Introductiontomathematicthinking.docx

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What is mathematics?
For all the time schools devote to the teaching of mathematics, very little (if any) is spent trying to convey just what the subject is about. Instead, the focus is on learning and applying various procedures to solve math problems. That’s a bit like explaining er by saying it is executing a series of maneuvers to get the ball into the goal. Both accurately describe various key features, but they miss the what and the why of the big picture.
Given the demands of the curriculum, I can understand how this happens, but I think it is a mistake. Particularly in today’s world, a general understanding of the nature, extent, power, and limitations of mathematics is valuable to any  Over the years, I’ve met many people who graduated with degrees in such mathematically rich subjects as engineering, physics, computer science, and even mathematics itself, who have told me that they went through their entire school and college-level education without ever gaining a good overview of what constitutes modern mathematics. Only later in life do they sometimes catch a glimpse of the true nature of the subject e to appreciate its pervasive role in modern
    More than arithmetic
Most of the mathematics used in present-day science and engineering is no more than three- or four-hundred years old, much of it less than a century old. Yet the typical high school prises mathematics at least that old—some of it over two-thousand years old!
Now, there is nothing wrong with teaching something so old. As the saying goes, if it ain’t broke, don’t fix it. The algebra that the Arabic-speaking traders developed in the eighth and ninth centuries (the word es from the Arabic term al-jabr, meaning “restoration” or “reunion of broken parts”) to increase efficiency in their business transactions remains as useful and important today as it was then, even though today we may now implement it in a spreadsheet macro rather than by medieval finger calculation. B