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Calculations Without Calculators

by J. M. Gilmour

158 pages; Black coil; illustrated; catalogue #03-1195; ISBN 1-4120-0827-1; US$24.00, C$29.95, EUR19.50, £13.51

Dispel your FEARS of NUMBERS!

Eliminate Frustration, Embarrassment, Anxiety, Regret, Stress.

Feel SAFER with NUMBERS!

Improve your Speed, Accuracy, Focus, Endurance, Recall.

GIVE YOURSELF A SKILL TO ENJOY FOR LIFE!

Read more!

about the book      about the author      sample excerpts      catalogue info

About the Book We were all happy when we went to school and learned about numbers with our "toys", fingers, coins, marbles, blocks, etc.. When they were removed, we had to look at the board, watch the teacher do things with numbers (+, -, x, ÷), and we faithfully copied them with pencils and paper, even though we had no idea where most of the numbers came from, because our calculating tools had been taken away, and we had nothing with which to replace them. We were lost, and this was the start of negativity towards self and numbers. The education system has assumed for generations that we all automatically make this transition from the physical to the abstract. Most of us don't!! As a result, our experiences with math, in school and beyond, brought Frustration, Embarrassment, Anxiety, Regret, and Stress to our lives. It is time to get rid of these FEARS, and you do so by mastering the system described in this book. You will learn to calculate by making physical movements on a visual grid. Preparation, Understanding, Learning, and Application make PULA, and that is the key to your success. Preparation entails eliminating all negativity, and believing that you will surely succeed if that is what you want to do. Understanding every word you read and every diagram you see is essential. If you don't, it is not your fault! Try again, and, if necessary, ask for help. There is no such thing as a stupid question. Learning takes concentration and effort. It is much easier to learn things you do understand than to memorize things you don't understand. Application happens because you believe in your new knowledge. There is no rush to master the system. When it does happen, you will have changed your FEARS into feeling SAFER with numbers. If SAFER stands for Speed, Accuracy, Focus, Endurance, and Recall, these are much more positive attributes than what FEARS stood for. Your mastery of calculating on the grid gives you the chance to TRAIN your BRAIN in these five areas. If you give yourself this GIFT for LIFE, you will do everything at a greater speed, more accurately, with greater focus, for a longer time, and remember it all. The book consists of nine very easy lessons, a set of blank grids and tables you are welcome to copy, eighty exercises, and a book of answers to selected exercises. There is no age limit. This system can be the first place where children see and learn about numbers. At the other end of the age scale, you are never too old to learn.

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Stories

There are thousands of stories which could be told about calculating skills and brain training. Here are two of my favourites:

"Over a 10 week period, I spent approximately 30 hours with a Grade 7 French Immersion class in a local Elementary school. During this time I taught the students my system, and, at the request of their teacher, 3 topics from Math 8 (Order of Operations, Integers, and my introduction to Algebra which uses Expanded Exponential Form as its base).

"At the end of this time I gave them a test consisting of 6 pages of work. 3 pages were on my system and one on each of the grade 8 topics. The students were given one hour for the test, which contained almost 1000 calculations. High school math teachers, who saw the test, estimated it would take at least a whole day to complete.

"Of the 22 students who wrote the test, 10 answered every question, the total number of errors made by the whole class was 311, the total number of omissions was 1043, 688 of which were accounted for by 3 students (whose marks on work done were 99.7%, 98.6%, and 96.9%. They obviously needed more time.). The average mark on work done was 97.5%. The average mark including omissions as errors was 90.9%.

"The class teacher was very pleased with the results of his students' efforts."

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"In my last year of teaching in Scotland before emigrating, I taught a class of 42 first year boys. The curriculum in Scotland required covering 2 text books in each of the six years of high school. With my principal's blessing, we spent the first three months of the school year working on calculating skills, speed, accuracy, focus, endurance and recall, and on self-esteem and confidence. This, of course, put us far behind all the other first year classes. However, as a result of all the brain training we had done, not only had we completed Books1 and 2 by the end of the school year, but were well into Book 3.

