“The Lost Art of Using Your Memory”

Many of the students I work with when tutoring them in mathematics struggle with basic math that I’m sure they learned as children.  Simple Addition, Subtraction, Multiplication, and Division; are skills they ought to have a good handle on long before they reach the High School level, but many do not.  Why?  What is the problem with students today?  We’ll learn the answer in just a little bit.

When my students have to stop and use their brains to figure out a basic math problem I hear over and over again, that they don’t know how to do it.  They did a few years ago, but now they don’t.  There’s no reason for this as far as I can tell, except for this basic explanation, “If you don’t use it, you lose it!”  They’ve become so dependent on using calculators they’ve forgotten how to use their own brains. 

Therefore, to try and counter the effects of this problem when I am tutoring my students, I have them do as much calculating in their heads as I can.  Whenever they try to use their calculators to do simple math they ought to be able to do without I stop them and have them work through the problem using what they don’t know they still know.  They get frustrated to start with, but after they find out they can still use their brains to do most of the math they start to develop a sense of self-confidence they haven’t really had in quite awhile.

 “The Greatest Calculator you will ever have,

Is sitting on their shoulders!”

When I was in school we didn’t have calculators to use and we managed to get through math problems tougher than the ones they are doing today.  I remember coming into class and my teacher asking us, “What’s the square root of 3!”  “1732”, we’d shout back, (or 1.732).  The next day, he when we would come into class again he would shout, “What’s the square-root of 2!”  “1414”, we’d shout back, (or 1.414).  Another trick he taught us was that 1732, was the year President George Washington was born.  So, you can imagine after a couple years of this we had those two figures memorized without too much trouble.

The same went for working with pi (π) or 3.14, we either had to leave problems in terms of π or use 3.14 to complete our calculations.  Not having calculators, we had to do our math the long way relying on our memories for much of the calculations we had to do.  All of us knew our x’s tables, and most could do division nearly as easily.  We didn’t use tables, or slide-rules (early manual calculator), simply because we were so use to using our brains for doing the calculations it wasn’t necessary to have any outside device to help us.  Since we never stopped using what we were taught in our early years of schooling, we never loss that particular skill.  There-in is the Secret to having a good memory.  You have to use your memory to keep your memories fresh and ready to be recalled at a moment’s notice. 

REPETITION IS THE MOTHER OF KNOWLEDGE

Using your memory is like exercise and practice.  The more you practice a particular skill, over and over, again and again, builds strong memory pathways that allow for improved technique.  It is said, that “Repetition is the Mother of Knowledge” and I have to agree with that strongly.  Athletes, practice their skills over and over until they master the techniques the need to succeed in their sport.  Surgeons practice their surgical techniques on cadavers until they master their techniques, hopefully preparing them for actual surgery on living patients.  Practice doesn’t ever make perfect however; but, it does make for improvement.

Many times I hear students say, “They can’t do it” or “I’m just not good at math”, I have to stop them and point out their negative attitude they keep expressing.  By saying these things out loud to reinforce the attitude they’re not able to do math and it reinforces their need for using a calculator.  My cure for this problem is to have them say out loud, “I love doing math!”  “I’m great at doing math!”  Over and over again to build new positive thought pathways over the old negative ones.

I explain to them that by repeating this simple statement to themselves that they create a positive frame of mind conducive to establishing good soil for planting the new memories they need for doing math.  It’s equivalent to opening the doors and windows of your home and letting the light come in.  All of a sudden learning math becomes easier for them!  I get the biggest kick out of their response when they realize their homework went faster and they actually understood what they were working on.

When it came time to prepare for their Regents Exams, I printed off several old exams from previous years, and we worked our way through them one at a time.  I explained to them, that on average during the exam, they will have ten minutes to complete each math problem.  At first that didn’t sound like much time for them until we began the test and I had them do their work solely in their heads.  I had them doing so much of their work without the use of their calculators that by this point I knew they really didn’t need them.

Right off the bat, with the first problem, I told them to just look at the problem, and tell me the answer.  Both my students trusted me and after looking at the problem for just a couple seconds, told me the correct answer.  Then we went onto the next problem for which I had them do the same thing, “Just tell me the answer, don’t use your calculator or even figure the problem on paper.”  Once again, they both told me the correct answer!

I reminded them that they had ten minutes to complete those problems that they just finished in less than a minute.  During tests they both struggled with getting over stressed, worrying about whether they would have enough time, and this was a good lesson for them.  I asked them, “Do you think you’ll have enough time, now, to take your exam?”  At this point they just laughed and said, “Yes.”  “So, relax when you go in for the exam.  You have an advantage most of your classmates don’t have, the ability to do your work in your head.”  Sure, they still have to show their work, but as I explained to them, “Won’t it make things easier when you can know the answer, before you start writing?” 

On test day, they both finished their work in less than two hours, a full hour less than they were allowed.  Not only had they been looking forward to taking their exam so they could prove themselves, they were ecstatic with the grades they received.

