Public Science & Reference

How to Excel in Mathematics

Lots of students consider mathematics to be quite a difficult subject. For many, mathematics studies represent endless effort, time consuming and frustrating overhead.

But, those who are into mathematics, do know that once you are familiar with the details, mathematics provide satisfaction, and even joy. It is true that being good at mathematics is, to some extent, a skill you are born with, but not only.

One of the most important principles in being good at mathematics is to be up to date with the items taught at college. Since the items of mathematics are built one on top of the other, similar to building a wall, brick by brick, it is good practice for any student, no matter what his skills are, to keep up following closely the mathematics subjects being taught. Once a student ignores a single subject, it will be difficult to catch up the new subjects, which are built on top.

Secondly, although college studies include much of mathematics theory, definitions, theorems, and more, knowing the theory is not sufficient at all. Only by tackling and solving lots of problems, can one get real expertise and excel in mathematics. Practice, practice, practice: this is the name of the game. (Actually, mathematics will become a game eventually).

These two important principles led me through my studies for my B.Sc. and my M.Sc. degrees. These principles do hold for all areas of mathematics and for all science subjects such as physics and others.

Having said that, still, there must be something else. Something that will really make he difference. That will make a student a great mathematician. Regardless of the born skills, regardless of the dedication, and commitment to mathematics studies, there should be some love, desire, or passion, to gently handle mathematics theorems and rules.

Is there a better way to learn mathematics as one progresses to higher level of education?

There are many ways to learn a subject. Different people has different learning style. However, regardless of learning style, there are two particular ways to learn knowledge within any style. The first way is memory method. This way of learning focuses on remembering facts and details, and recalling them when required. The second method is to understand the underlying concepts of the facts. It is the “what” versus the “how” and “why”. Either way has their merits and demerits. It depends on the education level and complexity of the subject matters. Sometimes, a hybrid of both are necessary to reap the best possible results, especially in learning mathematics.

For elementary mathematics level, the amount of mathematical facts and concepts to be learned are marginal, and only serves to lay foundation for further advancement into higher mathematics learning. At the basic level, memory method of learning may be acceptable and manageable. But how about maintaining this way when one progresses into higher mathematics studies?

At a higher level of mathematics learning, the learning taxonomy moves into the application level and beyond. Mastery of concepts becomes an important factor in analyzing and solving more complex mathematics questions. Mathematical equations and expressions get more integrated with detailed concepts. Pure memory will not be able to extract out the true meaning of these equations and expressions. A few mathematical tools may be required to solve a mathematics problem. This combination of solving methods and concepts rendered pure memory way of learning mathematics unacceptable. The scope to cover all possible combinations of solving tools and questions is far too wide to manage. Staying firm with this facts-remembering method will only cause the performance and outcome to dwindle low. This will reduce the motivation to study and may decline towards the fearful mathematics anxiety situation.

The achievements of Muslims in the field of mathematics are extremely remarkable. A regular study of this science, like all other sciences, was begun during the reign of the second Abbasi Caliph, Al-Mansür in. the second half of the eighth century A.C. During this period the work on mathematics was exclusively done by Muslims.1 Some stimulus came from Indian and Greek works which were later translated into ‘Arabic. The investigations were carried out, and until the end of the fifth century A.H. /the 11th century A.C., nearly all of the original and creative work was done by Muslims, and even the non-Muslims wrote all the works on mathematics in Arabic. In the 12th century the Christians and Jews started the work of translation from Arabic into Latin and Hebrew, and also began to conduct research in this field. But until, the end of the 13th century no mathematical work comparable to that of Muslims could be done by the Christians or Jews.

                                    The Muslims used numerals including zero for counting in contrast with writing the amounts in words, or counting with the letters of alphabet. Thus they made arithmetic simple and applicable to the problems of everyday life in connection with commerce and trade and the division of estates and inheritance. The zero has a great importance in arithmetic. Without zero it is not possible to indicate the figures like tens, hundreds, etc. If zero is not used it becomes necessary to use a table (named abacus) with columns of units, tens, hundreds, etc., to keep each figure in its place.2 The zero was used by the Muslims centuries before it was known in the West. The Latin word ciphra for zero is of Arabic origin; the Arabic word for it being sifr, meaning empty or nil.

WHY I  LOVE TEACHING MATHEMATICS ?

Friends, Why I teach mathematics? This is a question that does have many answers, depending on   where emphasis is placed. I teach mathematics because I am fortunate enough to have discovered that it is “my thing” to do. But mathematics is worth teaching in itself, for it is a powerful, useful thinking and communications tool. Why teach mathematics? My answer is because it has relevant content, structure, and form for each and every individual in our society.

I teach mathematics because of the personal satisfactions and self realization it brings to me in a sense of social purposive ness and self-identity. I teach mathematics because its lessons in learning fascinate me. I enjoy the look of insight in the eyes of students and the sense of achievement in relating to students when they drop by to “just mention” and share their subsequent attainments.

