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.

Representative samples of fourth- and eighth-grade public school students from 21 urban districts participated in the 2011 National Assessment of Educational Progress (NAEP) in mathematics. Eighteen of the districts participating in the 2011 NAEP Trial Urban District Assessment (TUDA) participated in earlier assessment years, while three districts…

Representative samples of fourth- and eighth-grade public school students from 21 urban districts participated in the 2011 National Assessment of Educational Progress (NAEP) in reading. Eighteen of the districts participating in the 2011 NAEP Trial Urban District Assessment (TUDA) participated in earlier assessment years, while three districts…

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…

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…

The author illustrates many problems in which drawing graphs of functions involving absolute values assists in the solution of algebraic equations and inequalities. (SD)