Why did I devote every blog post from 16 Oct to 27 Dec to The Big Four?
I will begin my answer by reviewing the names and the statements of each of The Big Four.
Distributive Property: If a, b, and c are real numbers, then a(b + c) = ab + ac.
Transitive Property: If a, b, and c are real numbers such that a = b and b = c, then a = c.
Law of Trichotomy: If a and b are real numbers, then exactly one of the following is true:
- a < b
- a = b
- a > b
Zero Factor Property: If a and b are real numbers and ab = 0, then a = 0 or b = 0.
In the collection of basic mathematics facts, these four may not be considered more important than some of the other facts. In fact, on October 11, I advocate that teachers know and use these other properties to give their teaching the proper perspective. However, The Big Four should be recognized as very important for teaching beginning algebra.
Recall The purpose of high school and early college algebra courses is to introduce the student to the use of abstraction, generalization, problem solving techniques, deductive reasoning, and critical thinking while exploring the structure, patterns, and relationships of a variety of algebraic entities including, but not limited to, relations, unary operations, binary operations, and mathematics objects such as equations, inequalities, algebraic fractions, polynomials, and functions.
The Big Four provide excellent opportunities to teach and illustrate:
- The value of unification.
- Deductive reasoning.
- The structure of mathematics systems.
- A systems viewpoint for mathematics.
- How to be a problem solver.
- Mathematics is not a collection of formulas, facts, and processes which are to be memorized.
- The use of abstraction, generalization, problem solving techniques, deductive reasoning, and critical thinking.