March 27, 2016-
I first became aware that there must be a faster way of doing math than what was being taught 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, and people on stage checked his answers with calculators. Before the problems could be entered in the calculators, he always had the answers. He also demonstrated very impressive memory tricks, and 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 libraries but found little about fast math techniques (this was the 1980’s and 90’s). 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 “The Trachtenberg Speed System Of Basic Mathematics”, printed in 1960. Since then, I have found other books and also ideas on the internet. I discovered techniques just by trying ideas that came to me. I give here what I consider the most useful of what I have found.
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 standard way students are taught to multiply. I understand and support the argument that it would confuse kids if they are taught a lot of different procedures to do math early on. They need to learn the basics well. While there are times when some students are eager for more, other students will not want to know more. Their experience with math has been like 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 them your own. After enough practice, the new thinking patterns will become reflexive, like an afterthought. How successful you are at learning and using the math techniques I give is up to you!
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. Students are getting limited help with this at home, because parents are lost not knowing the latest fad. 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.