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)

Investigates secondary mathematics teachers' concept definitions, mathematical understanding, and pedagogical content knowledge of slope. Indicates that geometric ratios dominated teachers' concept definitions of slope, and teachers' descriptions of classroom instruction included physical situations more often than functional situations. (Contains…

Investigated kindergartners' unary and binary understanding of additive commutativity using performance on tasks involving change-add-to and part-part-whole word problems, respectively. Found that data were inconsistent with models put forth by Baroody and Gannon and by Resnick and suggest three alternate theoretical explanations. Success on tasks…

Discovers and analyzes the proportions of the Golden Section in the rare stone tablet, Tablet of Sippar, representing the four main feats of the god Marduk. (ASK)

A total of 257 children in grades 2-5 were individually interviewed to find the grade level at which they demonstrated transitive reasoning and unit iteration in the measurement of volume. Concludes that the National Council of Teachers of Mathematics (NCTM) standard expecting children to understand units of measurement by grade 2 is unrealistic.…

Children shouldn't memorize mathematical facts and procedures like parrots, but should learn to think mathematically. In this article, the authors stress that mathematics involves making sense. They provide some simple mathematical challenges for readers to make sense of and to try with their classes.

Students should be given an opportunity to explore and conjecture with the help of new technology to become good problem solver. Ron Mclister, while using the Geometer's Sketchpad to explore the Pythagorean theorem, came upon a nice result about the relationship of some geometrical patterns.

A simple and practical application of mathematics is for fairly resolving the dispute of division of items for which two parties have equal claim. Basic properties of fair division are explained, which would enable students to learn concepts on optimization without introducing calculus.

This study investigated the development of children's knowledge of many-to-one counting. Four-year-olds ("n" = 51) either participated in a training or in a control group. The training taught children how to allot "Y" physically not present items to each of "X" objects and how to count these items in the process. It…

The Golden Ratio is sometimes called the "Golden Section" or the "Divine Proportion", in which three points: A, B, and C, divide a line in this proportion if AC/AB = AB/BC. "Donald in Mathmagicland" includes a section about the Golden Ratio and the ratios within a five-pointed star or pentagram. This article presents two computing exercises that…

This article presents a brief biography of Johann Carl Friedrich Gauss. Gauss was born on April 30, 1777, in the German city of Braunschweig (Brunswick). He was the only child of Gebhard Dietrich Gauss and Dorothea Benze. Neither of Gauss's parents had much education, his father could read and write, but earned his living doing menial jobs such as…

This study examined how 4 middle school textbook series (2 skills-based, 2 Standards-based) present equal signs. Equal signs were often presented in standard operations equals answer contexts (e.g., 3 + 4 = 7) and were rarely presented in nonstandard operations on both sides contexts (e.g., 3 + 4 = 5 + 2). They were, however, presented in other…

The aim of this research is to devise a cognitive tool for meeting the diverse needs of learners for comprehending new procedural knowledge. A model of affordances on teaching fraction equivalence for developing procedural knowledge for adding/subtracting fractions with unlike denominators was derived from the results of a case study of an initial…

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.

Many assertions about the occurrence of the golden ratio phi in art, architecture, and nature have been shown to be false, unsupported, or misleading. For instance, we show that the spirals found in sea shells, in particular the "Nautilus pompilius," are not in the shape of the golden ratio, as is often claimed. Some of the most interesting…