Describes research using a pedagogic strategy developed during an exploratory work called Active Graphing in which access to spreadsheets allows graphs to be used as analytic tools within practical experiments. Identifies aspects of student interaction with the experiment itself, the data collected and the graphs, and traces the emergence of…

Presents results from a study that examined students' understanding of connections between algebraic and graphical representations of functions. Discusses a possible reason for the inadequate and often absent connections that students made between them. (ASK)

In a classroom environment in which continual access to graphing calculators is assumed, items that have been used to assess students' understanding of functions often are no longer appropriate. Describes strategies for modifying such items including requiring students to explain their reasoning, using calculator-active items, analyzing graphs and…

Past research has shown that many scientists, when asked to interpret unfamiliar graphs that have nevertheless been culled from introductory undergraduate courses in their own field, experience problems and cannot give the standard answer accepted in the field. Yet, these same scientists turn out to be highly competent when it comes to graphs from…

An activity which stresses on identifying features of functions like the rate of change, intercepts, local and global behavior, zeros and asymptotes is designed to increase the level of understanding of the students and also to clear any doubts that they might have. The students are then asked to make a summary of what was discussed in the class,…

Some of the graphing capabilities of The Geometer's Sketchpad (GSP) in the "Technology Tips" are introduced. The new graphing features of GSP allow teachers to implement the software not only in geometry classrooms but also into their algebra, precalculus and calculus classes.

An evaluation designed to test basic graphical-thinking skills to students entering calculus or applied calculus at American University was given to use the assessment to discover the underlying causes for student's inability to use graphs effectively. The study indicates that graphical representation is not emphasized properly in the curriculum…

This paper examines the mathematical work of the French bishop, Nicole Oresme (c. 1323-1382), and his contributions towards the development of the concept of graphing functions and approaches to investigating infinite series. The historical importance and pedagogical value of his work will be considered in the context of an undergraduate course on…

An integral, either definite or improper, cannot always be computed by elementary methods, such as reversed usage of differentiation formulae. Graphical properties, in particular symmetries, can be useful to compute the integral, via an auxiliary computation. We present graded examples, then prove a general result. (Contains 4 figures.)

Inscriptions are central to the practice of science. Previous studies showed, however, that preservice teachers even those with undergraduate degrees in science, generally do not spontaneously produce inscriptions that economically summarize large amounts of data. This study was designed to investigate the production of inscription while a group…

Research findings show the difficulties younger students have in working with graphs. Higher mental operations are necessary for a skilled interpretation of abstract representations. We suggest connecting a concrete representation of the modeled problem with the related graph. The idea is to illustrate essential mental operations externally. This…

We describe a computer tutorial that introduces the concept of the steady state in enzyme kinetics. The tutorial allows students to produce graphs of the concentrations of free enzyme, enzyme-substrate complex, and product versus time in order to learn about the approach to steady state. By using a range of substrate concentrations and rate…

This study examines the practical work of a pair of students and an instructor using probeware in a mechanics lab. The aim of the study is to describe and discuss a type of interactional sequence that we refer to as "dark matter", the ordinary backdrop to the extraordinary sequences that are easily recognizable as clear-cut instances of learning.…

The objective of the research presented here was to study the influence of two types of instruction for using an argumentation diagram during pedagogical debates over the Internet. In particular, we studied how using an argumentation diagram as a medium of debate compared to using an argumentation diagram as a way of representing a debate. Two…

This paper suggests that mathematics teacher educators should listen carefully to what their students are saying. More specifically, it demonstrates how from one pre-teacher's non-traditional geometric representation of a unit fraction, a variety of learning environments that lead to the enrichment of mathematics for teaching can be developed. The…