Introduction: When I first started blogging as an experiment some of the early posts I made were regarding the philosophical question of defining the field of mathematics. Over time the responses I've received and practical questions about the needs...

I have been working mostly by myself for the last couple weeks on a course for the upcoming school year. Thus, I have postponed plans to write. Instead of adopting a pre-made course. I opted to use our existing materials and strategies to write a cou...

I was reading Euclid’s propositions and proofs of the Linear Pair Theorem and converse, and the vertical angles theorem. It finally occurred to me how I should prove the vertical angle theorem through superposition. In the past I always proved it i...

Last summer a coworker and I went to Fresno State and observed debate lessons in geometry. It is a method similar to Socratic seminar. Here is a summary of what it is about. What does a debate lesson look like?Each debate begins with a key quest...

First, I have to apologize. I have been trying to find more convenient ways to add pictures and diagrams to my blogs. The school district where I work is considering abandoning Microsoft Office for Google Docs. So, I’ve tried to start using their t...

The fifth proposition in the elements is the proves that the angles opposite the congruent sides in an isosceles triangle are congruent. Euclid proves this by extending the congruent sides of the isosceles triangle, shown above as the blue triangle,...

The new “common core” standards for geometry specifically state that congruence of figures is to be defined by the principle of superposition. In other words, two figures are congruent if and only if they can be superimposed upon each other throu...