Audience: High School Mathematics Teachers & Administrators: Fill & Download for Free

Boredom does not begin to describe it. It's nothing less than torture. Allow me to explain.I taught myself to read and do basic math at age 4. So obviously by the time I did get to school two years later, things were not ideal. Ages 6 through 12 were relatively manageable, because it was customary for kids to contribute a book to the class library. So during this time, when new material was presented I would spend the first class finishing all exercises for that year and the next year. In the following classes dealing with the subject, I would spend my time reading quietly while everyone else caught up.It's important to note that at this point, a lot of invisible damage had already been done to my psyche. I had already started adopting negative adjustment techniques, like purposefully wasting time before starting tasks to make them more challenging. To understand how this works, imagine owning a formula one car, but being forced to always drive on shabby roads where you can get up to maybe 1/8 of your maximum speed. So in this regard actively handicapping yourself helps, though at the time you're unaware of the long term damage you're inflicting. See, after a while your car starts deteriorating, simply because it's not being used to do what it was designed to do.Poor socialization starts happening as well, mostly due to the huge gap in development. I was literally told at age 12: "We don't want to play with you, you talk like a professor." In fact later in life I got dumped for similar reasons. Being intelligent is supposed to make your life better, right?Anyways, back to reading in the classroom. Most teachers were sensible enough to return the respect I was giving, and to not try and mess with me. However, in the last year before high school, they increasingly started making a problem out of the fact that I was quietly keeping myself busy. Initially they would tell me to stop reading, so I'd ask them for something else to do. Which they obviously could or did not want to offer me.This took away any kind of incentive I had to play nice. The lack of challenges and things to do in general drastically ramped up boredom, and as a result, creativity in dealing with the situation. So I started resorting to stuff like peeing my pants to get out of class, making the teachers look like idiots in front of the other students, sleeping in class, making weird noises, etc. This is what happens when you try to get a highly intelligent person to submit to blind authority. We always ask "Why?" If that question can't be answered to satisfaction, you're in a world of trouble.Also important was the fact that I'd been voicing my discontent and pain to my family, and they kept promising me things would be better in high school. I'd get challenged more, have some choice in what subjects I'd study, etc. I wish they hadn't.After a good month in the first year of high school studying Latin, I realized I was in for another 6 years of the same scam. Additionally, the amount of authoritarian teachers increased. I went from scoring 99% on the high school assessment test to intentionally scoring 50,1% on tests, refusing to do homework, sleeping in class, spending tons of time at the principal's office, etc.A year later my mom took me to Tessa Kieboom, the world's leading expert on gifted children. She begged her for a solution to my problems. Tessa tried to work with the principal and teachers at my school, but they were unwilling to help in any kind of way. She advised I skip a year, but the school refused. Didn't switch schools out of fear of losing the few social outcast friends I did have.All the bad stuff got progressively worse during the remaining five years. I developed severe clinical depression, and started trying to take my own life on a pretty regular basis. Stuff like coming up with a legitimate, novel solution for a geometry problem and getting a zero for the test because my answer wasn't in the textbooks obviously didn't help. Negative reinforcement doesn't get much worse.The bottom line is, society unwittingly inflicts a tremendous amount of pain and damage on anyone that deviates from the center. Schools are especially good at this. Their target audience is an average person, which doesn't exist. Every single child has different needs, regardless of intelligence levels.If civilization is to survive, we need a serious reorganization of society and the school system. With the current system, the more a person's intelligence deviates from the mean, the more social ostracization they face. For a species that thrives when cooperating, this is a terrible thing. It serves as a negative reinforcement, decreasing the chances that such persons will contribute to society. In the case of highly gifted children this is especially tragic. On the extreme end of this spectrum is radicalization. Consider in this regard the unfortunate case of Ted Kaczynski, mathematical prodigy turned Unabomber.As for me, I survived. At 29, I still have more suicide attempts than birthdays though. Ultimately, the things that saved me were:broadband internet access - this allowed me to learn at my own pacevideo games - they allowed me challenge myself and actually develop my consciousness, rather than having my entire being suppressed by an institution

As a high school calculus teacher of almost 30 years who has fine tuned the art of simplifying mathematics for a large spectrum of learners, let me offer an answer that can be appreciated by a wider audience.I was discussing the graphs of [math]y = \sqrt{x}[/math] and [math]y = \ln{x}[/math] in a calculus class once, graphs that increase at a decreasing rate, eventually rising so gradually and imperceptibly that they appear to be perfectly horizontal. If you are unfamiliar, you can graph each on Desmos.com/calculator.My students wondered how long it would take for each graph to reach the ceiling in the classroom. We placed the origin at the bottom left-hand corner of the whiteboard, marked off the x and y-axes at one-inch intervals, and performed a simple calculation for each graph to reach the 10-foot ceiling. The graph of [math]y = \sqrt{x}[/math] traveled to the right about 1,200 feet before it finally reached the ceiling. That was expected. But the graph of [math]y = \ln{x}[/math] rises so slowly that it would travel to the right trillions of times farther than the edge of the known universe and still would not reach a height of 10 feet. That shocked us all!!!Since I was flying to California the following week to visit my parents, and my father was a world-famous mathematician, I knew he would appreciate this fact. So I prepared an informal paper on the rise of various functions (exponential vs. radical vs. logarithmic) and couldn't wait to show him. My plane had just landed when my mom called and informed me that my father had unexpectedly passed away while I was on the flight. I never got to show him.

Depending what you're looking for, Lehoczky and Ruszczyk's The Art of Problem Solving is excellent, as is Zeitz's The Art and Craft of Problem Solving. The underlying material is accessible to middle-school and high-school students respectively, but if the math you've seen so far feels like "rote memorization" then either of these will be a big eye-opener, no matter how much of it you've learned. Both of them show you a great deal of math problems and help you learn to solve math problems creatively.In a different vein, John Allen Paulos's Beyond Numeracy is one of many excellent books that present mathematical ideas for a general audience with a focus on understanding the big ideas that get math people excited.Update: Not a book, but close enough: the authors of the first book I mentioned now have an online math-teaching application called Alcumus (http://www.artofproblemsolving.com/Alcumus/). Haven't used it myself, but it has a laudatory blurb from Vern Williams, who is the best math teacher I know (and may be the best in the country, as far as such a thing could be determined.) Worth a try, and I'd be curious to hear from anyone who has tried it.