And so I have begun on a course of study in Mathematics as part on my path to Masters of Special Needs Education.
As I review the basic materials that a child must learn at a very early age (pre school in the current system) regarding mathematics, I feel personally, that I am grappling with a complete neurological inability to understand mathematical concepts. I am curious if this is due to inadequate teaching when a child. While I can easily do the work and even teach the basic skills of arithmetic, algebra and even geometry, something seems to be fundamentally missing. Is it possible with a depth of understanding, a better way to teach basic mathematics can be found? Could better ways be discovered to teach mathematical principles at very young age, or to children with special needs including ADD, ADHD, and the wide range of spectrum autistic “disorders”?
Considering that a child begins to learn language from the moment he becomes sentient, would it not be that he or she also begins to learn the language of mathematics? If it is untaught or mis-taught from this early age, then could it be resolved through accurate teaching methods? These are my questions.
I imagine that as a teacher, I will encounter the need for answers to these questions. I also imagine, that if I can grasp the subject to its greatest depth that I can teach mathematics to a child successfully, even at a very young age, or a young age in terms of “intelligence” when these neurological pathways are just being developed or lay dormant awaiting development in the case of what we currently call “learning disorders”.
And so I enter into a series of experiments on myself, to trace just what is the mathematical mind and how can I develop it?
In the course of the next five days, I hope to overcome my own “disability” or apparent lack of “talent” or “intelligence” and integrate the entire subject of mathematics into my sensibility. Being able to provide, as a teacher, a rich understanding of mathematics, will enable me to teach mathematics to anyone, regardless of their past experience or learning disability or age. This hypothesis is based on the predetermination that a learning disability is actually a failure to develop intelligence and need not be permanent. This is a research theory that has yet to be proven, but seems very likely based on the most cutting edge neurological research of our times: that the pathways can be reformed through exercise and use. (For more information on this latest research, please see the references below.)
It is my hypothesis that I can re-pattern the neurological pathways in my mind to understand mathematics and that I can use what I learn in this experiment to teach others who maybe in a similar position for any reason.
A mathematics teacher is an expert who can help to mold the mind of the student, with a complete and rich understanding of a subject. Since the principles of mathematics are so intrinsic to the natural world, it seems possible that the patterns of mathematics may be intrinsic to our own minds as humans.
This leads me to a definition of mathematics that applies to all aspects of human existence. Searching for readily available definitions of mathematics in dictionaries and even by the best of modern teachers has left me unsatisfied. And so I have sought to first define mathematics in such a way that I can become enriched by it as a student, and teach with the purpose of developing the language of mathematics in any student.
Just like a child, I have no foresight to understand why this subject could be of value to me. Just like a baby or anyone with a developing “IQ”, I have no understanding of why this would be of value in the woof and warp of my daily existence. We are generally taught in school that mathematics helps us to learn how things work, and to eventually assume duties that involve the use of mathematics. But this is much later than the developing mind that needs to begin learning many years before any such concerns. Appreciating the beauty of mathematical patterns can be experienced by anyone without reason of such a complex understanding.
So here is my working definition of Mathematics: Mathematics is the science of properties, forms and patterns of our world.
Based on this definition of mathematics, Chemistry, Astronomy, Biology, Engineering, Geology are all sciences in the field of mathematics; where mathematically evident patterns and phenomenon occur and are studied scientifically and often harnessed or exploited, toward the development of technologies.
Math is often defined as a language, but in fact it uses its own language. The language of mathematics is not words, but symbols that directly express not concepts or ideas, but relationships in space-time.
To define math even further we can explain that mathematical observations can be described through symbols. It is a meta-language of the expressed patterns that create the forms, volume and properties of our physical world.
I searched to discover if others may have this understanding of mathematics, so as to determine whether this definition of mathematics could be useful in teaching this subject. So far, I have discover MIT Cosmologist Max Tegmark, who introduces such an understanding of mathematics. He explains that mathematics is all around us; in every step we take in our homes and our work, in every leaf, every food and every movement of our bodies and every natural phenomenon. “Mathematics captures the essence of what is going on in this very complicated universe.” According to Gallileo, “Nature seems to be a book in the written in the language of mathematics.”
BBC Two Film Production “Is Reality a Mathematical Structure?” posted Jan 18, 2011 by BBC retrieved Nov 27, 2012
BBC Autism Breakthrough retrieved from