How Should Science be Done?

Lately I keep running into the idea that the proper way to do science is to continually strive to disprove a hypothesis, rather than support it*.  According to these writers, this is what scientists are supposed to aspire to, but I've never actually heard a scientist say this.  The latest example was recently published in the Wall Street Journal (1).  This evokes an image of the Super Scientist, one who is so skeptical that he never believes his own ideas and is constantly trying to tear them down.  I'm no philosopher of science, but this idea never sat well with me, and it's contrary to how science is practiced. 
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