This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This…

Our study concerns the analysis of teacher and student activities. Secondary school 6th grade students were confronted, for the first time, with solving equations. We used our cognitive models of students and experts (in algebraic calculations) for analyzing the teaching process and the cognitive functioning of students. Our model led us to…

Building on previous research on the tendency in students of diverse ages to overrely on proportionality in different domains of mathematics (e.g., geometry, probability), this study shows that--when confronted with missing-value word problems--Flemish primary school pupils strongly tend to apply proportional solution strategies, also in cases…

This book is the result of the collaborative effort of nine AYA National Board Certified Teachers in Mathematics. Experiencing Mathematics, is a compilation of teacher-tested activities that prompt high school students to explore, conjecture and reflect on their mathematical adventures--thus "experience mathematics." The relevant nature of the…

Four worksheets are given to enhance the understanding of and facility with numerical concepts and relations for students in grades seven through nine. The focus is on enhancing deductive reasoning abilities with Venn diagrams and arrow diagrams. Teaching ideas are included. (MNS)

Problem solving that both requires and develops higher-order thinking skills is illustrated in the EQUATIONS Challenge Matches program, which consists of computer diskettes at the elementary, intermediate, and advanced levels plus a multi-level diskette. Samples of computer output are given, with the results of various types of experimentation…

This book is directed toward increasing students' ability to analyze problems and comprehend what they read and hear. It outlines and illustrates the methods that good problem solvers use in attacking complex ideas, and provides practice in applying these methods to a variety of questions involving comprehension and reasoning. Chapter I includes a…

Challenges the readers comprehension of mathematical induction by presenting four examples of arguments that misrepresent the concept. Discusses the reasons why the arguments lead to false conclusions. (MDH)

The paper provides a college mathematics student's concept maps, definitions, and essays to support the thesis that language-based prior knowledge can influence students' cognitive processes of mathematical concepts. A group of intermediate algebra students who displayed terms mainly from the spoken language on the first and the second concept…

The purpose of this research is to investigate students' cognitive behaviour in the subjects of function, limit, and derivative according to gender. The research was conducted with the participation of 67 female and 58 male 11th grade students of Gazi High School in Eskisehir in the academic year 2000/2001. The data were obtained through a test…

To be prepared for a successful college experience, students must know certain academic subjects and have the skills to demonstrate their competencies in these subjects. This booklet outlines what college entrants need to know and be able to do to enter college in Alabama. As of July 1989, admissions standards of all Alabama public colleges and…

The game "Pythagoras" is an adaptation of the tangram puzzle. Describes the process of finding all the possible convex polygons with seven sides to prove that the solution to a given puzzle shape of seven sides difficult to find was not possible. (MDH)

Creating ways to make a discipline come alive for those who are not experts--even for students who may not take more than one or two courses in the disciplines they study--requires rigorous thought about what really matters in a field and how to engage students in the practice of it. Faculty from Alverno College representing a range of liberal…