Geometry As It Can Be and Should Be Taught

Geometry is too perfect a subject not to teach logic in. It is wrong not to. An education without proof in geometry is a poor education. Unfortunately, most geometry text books I’ve seen don’t do a good job of integrating logic into the subject, either — if they mention it at all. And even the books who do mention logic treat it perfunctorily. The quality of education is getting worse, as the NCTM and others de-emphasize proof, and as logic becomes a lost and neglected art. According to NAEP tests, many high school and college students cannot write at the level they should — writing being a process which reflects the reasoning and logic going on in a student’s mind. Students today are, in general, not learning what they should, and are not being trained in reasoning. Students I tutor in geometry learn logic and reasoning, and have their mental tires hit the road. We don’t just mouth “geometry teaches logic” or “this aspect of logic is useful outside of geometry.” We are detailed, serious, and integrated about logic and proof in geometry. Recently, for example, some students were at a point where we were able to apply principles of logic we learned in geometry to analyze these paragraphs from a “commentary” entitled “Be afraid, be very afraid” (May 21, 2009, 4:15PM) by Lisa Falkenberg:

Critical thinking is gobbledy-gook. Public education is tyrannical and unconstitutional. Darwin was wrong and somebody’s gotta stand up to those menacing scientific experts! If you agree or at least feel comfortable with the above statements that have come from various Texas State Board of Education members in the past year, then fear not. … For the rest of us foolish enough to value critical thinking skills, public education, Darwin’s limitless contributions to science, and the opinions of educators, scientists and other people who have spent their lives accumulating invaluable expertise that can only make our schools better, be afraid. Be very afraid. Copyright © 2009 The Houston Chronicle

We analyzed what this said, what it implied, and what it presupposed. There are some interesting contradictions in this commentary. My students are learning reasoning skills and are being prepared for the cognitive demands of adult life. They are learning skills which will help in their reading, their writing, and their SAT performance. If you’d like your children to be educated in math as they can be and should be, contact me for tutoring!