-12 in a Penang International School. All approaches could be understood by pupils, but they preferred the area and fractional models. (MNS)

Several experimental studies are reviewed, the results of which suggest that students often fail to acquire an understanding of some of the concepts, relationships, principles, and processes that are fundamental to traditional high school course material. Questions of what it means to understand something and of how to assess understanding are…

Describes and presents an inventory for estimating primary grade students' ability to read mathematical vocabulary and their understanding of math concepts. (FL)

This is a qualitative study of 22 9th graders performing generalizations on a task involving linear patterns. Our research questions were: What enables/hinders students' abilities to generalize a linear pattern? What strategies do successful students use to develop an explicit generalization? How do students make use of visual and numerical cues…

The presentations address a variety of difficulties occurring in students' solutions of equations and inequalities, and suggest different reasons for these difficulties. When analyzing students' performances, [BB] and [TTT] mention students' tendencies to make irrelevant connections between equations and inequalities as a problematic phenomenon.…