The concept of symmetry is fundamental to mathematics. Arguments and proofs based on symmetry are often aesthetically pleasing because they are subtle and succinct and non-standard. This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical…

Some ways of thinking and acting geometrically are described which are related to the approach used by ancient humans. The focus is on intuitive geometric imagery, an attempt to resurrect a way of describing possible viewpoints of geometry outside of those commonly accepted. (MP)

Discusses teaching geometric concepts, including various shapes, patterns, and areas based on the NCTM Standards. Presented are activities for the geometric concepts. (YP)

Students with or without disabilities often experience difficulties with abstract math concepts. This paper is intended to help solve the mystery of math concepts through origami construction, a hands-on activity. Students are involved in constructing and deconstructing concepts by folding and unfolding a piece of paper which eventually leads to a…

Although geometry and spatial reasoning are important as a way to interpret and reflect on the physical environment and also form the foundation for learning mathematics and other subjects, many early childhood and primary school teachers spend little time instructing their students in these areas. This paper examines how young children learn…