"At my request, my best friend in Scotland tracked down one of the students in the class. I was curious to know if he remembered anything about that class. I was amazed to discover that he felt that that class had given him skills which he has used and developed throughout his life, and in his work as an engineer. He was extremely pleased to hear that I had written a book on calculating skills and brain training."

- John Gilmour

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About the Author The author was born and educated in Scotland, where he taught mathematics for six years before emigrating to Canada. Another 31 years in the classroom culminated in his retirement in 1999. Since then he has worked on his book "Calculations Without Calculators", and very successfully done presentations on its contents in classrooms and at math conferences in several countries.

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Excerpts

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MATH IS EASY

Marvel at your Memory.
Amaze yourself with your Accuracy.
Train your Brain.
Have Happy Math Health.

Invest in your Intelligence.
Secure your own Success.

Expect to Excel.
Acknowledge your Ability.
Seek mental Speed and Stamina.
Yes, this book is for YOU!

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Testimonials

"This book, in my opinion, encapsulates the basis of a very important and fundamental aspect of mathematics -- mental arithmetic. I had the good fortune to be in Mr. Gilmour's math class back in the early 70's in high school (every day for 4 years!), and my personal experience was a totally positive one. It was by far my favourite class, one that I greatly looked forward to each day.

"For me personally, the benefits gained from this focus on calculating skills and brain training learned as a teenager, are immeasurable. He helped sharpen my concentration skills and gave me an ability to perform math operations with significant speed and proficiency. He provided me with not only a life-long passion for Math but also, more importantly, a remarkable self-esteem based on this wonderful brainpower. Math became easy and it was a whole lot of fun!

"How delighted I am that a book such as this is available for a future generation of "brain-trained" individuals who will undoubtedly flourish in maximizing their mental capacity for math as I did. I didn't realize the true gem I was given until my 13-year-old son was experiencing difficulties in Math (an understatement at a 45% grade). Imagine my surprise at the amazing recall of all these skills and information that I was able to pass on to my son 30 years later! I now tutor Math to high school students and our first rule is "Forget the calculator!". In time they are amazed at their own ability for speed and accuracy in mental math, and based on Mr. Gilmour's convictions (and now mine) that Math is enjoyable, it has turned the most resistant student into one who sometimes can barely hold their enthusiasm.

"There is no doubt in my mind that highly developed calculating skills and brain training give students the extraordinary confidence and self-esteem so crucial to success and learning. This is the best way to popularize Math among students and, more importantly, to develop overall mental agility.

"I personally reaped the benefits of this system, and I am grateful for having attained these skills for life."

- Coreen Zubersky

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"Mr. Gilmour was my Math teacher every year of my high school career from 1971 - 75. The mental math skills I learned from him are priceless. I use them in the grocery store, on the golf course, and to do the complex calculations involved in drug doses in my job as a chemotherapy nurse.

"I get a lot of pleasure from my speed and accuracy, and confess that I enjoy impressing my friends with these skills. Most of all my calculating skills have given me high self-esteem and confidence, and provided me with an invaluable life skill."

- Cindy Sellers

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"I have worked with the concepts from this book for many years with my students from grades 5 through 7. The results were surprising and fantastic. I was amazed at how excited the students became while working with their grids and having challenging questions in multiple operations for the whole class.

"I would definitely recommend this method of working with numbers for any student strong or weak. All of my students loved doing math, and I saw outstanding improvement as soon as I started to teach them the strategies. One proof of this was seen when I realized that 70% of the students from one of my grade 5 classes ended up taking Math 12 seven years later. This number is extremely high as in most years I would have about 25% go on to Math 12.

"I attribute this to the combination of improving calculating skills along with training the brain, which has allowed these students to develop high confidence and self-esteem while doing math.

"I strongly feel that it is a good idea for students to start learning this system as early as possible."

- Mike Weeks
District Principal, Howe Sound School District #48, Squamish, B.C., Canada.

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Catalogue Information

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