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. He always gave the answer before the problem could be entered in the calculators. 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 sought out but found little information in local libraries about doing fast math. Convinced that there was another, faster way 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 in Atlanta, Georgia I finally got my start when I stumbled across a copy of “The Trachtenberg Speed System Of Basic Mathematics”, printed in 1960, at a used book sale. 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. It should help you be successful enough in math that those who see you will sit up and wonder how you do it. (Like I did!)
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 to most kids to be 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 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 football practice you are taught that to cut right or left quickly you plant the opposite foot and push in the direction you want to go. This process involves deliberate thinking and possibly stumbling at first, and then you get the hang of it and execute it to great benefit without thinking. Likewise, a tricky pattern or beat on the guitar or drums may take days of practice to get down, but then it becomes natural. You just do it, with added skill and confidence. 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 again and again to this web site to learn. I hope to have math notation difficulties solved soon. I now have another web site talking about trees I see around Atlanta, Georgia. You may check this website out 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 now there is much information available, from many sources. However, I am disappointed that so many different processes are being taught to children from the very beginning. They are confused, and do not know the basics. Because something is different does not make it better. I could substitute the word newer for different in the sentence, but there is nothing new under the sun. Parents, and others not informed about the latest educational fad, 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 that method, and when shown a straight forward way to get the answer they most often respond with “I don’t care about that, this is what I have been taught and that’s what I am going to use.” In these 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 to provide interest and added skill.