The sample mean is sometimes depicted as a fulcrum placed under the Dot plot. We provide an alternative geometric visualization of the sample mean using the empirical cumulative distribution function or the cumulative histogram data.

To become scientifically literate, students need to interpret science concepts using numbers, text, and visuals (Lemke 2004). Scientists use multiple modes to communicate their ideas to each other and the public, including images, text, mathematical notations, symbols, diagrams, charts, and graphs. Several of the science and engineering practices…

This article aims to illustrate a process of making connections, not between mathematics and other activities, but within mathematics itself--between diverse parts of the subject. Novel connections are still possible in previously explored mathematics when the material happens to be unfamiliar, as may be the case for a learner at any career stage.…

In this paper, the use of guided hyperlearning, unguided hyperlearning, and conventional learning methods in mathematics are compared. The design of the research involved a quasi-experiment with a modified single-factor multiple treatment design comparing the three learning methods, guided hyperlearning, unguided hyperlearning, and conventional…

This tricentennial tribute commemorates Euler's major contributions to mathematical and physical sciences. A brief biographical sketch is presented with his major contributions to certain selected areas of number theory, differential and integral calculus, differential equations, solid and fluid mechanics, topology and graph theory, infinite…

There has been a lot of material written about logarithmic spirals of golden proportion but this author states that he has never come across an article that states the exact equation of the spiral which ultimately spirals tangentially to the sides of the rectangles. In this article, the author intends to develop such an equation. (Contains 5…

The operation of rounding is shown to lead into an investigation of an abstract mathematical system. Properties of the system are discussed and graphs of the rounding function are drawn. Some questions for discussion are given. (MP)

This technical project report provides the National Science Foundation with information regarding the substantive achievements of the Social Science Education Consortium's project QUESST (Quantitative Understanding To Enhance Social Science Teaching). The report begins with a discussion of materials development and project publicity. Thirty-three…

Plotting a polynomial over the range of real numbers when its derivative contains complex roots is discussed. The polynomials are graphed by calculating the minimums, maximums, and zeros of the function. (MNS)

A collection of brief articles on mathematics and teaching mathematics. (FL)

Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)

Several problems involving "pi" and "e" can be approached by diagramming, flow charting, and computer programing. (SD)