I cannot teach anybody anything, I can only make them think.” ~ Socrates
From my 17+ years of schooling, and even today, schools systems teach facts and figures, and then have the students regurgitate them for a grade. In my opinion, the educational system, especially in this country, is deficient in the way the schools approach education. Like Socrates, schools should teach students how to learn. That is not to say that teachers are bad, there are many that are excellent in their profession. The system they work in, and the sometimes the way they are forced to teach, is the problem.
I couldn’t see how anyone could be educated by this self-propagating system in which people pass exams, and teach others to pass exams, but nobody knows anything.
Richard Feynman
When a person graduates from high school or college, they need to know how to learn as they enter the world of employment. Once employed, they must “learn” how to do the work assisgned them. Yes, they may have someone who “teaches” or “guides” them on their tasks, but they must make the effort to learn. We are human beings, not robots.
To learn, a person must first need to be willing to take the time to study and meditate on the subject, to do the necessary research, and to ask the appropriate questions. This leads to knowledge. Next, they need to see how that knowledge fits in with what we already know, discerning its benefit to us personally. That results in understanding. Finally, they should use what they have learned, putting it into action in our lives. This is wisdom.
What is the difference between knowledge, understanding, and wisdom? Let’s illustrate the difference this way: Imagine you are standing in the middle of a road and a bus is coming toward you. First, you recognize that it is a bus—that is knowledge. Next, you realize that if you remain standing there, you will be hit by the bus—that is understanding! So you jump out of the way of the bus—that is wisdom!
Wisdom is not a product of schooling but a lifelong attempt to acquire it.
Albert Einstein
What then is the best way to learn? Each individual is unique and may learn in a way different from others. Begin your quest on learning and find the something that was not taught in school, or while you are in school, that would help you understand a mathematical concept. I missed many “somethings” and have placed them in this website. I hope what I have placed here will help you to have an aha moment in understanding mathematics!
In Praise of Teachers
I have had many outstanding teachers (e.g., Mr. Jack Bowen and Mrs. Marion Kinzele of Perry High School, Massillon, OH), and have read many teachers blogs (e.g., Math Giraffe and iteachalgebra), use websites (e.g., CUEMATH and Math Is Fun), and learn teaching techniques from various websites (e.g., The Socratic Method: What it is and How to Use it in the Classroom and Asking Questions: Six Types). Many teachers are trying hard to make their students think on their own. It must be hard to work inside an educational system that wants teachers to teach how to take standardized test rather than how to think and learn. For all you teachers out there trying hard to improve the lives of your student: Take a bow! You deserve it!
I update the content on this website periodically to include more information that will help the reader understand a mathematical concept, or adding additional pages to cover mathematical topics that may be difficult to understand. Happy reading!
Mathematical Mysteries 