Research reveals that many mathematics teachers find it difficult to stimulate learners' interest in learning geometry. One major reason suggested is that geometric concepts are not well conceptualised and comprehended by both learners and teachers. The study explored learners' views on how polygon pieces and dictionary mediate learning of…

This paper provides historical insights and educational background of Froebel's Gifts, hands-on materials developed in the early 19th century. Based on an explorative study with 54 German children (aged 5 to 10) in 2016, we first took steps to explore how these materials meet the demands for early mathematics learning of primary children. Starting…

Spatial reasoning, which involves "building and manipulating mental representations of two-and three-dimensional objects and perceiving an object from different perspectives" is a critical aspect of geometric thinking and reasoning. Through building, drawing, and analyzing two-and three-dimensional shapes, students develop a foundation…

Reasoning is central to what Cuoco, Goldenberg, and Mark refer to as mathematical "habits of mind" (1996). "Reasoning is an integral part of doing mathematics. Students should enter the middle grades with the view that mathematics involves examining patterns and noting regularities, making conjectures about possible generalizations,…

The purpose of this classroom note is to provide an example of how a simple origami box can be used to explore important concepts of geometry and calculus. This article describes how an origami box can be folded, then it goes on to describe how its volume and surface area can be calculated. Finally, it describes how the box could be folded to…

Students enjoy origami and like making everything from paper cranes to footballs out of small, colorful squares of paper. They can invent their own shapes and are intrigued by the polyhedrons that they can construct. Paper folding is fun, but where is the math? Unless teachers develop lessons that address mathematical objectives, origami could be…

Making constructions with paper is called "origami" and is considered an art. The objective for many fans of origami is to design new figures never constructed before. From the point of view of mathematics education, origami is an interesting didactic activity. In this article, the authors propose to help High School students understand new…

Invented by English mathematician and pedagogist, Caleb Gattegno (1911-1988), the geoboard was designed as a manipulative tool for teaching primary geometry in schools (Williams, 1999). Traditionally made out of plywood and nails, geoboards today are usually made out of plastic and come in a variety of different sizes and colours. Rubber bands are…

The triangle congruence conditions are a central focus to nearly any course in Euclidean geometry. The author presents a hands-on activity that uses straws and pipe cleaners to explore and justify the triangle congruence conditions. (Contains 4 figures.)

Four geoboard activities for elementary school students are described. (SD)

Two ideas of mathematics that the students discuss here, demonstrate how sometimes a teacher can learn something new from the students. The examples given use geoboard and show relationships of the two ideas with the Pick's theorem.

Directions are given for folding paper to show geometric figures and relationships. Topics covered are folding the basic constructions, geometric concepts concerning triangles and quadrilaterals, circle relationships, products and factors, polygon constructions, symmetry, conic sections, and recreations. (DT)