We know Pythagorean's theorem. a^2 + b^2 = c^2. The square of the hypotenuse (the side opposite of the right angle) is equal to the sums of the other two sides.
When I was taking geometry which was an extra curricular class in high school, this example may have helped to create an understanding. Instead it was about memorizing the theories.However, the teacher did present a few examples with limited explanation. The text book was about memorizing proof examples. They have already been proved time and time again by mathematicians. Understanding them would have been more helpful. For ex: in elementary school I was introduced to the 'new' math developed by mathematicians that believed the way was to teach proving methods It was a failure and the easier old math became the norm.
The traditional curriculum of rigid memorization and rote based on limited predetermined parameters worked in its time but is now outmoded, including the "No child left behind act". Reform is needed, ie. many young adults that graduate from public High Schools are considered functionality illiterate. http://www.ed.gov/blog/2013/08/americas-kids-need-a-better-education-law/
Many institutions have continually complained that many 'American', young adults are not adequately educated to face the new era, compared to other countries. Especially in math and science.http://www.npr.org/blogs/thetwo-way/2013/12/03/248329823/u-s-high-school-students-slide-in-math-reading-sciencehttp://nces.ed.gov/fastfacts/display.asp?id=1
There are a few colleges and schools that have a great reputation. However, what about the other potential STEM students who may be the leaders of tomorrow that are hindered by out dated academic teaching methods? https://www.studentsfirst.org/pages/the-stats
All of this when the current administration is trying to promote science, technology,engineering and mathematics to the current generation.I did a thesis on the need for education reform in college and this is a serious concern that I feel needs to be addressed.