Education is not optional in the information age; it is a matter of survival in a world driven by accelerating demands for increases in productivity.
Education, to me, is fundamentally about making connections between powerful concepts and insights. For instance, the insight that we cannot experience the world as it is; we can only experience the world as it is transforming. This insight permits us to have insight into the art of mathematics. Mathematics is capable of simulating transformations and that is one of the powerful reasons that we can use the mathematics to gain insight into the physical world; transformation is where math and nature meet. When a scientist develops a model to explain some physical phenomenon, she is proposing a mathematical transformation that might emulate a transformation in nature. She will never know if the proposed transformation exactly replicates natures but if her transformation produces the same results as nature, the proposed transformation survives. Education is not about equations, it is about understanding the reasoning behind the models that gave rise to them.
I have over a decade of experience as a Research and Development Chemist and recently graduated with a MS in Chemistry as well as MS in Environmental Science. As a graduate student at Indiana University, I had the opportunity to be an Associate Instructor for Freshman Chemistry, Inorganic Chemistry laboratory and Energy Economics. Each semester I asked the students to step back from the symbolism of the mathematics and seek to understand the reasoning behind the symbolism. For instance, the equations that describe the ideal gas law are built on a model of very small, hard spheres bouncing off one another. A logical journey through that model's reasoning will lead to an intuitive understanding of much of thermodynamics. I also pointed out that the ideal gas law is not chemistry; it is what happens when the reactive and attractive forces of chemistry are removed or turned off. This often-overlooked insight can be immensely helpful for a freshman chemistry student trying to make sense of the deluge of information that confronts them.
An example of how I ask student how to think about Chemistry.
Observation 1: Chemistry is the study of the electron
Observation 2: Electrons have a negative charge
Observation 3: Negatively charged things are attracted to positively charged things
Observation 4: Electrons are modeled (can be thought of) as waves (standing waves)
Observation 5: There are only so many ways to fit a standing wave around a sphere (nucleus)
These 5 observations can be combined to explain a very large portion of chemistry. For instance, these observations can explain the periodic nature of the periodic table, electronegativity, ionization energy, reactivity, molecular geometry and on and on.