This study examined how 4 middle school textbook series (2 skills-based, 2 Standards-based) present equal signs. Equal signs were often presented in standard operations equals answer contexts (e.g., 3 + 4 = 7) and were rarely presented in nonstandard operations on both sides contexts (e.g., 3 + 4 = 5 + 2). They were, however, presented in other…

This study proposed practical ways to display mathematical formula on the Web and input mathematical formulae onto the Web according to the authors' successful experience of implementing mathematical forum which allowed displaying and inputting mathematical notations and equations. Authors believe that this study will pose more questions and…

A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.

Learning mathematics has traditionally been thought of as a sequential progression. Children learn to count to 10, then to 20, and then to 100. They learn to add without regrouping and then with regrouping. The authors teach addition before multiplication and the two-times table before the six-times table. They usually teach division as a separate…

Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…

Both mathematics and informatics share common characteristics. Several didacticians propose therefore to define didactic situations permitting learners to "co-construct" knowledge of mathematics and informatics. In this document, the idea is resumed and a certain number of "functional structures" are proposed. These sets of problems take on a…

This article gives a historical background, a discussion of the International Bureau of Weights and Measures, and an introduction to the International System of Units (SI). Base, derived, and supplemental units are discussed. Prefixes, matters of form, and possible adaption problems are also considered. (LS)

The purpose of this paper is to propose the combined use of distinct symbol sets to conduct multilevel process (MLP) analysis and to discuss the application of the technique through a case study example. In turn, consideration is given to the meaning of process analysis, the existent technology of representation, proposed new developments, and…

Using negative digits in writing numerals and in calculation is explained. This is the second article in the series; for the first, see Vol. 1, No. 7, Nov., 1972, pp. 8-9. (DT)

Responses to rate-of-change problems were collected during and after 24 hours of conceptual calculus instruction given to first-year university students. Analysis revealed three categories of error in which variables were treated as symbols to be manipulated rather than quantities to be related. Contains test questions. (Author/MKR)

Attempts to describe a notion parallel to number sense, called symbol sense, incorporating the following components: making friends with symbols, reading through symbols, engineering symbolic expressions, equivalent expressions for non-equivalent meanings, choice of symbols, flexible manipulation skills, symbols in retrospect, and symbols in…

Provides a brief historical explanation of the multiplication sign in mathematics. (ASK)