The way mathematics teaching and learning activities are presented to learners can make them hate or like the subject. The question of accomplishing the mathematics education of the learner from primary to post-secondary school levels is one which necessarily tasks, not only the teacher's stock of mathematical knowledge but also his skill, his…

The present study focused on the lack of knowledge of the double use of brackets in arithmetic expressions and the difficulty in the operatively of expression for mathematics application at the school level. Learning the other rules and formulas of mathematics involves learning the use of a bracket. Binding is useful in both arithmetic and…

Presents and investigates a theoretical perspective on the development of understandings of mathematical operations with a particular focus on addition. Presents a case study on the development of a young boy and concludes that his attainment of aspects of operation sense supported transitions into algebraic ways of thinking. Contains 46…

Examines arithmetic and algebra knowledge from a cognitive perspective in an effort to determine what constitutes a pre-algebraic level of understanding. Presents results of a longitudinal study designed to investigate students' readiness for algebra. Proposes a model for the transition from arithmetic to pre-algebra to algebra. Contains 29…

This study showed that Oksapmin children not only spontaneously use the indigenous numerical system of their nontechnical culture but also have created new forms of numerical symbolization and calculation to deal with schooling arithmetic problems. Novel conceptual developments, factors mediating the schools effect, and the influence of prior…

This instructional guide and set of three companion workbooks are intended for use in an arithmetic course based on the Tic Tac Toe method of addition and multiplication, which is an alternative means of learning to add and multiply that was developed for students whose learning disabilities (including difficulty in distinguishing left from right…

This paper presents the results of a pilot study conducted to examine Web-based instructional content for mathematics. Two research questions were posed during the study: (1) how is technology being used to represent mathematical concepts online? and (2) how do the representations work together as a system? A mixed method content analysis design…

The Education Technology Center (ETC) Fractions Group works to investigate well-documented difficulties that children have in understanding fractions. A central assumption underlying this group's inquiry is that students' difficulties in manipulating fractions arise from their lack of understanding about the nature of fractions. In order to learn…

This guide contains a collection of alternative techniques for teaching arithmetic that have proved useful in teaching both children and adults with various learning problems. Discussed first are several underlying principles of instructing individuals with learning disabilities, problems, and differences and special accommodations for…

Ongoing work toward developing a learning environment that will perform real-time diagnoses of students' difficulties in solving mathematical word problems is described. The learning environment designed consists of a microworld and expert modules. The microworld (or toolbox) is a collection of mouse-driven interfaces that facilitate a transition…

The associations among cognitive automatization, abstract problem solving, and educational performance were studied using 127 fourth to ninth grade students. A number of measures of fast, automatic, and fluent performance (FAF measures) were used: writing the alphabet; reading from a word list; and mentally performing arithmetic operations. The…

This document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr…