The Five Basic Concepts:

1. Mathematics is the study of numbers and all we can do with numbers is COUNT
2. The concept of SAME. The highest number we can count to (in base ten) is 9, the numbers tell you how many the places tell you what kind. Before we can count they must be SAME.
3. We form rectangles to facilitate counting.
4. O
Hero ZERO.
5. 1
No Fun Get Back To One. NFGBTO.

Math text books are always just variations on these five themes depending on subject matter. The trick (if there is one) is knowing how and when to apply them.

My students hear “hero zero, no fun get back to one” during problem solving and solving equations algebra constantly…and they realize very quickly just how easy it is when you apply these concepts. The reactions range from relief to joy to rage. Relief for some when they realize they aren’t stupid after all, joy for others who go from “F” to “A” so instantly that the teachers accuse them of cheating, rage by others who get mad when they realize all that fear, frustration and anxiety was for nothing.

Algebra as it turns out isn’t really that hard if you understand some basic concepts and can see what it is you are doing with the help of manipulatives. Even Algebra becomes child’s play: Once you understand the concepts doing the math is easy…and fun. At my website, Crewton Ramone’s House of Math students can actually see what they are doing because we do use base ten manipulatives to teach math concepts and along with detailed instructions and even some video parents, students and teachers alike can see what they are doing and it makes sense.

“Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.” ~Ernst Mach

All math is is counting. Every math problem counts something. Believe me I’ve had this argument in seminars with professors and teachers across the USA. If you aren’t counting something you aren’t doing math. Period. So one of the most basic concepts I teach ANY student is to ask “what are we counting?” when confronted with a math problem.

“Although I am almost illiterate mathematically, I grasped very early in life that any one who can count to ten can count upward indefinitely if he is fool enough to do so.” ~Robertson Davies, “Of the Conservation of Youth,” The Table Talk of Samuel Marchbanks.

In the mathematics there is a concept known as economy of symbol. That is, we use the fewest symbols possible to express an idea making the mathematics a beautiful concise language.

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