Fundamental of Mathematics for Secondary and Senior Secondary level

Secondary and Senior Secondary level

Secondary level is the stage where mathematics comes to the students as an academic discipline. It is a stage where students begin to perceive the structure of mathematics. Mathematical terminology gets sophisticated and the concept of proof becomes the central to curriculum. The new branch of mathematics Trigonometry and Co-ordinate geometry get introduced. The working of secondary level is somehow based on the learning the concept of primary and upper primary level. Mathematics at this stage is totally based on concept and reasoning. The theoretical part of mathematics begins and students find it irritating. A bigger question now arises: - What does mathematics really consist of? Mathematics in secondary and senior secondary level consists of Axioms, Theorems, Definitions, Theories, Formulas and Methods. Mathematics could surely not exist without these ingredients; they are all essential. Now the question is what a secondary student should do to enhance his mathematical skill. Polya says – To a mathematician, who is active in research, mathematics may appear sometimes as a guessing game; you have to guess a mathematical theorem before you prove it, you have to guess the idea of the proof before you carry through all the details. Mathematical facts are first guessed and then proven. If the learning of mathematics has anything to do with the discovery to do problems in which he first guesses and then proves some mathematical facts on an appropriate level.

• The student needs to integrate the techniques and basics learnt at the previous level.

• Students at this stage should have practical knowledge of why this and why not this. Reasoning helps to retain the learning for long and you not only understand the principle of mathematics but also understand its practical application.

• Students should have the knowledge of finding square, square root, cube and cube root of any number. It is also expected from the student in secondary level to have memorized the square up to 50 and cube up to 30 so that calculation can be done with ease without error. If possible learn the fourth power and fifth power up to 5 of first 10 numbers.

• They should learn some technique that can help them to calculate speedy. There are ample books available in market which will prove beneficial in order to calculate faster. Vedic Mathematics is now a popular book used by students for fast calculation. The best part of learning some trick to do arithmetical calculation faster is that you save ample time in your examination and the chance of your doing right calculation increase. Besides that student should also learn method to counter check calculation so that the chance of error is avoided. There is one simple and sophisticated technique to counter check the calculation in seconds. The method CASTING OUT NINES method will be beneficial to students in checking the calculation.

• In geometry, first learn about different shapes and its properties. Since the geometry of secondary level is highly based on some theorems so it is advised to students to learn the important statement of theorems so that they can write the statement or name of the theorem in proving a geometrical proof.

• Word problem is another area that needs to be addressed. Understanding mathematical language is equally important to do word problem. So before going through the exercise learn the most frequently used mathematical terms.

• Solving algebraic problem is considered a tough task but I have noticed students performing well in algebra once they understand the language of the word problem. Confusion creates when you don’t remember the formula to be applied at the appropriate problem and look for another way of solving the problem. Algebraic problem may be turned into a joyful game once you understand how to proceed with the problem. So before doing the algebra, learn algebraic identities, get mastery over understanding mathematical language of the problem.

• Trigonometry is introduced in Class 10th in India and students feel uneasy when they solve the problem or prove the identities. You must understand the fact that Trigonometry is the backbone of mathematics in senior secondary level. If you are not good at Trigonometry in secondary level, you will have baskets of problem as Differential and Integral Calculus taught in class 12 can’t be done without clear understanding of Trigonometry. In trigonometry, you must learn the formulas based on trigonometric ratios and understand the principle on which the finding of different angles such as 0, 30, 45, 60 and 90 are based so that when you go in class 11, you can extend these principle in finding the value of different angles such as-120, 135,150,180,---360 and more.

• Last but not the least, at the secondary stage; a special emphasis should be done on experimentation and exploration. Make model and visit mathematics laboratory whenever possible. Mathematics can’t learn alone by merely learning formulas until you master mathematics by practicing. This practical aspect of learning can be achieved only if you make mathematical model, play mathematical brain twister and visit mathematical laboratory to understand the mathematical concept with the help of diagram and mathematical shapes kept in laboratory. Activities in practical mathematics help students immensely in visualization.

Dr Rajesh Thakur
rkthakur1974@gmail.com