The analysis reported in this paper is part of a year-long first-grade teaching experiment and focuses on the teacher's proactive role in supporting students' mathematical growth in an inquiry mathematics classroom. Within the project classroom, the teacher often redescribed and notated students' responses so that what students had done…

Describes a procedure for helping students understand and work mathematical word problems. (MKM)

The relationship between eight skills and one concept used on maps and their companion spatial abilities in mathematics are presented and discussed: symbols, perspective, location, direction, distance, relief, elevation, scale, and territoriality. (MNS)

Two versions of a page of exercises using set ideas are presented, one in plain language and one in technical language. Some questions and answers about the appropriateness of set terminology and symbols are then given. (MNS)

This research study deals with the modes of representation that ninth-graders choose in order to communicate their problem solving paths and justifications, and the relation between these modes of representations and achievement level. The findings are based on analysis of 350 answers to problems that demanded communication of reasoning,…

The major idea in this paper is the formulation of a theory of three distinct but interrelated worlds of mathematical thinking each with its own sequence of development of sophistication, and its own sequence of developing warrants for truth, that in total spans the range of growth from the mathematics of new-born babies to the mathematics of…

In this paper we analyze the meanings of the "equal" sign as generated by sense production of the methods of substitution and comparison for solving problems and systems of equations of two unknowns. These methods are usually introduced through an extension process of the syntax and meanings recently learned by students in order to solve…

Children may perform computational operations readily when dealing with physical materials, but may have difficulty dealing with representational stimuli (pictures of objects) or symbolic stimuli. Describes and illustrates the function of mediators in moving from physical to representational or symbolic stimuli. (PR)

Mathematics is often referred to as a language. This paper attempts to explore the implied meanings of such statements and to outline a rationale for utilizing the language-structure of mathematics in mathematics instruction. (Author/MK)

Two major periods of development in proportional reasoning are identified by analysis of a 23-item experiment given to subjects between 6 and 16 years of age. (MP)

Explores the attempts of a group of preservice elementary school teachers to generalize a repeating visual number pattern. Discusses students' emergent algebraic thinking. Indicates that students' ability to express generalities verbally was not accompanied by algebraic notation, but participants often perceived complete and accurate solutions…

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)

Presents an episode in which a conflict arose as sixth-grade students attempted to create nonstandard units of measurement. Discusses the conflicting requirements of language and symbol use in mathematical communication in the activity. (MKR)

This article is the last keynote address of the Algebra Working Group of the Seventh International Conference on Mathematical Education held in Quebec City, Canada in August 1992. Attempts to integrate, and react to, the broad range of issues raised by the Algebra Working Group. (35 references) (MKR)