STUFF YA GOTTA KNOW
ENRICHMATH.COM is dedicated to bringing math and science together over the three years of math that most high-school students experience. The model used was developed for over 20 years at Carmel High School, Carmel Ca. and leans heavily on Jacob Brownowski’s Ascent of Man book and video series. From Algebra 1 through Geometry and Algebra 2 students were asked to write and explain how mathematics is used as the language of science, and how human culture evolved so quickly from 40,000 years ago to the present. From the first day in Algebra 1 the emphasis was to enrich the regular curriculum so that students gain an appreciation of how certain “species-specific characteristics” made humans successful, and gain a working knowledge of the human condition. Before each exam students were given a list entitled “Stuff Ya Gotta Know”, that included the important ideas they would be asked to write about.
As can be seen from the content outline, many topics were touched on during the three years, but they were all tied together with the idea that science is a progressive human endeavor, and that the models we build with our major symbol system (Mathematics) will be tested and open to revision when the data demands change. Students were expected to know the difference between an inductive conclusion based on many observations and a deductive conclusion based on accepted axioms.
The theme that ran through all three years was how and why the modern conception of our universe changed over time. It was great fun to listen to 9th graders argue about where the rest of the moon goes when it is a thin crescent, and to remind them that the “sunset” should really be called the “earthrise”. Geometry students were empowered when they could explain the concept of finite-unbounded space, and the story of Galileo, Newton, and Einstein capped off the enrichment in Algebra 2.
I hope this website will become a source of activities (Sourcebook) and new investigations to strengthen the model. I encourage input from all interested parties, and hope to create a forum for new information that can be applied. For example, there is a fun page called “Mind Games” by Scott Kim in the Aug. 2007 issue of Discover magazine. It includes three key ideas from Douglas Hofstadter’s new book I Am a Strange Loop (Basic Books, 2007). The section on “Levels of Structure” ties in nicely with the enrichment unit in chapter 4 of the book dealing with second-order abstractions. It challenges you to sort several lists from lowest level to highest, e.g. LIFE: cell, community, ecosystem, molecule, organ, organ system, organism, population, tissue. The section titled “Strange Loops” gives 11 self-referential statements to classify as true or false or something else. Number 1 is “This sentence is true” (classified as “other”), #2 is “This sentence is neither true nor false”, and #11 is “Thit sentence is not self-referential because ‘thit’ is not a word.” Geometry kids love thit stuff.
The July 21, 2007 issue of Science News contains a report that the game of checkers has now been solved completely, which would have been of great interest to my Algebra 2 students. We played enough tic-tac-toe to convince ourselves that it was not a “real” game, just a process of calculation (there are just a few different possible positions). See chapter 14 for our enrichment unit on games-theory. I will try to update the website as often as possible, so WELCOME ABOARD. Vic Selby