One of the main problems in undergraduate research in pure mathematics is that of determining a problem that is, at once, interesting to and capable of solution by a student who has completed only the calculus sequence. It is also desirable that the problem should present something new, since novelty and originality greatly increase the enthusiasm…

Graphs are vital components for analyzing data in the experimental analysis of behavior using single subject research methods. This paper extends the previous literature on the construction of single subject graphs by providing instructions for using Microsoft[R] Power Point[TM] and Microsoft[R] PowerPoint for Mac[R], and describes improved…

The fortunes of chance and data have fluctuated in the mathematics curriculum in Australia since their emergence in the National Statement in the early 1990s. Their appearance in Australia followed closely on similar moves in the United States. In both countries the topics, taken together, were given a section status equal to other areas of the…

Using "error bars" on graphs is a good way to help students see that, within the inherent uncertainty of the measurements due to the instruments used for measurement, the data points do, in fact, lie along the line that represents the linear relationship. In this article, the author explains why connecting the dots on graphs of collected data is…

With regard to transfer, is it better to provide pupils with ready-made representations or is it more effective to scaffold pupils' thinking in the process of generating their own representations with the help of peers and under the guidance of a teacher in a process of guided co-construction? The sample comprises 10 classes and 239 Grade 5…

These proceedings contain the papers of the 14th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2017), 18-20 October 2017, which has been organized by the International Association for Development of the Information Society (IADIS) and endorsed by the Japanese Society for Information and Systems in…

We present a simple activity that permits students to determine the coefficient of restitution of bouncing balls using only a stopwatch, a metre stick and graphical analysis. The experiment emphasizes that simple models, in combination with careful attention to how students make measurements, can lead to good results in a straightforward way.

This brochure contains an activity for grades 9-12 that involves students in an examination of real versus perceived risks. Students perform a risk factor analysis, and evaluate benefits and risks of energy sources. The activity can be conducted by individuals or small groups. Students rank a series of life-threatening risks and compare them to…

The information that is gained through various analyses of the residual scores yielded by the least squares regression model is explored. In fact, the most widely used methods for detecting data that do not fit this model are based on an analysis of residual scores. First, graphical methods of residual analysis are discussed, followed by a review…

A modification of the usual graphical representation of heterogeneous regressions is described that can aid in interpreting significant regions for linear or quadratic surfaces. The standard Johnson-Neyman graph is a bivariate plot with the criterion variable on the ordinate and the predictor variable on the abscissa. Regression surfaces are drawn…

The aim of good data graphics is to display data accurately and clearly. This definition is used as a point of departure for developing 12 rules of bad data display: (1) show as little data as possible (minimize the data density); (2) hide what data you do show (minimize the data-ink ratio); (3) ignore the visual metaphor altogether; (4) only…

This document presents an application of cost-benefit analysis to a hypothetical university parking problem. After discussing cost-benefit analysis in general, the document applies this technique to hypothetical data in light of a checklist for general cost-benefit procedure. The checklist includes the following steps: (1) examine and quantify…

The aim of this catalogue of wallcharts is to provide a list of charts and flannelgraphs suitable for use in schools so that teachers, education authorities, and others may have on hand a concise reference to all charts available on any particular topic. All charts of specific teaching value designed especially for wall display and at least 10…

Graphical methods for evaluating the fit of Johnson's hierarchical clustering schemes are presented together with an example. These evaluation methods examine the extent to which the clustering algorithm can minimize the overlap of the distributions of intracluster and intercluster distances. (Author)