Tests of (n=105) ninth-grade algebra students involving the addition and multiplication of monomials found that common, systematic errors made when multiplying monomials were related logically to the symbolism used and the algebraic convention of using an implicit 1 as an exponent. (16 references) (MKR)

Presents suggestions for developing algebraic concepts beginning in the early grades to develop a gradual building from informal to formal algebraic concepts that progresses over the K-12 curriculum. Includes suggestions for representing relationships, solving equations, employing meaningful applications of algebra, and using of technology. (MDH)

Explores two hypotheses about the effect of symbolic systems on psychological functions: (1) culturally elaborated systems of signs affect psychological functioning in a general way; and (2) systems of signs, when used to support skilled action, affect the organization of human activity. Reviews research that supports the second hypothesis. (LB)

Proposes helping students understand fractions by establishing connections between students' informal knowledge of fractions and the mathematical symbols used to represent fractions. Sample dialogues demonstrate how these connections can be made. (MDH)

This study compares reading comprehension of three different texts: two mathematical texts and one historical text. The two mathematical texts both present basic concepts of group theory, but one does it using mathematical symbols and the other only uses natural language. A total of 95 upper secondary and university students read one of the…

In an age of scientific method much of any individual's thinking is quantitative. He lives in a world in which every situation involves concepts of quantity, amount, size, or number. He employs number language, that is, number names and signs to express his quantitative ideas. These various number names and signs constitute the medium for his…

Although mathematics can be described as a formalized language, the signs and symbols of mathematical representation are subject to individual interpretation, which, if inaccurate, can lead to inhibitions about and interferences with the mathematical learning process. The purpose of this study was to explore communication in an intermediate-level…

Research on routine problem solving (e.g. the typical "story" problem) was reviewed to facilitate the identification and dissemination of promising practices for teaching routine problem solving, and to provide suggestions and directions for further research in the area. Promising teaching practices which were identified included giving attention…

Reports on the findings of an examination of 32 linear algebra textbooks. The examination, to determine existing approaches to teaching the topics, was in preparation for developing a linear algebra program for high school students. (PK)

Provides a thorough review of the software package "MathType, Mathematical Equation Editor." Includes hardware specifications, a description of the program, and evaluative comments. (PK)

Discusses the application of cognitive processes of physics teaching including idea first and name afterward; translating symbols into words; describing phenomena in words; reversing a line of thought; making decisions; inapplicability of formulas; recognizing the importance of non-examples; comparison and serial ordering; and estimating and…

The paper commences by reviewing some of the issues currently being raised with respect to the use of technology in undergraduate mathematics teaching and learning. Selected material from three research projects is used to address a series of questions. The questions relate to the use of symbolic manipulators in tertiary mathematics, to…

The tension between providing opportunities for mathematical understandings and the need to teach widely-used notations and algorithms is explained in terms of a folk pedagogical conflict. Divergent pedagogical practices are shown to follow from different mental and epistemological assumptions and manifest themselves in equally divergent student…

Our minds are shaped by youthful learning opportunities. Different forms of cultural representation (art, poetry, or mathematics) influence the processes and products of thinking, develop different cognitive skills, influence perceptions, can be combined to provide enriching experiences, and call on different skills and forms of thinking.…

This article examines the level of understanding by children (six- to seven-year-olds) of the addition and equality symbols. The article reports that about half of the subjects were unable to write the mathematical expression of simple addition while they were able to do it verbally. (YP)