Answers to mathematical problems come in all forms and most come with a variety of questions. Students often forget to ask questions once they have found an answer. This paper suggests that students would always benefit by questioning answers.

A simple car following model based on the solution of coupled ordinary differential equations is considered. The model is solved using Euler's method and this method of solution is itself interpreted as a mathematical model for car following. Examples of possible classroom use are given. (Contains 6 figures.)

The Proceedings of PME-XVI has been published in three volumes because of the large number of papers presented at the conference. Volume 1 contains: (1) brief reports from each of the 11 standing Working Groups on their respective roles in organizing PME-XVI; (2) brief reports from 6 Discussion Groups; and (3) 35 research reports covering authors…

This study investigated the ways in which the technological tool, The Geometer's Sketchpad, mediated the understandings that high school Honors Geometry students developed about geometric transformations by focusing on their uses of technological affordances and the ways in which they interpreted technological results in terms of figure and…

Teaching and learning mathematics with technology poses a unique dilemma. If technology is to enhance mathematical achievement (NCTM, 2000), why do documented studies indicate that this may not be the case (Waxman, Connell, & Gray, 2002)? This study looks at the learning environment used when teaching with technology. What in the instructional…

In 1983, the Ohio State Board of Education responded to the public's expectations for schools by adopting minimum standards requiring competency-based education in mathematics on a 5-year cycle, of each school district's competency-based education program; and to publish an annual report on competency-based education in Ohio. This document is the…

This book explores current theory, research, practice, and policy in the assessment of higher order thinking in mathematics, focusing on the elementary and secondary grades. Current knowledge and research on mathematics learning and testing is synthesized. Examples of innovative test items for classroom use and state assessment programs are…

The purpose of this report is to see what the literature has to say about motivation and group interactions, both with and without the assistance of computers. The ultimate purpose is to examine in detail how the emerging ideas can be used to enhance the teaching and learning of arithmetic using computers. This report is divided into the following…

This guide describes 20 learning activities that can be used with elementary school students on the topic of probability and statistics. These activities have been developed using the mathematics laboratory approach. This publication is designed to serve as a stimulant to encourage teachers to open their minds and employ their imagination in…

This guide focuses on the Square One TV game shows, which explore areas ranging from probability and statistics to geometry. Eight game shows are described including the game rules, materials, directions, strategies for playing the games, actual game questions, and reproducible student pages. Follow-up activities provide ideas for using the games…

This issue of the journal contains abstracts and critiques of 11 research reports. Three of the reports concern problem solving; the remainder pertain to the following topics: the impact of secondary schooling and secondary mathematics on student mathematical behavior; figural matrices; computer-video instruction in mathematics; equivalent…

This unit is designed to acquaint middle school students with Pascal's Triangle. The unit is intended to be completed in small groups with a minimum of teacher direction. Students complete the activities by using manipulatives, calculators and computers and then report the results to the teacher and the class. The activities include: (1) patterns…

A delegation of 22 mathematics educators sponsored by the Illinois Council of Teachers of Mathematics visited Japan September 23-October 11, 1988. The group included teachers from elementary through university levels. The group visited 16 schools, 2 teacher training colleges, a scientific university, and 2 juku schools in the four major population…

The National Assessment of Educational Progress (NAEP) reports on the status and progress of educational achievement in the United States. Based on its surveys, "The Nation's Report Card" provides comprehensive information about what students in the United States can do in various subject areas. The framework for the 1990 mathematics…