Plane Geometry - Bruce E. Shapiro

Section 1PrefaceReflectionsFoundations of Geometry is a content class for future high school teachers.In most college math classes, the focus is on a logical developmentof mathematical tools and techniques; their underlying theory, derivationsand proofs; and application to the real world or other mathematical subdisciplines.As a content class we will do all this, but we will also makean (albeit limited) attempt to integrate the material in a way that it ispertinent to your future as a an educator.On Pedagogy. As teachers you will need to know the most effective wayto present the material to others. To be effective, you should be clear, concise,and interesting. To be successful your presentation needs to promoteunderstanding and retention.Most of this cannot be learned in the classroom. It requires hard workand lots of practice. I can tell you what I find effective but that might nothelp very much. My students are more mathematically mature than yourswill be - after all, they are college mathematics majors. My students arepeople who like math, want to learn more about it, and (in the your case)are anxious to share that excitement with others. Middle school and highschool is different. So most of what works for me probably won’t work verywell in your classrooms.As you progress towards your California teaching credential you will takea lot of classes in pedagogy, the art or science of teaching. Some of thesewill focus on pedagogy in mathematics and others will not. A few of you1