In this article, I argue for a renewed focus in mathematics education research on procedural knowledge. I make three main points: (1) The development of students' procedural knowledge has not received a great deal of attention in recent research; (2) one possible explanation for this deficiency is that current characterizations of conceptual and…

This paper is a report on an attempt to teach students in their first and second year of university how to write mathematics. The problems faced by these students are outlined and the system devised to emphasize the importance of communicating mathematics is explained.

Literature suggests that the type of context wherein a task is placed relates to students' performance and solution strategies. In the particular domain of logical thinking, there is the belief that students have less difficulty reasoning in verbal than in logically equivalent symbolic tasks. Thus far, this belief has remained relatively…

In this paper we develop our theory of "Bi-numeracy" and show the importance of children's own invented symbolism. Most studies to date have concentrated on the analysis of children's number representations in clinically set-up tasks (Hughes, 1986; Sinclair, 1988; Munn, 1994). These studies have added to our knowledge of and…

Teaching teachers to become observers and inquirers into mathematics will help change how they teach math to students. Essential to all professional development in mathematics is the idea that making sense of mathematics is key to learning. Just as learning to read calls for bringing meaning to the printed page, learning math calls for bringing…

One in a series of core instructional materials for apprentices to use during the first or second years of apprentice-related subjects training, this booklet deals with sketching, drawing, and blueprint reading. The first section consists of an outline of the content and scope of the core materials as well as a self-assessment pretest. Covered in…

This bibliography lists books and articles discussing graphic aspects of human communication. References have been selected for their relevance to the design of self-instructional texts for the adult learner; for the most part, research on younger children, on non-text media, and on non-educational texts is not included. Items are organized into…

The development of number concepts from conservation through order and place value notation is discussed in the context of applications to classroom instruction. Activities designed to motivate, build, and reinforce these concepts are described, and a list of objectives is presented in the form of a suggested progress record. (SD)

Difficulties inherent in the reading of mathematics at secondary and college levels are discussed. Special emphasis is placed on the reading of arithmetic numerals, literal numbers, operational symbols, and expressions of relationships, as well as the reading of technical vocabularies and specialized meanings of general words. While each…

There are today some 5,000 languages and dialects in use throughout the world; in most instances, intercommunication among them ranges from difficult to impossible. This sourcebook of graphic symbols was compiled as a first step toward a basic means of communication through a system of universally recognizable symbols. The sourcebook is limited to…

Presented is the basis for an integrated approach to teaching reading skills and mathematics concepts at the elementary school level. A general explanation of concept formation, of oral and written language, and of mathematics symbols, with specific suggestions as to their application in mathematics, is included in the first section of the…

Intended for teachers of the visually impaired, the article provides information on the terminology; symbols; and use of metric ladders for area, volume, and temperature to covert from one denomination to another denomination of metric units. (SB)

Presented is a theory of how competence with written mathematical symbols develops, tracing a succession of cognitive processes that cumulate to yield competence. Arguments supporting the theory are drawn from the history, philosophy, and psychology of mathematics. (MNS)

How children can be guided to see and feel the power of thinking with and about mathematical symbols is discussed. A strategy to help them bridge the gap between manipulative models and symbols is detailed. (MNS)