Transformations are a central organizing idea in geometry. They are included in most geometry curricula and are likely to appear with even greater emphasis in the future, given the central role they play in the "Common Core State Standards" for K-12 mathematics. One of the attractions of geometry is the ability to draw and construct the…

A geometry textbook or mathematics journal that prints all the work that mathematicians use as they generate proofs of mathematical results would be rare indeed. The false starts, the tentative conjectures, and the arguments that led nowhere--these are conveniently omitted; only the final successful product is presented to the world. To students…

This article explores the notion of collateral learning in the context of classic ideas about the summation of powers of the first "n" counting numbers. Proceeding from the well-known legend about young Gauss, this article demonstrates the value of reflection under the guidance of "the more knowledgeable other" as a pedagogical method of making…

When properly implemented, the vision of "Beyond Crossroads" will result in classrooms where students are actively engaged and responsible for their learning. They are able to share their thinking and the teacher, in turn, can use the emerging understanding as a foundation for learning. According to "Beyond Crossroads," students will be expected…

Formal requests were recently introduced for integration of ICT in secondary school mathematics. As the main issue, students must develop competence to decide when and how it is appropriate to use available ICT tools and to use them. These new requests put demands on those teachers who have not developed corresponding competencies themselves.…

This paper discusses the basic concepts of reflection and its related concepts in optics. It aims at providing examples on how to apply the principle of reflection in geometry. Explorations of the concepts involved via dynamic geometry software are also included.