Students often struggle with concepts from abstract algebra. Typical classes incorporate few ways to make the concepts concrete. Using a set of woven paper artifacts, this paper proposes a way to visualize and explore concepts (symmetries, groups, permutations, subgroups, etc.). The set of artifacts used to illustrate these concepts is derived…

Developments in mathematics education tend to emphasize mathematics teaching with the help of activities that will allow the students to create these concepts rather than to make them memorize mathematical rules. The purpose of this study is to analyze the applicability of the application of multiplication with fingers developed by the researcher.…

Algebra is often considered as difficult and mysterious doctrine due to numerous symbols that represent mathematical notions. Results of the research on students' interpretation of literal expressions show that only a small number of students are ready to accept that a letter can represent a variable. The aim of this research with students of the…

This study aims at exploring processes of flexibility and coordination among acts of visualization and analysis in students' attempt to reach a general formula for a three-dimensional pattern generalizing task. The investigation draws on a case-study analysis of two 15-year-old girls working together on a task in which they are asked to calculate…

Many students have traditionally found the processes of algebraic manipulation, especially factorisation, difficult to learn. This study investigated the value of introducing students to a Vedic method of multiplication of arithmetic numbers to algebra that is very visual in its application. This research considered a possible role of the…

Presented are three cases for intuitive understanding in secondary and college level geometry. Four ways to develop the intuition (physical experience, mutable manipulatives, visualization, and looking back) step are discussed. (YP)

Shows that graphs can reveal much about feedback systems that formula conceal, especially as microcomputers can provide complex graphs presented as animations and allow students to interact easily with them. Describes feedback systems, evolution of the system, and phase diagram. (YP)

Describes five skills underpinning the understanding of geometry for primary and lower secondary mathematics students. Skill categories identified include (1) visual; (2) verbal; (3) drawing; (4) logical; and (5) application. Gives examples of skills appropriate for Van Hiele levels 1-3. (MDH)

Reports part of the results of the Design, Development, and Assessment in Mathematics Education Project that tested the booklet on descriptive statistics called "Data Visualization" in six experimental algebra classes in Whitnall, Wisconsin. Describes examples of problems presented, use of cooperative learning during instruction, and…

The 1989 document, "Curriculum and Evaluation Standards for School Mathematics" (the "Standards"), provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. This book, one in a series…