Introduction Humans use language in creative ways to make us laugh, cry and, most importantly, to give us the ability to cooperate and adapt. We create the abstractions that power cultural evolution. When a student is introduced to the world of the abstract in Algebra 1 and can explain how Archimedes turned the idea of leverage into a mathematical model we have a good start. When we complete the story of how that idea was used to build catapults that were used to kill many Romans, the connection of mathematics to the human condition begins to become clear.
During my 30 years of teaching high school mathematics I found that certain topics could easily be used to show the impact and importance of the mathematical symbol system. Some of the examples in this book connect directly to the standard texts and some would be considered enrichment (for example, the Drake equation, 4-D curved space, and relative time). The notion that students should write in a math class has been advocated for many years. But what I present in this book is a 3-year curriculum that brings mathematics together with science and sociology and allows students to write about topics that impact their lives in a multitude of ways. I believe it is a way to foster critical thinking at the highest level. It also allows for these ideas to gain depth over a three year period.
One of the amazing things about teaching is the feedback from students
10 to 30 years after they graduate. Just when we think that kids don’t
remember much of what we teach, they surprise us by recalling that “great joke” or the day we played the happy birthday song on the vacuum cleaner. This is nice, but the feedback that confirms that I did some good teaching comes from the students who recall the connection of jokes to mathematics or the many discussions about how humans use and abuse power. By connecting mathematics to the human condition and cultural evolution we can be assured that students will internalize and retain the truly important aspect of the subject.
One of the jokes happened to be from Groucho Marx and goes something like “Outside of a dog, man’s best friend is a good book. Inside of a dog, it’s too dark to read.” My dog T-Bone has a great sense of humor and knows many ways to joke around, but he has never really caught on to the Marx joke. Double-entendres are just not his thing. In teaching about the human condition it’s important to talk about how the human critter is different from the canine critter. They talk, we write. They sing, we compose. They count, we do math and science. It’s the symbol systems and the power they give us to evolve culturally that allow us to call ourselves artists, mathematicians, or scientists.