Examined how student's strategies and associated conceptions emerged and changed over a 6-session tutoring curriculum designed to develop conceptual knowledge of linear functions. Found that the student did not erase his original conception or replace it with a conception supported by instruction, but instead refined his initial strategies and…

The National Council of Teachers of Mathematics' "Curriculum and Evaluation Standards" in 1989 was pivotal in mathematics reform. The National Science Foundation funded several curriculum projects to address the vision described in the "Standards." This study investigates students' learning in one of these "Standards"-based curricula, the…

This article explores the graphic development of a five-year-old girl with autism during Saturday morning art classes. It attempts to uncover what particular methods of consideration are useful in the examination of the art of such a child. Drawing systems and early mathematics are found to be of value in discussing Sung's art making since both…

As the class is learning new names and new faces at the beginning of the school year, it's the perfect time to have fun with names and learn some math concepts at the same time. This document describes examples of different number games that can be played with students.

A simple model for how traffic moves around a closed loop of road is introduced. The consequent analysis of the model can be used as an application of techniques taught at first year undergraduate level, and as a motivator to encourage students to think critically about model formulation and interpretation.

This article discusses a relatively unnoticed application of mathematics by describing its connection with an aspect of music, in particular, the musical scales. Stemming from a problem found in a Year 9 mathematics textbook commonly used in Singapore, the article illustrates the role of mathematics in musical scales by first considering the…

This article describes a set of problem-solving tasks that may provide opportunities for students to make sense of proportional reasoning. (Contains 1 figure.)

This article describes how we have used children's picture books to explore linear and exponential functions with prospective teachers and middle-grades students. (Contains 2 tables and 2 figures.)

This article examines research to explore whether the use of manipulatives is an effective tool in teaching mathematics concepts and reasoning to middle-grades students.

This study argues that maximizing early childhood educators' abilities to create social opportunities for co-construction of knowledge rests on two understudied assumptions, one theoretical and one empirical. Theoretically this study rejects the notion of language as an impartial conveyor of knowledge in favor of one in which math and language…

Teachers can help students build a disposition to use connections in solving mathematical problems, rather than mathematics as a set of disconnected, isolated concepts and skills. One activity that addresses the criteria that involve problem solving, reasoning, communication, and representation that together create a vision that encourages…

In this paper, we give a detailed account of the design principles and construction of activities designed for learning about the relationships between position, velocity and acceleration, and corresponding kinematics graphs. Our approach is model-based, that is, it focuses attention on the idea that students constructed their own models--in the…

Mathematical fiction has probably existed since ideas have been written down and certainly as early as 414 BC (Kasman, 2000). Mathematical fiction is a recently rediscovered and growing literature, as sales of the novels: "The Curious Incident of the Dog in the Night-time" (Haddon, 2003) and "The Da Vinci Code" (Brown, 2004)…

Previous studies have shown that even preschoolers can solve inversion problems of the form a + b - b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d x e [divided by] e was also examined. Grade 6 and 8 students solved inversion problems of both types as well…

The purpose of this paper is to focus on the nature of the thinking processes supporting pupils' construction and understanding of mathematical concepts. We assume that interaction with reality plays a crucial role in learning. In particular, human perception and action and, more generally, interaction with artefacts, are very important for…