This brief investigation exemplifies such considerations by relating concepts from number theory, set theory, probability, logic, and calculus. Satisfying the call for students to acquire skills in estimation, the following technique allows one to "immediately estimate" whether or not a number is prime. (MM)

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)

Introduces data collated by Glendon Lean on nearly 900 counting systems in Papua New Guinea, Oceania, and Irian Jaya (West Papua) which came from a questionnaire completed by students and talks with village elders. Lean's thesis on the spontaneous developments of these ancient cultures challenged traditional theories describing the spread of…

For the last several years teachers have been using counters and connected cube "trains" and creating base-10 block models to help students develop number sense and understand number concepts. It is described how ten-frame tiles could be more useful tool for building number understanding for many students.

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…

Within the set of points in the plane with integer coordinates, one point is said to be visible from another if no other point in the set lies between them. This study of visibility draws in topics from a wide variety of mathematical areas, including geometry, number theory, probability, and combinatorics.

Two experiments were conducted to test the hypothesis that toddlers have access to an analog-magnitude number representation that supports numerical reasoning about relatively large numbers. Three-year-olds were presented with subtraction problems in which initial set size and proportions subtracted were systematically varied. Two sets of cookies…

In this paper, the author gives a further simple generalization of a power series evaluation of an integral using Taylor series to derive the result. The author encourages readers to consider numerical methods to evaluate the integrals and sums. Such methods are suitable for use in courses in advanced calculus and numerical analysis.

Authors use combinatorical analysis to prove some interesting facts about the Fibonacci sequence.

The paper details a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts to force limit discussion into the language of individual real numbers and equality. The system of near-numbers…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

This article explores the origins and potential benefits of the empty number line for the development of mental computation. It also provides a learner's perspective of its use through the reflections of nine-year-old Emily. (Contains 3 figures.)

This article describes how the story of Alice in Wonderland helps students understand the operation of multiplying by a rational number less than 1 and related aspects of ratio and proportion. Included with this article is a "How Tall Is Alice?" Worksheet. (Contains 1 table and 6 figures.)

In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed…