Investigates 10th grade students' ability to handle data and interpretation by using a variety of tasks. Discusses the importance of developing student discussion as a route to better conceptual understanding of data presented in graphical form. (Contains 15 references.) (Author/YDS)

Reports on a study designed to find out what scientists and science students actually do when they are reading familiar and unfamiliar graphs. Describes changes in ontologies of scientists and science students as they engage in the reading tasks assigned to them. Theorizes a transition of graphs from things to signs that come to stand for natural…

Presents concrete graphing experiences from the United States. (Author/CCM)

Mathematics should not be studied simply because it is useful; mathematics should be also studied because it nurtures both the mind and soul with its beauty. By completing the four activities described in this paper, students will appreciate mathematical ideas both rationally and emotionally. Since students' appreciation of mathematical ideas…

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…

When discussing the topic of elementary complex variables, students are often mystified by the fact that ii is real. After seeing a proof of this statement, a standard question is "well, what about iii or iiii etc., are these real or complex?" In this paper the meaning of the infinite power-tower iii...is considered both from the "bottom-up" and…

William Playfair's pie chart is more than 200 years old and yet its intellectual origins remain obscure. The inspiration likely derived from the logic diagrams of Llull, Bruno, Leibniz, and Euler, which were familiar to William because of the instruction of his mathematician brother John. The pie chart is broadly popular but--despite its common…

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.

Quadrature methods for approximating the definite integral of a function f(t) over an interval [a,b] are in common use. Examples of such methods are the Newton-Cotes formulas (midpoint, trapezoidal and Simpson methods etc.) and the Gauss-Legendre quadrature rules, to name two types of quadrature. Error bounds for these approximations involve…

This article describes a solution, using CAS, to graph theory problem that was presented in the movie "Good Will Hunting."

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…

Students in undergraduate chemistry courses find, as a rule, topics with a strong mathematical basis difficult to master. In this study we investigate whether such mathematically related problems are due to deficiencies in their mathematics foundation or due to the complexity introduced by transfer of mathematics to a new scientific domain. In the…

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…