March 15, 2012

How To Tackle Mathematics By its Horns?

There was a time in my childhood when I used to hate mathematics. I hated mathematics more that Hitler hated Jews (never intending to be racist in any manner). I was so biased against maths that I used to deliberately forget maths books at home daily. I thought maths was unworthy of my concentration, so I never concentrated on it. But maths always took its revenge. Maths syllabus and course used to hide unnoticed all semester long. But at the very end of the semester it used to appear like a demon.

I had all sorts of mathematical problems. When it came to tables I always used my fingers to compute the results but my lack of belief always handed me a wrong answer. Even when I knew the right answer I was never encouraged to speak out in the classroom. I would just let the teacher tell the answer and then I would whisper to my friend saying "I knew the answer".

When I aimed at learning algebra I couldn't dissect it from the other parts of maths such as algorithm and trigonometry. When I used to give time to trigonometry, I also found algebraic calculations intermingling with trigonometry. I was like when I intended to diagnose one branch of mathematics the other parts always pinched me. I required me to device a good strategy to cure my illness relating to maths.

First of all I tried to understand what was it that was annoying me about maths in general. And I soon understood that my core concern was getting to understand various disciplines of mathematics (like calculus, arithmetic, algebra, geometry, trigonometry etc) together. This caused many difficulties and frustration. Normally I would start with a trigonometry question and when that question posed a concept of algebra I would try to consult algebraic expressions and leave that trigonometry question on its fate.This caused a wastage of time, and after a while I would lose my concentration and leave studying mathematics.

Then I changed my style. I started with the simplest questions of algebra. The reason behind starting with algebra was that algebra is basic branch of mathematics. It has many implications on other disciplines like trigonometry and calculus. So I narrow down 15 to 20 basic algebraic questions and tried to solve them on daily basis. I made it my routine. No matter even if I had to miss the other homework, doing 15 - 20 basic algebraic questions became a part of my routine. After a few weeks the very first thing I noticed was that I was not falling asleep in the maths class any more.

The next step for me was the revision session. I never knew the importance of the phrase " Practice makes a woman perfect " until I actually practised and re-practised these algebraic questions. It was the revision sessions that I started to understand the logic behind various algebraic expressions. Before now I always used to memorize the various formulas. But now that I new the logic behind it, I was quite comfortable with trying more complex mathematical questions. I could see my confidence developing.

But the best help on mathematics came from my friends, colleagues and tutors. When I started learning maths, quite often I was faced with many problems that frustrated me a lot. I could understand the point even after looking at the solution. And here is where my initiative oriented personality played its part. I was always asking from help. Many of my mathematical problems were straightened out by my friends. When I used to describe my problems to others I used to gain their take on it and this also helped me to express what I thought about those mathematical situations.

When I kept on moving forward I learned yet another beautiful trick to solve various equations. Previously I thought of mathematics as a passive activity. But now as I was gaining exposure I understood that there are many ways to phrase an equation. I rephrased many equations and develope

Now my transition to the other disciplines of mathematics was an easy one. Next I started trigonometry. I did the same thing here as well. I started with the basic and the most easy questions and attempted them twice (sometimes trice as well).

I never used an particular book for learning mathematics. I used various notes and other explanatory material written by many authors. Had I remained content with only one book, I would have found it hard to have a complete grasp of the subject. Different authors have different view points and when you consult various books it widens your mind. So I consulted various books on mathematics.

Gradually I developed another fruitful habit. Previously I was very curious on whether or not I am doing the question rightly. So I used to check the answer when I was mid-way through the solution. This was not a productive thing to do because it reduced my mental creativity, and when ever I was faced with a new type of question, I was unable to solve it. But now I changed this habit. I used to solve the question completely before referring to the answer. Even if I was unable to answer the question rightly, still I used to wait until I was finished. I noticed that almost every time I was just a couple of steps in the wrong direction. And while repeating the question I used to get it right. This helped in developing my confidence as well.

But the most beneficial activity that helped me the most while learning mathematics was consulting my friends, colleagues and tutors. Previously when I was faced with a problem it made be gravely frustration. I couldn't understand the point even when I used to consult the solution. And here is where my initiative oriented personality played its part. When I used to ask a mathematical query from a colleague, this helped me understand his/her point of view as well. It also enabled me to address my mathematical problems in a better way. Now I could answer others in a more concrete and mathematical way. Plus my increasing grasp on the subject enable me to include various suggestions and postulates in my sentences.

