Geometry is one of the first real exposures to the mathematical structure of axioms, propositions, postulates, theorems and proofs. It’s also one of the first courses that will push a student to make real mathematical connections on his or her own, rather than just learning patterns of solving particular types of problems and repeating them. Geometry is also one of the oldest branches of mathematics, with early forms of analytic geometry being used to solve complex algebraic problems centuries before the development of a formal symbolic algebra.

Geometry begins with definitions and axioms. Definitions are often self-reflexive or seemingly meaningless on close examination but can be understood intuitively and through graphical representation. More important than the essences of the definitions are the axioms which relate defined entities to each other and the conjectures which can be proved using said axioms. Axioms are things that are assumed to be true, not because they may be proven or not proven, but because if they are assumed, then they can be used to prove or disprove conjectures.

If a Geometry course is sufficiently advanced, it may explore non-Euclidian geometries, which are geometries constructed by picking and choosing different sets of axioms and discovering what sets of theorems can be derived from these.

Geometry can be a difficult and frustrating class for students who are used to more straight-forward courses which focus more on methods for solving particular types of problems than analysis of the methods themselves. Success demands intuitive understandings of definitions, axioms and their uses, and practice in making connections to prove theorems. More than many other classes, geometry demands personal coaching through the process of learning strategies to make connections and the help of a tutor for clues to difficult proofs that may otherwise demand hours of pondering to find needed insights.

I provide supplementary instruction (tutoring) for Geometry for $35 an hour. I provide more comprehensive homeschool instruction, including assigning homework and administering tests and quizzes for $50 an hour.