This article reports on results of an exploratory study on undergraduate pre-service teachers' understanding of graphical representations of motion functions. The study described pre-service teachers' explorations using a CBR device. Pre-service teachers' growth was studied in two dimensions: (a) in their learning of the mathematics involved and…

Graphs don't always show what the graphers say they do. The most notorious recent example of a misleading graph is the one produced by the U.S. Department of Education that plots National Assessment of Educational Progress (NAEP) reading scores against total federal spending on education. This graph was taken apart by Howard Wainer and Daniel…

One of the most remarkable devices embedded in a Microsoft Excel spreadsheet is known as the spinner. Its staggering simplicity is undoubtedly its strength. As an incrementing device that allows graphs to dance across the screen, it gives the concept of variability a whole new meaning. Spinners and their close cousins scroll bars can be grabbed…

This paper analyses the answers of a group of first-year university Mathematics students to a questionnaire, with the aim of determining the difficulties they have when carrying out non-routine tasks related to improper integrals. The questionnaire consisted of nine questions including not only calculus tasks and determining the convergence of…

Resistance destroys symmetry. In this note, a graphical exploration serves as a guide to a rigorous elementary proof of a specific asymmetry in the trajectory of a point projectile in a medium offering linear resistance.

The five Platonic solids are constructed (as graphs) from their rotational symmetry groups. The constructions are based on an idea of Bertram Kostant and are quite simple; conjugacy classes in the group are the vertices of the graphs and products determine adjacency.

When technologies are used in mathematics education it is important to assess how activities will support the development of mathematical understanding and the technical expertise that students will need. The two issues are discussed in this paper. Literature is reviewed and findings from a recent study in a high-school class are reported. The…

The motion of a magnet through a coil is analysed through a model of magnetic monopoles. The magnetic flux of a monopole passing through a loop is explained and also its rate of change. By a superposition of voltages produced by the monopoles on the coils the shape of the voltage versus time graph is explained. Also examined is the interaction of…

Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…

Sorting networks, used in graph theory, have instructional value as a skill- building tool as well as an interesting exploration in discrete mathematics. Students can practice mathematics facts and develop reasoning and logic skills with this topic. (Contains 4 figures.)

This article is concerned with the meanings that employees in industry attribute to representations of data and the contingencies of these meanings in context. Our primary concern is to more precisely characterize how the context of the industrial process is constitutive of the meaning of graphs of data derived from this process. We draw on data…

It is in the field of numerical analysis that this "easy-looking" function, also known as the Runge function, exhibits a behavior so idiosyncratic that it is mentioned even in most undergraduate textbooks. In spite of the fact that the function is infinitely differentiable, the common procedure of (uniformly) interpolating it with polynomials that…

The Cognitive Tutor Authoring Tools (CTAT) support creation of a novel type of tutors called example-tracing tutors. Unlike other types of ITSs (e.g., model-tracing tutors, constraint-based tutors), example-tracing tutors evaluate student behavior by flexibly comparing it against generalized examples of problem-solving behavior. Example-tracing…

In contemporary academic literature and in many national curricula, there is a widespread acceptance that critical thinking should be an important dimension of Education. Teachers and researchers recognize the importance of developing students critical thinking, but there are still great difficulties in defining and assessing critical-thinking…

This study documented efforts to facilitate ideas of beginning inference in novice grade 7 students. A design experiment allowed modified teaching opportunities in light of observation of components of a framework adapted from that developed by Pfannkuch for teaching informal inference with box plots. Box plots were replaced by hat plots, a…