Reports on a study of students' responses to two types of questions on final examinations in calculus. Concludes that the two kinds of understanding--pointwise and across time--are clearly distinguishable. Discusses the differences between these two types of understanding. (ASK)

Focuses on the role of graphs as part of the statistical investigation process. Recommends that teachers explore students' thinking in terms of what it says about their graph sense. Suggests that teachers take time to reflect on how their thinking may be changing as they listen more closely to their students. Contains 17 references. (DDR)

Examines the impact of the recent shift towards calculating and computing tools on the nature of learning in traditionally difficult curriculum area. Focuses on the use of graphic calculators by undergraduates taking an innovative new mathematics course at Open University. Indicates that graphic calculator technology acted as a critical mediator…

Describes an index of cohesion for the investigation of communication between authors or academic units and compares it with the Brillouin-Shaw index. Communication and cooperation between researchers is discussed and graph theory is explained, especially cooperation graphs. (Author/LRW)

Using a computer and thermistor probes, students analyze graphs of temperature versus time. The experiment demonstrates phase changes in water, which can lead to a broader interpretation of matter, its properties, and the laws of thermodynamics. (Author/AIM)

Introduces the use of Formal Concept Analysis (FCA) as a methodology to visualize the data in computer-mediated communication. Bases FCA on a mathematical lattice theory and offers visual maps (graphs) with conceptual hierarchies, and proposes use of FCA combined with content analysis to analyze computer-mediated communication. (Author/LRW)

This article reports on results of an exploratory study on undergraduate pre-service teachers' understanding of graphical representations of motion functions. The study described pre-service teachers' explorations using a CBR device. Pre-service teachers' growth was studied in two dimensions: (a) in their learning of the mathematics involved and…

Graphs don't always show what the graphers say they do. The most notorious recent example of a misleading graph is the one produced by the U.S. Department of Education that plots National Assessment of Educational Progress (NAEP) reading scores against total federal spending on education. This graph was taken apart by Howard Wainer and Daniel…

One of the most remarkable devices embedded in a Microsoft Excel spreadsheet is known as the spinner. Its staggering simplicity is undoubtedly its strength. As an incrementing device that allows graphs to dance across the screen, it gives the concept of variability a whole new meaning. Spinners and their close cousins scroll bars can be grabbed…

This paper analyses the answers of a group of first-year university Mathematics students to a questionnaire, with the aim of determining the difficulties they have when carrying out non-routine tasks related to improper integrals. The questionnaire consisted of nine questions including not only calculus tasks and determining the convergence of…

Resistance destroys symmetry. In this note, a graphical exploration serves as a guide to a rigorous elementary proof of a specific asymmetry in the trajectory of a point projectile in a medium offering linear resistance.

The five Platonic solids are constructed (as graphs) from their rotational symmetry groups. The constructions are based on an idea of Bertram Kostant and are quite simple; conjugacy classes in the group are the vertices of the graphs and products determine adjacency.

The motion of a magnet through a coil is analysed through a model of magnetic monopoles. The magnetic flux of a monopole passing through a loop is explained and also its rate of change. By a superposition of voltages produced by the monopoles on the coils the shape of the voltage versus time graph is explained. Also examined is the interaction of…

Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…

In this article, the authors present a laboratory exercise in data collection and statistical analysis in biological space using clustered stomates on leaves of "Begonia" plants. The exercise can be done in middle school classes by students making their own slides and seeing imprints of cells, or at the high school level through collecting data of…