Mathematical definitions are central to learning and doing mathematics. Research has uncovered significant differences between how mathematicians and non-mathematicians construct, reason about, and refine mathematical definitions. Various strands of research provide insight into the development of definitional practices, yet an integrated approach…

The purpose of this study was to examine adult developmental mathematics (ADM) students' knowledge of fraction addition and subtraction as it relates to their demonstrated fraction schemes and ability to disembed in multiplicative contexts with whole numbers. The study was conducted using a mixed methods sequential explanatory design. In the first…

Discussed are the concepts of intuition, the general properties of an intuitive knowledge, and the classification of intuitions as problem solving of affirmative. An example of intuition using multiplication and division is described in some detail. (MNS)

This research focused on preservice elementary teachers' understanding and reconstruction of understanding about multiplication in the domain of fractions. At the start of the study, 44% of the 50 preservice teachers studied reported that they had a method for reasoning about multiplication with fractions, and 28% were able to describe a situation…

This study, written in French, presents the hierarchy of strategies used by children in solving multiplication and division problems, as they acquire the linear function concept. It is based on analysis of the different classes of problems, of specific tasks, and of strategies actually used in solutions. (MP)

The purpose of this study was to determine whether a process model could be constructed using steps identified from flow charts which accounted for somewhat more variance in predicting the difficulty of two-digit multiplication problems than did a process model developed by Cromer. Cromer's data and variables were used as a starting point. Ten new…

The purpose of this study was to determine whether a process model could be constructed using steps identified from flow charts which accounted for somewhat more variance in predicting the difficulty of two-digit multiplication problems than did a process model developed by Cromer. Cromer's data and variables were used as a starting point. Ten new…

The learning of word problems in mathematics is viewed as particularly difficult. The first paper in this report takes into consideration the semantic aspects of problems, by viewing the difficulties that children have solving two-step multiplication problems. An initial study was carried out with 36 children between the ages of nine and fourteen…

Describes the psychological analysis of the instruction of the concept of multiplication in the former Soviet Union. Presents a system of instructional situations in introducing multiplication and the main results of instruction for grade two. (MDH)

This report describes a simulation of adults' retrieval of arithmetic facts from a network-based memory representation. The goals of the simulation project are to: demonstrate in specific form the nature of a spreading activation model of mental arithmetic; account for three important reaction time effects observed in laboratory investigations;…

After a year of instruction, 70 kindergarten children were individually interviewed as they solved basic, multistep, and nonroutine word problems. Thirty-two used a valid strategy for all 9 problems, and 44 correctly answered 7 or more problems. Modeling provided a unifying framework for thinking about problem solving. (Author/MDH)

Children's (n=70) solution strategies to a variety of multiplication and division word problems were analyzed to determine performance levels and strategies used. Solution strategies were classified at three levels: direct modeling with counting; no direct modeling with counting, additive, or subtractive strategies; and use of known derived facts.…

An editorial comment on the computer and the mathematics educator is included first. Then, abstracts and comments are presented for 11 articles. Studies included focus on mental addition, problem solving by sixth graders, mathematics anxiety, tutoring, direct instruction, a bilingual program, thinking strategies for multiplication basic facts,…

This issue of the journal contains abstracts and critical comments for ten published reports of research in mathematics education. The reports concern teaching probability and estimation of measurements through microcomputer games, mental addition, use of calculators at the intermediate level, logical reasoning hierarchies, two approaches to the…

These conference proceedings include two invited lectures, three working group reports, three topic group reports, two Ad Hoc group reports, a round table report, a list of participants, and a list of previous proceedings. The invited lectures were: "Values in Mathematics Education" (Ubiratan D'Ambrosio) and "Remarks on…