This note describes a large-scale modelling activity involving geometry that can be solved with the help of uni-variable calculus. More specifically, it introduces and proves the following theorem: given any non-equilateral triangle, there exist infinitely many mutually non-congruent triangles with the same area and the same perimeter as the given…

If larger and larger samples are successively drawn from a population and a running average calculated after each sample has been drawn, the sequence of averages will converge to the mean, [mu], of the population. This remarkable fact, known as the law of large numbers, holds true if samples are drawn from a population of discrete or continuous…

It has been a practice at the University of Washington to begin their workshops on investigative sciences for preservice and inservice K-8 teachers with the discussion of variables. The teaching of the concepts of variables is important, as it provides students with the opportunity to understand other aspects of an investigation, such as the use…

Trypsin and soybean trypsin inhibitor (Kunitz inhibitor) can be used in a relatively simple and inexpensive student exercise to demonstrate the usefulness of enzyme kinetics. The study of enzyme kinetics is essential to biology because enzymes play such a crucial role in the biochemical pathways of all living organisms. The data from enzyme…

Classroom climate, though difficult to define and assess, affects student learning especially in the elementary schools. Much of the current research focuses on the primary architect of classroom climate--the teacher. There is little doubt that teacher behaviors determine the overall climate of the classroom, but peer actions and reactions also…

We give an example of a student project that experimentally explores a topic in random graph theory. We use the "Combinatorica" package in "Mathematica" to estimate the minimum number of edges needed in a random graph to have a 50 percent chance that the graph is connected. We provide the "Mathematica" code and compare it to the known theoretical…

We examine the behavior of the curvature function associated with most common families of functions and curves, with the focus on establishing where maximum curvature occurs. Many examples are included for student illustrations. (Contains 18 figures.)

In this paper, results of a questionnaire about continuity of functions are analysed. The tested students attend Novi Sad grammar school. The aim of this test was to check the student's theoretical and visual knowledge of continuous functions at the end of their high school education. The questions were given with and without the graphs of…

Using Freudenthal's method of historical phenomenology, the history of statistics was investigated as a source of inspiration for instructional design. Based on systematically selected historical examples, hypotheses were formulated about how students could be supported in learning to reason with particular statistical concepts and graphs. Such a…

The purpose of this study was to investigate the effects of formative assessment as a teaching strategy through an internet-mediated assessment portal (ImAP) on preservice elementary student understanding of kinematics graphs as opposed to traditional lecturing. A quasi-experimental design was used for this purpose. Findings revealed that…

Some students at the master-level viewed research methodology courses negatively. This study investigated six factors that changed attitudes of graduate school students toward research during the course of a semester at a mid-sized university (University X) located in a western state. To facilitate this study, a survey instrument (Student Research…

The U.S. Department of Education's National Center for Education Statistics (NCES) annually publishes a statistical report on the status and progress of education in the United States. This pamphlet provides 14 charts that represent a small sample of the 60 indicators contained in the "Condition of Education, 1995" report. The charts present…

Many students find climate classification laborious and time-consuming, and through their lack of repetition fail to grasp the details of classification. This paper describes an expert system for climate classification that is being developed at Middle Tennessee State University. Topics include: (1) an introduction to the nature of classification,…

This 50 slide set of presentation graphs and maps illustrates some of the major conditions and trends in population, agriculture, biodiversity, forests, water resources, energy, climate, and social and economic development that determine the state of the world's environment. Graphs and maps can be used by those in academic, professional, and…

This study investigated six students' understandings of and difficulties with qualitative and numerical methods for analyzing differential equations. From an individual cognitive perspective, the obstacles found to influence the development of students' understandings included the function dilemma, the tendency to overgeneralize, interference from…