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Insight on Insight is Insightful

We have all perhaps experienced an "aha"...that special moment when a problem is solved unexpectedly. This is often called insight.

Now, researchers Sascha Topolinski (Germany) and Rolf Reber (Norway) have hypothesized that insight integrates these four characteristics:

  1. Suddenness: The experience is surprising and immediate
  2. Ease: Compared to previous obstacles, the problem's solution now surfaces smoothly and easily
  3. Positive Affect: Each insight leads to postive feelings
  4. Feeling of Being Right: After an insight, we judge the solution as being correct and are confident
These hypotheses have been verifed by a combination of multiple research studies, and are confident that they are right. So, I guess their insight was truly insight!

So what does this have to do with teaching and learning mathematics? Characteristics #2-#4 obviously are important to the doing of mathematics, especially in a problem solving moment. But, it is that first characteristic--suddeness-- that is so elusive, as one never knows when or if insight will happen. And, if it does not, then what happens to the other three characteristics?

Source: ScienceDaily, December 15, 2010