A proper mathematical education should develop a conceptual understanding of the subject while also building up proficiency.  Mathematics is well-suited for this endeavor. Beginning with clearly understood first principles, reasoning is used to develop the logical consequences of those initial assumptions. This is true at all levels of the curriculum. Properly implemented, a mathematical education is not the memorization of seemingly unrelated facts but allows students to understand the relationships between seemingly disparate ideas taught on different days, weeks, or even across the years. 

In this talk, we will use geometry and its relationship to other areas of the K-12 mathematics curriculum to illustrate these ideas.