For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

Learners are all different and teachers are all different, so why do we often ignore this reality when trying to explain, or demystify, some aspect of mathematics in the classroom? Enabling learning can be challenging, demanding of creativity, and needy of alternatives if understanding is the real goal. Here the authors offer ideas that are aimed…

In this article, the authors explore framing, a non-multiplicative technique commonly employed by students as they construct similar shapes. When students frame, they add (or subtract) a "border" of fixed width about a geometric object. Although the approach does not yield similar shapes in general, the mathematical underpinnings of…

The concept of "function" spans elementary school through high school. When introducing the topic to elementary school and middle school students, the authors ask them to work with a variety of examples and representations of functions, since a formal definition of a function is rather abstract. They give the most accessible geometric functions…

An online interactive geometry item was developed to explore students' abilities to create prototypical and "tilted" rectangles out of line segments. The item was administered to 1,002 students. The responses to the item were hand-coded as correct, incorrect, or incorrect with possible evidence of a misconception. A variation of the nearest…

In this paper, the development of an innovative Virtual Manipulatives and Whiteboard (VMW) system is described. The VMW system allowed users to manipulate virtual objects in 3D space and find clues to solve geometry problems. To assist with multi-representation transformation, translucent multimedia whiteboards were used to provide a virtual 3D…

"Mathematics is more than skills... it is also the excitement of discovery." This is how Derek Holton, one of the contributing authors to this book, defines mathematics. His enthusiasm and energy are echoed throughout by many of the other writers. This is a book to delight mathematics teachers at all stages: experienced and inexperienced;…

In this article we discuss nine common misconceptions about learning and teaching mathematics for young children that are widespread among prospective and practicing early childhood teachers in the United States. These misconceptions include: 1. Young children are not ready for mathematics education; 2. Mathematics is for some bright kids with…

This present study investigated engineering students' conceptions and misconceptions related to derivative, particularly interpreting the graph of a function and constructing its derivative graph. Participants were 147 first year engineering students from four universities enrolled in first year undergraduate calculus courses with or without the…

The concept of function is the single most important mathematical concept studied from kindergarten to graduate school and is critical throughout the full range of education. Thus, the goals of this book are to contribute to research in learning the concept of function and to provide a resource for mathematics teachers that could help them in…

Contains six abstracts of papers from the National Educational Computing Conference of 1986. Topics of the papers focus on the effects of teacher involvement, computer programs in applied mathematics and physics, microcomputer labs in science, graphing misconceptions, science simulations, and mastery learning with computers. (ML)

The Probability Inquiry Environment (PIE) is being designed as a computer-mediated collaborative inquiry environment to aid middle school students in learning elementary probability. This paper reports on a study in which seventh grade students engaged in probabilistic reasoning while interacting with a preliminary version of PIE. By analyzing the…

These proceedings contain the papers presented at the 1995 annual meeting of the Canadian Mathematics Education Study Group. Papers are organized into four sections: (1) plenary lectures; (2) working groups; (3) topic sessions; and (4) ad hoc sessions. Papers include: (1) "The Role of Epistemology in the Analysis of Teaching/Learning…

This publication provides an introduction to teaching and learning approaches for the extension topics within GCSE Physics. It highlights some specific ideas that teachers can adopt and where to find further information. It also outlines issues for managing the change. This guide contains sevens sections: Section 1 presents the policy context;…

This document is the first of three volumes of the proceedings of an international seminar which focused on student misconceptions in science and mathematics as well as teaching strategies intended to deal with those misconceptions. An introduction to the volume explains the format of the conference and the organization of the sessions. It…