1. Watch/timer function. Some people are lazy to wear their watch and use cell phone instead. They also use cell phone as an alarm clock by setting the alarm feature provided in the cell phone menu. As we all know, alarm feature in a cell phone has many sounds to get us up from sleeping. Stop watch may also support you in your exercise.
2. Calendar-schedule function. Besides time function, cell phone has calendar-schedule feature to organize your activity. You can insert a message as a reminder so that you will never forget you schedule.
3. Calculator function. We use calculator feature to solve simple calculation like addition, multiplication, deduction, and division.
4. Computer function. Modern cell phone has computer function like internet browsing, sending and receiving email, and social networking. Some cell phones even have spreadsheet and word processing application to help your business.
5. Games feature. While waiting for a bus, train, or somebody to pick us up, we spend our time by reading book, newspaper, playing a game or just sight seeing around us. Most cell phone has interesting games feature to play so that you will never bore any more.
6. Image or video camera function. You can use your cell phone to capture an image or take a motion picture of unforgettable moment or sudden event that may happen once in your life time. You can also play the image result at the same time without using additional devices. If you are not satisfied, you may re-take the picture.
7. MP3 Player/Voice recorder function. Cell phone has music feature to turn you favorite songs on. Voice recorder feature is used to record speech, interview, or sound that make you are interested in.
8. TV/Radio function. Some cell phones have television or radio feature so that you can watch and follow the news anywhere anytime.

The eating habits of AmericansAmericansare responsible for 5% of total emissions of greenhouse gasesgreenhouse gases in the world. If we could make them citizens understand the difference between the different foods you can consume, and replace the more polluting alternatives which can be just as tasty and attractive, this figure could be reduced significantly.

Meat and dairy products, fruit and vegetables out of season, consumption of fossil fuels by conventional agriculture, transport of food from all corners of the planet, its storage to the point of sale … All these factors make for a polluted world.

Bon Appétit Management Company(BAMC) is a catering company that provides catering services to businesses, universities, schools, events … The firm, which has over 400 stores in 29 states, offers dishes based on local and seasonal ingredients, harvested in a radius of 150 miles. The company, which has spent years promoting responsible decision-making power, and has been honored numerous times for its environmental contribution, has developed the calculator for the impact of food. 

Assuming that we can all contribute our bit to create a better world, and that “we are what we eat, BAMC has created a tool for the user to check the impact of their food and make more environmental-friendly decisions when shopping for groceries. 

The calculator, based on the results of several studies on foods available in North America, aims to educate the public about how your shopping cart may be part of the solution  to reduce   environmental footprins. 

With this calculator, created from scientific data and analysis, foods are grouped into three main categories: 

1) Create your own menu (Make Your Own Meal), where you can select the ingredients one by one.

2) Menu Items, from which you can select a complete meal.

3) The third option, Sample Meals, including examples of foods that can be eaten for breakfast, lunch and dinner, and suggests sustainable substitutes. 

The user must drag the ingredients to the pan to compose your daily menu, change the size of its portions, and learn about the environmental impact of their diet. An index of around 4,500 points a day is considered a diet high impact equivalent to 3 tons of CO2 emissions per year (one point equals one gram of carbon dioxide equivalent, CO2e). 

In addition, the calculator offers a number of directions for improving your environmental footprint, such as focusing on local seasonal food and reducing your consumption of meat and cheese, avoiding the consumption of processed and packaged foods, and other helpful tips.

Evolution

The abacus evolved along with the science of mathematics. In 1800 BC a Babylonian mathematician developed algorithms to resolve numerical problems with the help of the counting device, and the secrets of the new super-computing machine soon spread throughout the civilized world. The empires of China, Japan, and Rome used them. An early engineer in Egypt drilled holes in the pebbles and strung them on wire. This innovation, about 2,500 years ago, generated a huge increase in the speed of calculation.

The wire-frame abacus became more sophisticated in China, where it is called Suan Pan, and later in Japan, where it is called Soroban. In Europe, Pope Sylvester II devised an efficient abacus at the end of the first Millenium (1000AD.) Unsubtle Occidentals opted for a simple design, with one tier, and an empty wire to represent zero. The current European form of the abacus is Russian, with 10 beads in ten rows.

The Modern Abacus

Bead counters are still being manufactured in the USA and other countries. A beginner’s model has two rods of 9 beads, and is for children between the ages of five and seven. The Cranmer model, made of black and white high-impact plastic is a pocket-sized calculating device like ones used in Japan, and there is a coupling device that will link two Cranmers together for experts, and a large Cranmer designed for persons with limited manipulative or visual skills. All three abaci come with thoroughly modern video training tapes. The abacus is still part of the school curriculum in areas of the Far East, and is still used as a calculator.

Legacy of the Abacus

From small business deals between single individuals to the economies of large sophisticated civilizations, the humble abacus helped pull together the economic sinews of much of mankind for a long time. It allowed us to manipulate numbers and become as familiar and confident in their use as we are with words. It provided us with a solid stepping-stone to higher mathematics, and is a fitting ancestor to the powerful computer network that spans the globe today.

The abacus today survives as a usable tool, a collector’s item, an art form, and a reminder that our supercomputers still have viable ancestors that emerged at the dawn of civilization. A couple of links to this remarkable invention appear below.