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 document is one of six which set forth the mathematics components of the Project SEARCH Articulated Curriculum developed by the Utica (New York) City School District. Each volume deals with a broad area of mathematics and lists objectives related to that area for all grades from K through 12. Each objective listed is described first in…

This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)

Reasoning patterns and learning difficulties of six students are illustrated in support of the contention that language and notation often disguise thought. (MN)

Considers the problem of constructing Venn diagrams for more than three sets. Presents an unusual geometric display of a Venn diagram for five sets. (PK)

Many children with learning handicaps have difficulty learning to write numerals. The source of numeral-writing difficulties and some things which can be done to teach or remedy this skill are presented. (MNS)

Proposes a method for dealing with units that require involvement of units of each physical quantity at every stage of a calculation. Preliminary ideas on algebra and the concept of a physical quantity, equations relating two or more units, calculations of physical quantities, and logarithms are considered. (JM)

This research offers empirical evidence of the importance of supplying diverse symbolic representations in order to support concept development in mathematics. Graphical representation can be a helpful symbolic tool for concept development in the conceptual field of additive structures. Nevertheless, this symbolic tool has specific difficulties…

Practical examples from everyday life, spanning personal financial matters to traveling and even cooking conversions are the lessons offered in this useful guide. The vast majority of older students and adults who come to America come from countries that use the metric system. Learning a new system for measuring, telling time, and so forth is…

This paper reports on part of a wider study on the teaching and learning of the conventions of formal algebraic notation. Through the analysis of paper tasks given to teachers I argue that not only does the inherent mathematical structure have an effect on the way in which an equation is manipulated but also the visual impact of notation itself.…

A review of several studies on the role of concrete and symbolic models in facilitating the learning of mathematical ideas, and a discussion of their implications for instruction are presented. (DT)

The roles and uses of symbols in mathematical thinking are discussed. The thinking process is further subdivided into specialization, generalization, and reasoning. (MP)