This class is about to embark on the study of the primary rules of Mathematics, that said, we should start with the definition of Mathematics.
Science of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation. Since the 17th century it has been an indispensable adjunct to the physical sciences and technology, to the extent that it is considered the underlying language of science. Among the principal branches of mathematics are algebra, analysis, arithmetic, combinatorics,Euclidean and non-Euclidean geometries, game theory, number theory, numerical analysis, optimization, probability, set theory,statistics, topology, and trigonometry.
In the definition above it is spoken of as a "science" and as a "language".
One must use care in siting information from Wikipedia but I find their definition a great place to start a discussion on how to view the topic of Mathematics from the beginners view.
From Wikipedia, the free encyclopedia
Mathematics is the abstract study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.
Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science. A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. Some just say, "Mathematics is what mathematicians do."
: a specialist or expert in mathematics
Does the above define what you are? If not, how can we do Mathematics? I propose that for the purpose of beginning to study Mathematics we consider it a language, in fact, the language of science. If we opt for this definition which puts Mathematics in the Art arena then we can begin to study and develop our skills using the same pedagogy as learning a language. In this course of study we can make references to our own native language and it's syntax, definitions, and rules which should draw parallels to concepts we already know thus making the study of Mathematics more familiar.
Links to definitions from Webster's On-Line Dictionary & Wikipedia
Webster's definition of Algebra