This paper describes the difficulties faced by a group of middle school students (13- to 15-year-olds) attempting to translate algebraic statements written in verbal language into symbolic language and vice versa. The data used were drawn from their replies to a written quiz and semi-structured interviews. In the former, students were confronted…

In the study presented, as we report in this paper, we describe our theoretical and practical consideration to engage first-year pre-service teachers in proving activities in the context of a transition-to-proof course. We investigated how students argued to verify a claim of elementary number theory on entering university and compared the results…

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…

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

Traces three major stages in the development of algebraic notation: (1) rhetorical or prose; (2) syncopated; and (3) symbolic. Illustrates the development of a standardized, efficient symbol system by tracing the evolution of some common symbols, including the symbols for equals, addition, subtraction, multiplication, and division. (Author/WRM)

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)

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…