Students' difficulty with reasoning and justification in the context of proofs in geometry has been well documented. Studies reveal that many of the ideas that students are asked to prove are known to be true, and therefore, the process of such proof is likely to remain meaningless and purposeless. The implication of this claim is that students…

The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…

Two heuristic and three rigorous arguments are given for the fact that functions of the form Ce[kx], with C an arbitrary constant, are the only solutions of the equation dy/dx=ky where k is constant. Various of the proofs in this self-contained note could find classroom use in a first-year calculus course, an introductory course on differential…

In this short note, a mathematical proposition on a functional equation for f(xy)=xf(y) + yf(x)for x,y [does not equal] 0, which is encountered in calculus, is generalized step by step. These steps involve continuity, differentiability, a functional equation, an ordinary differential linear equation of the first order, and relationships between…

In order to learn the concept of statistical techniques one needs to run real experiments that generate reliable data. In practice, the data from some well-defined process or system is very costly and time consuming. It is difficult to run real experiments during the teaching period in the university. To overcome these difficulties, statisticians…

This paper gives a broad descriptive account of some activities that the author has designed using Sketchpad to develop teachers' understanding of other functions of proof than just the traditional function of 'verification'. These other functions of proof illustrated here are those of explanation, discovery and systematization (in the context of…

This article describes a general instructional strategy designed to help students in the learning process from textbooks and to furnish opportunities for practice in critical reading. Students participate in cooperative learning by breaking the class up into small groups--the Study Teams--and providing them with worksheets and reading organizers,…

Two techniques for determining a straight line fit to data are compared. This article reviews two simple techniques for fitting a straight line to a set of data, namely the method of averages and the method of least squares. These methods are compared by showing the results of a simple analysis, together with a number of tests based on randomized…