Philosophy

Mathematical ideas only exist in our minds.

Mathematical truths and ideas are discovered, only mathematical symbols are created.

Mathematics is both a logical and a creative endeavor, which both requires and improves ones reasoning and imagination.

Mathematics describes the world around us so well, because it’s possible that every object in the universe, at its core level, is actually a mathematical object itself.

Mathematics is about asking questions, discovering patterns, and then making and confirming connections, which leads to more questions, more patterns, and more connections, ad infinitum.

Doing arithmetic should not be confused with doing mathematics, but being good at arithmetic can boost ones confidence and enable one to concentrate on the bigger ideas (Mathematics is not about being right and getting answers, mathematics is about discovering truths and asking questions).

Outside of the multiplication chart, memorization can come in handy, but it is not necessary to learn mathematics. Remembering all of the mathematics you ever learned is not necessary either (or possible). Understanding the big ideas and knowing how to look up the rest when necessary is all you need.

Learning mathematics is more about learning, thinking, and abstraction, than the actual mathematics being used to deliver this training. The mathematics learned however, turn into the skills needed to learn more mathematics and further your training.

Algebra is not just a gateway course, it’s a powerful and beautiful branch of mathematics in its own right.

Algebra and geometry should not be thought of as two different branches of mathematics, but as a union of abstract and concrete views of a collection of mathematical ideas.

The study of polynomials is a rich and rewarding endeavor, which as a common theme, allows for a better understanding of the mathematical ideas commonly found in algebra and geometry courses. "Succinctly put, algebraic geometry is the study of geometry using polynomials and the investigation of polynomials using geometry." - The Princeton Companion To Mathematics

Mathematics teachers try to teach their students mathematics, but teachers of mathematics try to encourage and facilitate their students as they learn how to teach themselves.

Mathematics is not only a fulfilling personal endeavor, but a social endeavor as well, the learning of which is only helped through both personal sustained effort and reflection, and mathematical discourse with others.

Students should learn mathematics by being allowed to discover and to do mathematics, and to do so at their own pace.

Given a safe physical and psychological environment, students who demonstrate an appropriate level of readiness, will be successful.

Kids are people first and students second.

Education is about learning how to learn and becoming an independent thinker.

Being a life long learner and independent thinker, can lead to a better appreciation of life and inner peace.