This paper presents a derivation of all five Lagrange points by methods accessible to sixth-form students, and provides a further opportunity to match Newtonian gravity with centripetal force. The predictive powers of good scientific theories are also discussed with regard to the philosophy of science. Methods for calculating the positions of the…

Inequalities are considered among the most useful tools of investigation in pure and applied mathematics; yet their didactical aspects have not received much attention in mathematics education research until recently. An important aspect of teaching problem solving at the secondary level deals with the notion of equivalence of algebraic…

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…

With regard to transfer, is it better to provide pupils with ready-made representations or is it more effective to scaffold pupils' thinking in the process of generating their own representations with the help of peers and under the guidance of a teacher in a process of guided co-construction? The sample comprises 10 classes and 239 Grade 5…

These proceedings contain the papers of the 14th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2017), 18-20 October 2017, which has been organized by the International Association for Development of the Information Society (IADIS) and endorsed by the Japanese Society for Information and Systems in…

We present a simple activity that permits students to determine the coefficient of restitution of bouncing balls using only a stopwatch, a metre stick and graphical analysis. The experiment emphasizes that simple models, in combination with careful attention to how students make measurements, can lead to good results in a straightforward way.

This study tested the effectiveness of teaching concepts in high school economics first by verbal instruction and then by graphs or other imagery. Eighty-three high school seniors were taught by the method above, by reversing the order of that method, and by verbal instruction only. Results are discussed. (Author/MT)

The present study investigates the differential effects of cooperative learning with or without metacognitive instruction on making sense of graphs. Participants were 196 eighth-graders who studied in six classrooms. Data were analyzed by using quantitative and qualitative methods. Results indicated that students who were exposed to the…

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…

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…

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.

Graphing skills are growing in importance in our information society, presenting facts and concepts in newspapers, magazines, and on television. Graphs incorporated into teaching develop children's problem-solving skills. Ways to use graphs in the classroom are discussed, and examples are given. (MT)