Motivated by cognitive theories of graph comprehension, this study systematically manipulated characteristics of a line graph description task in a speaking test in ways to mitigate the influence of graph familiarity, a potential source of construct-irrelevant variance. It extends Xi (2005), which found that the differences in holistic scores on…

This article presents a procedure for generating a sequence of data sets which will yield exactly the same fitted simple linear regression equation y = a + bx. Unless rescaled, the generated data sets will have progressively smaller variability for the two variables, and the associated response and covariate will "regress" towards their…

To date there has been very little work on the machine understanding of imprecise diagrams, such as diagrams drawn by students in response to assessment questions. Imprecise diagrams exhibit faults such as missing, extraneous and incorrectly formed elements. The semantics of imprecise diagrams are difficult to determine. While there have been…

Information systems increasingly provide options for visually inspecting data during the process of information discovery and exploration. Little research has dealt so far with user interactions with these systems, and specifically with the effects of characteristics of the displayed data and the user on performance with such systems. The study…

The authors describe a collection of dynamic interactive simulations for teaching and learning most of the important ideas and techniques of introductory statistics and probability. The modules cover such topics as randomness, simulations of probability experiments such as coin flipping, dice rolling and general binomial experiments, a simulation…

Coach is an activity-based, open computer environment for learning and doing mathematics, science, and technology in an inquiry approach, developed in the last twenty-five years at the AMSTEL Institute of the University of Amsterdam. It offers a versatile set of integrated tools for data collection, data analysis, modelling and simulation, and for…

Textbook companies are increasingly including larger numbers of animations as complementary resources for students and teachers. Are all animations useful as teaching tools? The answer is no. Animations can be useful for communicating dynamic events and processes but only when specific rules are followed. The authors review the important…

This work presents an introductory development of fractional order derivatives and their computations. Historical development of fractional calculus is discussed. This paper presents how to obtain computational results of fractional order derivatives for some elementary functions. Computational results are illustrated in tabular and graphical…

The author presents a geometrical framework in which the inability of discretionary policy (consistent policy in the sense of Kydland and Prescott) to be socially optimal is demonstrated. Policy based on a rule results in a higher level of utility. The author extends the model to demonstrate that policy of a Rogoff conservative central banker…

Ballistocardiograms (BCGs) are graphical representations of the recoil from the pumping action of the heart. Introductory mechanics and a basic knowledge of the circulatory system are sufficient to understand the key features of a BCG. BCGs with adequate detail for instructional purposes may be produced easily and rapidly using hardware (a force…

Two experiments investigated effects of emergent features on perceptual judgments of comparative magnitude in three diagrammatic representations: kiviat charts, bar graphs, and line graphs. Experiment 1 required participants to compare individual values; whereas in Experiment 2 participants had to integrate several values to produce a global…

The purpose of this study is to determine whether educators believe mathematics should be taught to liberal arts students, what topics are taught in liberal arts mathematics courses, and what the motivation is for teaching such topics. The study consists of two parts, a review of the opinions of educators regarding liberal arts mathematics, and a…

In an English as a second language (ESL) or English as a foreign language (EFL) class, special emphasis is often put on interaction and negotiation as a means of learning and understanding the language being taught (Long, 1981; Pica, 1994). However, student-student interaction as well as student-teacher interaction could be difficult to achieve in…

This article is the third in a series describing the steps in using data-based decision making to inform intervention and, ultimately, improve outcomes for children. Whereas the first two articles describe identifying and measuring important behaviors to target for intervention, the purpose of this article is to describe basic considerations in…

This paper presents an investigation by pre-service secondary school teachers in a geometry class of the relationship between the perpendicular distance from the eyeball to the wall (x) and the viewable vertical distance on the wall (y) using a view tube of constant length and diameter. In undertaking the investigation, students used tabular and…