A theory is proposed for how students develop competence with the written symbols of decimal fractions. Competence is viewed as the cumulative and sequential mastery of four separate cognitive processes. The theory was tested with small groups of students, most of whom were able to acquire the first two processes. (MNS)

Presents activities to visually explore the algebraic concepts of variable, constant, the distributive property, and combining like terms. Presents four transparencies that use visual models to understand exercises in students perform the same mental calculations on a number of their choice and obtain the same result. (MDH)

Relates research findings on the way primary-grade students communicate mathematical ideas through the use of symbols to a framework for students to investigate the part-whole relationship of quantity. Discusses children's problem-solving abilities, linking word problems and symbols, the importance of context for understanding symbols, and the…

Discusses duality between process and concept in mathematics, ambiguity of symbolic notation, and flexibility in thought processes of successful students. Content analysis and empirical evidence suggest a qualitatively different kind of mathematical thought in more able compared to less able elementary students (n=72) in arithmetic. (Contains 42…

Effects of 3 different types of instruction (use of manipulatives, use of diagrams, and use of symbols only) of rational number content and teaching techniques were compared for 75 preservice teachers in a course in elementary mathematics. Only the manipulatives group showed significant improvement pretest to posttest. Implications are discussed.…

Teaching in a manner consistent with reform recommendations is a challenging and often overwhelming task. Part of this challenge involves using students' thinking and understanding as a basis for the development of mathematical ideas (cf. NCTM, 2000). The purpose of this article is to address this challenge by developing the notion of "pedagogical…

Students' performances on mathematical problems varying in symbolic form and the kinds of symbolic representations and translation used in instruction were explored. The sample consisted of 29 students enrolled in Algebra II in a summer program for minority students. All students were Black or Hispanic American and most were about to enter grade…

This document presents Core Course Proficiencies for the State of New Jersey whose purpose is to ensure that all students have equal access to the fundamental knowledge and skills critical to achieving success in mathematics. After an introduction providing rationale and background, the Core Course Proficiencies are presented in three sections.…

Intended for college bound students, this booklet explores textbook components to help students in their approach to studying technical information. After defining technical material and describing how to recognize it, the booklet discusses (1) symbols, (2) equations, (3) formulas, (4) theorems, (5) placement of symbols in textbooks, (6) tables,…

A study explored the effectiveness of an instructional approach designed to help students establish connections between their understanding of the decimal system and the stardard symbols and procedural rules used to solve decimal problems. Ten children each in grades 4 through 6 participated. They were individually interviewed prior to and six…

This paper describes the BUD project which surveyed childrens' conceptions of division, and of fractions and decimals. The lack of connection between counting skills and conceptual understanding is discussed. The expectations for new algorithms and the basic idea in planning the BUD project are summarized. Some previous studies on counting, the…

This pamphlet is a guide to the equipment, procedures, instruments, and resources needed in teaching a course of technical typewriting to prepare a typist for a job in a science-related office where correct spelling and use of scientific and technical terminology are of paramount importance. Described are course guidelines, performance objectives,…

Science and technology use a large variety of symbols to represent physical properties, chemical formulas, and mathematical expressions. Since data centers which codify and evaluate physical properties need to use this conventional symbolism, it is recommended that they adopt the symbols and terminology specified by the various International…

The purposes of this booklet are to acquaint both mathematics teachers and reading teachers with some skills which students need for effectively reading the language of mathematics and to provide sample activities which may be used as an integral part of the mathematics class, in an effort to help students develop those skills. Since mathematics…

This paper presents the idea of multimodal teaching and learning and discusses how this perspective can help better understand the learning of students. The discussion is based on data gathered in a qualitative study of a fifth-grade bilingual classroom where at-risk students were successful in mathematics. We report on one class episode and one…