Using a joystick module, we followed the movement of a chaotic magnetic pendulum. The pendulum bar was attached to a joystick that served as a pivot point and biaxial angular motion sensor. Using an Arduino board, we could follow the position as a function of time along both the "x" and "y"-axis and draw a graph showing the…

Too often, high school algebra students encounter topics in a discrete, disconnected fashion. In the authors' first years of teaching, they found students to be adept at solving problems they were currently studying; for instance, they could solve quadratics during a quadratics unit. Too often, however, students struggled with that same content…

In order to use dialogue systems for computer assisted second-language learning systems, one of the difficult issues in such systems is how to construct large-scale dialogue knowledge that matches the dialogue modelling of a dialogue system. This paper describes how we have accomplished the short-term construction of large-scale and…

Box-and-whisker plots or simply boxplots are powerful graphical representations that give an overview of a data set. In this work five different examples illustrate the applications of boxplots in food chemistry. The examples involve relative sweetness of sugars and sugar alcohols with respect to sucrose, the potassium content of fruits and…

This paper presents a rule-based task-oriented dialogue system for second language learning and a knowledge extraction method which automatically extracts the training data for Natural Language Understanding (NLU) and dialogue rules for dialogue management from a Dialogue Map (DM). The DM consists of turn-by-turn utterances between the system and…

The research literature on L2 writing processes contains a multitude of insights that could inform writing instruction, but writing teachers are constrained in their capacity to make use of these insights insofar as they lack detailed information about how their students actually engage in the processes of writing. At the same time,…

Literature in "Physics Education" has shown that students encounter many difficulties in understanding wave propagation. Such difficulties lead to misconceptions also in understanding sound, often used as context to teach wave propagation. To address these issues, we present in this paper a module in which the students are engaged in…

We have recently developed a Graphs and Tracks model based on an earlier program by David Trowbridge, as shown in Fig. 1. Our model can show position, velocity, acceleration, and energy graphs and can be used for motion-to-graphs exercises. Users set the heights of the track segments, and the model displays the motion of the ball on the track…

Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this paper, we describe lesson sequences utilizing dynamic tools for teaching the epsilon-delta definition of the limit and the…

One sign of a good task is that it will work just as well with Year 7 as with Year 13. The author asks learners to use graph-drawing software to draw a picture with graphs. He uses his imagination to suggest what a particular curve might resemble and helps learners to adjust their drawings to achieve what they are trying to make. Sometimes, one…

A simple way is given to create residual plots that are words or pictures. Three illustrative examples are presented.

This article presents a web-based tool designed to compute certified equations and graphs of geometric loci specified using standard Dynamic Geometry Systems (DGS). Complementing the graphing abilities of the considered DGS, the equations of the loci produced by the application are remotely computed using symbolic algebraic techniques from the…

Some interesting and unusual loci are generated by a familiar mechanical system.

This paper examines the relation between bodily actions, artifact-mediated activities, and semiotic processes that students experience while producing and interpreting graphs of two-dimensional motion in the plane. We designed a technology-based setting that enabled students to engage in embodied semiotic activities and experience two modes of…

Many popular mathematical software products including Maple, Mathematica, Derive, Mathcad, Matlab, and some of the TI calculators produce incorrect graphs because they use complex arithmetic instead of "real" arithmetic. This article expounds on this issue, provides possible remedies for instructors to share with their students, and demonstrates…