An even more beautiful advantage that I gained with the passage of time was the ability to solve various equations in different ways. Now I could rephrase my equations and apply different formulas to derive the same solution. I learned a very key fact that almost all the mathematical problems that involve variables can be solved by using graphs. This simple fact was very effective to understand different relationships and enabled me to exploit different paths on theoretical mathematics. Previously I thought that maths is a boring activity where only numbers are involved. But now I understood that maths was not at all a passive activity. Solving variables by graphs can be a very interesting and thought provoking activity. Such graphs could be used in every you-name-it disciplines of our daily business routines. If the appropriate data is graphically represents on a piece of paper, we can develop budgets, build productive forecasts and undertake surveys.

But I did all this slowly and gradually. I never intended to read a complete book in one go. I started chapter-wise. Sometimes even topic-wise or page-wise. The most important fact that I always kept in my mind was that I never intended to jump forward and leave a point behind. I never step ahead until my previous queries were properly addressed.

I will leave you all with a couple of mathematical tricks that might help someone (hopefully):

Trick 1:
When I was young, I couldn't make up when to use sin, cos and tan while solving right-angled triangles. I used to mix it all up. Then a friend of mine taught me this following trick.

He taught me this sentence: "Some people have curly brown hair. They prove beauty."

I did know what it meant and how it will eventually help me. But it was a great idea. Now let me teach you how it was helpful.

He used the beginning alphabet of each of the nine words used in the above sentence ( namely S, P, H, C, B, H, T, P, B) and produced the formulas of sin, cos and tan. Now all I had to do was to remember the sentence 'Some people have curly brown hair. They prove beauty', and the formulas became much much each to recall.

Sin = Perp./Hyp (Some People Have)

Cos = Base/Hyp (Curly Brown Hair)

Tan = Perp./Base (They Prove Beauty)

Use can obviously see that the bold alphabets are the initial alphabets of the sentence that I used. If you are teacher or a mother you can teach this simple trick to your students or children to memorise this basic trigonometry formulas.

Trick 2:
This trick is a bit of a smartness check trick. As a new teacher you will always be wanting to get some knowledge about the students of the class so that you can pinpoint which student requires more efforts and which student can be an asset of the future.

It is a simple trick but it checks the alertness of many individuals. The beauty of this trick is that you can also use it during flirting. It is a harmless little trick but it can attract an audience that is interest in the subject of mathematics. As a new teacher, you must try this trick on the very first day of the new session. No matter whether the class is of sixth graders or of a sufficient acquaint individuals. This can be an impression building trick.

Here is how it goes:

Imagine someone using simple mathematics to make you feel as if he/she is playing some kind of a magic with you. Just ask someone to imagine a number. Set the range from 1-100 so that you can easily do mental calculations. Lets assume that the person imagined 25 as his/her secret number. Now he/she is the only one that knows what the real number is. As far as you are concerned just let it be x. Then ask him/her to add and then subtract a few easy mathematical numbers into x.

Lets suppose you ask him to add 15 into his secret number and then subtract 10 from it. You will get as follows:

x + 15 - 10

= x + 5

Now you can find out any calculations you want him to add or subtract.... The only digit you don't know is x.

Keep making his mind work over. Keep asking him to add and subtract numbers randomly. For example ask him to add 20 further and then add 5 more and then finally subtract 17.

You will have the following resultant figure.

x + 5 + 20 + 5 - 17

x + 13

After making him do these sort of calculations for about 4 to 5 times, you should never forget that the resultant figure is x + 13. The other person knows that the answer is 38 (25 + 13). But you only know that the answer is x + 13. Now here is the trick. Ask that person to subtract the original number he thought at the beginning (which for him would be 25 and for you would be x). When he subtracts that number now he and you have the same amount of information (i.e 13).

At this point almost all the average students will unconsciously subtract 25 (or for you x) from the resultant solution.

When its done. Just ask them "Is you answer 13".

You will get some bizarre and questioning faces you have never seen before. You will get the exact attention you were dreaming off on the very first day at your new place.

Now at this point (as I give a full-stop to my pen) I will just want you to remember only one word when ever you think of mathematics. PRACTICE.