Euler's famous formula, e to the (i, pi) power equals -1, is developed by a purely algebraic method that avoids the use of both trigonometry and calculus. A heuristic outline is given followed by the rigorous theory. Pedagogical considerations for classroom presentation are suggested. (LS)

The paper presents reasons for teaching topics from number theory to elementary school students: (1) it can help reveal why numbers "act" in a certain way when added, multiplied, etc., (2) it offers drill material in new areas of mathematics, (3) it can develop interest - as mathematical enrichment, (4) it offers opportunities for students to…

Three-, four-, and five-year-olds were given problems to test their ability to recognize absolute number and relative order. Results suggest that children understand number as an absolute amount before they understand it as part of a progressive sequence in contradiction to the "ordinal theory of number." (Author/DST)

"How Students Learn: Mathematics in the Classroom" builds on the discoveries detailed in the best-selling "How People Learn." Now these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. This book shows how to overcome the difficulties in teaching math to…

Mathematical Induction is used for direct proofs of many theorems; its logical equivalent, the Well-Ordering Property, replaced it to yield indirect proofs by contradiction. The author claims the later property is easier to comprehend and that it affords a non-geometrical example of proof by contradiction. (JP)

The minimum number and type of whole-unit weights needed to balance any object is extended to the situation where weights may be placed on both pans of a balance scale. (DT)

A method for finding a fraction having a value between two given fractions is illustrated and proved. (DT)