Analyzes the nature and growth of students' algebraic knowledge and thinking from an epistemological perspective supported by historical observations. Focuses on two crucial transitions: from the purely operational algebra to the structural algebra of a fixed value of an unknown and then to the functional algebra of a variable. (Contains 58…

After discussing the role of supercalculators within the business calculus curriculum, several examples are presented which allow the reader to examine the capabilities and codes of calculators specific to different major manufacturers. The topics examined include annuities, Newton's method, fixed point iteration, graphing, solvers, and…

Proposes a perspective on mathematical symbolism as a communication and conceptualization tool. Describes research in which first graders, solving mathematical problems in small groups, invented symbolic representations as both a part of the knowledge construction process and a means of communicating their conceptualizations to each other. (SV)

Introduces a new sign convention for the object and image distances involving mirrors and lenses. Proposes that the method is easier for students to understand and remember and that it helps clarify the physics concepts involved. (MDH)

Symbol-and-arrow diagrams are helpful adjuncts to equations derived from pharmacokinetic models. Both show relationships among dependent and independent variables. Diagrams show only qualitative relationships, but clearly show which variables are dependent and which are independent, helping students understand complex but important functional…

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)

The use of Symbolic Mathematics Engines (SMEs) in chemical education as a part of the Division of Computers in Chemistry was discussed by a panel of educators at the Symbolic Calculation in Chemistry symposium in Philadelphia in 2004. The panelists agreed that many more topics in chemistry are amenable to SME's exploration and that symbolic…

Substitution tests have a long history in psychology because of their simplicity of administration and their sensitivity to individual differences related to complex cognitive performance. Despite their widespread use there is no agreement on what the substitution test measures. The present study approached this question by applying a method of…

This study investigated how understanding of the equal sign changes as a function of experience in mathematics and variations in context. Students with different levels of mathematics experience (elementary school, seventh grade, undergraduate, and graduate) were randomly assigned to view the equal sign in one of three contexts: (a) equal sign…

Mathematical signs and symbols have a decisive role for coding, constructing and communicating mathematical knowledge. Nevertheless these mathematical signs do not already contain mathematical meaning and conceptual ideas themselves. The contribution will present basic elements of an epistemology of mathematical knowledge and then apply these…

The focus of this document is on students' understanding of symbolization processes in algebra, and specifically their understanding of semantically laden letters. In the first four sections, four inappropriate ways in which many college students use semantically laden letters are described. Evidence from clinical interview protocols demonstrate…

Reading the language of mathematics textbooks is very different from reading the narrative in traditional basal textbooks, and children should be taught how to read in a mathematics course; teachers should not assume a transfer of skills will occur. Specific skills, such as noting details, following directions, and seeing relationships, should be…

Instruction on properties of whole numbers, the meanings of operations on whole numbers, symbolic representation and algorithms for completing these operations is discussed. Many activities appropriate to each of these topics, and suitable for primary school children, are presented. (SD)

A series of activities designed to help primary school children understand the meaning of the term "fraction," the symbolization, and equivalence of fractions are presented. Identification of units and pictorial representation are stressed, as is the uses of concrete materials. (SD)

Excerpts from interviews with pupils in grades 1, 2, 3, and 6 to ascertain their interpretations of mathematical sentences and symbols are presented. Children were found to consider the equal sign as an operator symbol ("do something") and not as a relational symbol. Implications for teaching are briefly discussed. (MS)