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Showing posts from January, 2018

The Calculus Trap

https://artofproblemsolving.com/articles/calculus-trap The Calculus Trap by Richard Rusczyk You love math and want to learn more. But you're in ninth grade and you've already taken nearly all the math classes your school offers. They were all pretty easy for you and you're ready for a greater challenge. What now? You'll probably go to the local community college or university and take the next class in the core college curriculum. Chances are, you've just stepped in the calculus trap . For an avid student with great skill in mathematics, rushing through the standard curriculum is not the best answer . That student who breezed unchallenged through algebra, geometry, and trigonometry, will breeze through calculus, too. This is not to say that high school students should not learn calculus – they should. But more importantly, the gifted, interested student should be exposed to mathematics outside the core curriculum, because th

Kids, Would You Please Start Fighting?

https://www.nytimes.com/2017/11/04/opinion/sunday/kids-would-you-please-start-fighting.html   When Wilbur and Orville Wright finished their flight at Kitty Hawk, Americans celebrated the brotherly bond. The brothers had grown up playing together, they had been in the newspaper business together, they had built an airplane together. They even said they “thought together.” These are our images of creativity: filled with harmony. Innovation, we think, is something magical that happens when people find synchrony together. The melodies of Rodgers blend with the lyrics of Hammerstein. It’s why one of the cardinal rules of brainstorming is “withhold criticism.” You want people to build on one another’s ideas, not shoot them down. But that’s not how creativity really happens. When the Wright brothers said they thought together, what they really meant is that they argued together. One of their pivotal decisions was the design of a propeller for their plane. They squabbl