Describes Fermat's last theorem and shows the proof for the case when the exponent is four. Outlines other works for the proof of the theorem, including Kummer's. Twelve references are listed. (YP)

This dictionary explains 225 terms used in bibliometrics, and it provides nontechnical definitions of bibliometric concepts and suggests sources where more information can be found about the defined term. Special features include sample references, cross references, variants (synonyms), and an index of names. The introduction relates the terms of…

In this paper, Piaget's theory is analyzed using Locke's philosophy. The first part, "Mental Experiences," describes the author's view (with a tentative interpretation of Piaget's position) of reflection, abstraction, re-presentation, and the use of symbols. The second part, "Piaget's Theory of Abstraction," has four sections:…

Discussed are students' understandings of the relationship between fraction and decimal interpretations of rational numbers, where both interpretations are represented symbolically. The methodology employed in this study, interviews, results, and a discussion of the implications of the results are presented. (CW)

The focus of this document is on students' understanding of symbolization processes in algebra, and specifically their understanding of semantically laden letters. In the first four sections, four inappropriate ways in which many college students use semantically laden letters are described. Evidence from clinical interview protocols demonstrate…

Discussed are the background and implementation of a method of teaching fractions to primary children referred to as "The Visual Concept of Fractions." The advantages and criticisms of the use of this method are stressed. (CW)

Results of empirical research relating computer programming instruction and understanding of the concept of mathematical variables is unclear. While some studies have found a positive relationship, others have reported nonsignificant results. The purpose of this study was to investigate high school students' (n=36) understanding of the concept of…

This exploratory study describes fourth-grade students' opinions and knowledge about fractions. A coherent and elaborate fraction knowledge base results when students establish connections between their conceptual knowledge and procedural knowledge of fractions. One possible juncture between concepts and procedures might involve establishing…

Described is the notion of multiple alternative representations of mathematical reasoning, particularly as they relate to algebraic notation and the potential of computers to change representations. Features of a desirable notation for algebraic problem solving are described. This is followed by a description of the RAND Corporation's intelligent…

This study investigated the ways students represented fractions on number lines and the effects of instruction on those representations. The instruction primarily concerned representing fractions and ordering fractions on number lines. (Author/PK)

The ability of students to sort cards based on surface features and deep patterns is investigated. The effect of the presence of variables and what makes a pattern difficult or easy for students to recognize are discussed. Study revealed that students are unsuccessful at making connections between expressions, sentences, and sequences which share…

College students were asked to write equations using one of two sets of notational systems. Results indicate that the use of more explicit notation did not help problem-solving performance. (Author/PK)

Seventh-grade students were tested to uncover arithmetic errors. Answers and intermediate steps were analyzed and models to represent students' behavior were developed. Certain errors were common across students. Others were tied to the format of the test item. Some superficial understandings of mathematical concepts were exposed. (Author/DC)

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…

Language syntax is discussed, followed by an overview of algbraic syntax. Evaluating algebraic expressions was chosen as the means to investigate the psychological basis of syntactic skills. Subjects' ability to perform evaluative tasks appropriately using standard algebraic notation was ascertained; then similar tasks were presented using a…