Archive for category Mathematics
Was your Math Education a Waste of Time?
Posted by Scott Andrews in Mathematics on August 30, 2010
Reflections on the book A Mathematician’s Lament by Paul Lockhart
Because I am an IT professional, many people assume I must love math. While I did OK at math in school, I never really enjoyed it. A Mathematician’s Lament goes a long way to explaining why.
In contrast, I remember vividly my first contact with computers. I was in grade 5. I had Mr. B. (one of those cool male teachers who went by his initial only). The computer was an Apple II E. The code he showed us was simple:
10 PRINT “HELLO”
20 GOTO 10
Of course, this meant the computer would print HELLO forever, or at least until you hit the ESC key. I was immediately stuck by the infinite potential of a machine that did exactly whatever you said. I would go on to spend years tinkering with code, writing home-made computer games and otherwise experimenting with these great machines (one silly experiment involved seeing how much abuse a 5 1/4″ disk could take before becoming completely unreadable – surprisingly, it could take a lot!) I went on further to win multiple awards as a top computer student and yet never really pictured myself working with them, doing a business degree instead. Computers were for fun!
Math, on the other hand, was pure drudgery. The timed multiplication table quizes in elementary school were the worst – to this day I freeze up on any short timed event (I am unable to play Scategories with the timer). Throughout my mathematical education, I often thought “if only I could get a computer to do all this!” Mathematical proofs in high school were no better – I took them as exercises in irrelevance that simply had to be memorized. My success in high school math came only from monotonous repetition of exercises. I took out my frustrations in math with a doodled character I named “Math Man” who had gone insane because of math, loosely based on Bloom County’s Bill the Cat.
Once in second-year university, an economics professor realized that most of us had no clue about calculus (even after finishing 2 courses on it) so he took the time to give us an economist’s eye view of calculus, and for the first time calculus actually made sense. Sadly, moments of inspired understanding such as this were few and far between.
What Lockhart tells us is that the way math is taught in schools is wrong. It kills creativity, innovation and true understanding. I agree completely. Lockhart argues that if music were taught in the same way, students would spend years transposing written music from one key to another but never hear a song. He argues that high school math proofs are written in jargon and incomprehensible, even to most mathematicians. For a truly successful mathematical education, it needs to be experimentational and even fun. Math education should involve play and discovery, puzzles and games, and moments of eureka!
In a sense, my education in computers and mathematics gave me very opposite experiences. One was fun, free-spirited adventure; the other boring, formalized and sterile. Lockhart tells us it doesn’t have to be this way. I highly recommend his book to anyone who felt that his or her mathematical education was a waste of time.
As Easy as 1-2-3
Posted by Scott Andrews in Mathematics on August 5, 2010
A Book Review of The Math Instinct by Keith Devlin
As part of my summer reading, I read the fascinating and informative book The Math Instinct. This included an interesting journey through mathematics in the natural world, plus a review of how math works in the human mind. It was this latter part that really intrigued me the most.
The book opens with recent studies that show newborn babies have the innate ability to count to 3, even at a few days old. It turns out all humans, including the ancients, have the natural ability to count one, two and three. In fact all numbering systems use a similar system to show these numbers as either a dot or line. What about our representation of 1, 2, 3? Looking back at the ancient Indian script these numbers are based upon, they match the pattern as well:
1, 2, 3 in Ancient Indian script
1, 2, 3 in modified Ancient Indian script (without lifting the pen)
What’s more, studies show that people are very good with arithmetic when it is used in a meaningful context. Children shopkeepers in Brazil were shown to have good math skills at their market stalls, but failed abysmally at identical math questions in a formal classroom setting. The same was found with adult shoppers and carpenters. Why? Because when math is reduced to symbols it quickly loses its meaning to most of us.
And what about those pesky times tables? Our minds are made to recognize patterns, and it is this pattern recognition that messes us up when it comes to multiplication. A typical six year old child has a vocabulary of between 13,000 and 15,000 words but will struggle to learn the 18 numbers in the single digit times tables times (removing repeats and simple ones like times 1, times 2, and times 5). It is pattern interference that prevents us from learning this easily.
In short, we are all better at math than we give ourselves credit for. We have no trouble determining the larger size of a product when shopping and we are very good to spot a bargain. This book will help you see math differently, and open up your mind to the possibility that we may all be math-smart after all.