This article describes how we used the context of mailing a package with seventh-grade students to explore and connect the different representations of step and linear functions. (Contains 2 tables and 7 figures.)

Using MAPLE enables students to consider many examples which would be very tedious to work out by hand. This applies to graph plotting as well as to algebraic manipulation. The challenge is to use these observations to develop the students' understanding of mathematical concepts. In this note an interesting relationship arising from inverse…

Geometric constructions have previously been shown that can be interpreted as rays of light trapped either in polygons or in conics, by successive reflections. The same question, trapping light in closed Fermat curves, is addressed here. Numerical methods are used to study the behaviour of the reflection points of a triangle when the degree of the…

This article describes two alternative coordinate systems and their use in graphing conic sections. This alternative graph paper helps students explore the idea of eccentricity using the definitions of the conic sections.

In this qualitative study of mathematical discourse between elementary teachers, we examined linguistic invention and semantic warrant production as participants made successive attempts to communicate mathematical ideas. Linguistic invention is a creative practice of describing mathematics in terms of personal experience. We introduce semantic…

The purpose of this article is to describe a simple laboratory activity in which students collect a series of measurements and then use graphical analysis to determine the nature of the relationship between an object's mass and the volume of water it displaces. In this activity, students explore the relationships between the mass of a floating…

The inertial balance is one device that can help students to quantify the quality of inertia--a body's resistance to a change in movement--in more generally understood terms of mass. In this hands-on activity, students use the inertial balance to develop a more quantitative idea of what mass means in an inertial sense. The activity also helps…

This study sought to improve students' comprehension of scientific graphs by adapting scaffolding techniques used to aid text comprehension. In 3 experiments involving 121 female and 88 male college students, some students were shown cognitive aids prior to viewing 4 geography graphs whereas others were not; all students were then asked to write a…

Collecting data and analyzing the results of experiments is difficult for children. The authors found a surprising way to help their third graders make graphs and draw conclusions from their data: digital photographs. The pictures bridged the gap between an abstract graph and the plants it represented. With the support of the photos, students…

The 11th International Conference on Educational Data Mining (EDM 2018) is held under the auspices of the International Educational Data Mining Society at the Templeton Landing in Buffalo, New York. This year's EDM conference was highly competitive, with 145 long and short paper submissions. Of these, 23 were accepted as full papers and 37…

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…

Hammond's Cognitive Continuum theory posits that certain task features induce distinct processing modes (e.g., intuitive or analytic) and thus result in qualitatively different decision performance. Although the theory suggests the relation between task features and performance characteristics a priori, the validity of these predictions requires…