March 27, 2016 –
I first became aware that there must be a faster way of doing math than what was being taught in school when attending a class at the University of Alabama. My calculus teacher would stand back from the board, pause a moment, and say “…and that would be -“. It’s funny when I look back now, that though we were amazed he could do this, no one asked him how he did it.
Later, I saw another example of fast math when I took a date from my psychology class to a magic show. The magician got people from the audience to call out numbers for him to multiply in his head, after people with calculators were called on to the stage to check his answers. Before the problems could be entered in the calculators, he always had the answers. After also demonstrating very impressive memory tricks, he told the audience something that I found amazing- that he had only finished high school and did not consider himself smart. He said he sought out and learned techniques that made it all possible.
After this, I searched but found little information in local libraries about doing fast math. Convinced that there were other, faster ways to get math answers, I became angry that the educational system did not teach something so important. How many tests had I taken in which time ran out before I could finish and check all the answers? I vowed to share any techniques I might learn with anyone interested.
Several years later, at a used book sale in Atlanta, Georgia, I stumbled across a copy of “The Trachtenberg Speed System Of Basic Mathematics”, printed in 1960. Since then, I have found other books and also ideas on the internet that have helped me in my examination of math relationships. I have discovered techniques just by trying ideas that come to me. I give here what I consider the most useful of what I have found. They should enable you to be successful enough in math that those who see you using it will sit up and wonder how you do it. (Like I have done!)
April 10, 2016 –
“If the only tool you have is a hammer, everything is going to get a lick.” That is a phrase that often comes to mind when I think of the one way students are taught to multiply. I understand and support the argument that it would be confusing for most kids if the are taught a lot of different procedures to do math early on. They need to learn the basics well. However, there are times when some students are eager for more. At the same time, other students don’t want to know more. Their experience with math has been like the training in a flea circus- they’ve bumped their heads on their limits so much that they feel defeated and unmotivated, and their failures have effectively trained them to no longer try. A person’s attitude approaching a problem is important, as is evident in this quote by British mathematician John Baines: “The first step toward the solution of any problem is optimism”. Sometimes it takes showing a neat trick or two along the way to “prime the pump” of interest and capability. With encouragement, appropriate tools, and practice any student can learn to like and do better in math.
It is worth mentioning that techniques to help with math should be practiced and learned before it is necessary to use them. Once, to help me remember all the facts for a big test, I used precious study time reading a book that a friend recommended called “The Memory Book” by Harry Lorraine and Jerry Lucas. It didn’t help. In my test preparations, my mind wasn’t properly focused on the subject but on the struggle to handle information in unfamiliar and often awkward ways. Though information in the book was very helpful later, at this time I should have put all my effort on studying in a more focused manner. What I learned from this was that to be useful, techniques for memory (or math) must be learned and ready to use before there is a need for them.
Review and practice these techniques to make make them your own. Actions requiring effort become reflexive (like an afterthought) after enough practice. In ball practice you are taught that to cut right or left quickly, you should plant the opposite foot and push in the direction you want to go. After deliberate thinking and possibly stumbling at first, you get the hang of it and execute it quickly and to great benefit without thinking. Likewise, a tricky pattern or beat on the guitar or drums may take days of deliberate practice to get down, but then it becomes natural. Practice to make math techniques not an effort but an afterthought. How successful you are in learning and using the math techniques I give is up to you!
December 18, 2016 –
I am very exited to see so many people around the world coming back to this site again and again to learn math techniques. Improvements will be made once math notation difficulties are solved. I now have another site that examines trees I see around Atlanta, Georgia. You may check out this website at chasingtrees.net. I wish you much success in your efforts, and I welcome your comments.
August 23, 2018-
When I created this website on math shortcuts, it was very hard to find information on the subject. I am pleased to find that there is now much more information available. However, I am disappointed that so many different math processes are being taught to children from the very beginning, thinking they are an improvement over basic techniques. Parents, and others not informed about the latest educational fads, are losing the ability to help with homework. When I try to help children with math, I often find that they are struggling to force convoluted ways on simple problems in ways that have been taught to them. They are stuck in the struggle to find what they are doing wrong using those methods, and when shown a straight forward way to get the answer they most often respond with “I don’t care about that, I want to do it the way I was taught- that’s the right way.” In those situations, I am frustrated and unable to help. The child is frustrated and ready to give up. We are speaking different languages, unable to communicate. The bottom line is, alternative methods and shortcuts are great, but they have their place. I encourage teaching math basics that are used universally, with other methods shown strategically to provide interest and added skill.