| In continuation of my series on arithmetic, I present | | | | which when germinated, leads to negative attitudes |
| here a topic that was one of the cornerstones in my | | | | toward mathematics and ultimately crystallizes into |
| book "Arithmetic Magic." To fully understand how this | | | | self-doubt, fear, and dread of this most wonderful |
| concept aids one in arithmetic operations, we need to | | | | subject. The consequences are truly disastrous as |
| lay some foundational ideas first. The "Quick-Add" is | | | | many students I have worked with realize--after I |
| an enormously valuable tool to help children master | | | | healed them of their mathematical ills--that they were |
| quick arithmetic, particularly applied to summing | | | | actually good at math. Imagine what better problem |
| numbers. Today the calculator has crippled even the | | | | solvers we would be in general if we had math on |
| ablest students. Hardly a one knows his fundamental | | | | our side rather than against us! |
| multiplication facts, as the omnipresent calculator | | | | Let's return to the idea of complements. In the 8 + 9 |
| does this operation for him. This situation is | | | | example, we see the sum is 17. How much faster |
| understandable, and a comparison I can make is one | | | | would a child come up with the answer 17, if I said |
| regarding remembering telephone numbers. Since the | | | | "What is 10 + 7?" Now the careful analysis of the |
| ubiquitous cell phones store numbers, I no longer | | | | difference between 8 + 9 and 10 + 7 reveals some |
| memorize people's numbers as I have no need to. | | | | very interesting things, and shows how the circuitry |
| Analogously, students no longer can add or multiply | | | | of the brain capitalizes on some very important |
| because the calculator does it for them. This is a | | | | mathematical facts. Let us examine these. It is indeed |
| problem for the following reasons: 1) not mastering | | | | true that 0 and 1 are two very special numbers, but |
| arithmetic leads to problems in mathematics down | | | | for addition, 0 is the number whose special property |
| the road; 2) not being able to add or multiply | | | | applies here. The number 0 has the "Additive Identity |
| engenders frustration when doing basic homework | | | | Property." This simply means that 0 plus any other |
| assignments; and 3) lack of doing = future lack of | | | | number yields the given number. That is 0 + 5 = 5; 0 |
| doing, which further increases the chance of | | | | + 4 = 4, etc.(From an addition perspective, I guess |
| mathematical illiteracy. | | | | one could say that 1 is special in that adding 1 to any |
| The Quick-Add method gives students a viable | | | | number is quite intuitive as we are only incrementing |
| alternative to performing quick sums without the aid | | | | said number one unit: thus 8 + 1 = 9--you get the |
| of calculators or pencil and paper. This method is | | | | idea.) |
| based on the idea of "complements." The word | | | | Now complements of a number are those numbers, |
| "complement" means "to complete," and this is | | | | which when added to the given number, yield a sum |
| exactly what these numbers do. A "10-Complement" | | | | of 10. For example, the 10-complement of 8 is 2, |
| completes the 10; a "100-Complement" completes the | | | | since 8 + 2 = 10. The 10-complement of 3 is 7, since |
| 100, and so on. Why this idea is so useful is that it | | | | 3 + 7 = 10. How we tie the concept of complements |
| aligns itself with the simplicity inherent in the metric | | | | to the Quick-Add is as follows: in analyzing 10 + 7, |
| system, in which all units and measurements are | | | | we rewrite this example as 10 + 07. We insert a 0 in |
| based on the number 10 and its multiples. To begin to | | | | front of the 7 as a placeholder for the empty "tens |
| understand this idea, let me present the following | | | | column," and to bring the numbers into parallel |
| scenario: If I said to a child, "What is 8 + 9?", and | | | | structure. Now let us examine how the brain circuitry |
| wanted a fast answer, the child would probably start | | | | works in doing 10 + 07. The brain performs 1 + 0 in |
| and stumble, resorting to counting on his fingers or | | | | the "tens column" and 0 + 7 in the "ones column," |
| trying feverishly to reckon the sum. Granted, there | | | | thus capitalizing on the "Additive Identity Property" of |
| are those children who are quick with this type of | | | | 0. This is in fact a "no-brainer." Therefore, our |
| thing and, rather fast, can come up with the answer | | | | strategy tool for addition will be to convert addition |
| of 17. My focus, however, is not on these children. | | | | problems into their associated "Quick-Adds." Once |
| The healthy have no need of a doctor. My focus is | | | | done, this simplifies additions enormously. |
| on the children who struggle with basic arithmetic | | | | Stay tuned, as in Part II I will go into much more |
| operations and experience tremendous frustration: | | | | detail about this whole procedure. |