ARITHMETIC and MATHEMATICS
Arithmetic is the understanding, manipulation and basic operations of numbers. Mathematics involve variables, functions, expressions and logical operators in addition to numbers. It is important that concepts and skills are instilled correctly lest difficulties arise.
Most students are unable to perform mental math, solve word problems, or recall definitions and rules. This is due to premature calculator usage, learning by rote and procedure, and shirking proper study techniques. This leads to numerous problems in mathematics courses such as algebra, geometry and calculus. These deficiencies must be corrected at the earliest possible time.
Mental math skills are supremely important. Without mental math, it is impossible to follow lectures in mathematics as students will not understand instantly the numerical portion of the procedure or concept. A good example is the learning of factoring and binomial expansion. Without rapid mental calculations, this becomes tedious if not impossible. Simple mental math is not an option, it is a necessity in life.
The inability to solve word problems is an indication of conceptual incompetence. An infinite number of procedures can be derived from each concept; unfortunately, with a rote procedural approach engaged by schools, it is impossible to do these problems unless stated in one specific way. Real life is not that accommodating. It is indeed impossible to memorize hundreds of procedures involved in solving problems worded differently. Concepts.
The recollection of definitions and rules are required for progress in math and science. All operations and procedures must be justified by definition or rule (postulate, axiom, corollary, thorem, etc.). Students do not understand the relevance and significance for learning these principles; hence, they are unable to follow instructions or solve problems.
Arithmetic involves whole numbers, fractions, decimals, percents, integers, and operations involving them. Often, arithmetic is coupled with pre-algebra so that procedures involving basic figures, pi, and basic formulas are introduced.
Algebra is the first level of mathematics. Everything before algebra is arithmetic. Variables and functions are introduced here. Algebra is the mathematics of patterns and sequences. All algebraic expressions are patterns or sequences of some sort.
Geometry is the second level of mathematics, and perhaps the most important for the development of critical thinking. Geometry is the mathematics of logic, not shapes as is popularly believed. Shapes are used merely to develop logical thinking. It is important to understand this distinction as most students do not consider geometry relevant to them. Unfortunately, those who do not develop in geometry is unlikely to succeed in the mathematics, science and engineering professions as critical thinking skills will be lacking.
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David K. Yoshinaga, Ph.D., Ph.D., Sc.D.