The purpose of this study is to present a multimodal languaging model for mathematics education. The model consists of mathematical symbolic language, a pictorial language, and a natural language. By applying this model, the objective was to study how 4th grade pupils (N = 21) understand the concept of division. The data was collected over six…

Before the advent of symbolism, i.e. before the end of the 16th Century, algebraic calculations were made using natural language. Through a kind of metaphorical process, a few terms from everyday life (e.g. thing, root) acquired a technical mathematical status and constituted the specialized language of algebra. The introduction of letters and…

An historical perspective reveals that sophisticated mathematical activity has been going on in the Latino culture for thousands of years. This paper provides a general definition of the area of mathematics education that deals with issues of culture and mathematics (ethnomathematics) and defines what is meant by the term Latino in this essay.…

The internal operations of this computer symbolic mathematics system are described in detail in order to explain the accomplishments of the computer. (MP)

Provides a categorization of the processes and products of science and discusses the need for science educators to provide quantitative and symbolic understandings of science using the mathematical ideas of symbols, proportions and scaling, and axiomatic methods of inductive and deductive proof. (MKR)

A major component of student difficulty with algebra is the inability to make sense of the algebra symbol system as a language. Accordingly, remedies should be sought by considering algebra in a linguistic sense. (PK)

Argues that intuitive and computational knowledge can be combined by focusing more explicitly on referential and quantitative meanings in division of fractions problems. Recommends teaching mathematics as problem solving, communication, reasoning, and connections to help students overcome misunderstandings and connect their intuitive knowledge…

The dual purpose of this paper is to put forward the problem of goal orientation in mathematics education in general and to consider a specific goal that is not seen as central in traditional teaching practice. The goal orientation approach in education aims to construct the teaching process considering the goals of the students, i.e. the expected…

Researchers have reported that children's writing about mathematical concepts can give teachers valuable insight into students' mathematical understanding. There are, however, factors which place constraints on the adequacy of written products to reveal the quality and degree of children's conceptual understanding. This study examined the…

This paper explores languages for communicating precise ideas within limited domains, which include mathematical notation and general purpose and high level computer programming languages. Low-level properties of such natural artificial languages are discussed, with emphasis on those in which names are chosen for concepts and symbols are chosen…

Describes a general education course addressing the linguistic and logical aspects of the language of mathematics which is intended to develop students' abilities to read mathematics, express mathematical thoughts clearly, reason logically, and grasp the nature of proof. Students improved their algebraic procedural skills and attitudes toward…

This longitudinal study investigated the ways in which two groups of eight students used spreadsheets to represent and solve algebra problems and related this to their previous arithmetical experiences and evolving use of symbolic language. The spreadsheet environment supported students to move from specific to general thinking. Includes story…