The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

Using the correct materials and manipulatives appropriately allows the richness of geometrical concepts to be fully investigated to enable students to explore and reason about shapes. This article explores some of the key ideas involved in learning about two dimensional shapes and discusses how materials can be used to support learning.

The importance of mathematical reasoning is unquestioned and providing opportunities for students to become involved in mathematical reasoning is paramount. The open-ended tasks presented incorporate mathematical content explored through the contexts of problem solving and reasoning. This article presents a number of simple tasks that may be…

A Steiner chain is defined as the sequence of n circles that are all tangent to two given non-intersecting circles. A closed chain, in particular, is one in which every circle in the sequence is tangent to the previous and next circles of the chain. In a closed Steiner chain the first and the "n"th circles of the chain are also tangent…

The educational project "From Soccerene to Fullerene" (FSTF) was a pioneering interdisciplinary experience accomplished by six pupils who discussed it in the 2013 Italian school-leaving examination. The author illustrated the FSTF in the 2014 national conference of the Italian Physical Society (Pisa) eliciting a genuine interest. Here we…

Art uses mathematics in many ways. The author's teaching and involvement with mathematics and art in the Bridges Conference connecting the two have convinced him more and more that concepts for understanding mathematics can be achieved by the use of art. The author states that one reason he believes in teaching mathematics through art is that it…

Assigning difficulty level indicators to the knowledge units helps the learners plan their learning activities more efficiently. This paper focuses on how to use the topology of a knowledge map to compute and rank the difficulty levels of knowledge units. Firstly, the authors present the hierarchical structure and properties of the knowledge map.…

In this paper the didactically-methodological procedure named the MTE-model of mathematics teaching (Motivation test-Teaching-Examination test) is suggested and recommended when the teacher has subsequent lessons. This model is presented in detail through the processing of a nonstandard theme--the theme of decomposition of planes. Its efficiency…

The third session of IT@EDU98 consisted of five papers on educational software and was chaired by Tran Van Hao (University of Education, Ho Chi Minh City, Vietnam). "Courseware Engineering" (Nguyen Thanh Son, Ngo Ngoc Bao Tran, Quan Thanh Tho, Nguyen Hong Lam) briefly describes the use of courseware. "Machine Discovery Theorems in Geometry: A…

Describes attempts to instruct 12 children, aged between 10 and 11, during a 12-hour course in LOGO that proper attention should be paid to the external angles through which the turtle rotated. Results suggest that using LOGO to draw closed figures may lead to confusions about angle that are not amenable to conventional intervention techniques…