Math encompasses so much more than number and geometry. It's one of the oldest fields of knowledge, rooted in star-gazing and hut-building. Even the "hard" subjects taught in high school, trigonometry and algebra, are over one thousand years old. Calculus has been around for three centuries. None of the really interesting new stuff like statistics and fractals is taught until college.
The main problem with math classes is that we expect every student to become a mathematician. There should be some math appreciation classes. Music Appreciation wouldn't be popular (or even useful) if you were expected to master an instrument. Intro to Art is fun because you can dabble and experiment. Every math class says you will learn every detail of this equation or proof and people stick it out until they fail and then say they're no good at math. One of my professors even told me that other college majors use a calculus or statistics prerequisite to weed out students instead of incorporating the necessary (or often unnecessary) mathematics into their own classes.
With this history, I'm sure most readers wonder how math could possibly be appreciated.
Just basic numbers can be fascinating. How many are there? Infinity was investigated by a mathematician, Georg Cantor, who committed suicide. There are many different types of numbers: imaginary, transcendental, rational. The discoverer of irrational numbers was thrown overboard to protect a church established by followers of Pythagoras. Numbers have inspired and confounded people throughout history.
Not only numbers warrant awe. There are several different geometries besides the one we all spent a year in high school learning by proving theorems that had been codified 2300 years ago by Euclid. The person who discovered other varieties of algebra was killed at age 19 in a duel. Calculus is actually the art of dividing zero by zero.
For most people, the only math they truly need is arithmetic -- addition to long division. Even fractions and percentages should probably be taught in later grades when minds are more analytical. Most other math is unnecessary except to scientists and engineers. Providing an overview of all mathematics including the latest discoveries and the timeless paradoxes could prevent boredom, present a vital component of human knowledge, and perhaps entice some students to pursue studies, to stick it out through the tougher equations.
A math enjoyment component could also help develop needed analytical skills. What if every Friday were spent discussing statistics used in news reports? Citizens would grow up with a better understanding of how results can be misinterpreted and studies skewed with faulty premises, possibly preventing poor policies based on bad numbers. And what student isn't interested in the Nielsen ratings?
Or teachers could show how a word problem can be converted into algebra or calculus. Saying, "You don't need to know this," would allow the students to see the power of math without the fear of failure. Regular exposure to presentations on fractals or projective geometry may attract the artistically inclined to pursue math. Showing how algebraic groups and rings explain the concept of harmony may attract musicians.
Presenting many of the concepts of math each year during other classes, or demonstrating them in overview or introductory courses could result in more mathematically inclined graduates instead of the current way schools produce a few accomplished geometers or algebraists and a majority of proud mathematical incompetents.