William Playfair's pie chart is more than 200 years old and yet its intellectual origins remain obscure. The inspiration likely derived from the logic diagrams of Llull, Bruno, Leibniz, and Euler, which were familiar to William because of the instruction of his mathematician brother John. The pie chart is broadly popular but--despite its common…

Quadrature methods for approximating the definite integral of a function f(t) over an interval [a,b] are in common use. Examples of such methods are the Newton-Cotes formulas (midpoint, trapezoidal and Simpson methods etc.) and the Gauss-Legendre quadrature rules, to name two types of quadrature. Error bounds for these approximations involve…

This article describes a solution, using CAS, to graph theory problem that was presented in the movie "Good Will Hunting."

This study examines the practical work of a pair of students and an instructor using probeware in a mechanics lab. The aim of the study is to describe and discuss a type of interactional sequence that we refer to as "dark matter", the ordinary backdrop to the extraordinary sequences that are easily recognizable as clear-cut instances of learning.…

In this book, parents will find ways to help teachers nurture important emerging math skills, from sorting and division of materials to early counting. Basic ideas and tools, including classroom-tested activities, will help support their child's math learning, both at home and in child care. Following an introduction, the book contains three…

In this article, the author considers a student exercise that involves determining the exact and numerical solutions of a particular differential equation. He shows how a typical student solution is at variance with a numerical solution, suggesting that the numerical solution is incorrect. However, further investigation shows that this numerical…

Metal rods of high purity for many elements are now commercially available and may be used to construct a display of relative densities. We have constructed a display with nine metal rods (Mg, Al, Ti, V, Fe, Cu, Ag, Pb, and W) of equal mass whose densities vary from 1.74 to 19.3 g cm[superscript -3]. The relative densities of the metals may be…

This paper analyses technology-based instruction on data-analysis with box plots. Examples of instruction taken from the research literature inform a study of two classes of 17 year-old students (upper secondary) in which the mathematical relationships that their teachers targeted are distinguished as being, or not being, relevant to statistical…

This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in…

This case study investigated the impact of a spreadsheet (EXCEL) exploration on the understanding of statistical graphs among twenty Singapore secondary school students of average ability. Four EXCEL templates were constructed to allow students to explore four aspects of statistical graphs: zero in scale, effect of different scales, size…

The purpose of this study was to determine whether there were significant differences in students' performances amongst conceptual, algorithmic and graphical questions tests. Seventy-one eleventh-grade students were involved in this study. In order to assess students' performance, conceptual, graphical and algorithmic questions tests were…

In light of evidence indicating that errors in making accurate pie charts are prevalent, an alternative method for constructing pie charts is proposed. It involves the use of a simple trigonometric formula to compute a factor of the length of the chord that defines a given percentage sector. This factor is multiplied by the radius of the circle to…

This article briefly describes the topics "beta coefficient"--a measurement of the price volatility of a company's stock in relationship to the overall stock market--and "market share"--an average measurement for the overall stock market based on a specified group of stocks. It then selectively recommends a database (file) on…

A study tested the data-ink ratio theory, which holds that a reader's recall of quantitative data displayed in a graph containing a substantial amount of non-data-ink will be significantly less than recall from a graph containing little non-data-ink, as it might apply to graphics used in mass circulation newspapers. The experiment employed a…

A study investigated the effects of chartoons--cartoon-like informational graphics--and three-dimensional graphs on the attractiveness of graphs and on the information gain from graphs. Subjects, 86 students from a mass communication course at the University of Texas, were randomly assigned to two experimental groups, each of which was shown a set…