In this article we compare two frameworks for analysing young children's responses to the task of copying and extending a 6-dot triangle pattern. We used Mulligan & Mitchelmore's Awareness of Mathematical Pattern and Structure (AMPS) and then Biggs & Collis' SOLO taxonomy, both of which provide criteria for assigning levels. In comparison…

An extraordinary variety of experimental (e.g., flicker, magnetic fields) and clinical (epilepsy, migraine) conditions give rise to a surprisingly common set of elementary hallucinations, including spots, geometric patterns, and jagged lines, some of which also have color, depth, motion, and texture. Many of these simple hallucinations fall into a…

Research on naive physics and naive optics have shown that people hold surprising beliefs about everyday phenomena that are in contrast with what they see. In this article, we investigated what adults expect to be the field of view of a mirror from various viewpoints. The studies presented here confirm that humans have difficulty dealing with the…

The present study investigated (a) whether the perceived cognitive load was different when geometry problems with various levels of configuration comprehension were solved and (b) whether eye movements in comprehending geometry problems showed sources of cognitive loads. In the first investigation, three characteristics of geometry configurations…

Described are activities for thinking through patterns using toothpicks, paper strips, wooden cubes, and people patterns; thinking with attribute items such as geocards, namestrips, and treasures; and thinking with geometric materials such as geoboards and dot paper, cubes, and simple puzzle pieces. (MNS)

Games and activities which involve problem solving are presented in order to help teachers develop the numeric, geometric, and logical thought processes of elementary school students. The activities and games (many of which are pencil-and-paper) require using logic, plan-ahead strategies, spatial reasoning, strategies based on prior patterns or…

Described is a project in a third grade class in which problem-solving skills are developed through activities with patterns. Activities for growing picture patterns, making number tables, and developing open sentences or formulas are discussed and illustrated. (MNS)

This document contains the fourth volume of the proceedings of the 30th 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 59 research reports by presenters with last names beginning between Kun and…