This article explores the transmission of practical knowledge in the XV and XVI centuries. According to cosmographer Egnatio Danti, optics and other mathematical sciences had "been banished" from the main philosophical schools of his period, and "the little which remains to us is limited to some practical aspects learned from the mechanical…

Formulas presented for the calculation of [Summation of n over j=1] j[superscript k] (n, k [is a member of] N) do not have a closed form; they are in the form of recursive or complex formulas. Here an attempt is made to present a simple formula in which it is only necessary to compute the numerical coefficients in a recursive form, and the…

This article employs the Archimedean method of estimating the value of pi within an inscribed pentagon. We show how to write these approximations in terms of the golden ration.

The article deals with the area of polygons that are inscribed in a given circle. Naturally, the following question arises: Among all n-polygons that are inscribed in a given circle, which one has the biggest area? Intuitively, it may be guessed that is suitable for secondary students, and without any use id calculus, but only using very…

This note presents a brief and partial review of the work of Broom, Cannings and Vickers [1]. It also presents some simple examples of an extension of the their formalism to non-symmetric matrices. (Contains 1 figure.)

This article explores how different proofs of a solution to the Surfer Problem provide answers to the question "Why"?

This article describes a development of conic surfaces that connects different definitions of the conics. A classroom project using Dandelin Spheres is also described.

This article describes a polyhedra construction project that illustrates how one activity can address several of the mathematics content standards in the NCTM Principles and Standards for School Mathematics.

Geometry is the study of shape and space. Without spatial ability, students cannot fully appreciate the natural world. Spatial ability is also very important for work in various fields such as computer graphics, engineering, architecture, and cartography. A number of studies have demonstrated that technology has an important potential to develop…

The study investigated the effect of using mathematics laboratory in teaching on students' achievement in Junior Secondary School Mathematics. A total of 100 JS 3 Mathematics students were involved in the study. The study is a quasi-experimental research. Results were analyzed using mean, standard deviation and analysis of covariance (ANCOVA).…

Spring term of 2005, three Web-assisted undergraduate mathematics courses were taught at the University of Idaho: Math 235 Mathematics for Elementary Teachers 1; Math 236 Mathematics for Elementary Teachers II; and Math 391 Modern Geometry. While the content of these courses differ, they share common goals: to foster a deep understanding of…

The paper presents a case study of the educational exploitation of group blogging for the implementation of a "learning by design" activity. More specifically, a group of students used a blog as a communication and information management tool in the University course of ICT-enhanced Geometry learning activities. The analysis of the designed…

Reading, writing, and mathematics are best learned by children in meaningful, integrated experiences. In an engaging project combining math and literacy, primary children in Michelle Piwko's classroom followed the framework of verses from a classic children's book to structure their own writing about geometric forms. They brainstormed geometric…

This article offers some ideas about creating mathematical art based on number patterns. It includes a process for students that integrates number and geometry and results in attractive and useful patterned squares. Students may pursue the activity with paper and pencil or they may use computer software like The Geometer's Sketchpad to achieve…

Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…