From the prospective of ex-salesman, Insurance agent, office worker, engineer, and graduate student, I have found teaching mathematics to be most satisfying of my experiences. The small exciting bit of anticipation in the morning, the moment before entering to face a class of students, the rush of involvement, and the bits of fulfilment as well as, alas, the failures all persist day after day, year after year, as reasons why I teach mathematics.

With classes over, the anticipation, planning, preparation and development of strategy for lessons is a continuing and satisfying activity. The challenge of each succeeding day, looking forward to a small improvement, overcoming the failures and faults, and giving each day its opportunity for fulfilment are reasons why I teach mathematics.

HOW TO TACKLE THE PROBLEM OF MATHEMATICS IN SCHOOLS

Mathematics in general is construed as a subject which is very difficult and thus students fear this subject resulting in low scores. However the fact is otherwise. In order to tackle this problem, the teaching of mathematics has to change. It should be child centred.

Firstly, the child should be made to master tables up to 19. For this quizzes may be designed by the teachers by dividing the students into two groups and asking tables randomly. A game may also be designed on this and may be played on knockout basis.

Next the child should be made to have command over addition, subtraction, multiplication and division and the BODMAS rule.

It is found that the child gets confused as to whether his/her addition, subtraction etc is correct or not? For this the method of 9’s for checking addition, subtraction and multiplication should be introduced to the students (Details are available in the accompanying CD).

The teacher should divide the students into bright, average and under-achievers. The teacher should make the seating arrangement in his class in such a way that the under-achievers should be made to occupy the first two rows in the class. Each bright child should be made to sit beside each under-achiever and the average students and the remaining bright students should be made to occupy the subsequent rows. In this way the teacher will have an eye to eye contact with his/her under-achievers. Further, the under-achievers will receive a dual guidance while a class is on- one, directly from the teacher and two, from his neighbour who is a bright student. This will certainly help him to learn the topic/subject more effectively.

TEACHING OF MATHEMATICS

Every teacher of mathematics needs to be informed and convinced about the educational values of his subject. His own conviction enables him to convince the students, parents and the society. These are as under:-

a)     Practical value—He cannot do without learning how to count and calculate. Any person ignorant of it is easily cheated counting, notation, addition, subtraction, multiplication, division, weighing, measuring, selling, loving are fundamental processors of mathematics having immense practical value. It has become the basis of world’s entire business and commercial system.

b)    Disciplinary value—It trains and disciplines the mind. It is exact time and point knowledge and therefore creates discipline in the mind. It develops reasoning and thinking powers more and demands less from memory. Reasoning in mathematics possesses certain characteristics which are suitable for the training of learner’s mind. These are:-

1)      Characteristic of simplicity—it teaches that definite facts are always expressed in simple language which are always easily understand.

2)    Characteristic of Accuracy—Accurate reasoning thinking and judgment are essential for its study. Accuracy, exactness and precision compose the beauty of mathematics

3)    Characteristic of certainty of results— The answer is either right or wrong. Subjectivity or difference of opinion between the teacher and the taught is missing. The student can verify his result by reverse process. It is possible for the child to remove his difficulty by self-effort and to be sure of the removal. He develops faith in self-effort which is the secret of success in life.

4)    Characteristic of originality— Most work in mathematics demands original thinking, reproduction and cramming of ideas of others is not very much appreciated. When the child has a new or a different mathematical problem, it is only his originality which keeps him going. The discovery or establishment (derivation) of a formula or conversion of formula in one form to another is also his original work. This practice in originality enables the child to face new and challenging problems with confidence.

FALLING MATHEMATICS RESULTS- AN INTROSPECTION

It is a matter of great concern and serious consequences that the results of Mathematics in the AISSE examination at the end of class-X and AISSCE examination at the end of class-XII conducted by CBSE is falling at an alarming rate of 3 to 5% every year. Same is the case with other state boards too.

To check this shocking downslide, the syllabi have been modified a number of times, the question papers have been simplified, the evaluation of answer scripts have been made lenient, but all these efforts are yet to give better results in the subject or make it student friendly.

Introspection in this respect is an absolute necessity. I feel that such a state of affairs is because there have been weaknesses in Mathematics education today which are as below:

1)      Mathematics is taught as an abstract subject.

2)      Mathematics education is far removed from applications.

3)      Mathematics is taught as an isolated subject.

4)      There is too much emphasis on symbols; manipulation and very little on problem solving.

5)      Too much time is spent on routine, monotonous drill type arithmetical calculations.

6)      The goal of mathematics education appears to be passing examinations in mathematics and not understanding mathematics and its applications or developing the capacity to think mathematically.

7)      Instead of developing creativity, mathematics education encourages conformity to standard methods.

8)      The present mathematics education trains students to think that there can only be one solution to a problem- it make students’ thinking convergent.

9)      The present mathematics education trains students to think that there should be only one method to solve a mathematics problem-it never encourages them to think in a diversified way.