First let us start with a simple addition problem and discover the omission. You are telling yourself, I know how to add – just wait and see. Let us begin with the classic two plus two. Seems simple enough the answer is four. Are you sure? When we are first learning the arithmetic tables, over and over we never question can we add the numbers. Take a moment and really think about the question; can we add the numbers together? If the “meaning” of the value of the two two’s are different, we cannot add the numbers. Two apples plus two oranges we cannot add the values.
The key to unlocking math is the meaning of the each value determines how and what we can do mathematically. The values have nothing to do with the mathematical operation. We can increase the value to ten apples and two oranges we still cannot perform the operation due to the meaning of the values. Only when the units apples to apples or oranges to oranges does the meaning of the units allow the addition operation.
Go look at any mathematics textbook and rarely do you see meanings or units next to the numbers. The meanings of the values are strip from the textbook. Go use your calculator, you must know that the numbers can be added base on the meaning. Or, the computer computes the numbers therefore it is RIGHT?
The control is at an early age, we are taught to memorize the addition tables and rules to add larger numbers, for example carry the one. Rarely reinforcing the knowledge that the meaning of the value determines what you can and cannot do in math. The secret to mathematics and science is to understand the meaning of the values. The meanings of the values lead us through the problem and the correct solution.