The reason I was seeking an education degree was because I had developed methods that would allow school to teach Calculus at a much earlier age. Bringing this method to fruition became a primary goal of my education career. I had hoped to turn it into a real career.
In my opinion, calculus should be taught immediately after or at in concurrence with algebra. Everything becomes easier when one knows calculus. Calculus is the basis of physics. Physics is the basis of chemistry and chemistry the basis of biology. In finance, you can't understand interest rates without calculus. Statistics leans heavily on calculus. Trigonometry is easier to understand once you know calculus. Calculus is primary and it should be taught earlier.
If we had a good method for teaching Calculus to your average high school student, then we would dramatically improve the quality of our math and science education and would dramatically improve the quality of life.
On a side note, my mother was interested in the history of logic. Logic was the center of education from the days of Aristotle through to the modern era. In this 2300 years history of teaching logic, there developed a plethora of approaches to the subject. Interestingly, the very first thing the left did when they gained hegemony in education was to rip the logic class out of the school. That is a different story.
… back to calculus ...
There are multiple ways to teach calculus. The traditional Cauchy method is a college level course. Proponents of new math favor a set theoretic approach which presents calculus as a construct of language. This method fits in well with the tradition of Hegel, Marx, Cantor, Russell and Chomsky. I find the approach paradox ridden. Again, I don't think it is suitable for high school. Marvin Kline proposed an Intuitive Approach to Calculus. His method fits in with the thinking of Montessori, however, it really depends on the skill of the teacher.
Not surprisingly, the method I wanted to develop fell squarely in the classical tradition of Aristotle, Descartes, Leibnitz, Newton, Gauss, Reimann, Einstein, etc.. It would work even better if schools taught logic.
I believed that there was merit to my method. Regardless of my personal thoughts, I would never force it on anyone without data to back up the claim. At the time, I figured I would need about $200,000 to develop and do alpha testing of the curriculum. If the data looked good, I would want to role out a controlled beta test. If the average high school student was able to master Calculus with my method, as I contended, then I would want it to compete with all of the other ideas on the market.
There are multiple ways of teaching subjects like logic and calculus. So, the question is: How do you create a mechanism that simultaneously allows for the development of multiple curriculums with the majority of students getting the best methods?
Unfortunately, in our current single payer system of education, there is market mechanism to allow for diversity of ideas.
In Utah, 96% of students go to public schools. The curriculum is set in Universities that have zero interest any method beyond New Math. Ideas, other than new math, don't even have the potential to survive.
With one extraordinarily corrupt group, the UEA, having absolute power over 96% of the education market, there is no longer any place for ideas such as teaching logic to primary students or teaching Calculus to all students in high school to exist. Survival for diverse ideas is not even possible. It is a stagnant system.
It is possible that new math really is the way to go, and that my method really should fail. That is entirely fine with me. Trying ideas and failing is part of life. For every profound scientific discovery, there are at least a thousand ideas thrown on the table that fail. For every blockbuster toy, there is a thousand flops. This method of developing and testing ideas through open inquiry is called science. The marketplace leads to prosperity. Our left dominated public school has destroyed the marketplace for ideas.
The fact that I never even got the opportunity to put any of my ideas on the table because a group of brownshirts in the education department weeded people out for political reasons is inexcusable and greatly devalues the value of our education.
In the past, I had rejected vouchers. I don't think it is as good as tax credits, neither is as good as a world where taxes are low and people have sufficient personal resources to send students to the school of their choice. In looking at the diversity of the charter and private schools that is starting to come to life in the wake of the State's legislature commitment to diversified education, I decided that the vouchers are a good interim step for breaking the monopoly in education.