This study examined the links students are able to make between formal expressions and situations to which they might refer. Students' understanding of a basic set of transformational rules in elementary algebra sign changes in addition and subtraction expressions with parentheses was assessed, exploring: (1) informal intuitive understanding of…

The goal of this study was to find a way to quantify three criteria of representational quality, described by Greeno, so that it would be possible to examine statistically the relationship between representational quality and other variables related to problem solution. The sample consisted of 18 college students, 84 percent of whom had…

This study, part of a longitudinal investigation, examined the kinds of thinking which children aged 10 and 11 could carry over from Logo instruction to an algebraic context. Interviews focused on their ability to construct meaningful symbolization for the concept of variable and to construct formalized algebraic rules. (MNS)

Previous studies were conducted with 14- to 15-year-old students on the nature of the processes they used to solve tasks given the incorrect/buggy/mal-rules. The computer-based Leeds Modelling System (LMS) was implemented and a database of examples, correct and incorrect, or mal-rules had been established which was sufficient to diagnose the…

High school students (n=295) were administered variants of the student-professor problem to ascertain whether errors could be traced to implicit versus explicit relationships between the variables. Concludes that implicit variable relationship problems were harder than explicit variable relationship problems. A follow-up study to explore why is…

A group of 24 14-year-old students were presented with sets of algebra tasks using the Leeds Modelling System (LMS), a computer-based modeling system. Four months later, these same students were given a paper-and-pencil test which covered comparable tasks set by LMS. In addition, certain students were given detailed diagnostic interviews. A…

This paper reports the results obtained with a group of 24 14-year-old students when presented with a set of algebra tasks by the Leeds Modelling System (LMS). These same students were given a comparable paper-and-pencil test and detailed interviews some 4 months later. The latter studies uncovered several kinds of student misunderstanding that…

Research on Teacher Education was the theme for the plenary sessions of the eighth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. More than 50 papers were selected for presentation at the conference. These papers are grouped into seven categories in these conference proceedings.…

Argues that computer instantiations of abstract concepts could assist mathematics education by providing concrete experiences and by inducing the mental process of construction that Piaget called reflexive abstraction. College students with computer experiences scored higher than those taught with traditional methods on a test of functions and…

Describes a hierarchical system of problem-solving strategies employed for the solution of a specific kind of problem about speed. Presents the results of 563 high school students tested with problems relating to distance, speed, and time. Provides a rationale for the methods used. (TW)

Knowledge about the structure of arithmetic expressions enables people to reason effectively about such expressions, including an ability to judge equivalence under transformations. This paper reports an empirical study of six middle-school children who judged the equivalence of three sets of three-term arithmetic expressions with an addition and…

This fourth yearbook on research on mathematics teaching in Finland contains five articles, four in English and the fifth in German. "Mathematics as a Cognitive Science" (C. Letteri) examines cognitive aspects related to teaching and learning mathematics, with the focus on the different levels of comprehension and an analysis of basic…

This study examined the benefits to teachers who used impromptu writing prompts in first- and second-year algebra classes. Interpretive research methodology was used to collect and analyze data. Concluded that teachers' assessment of students' understanding was enhanced by reading their students' responses to impromptu writing prompts, thus…

A theory of how people learn certain procedural skills is presented. It is based on the idea that the teaching and learning that goes on in a classroom is like an ordinary conversation. The speaker (teacher) compresses a non-linear knowledge structure (the target procedure) into a linear sequence of utterances (lessons). The listener (student)…

This document contains 53 plenary and contributed papers presented at the eighth Psychology of Mathematics Education (PME) meeting. Two plenary addresses focused on mathematics research in Australia and Japan, and problem solving and symbolism. Contributed papers were classified under 13 headings including: teaching and learning theory; cognition;…