Insights into the world of “broken math”
My wife is a certified math teacher, and I am a web developer by trade. Initially this statement seems rather bland and not out of the ordinary. But when I say the result of this combination is: “I subtract when I add,” people tend to look at me funny, first and foremost my wife!
1 + 1 = 2, that part doesn't change, what does change is when you cross a power of 10. For example, most people would look at the problem: 6 + 7 and count up on their fingers (or in their head) from seven, (8, 9, 10, etc…) ending up with 13. I don’t.
When I see this problem, I think 7 is 3 less than 10 so 6 – 3 = 13.
Welcome to the world of “broken math.” Broken math is math that works, but they don’t teach it to you in school. These are the shortcuts that we create in our minds using mathematic principles in a non-standard way to get the correct answer. Here is another example:
If I am baking and the “1 Cup” measuring cup is dirty and I need to measure 2 cups of something, I simply reach for the 2/3 Cup and dump three measures in the bowl. “How does that work?” you ask. If you take the denominator (in this case 3) and pour that many in the bowl, you will get the numerator (in this case 2) of the size of your measure (in this case cups). This works with all fractions. (My wife explained it this way: 3/1 * 2/3 = 2. I just know it lets me continue baking bread when the ideal measuring cups are dirty.)
Another reason they don’t teach broken math in school: it is a lot more complicated to explain.
When most people need to count something, they usually start at 1. When you start working with computers, this is not necessarily true. One type of variable (called an array), begins counting at 0. So, if I am writing a calendar program for example, 0 = January, 1= February, and so on. If I want to loop through the year and do something to each month, I start my count at 0, not 1. (I believe this is leftover from Binary, but I’m not 100% certain on that. If so, computers use broken math too!)
Am I wrong for using “broken math” to get through the day? I don’t think so. What I do believe is that when a student asks a teacher “When am I ever going to use this?” they should think twice about the math they already do on a daily basis. You can’t fill up your car without knowing subtraction (and if you do, you learn about negative numbers real quick!). You get a job because of addition, and you invest because of percentages. I may not use math the way it was taught out of a text book, but broken or not, I use it every day.