Algebra has been bugbear for several students since time immemorial. Especially by Class 12, algebra is almost like an inscrutable monster with tentacles going into every other topic in the syllabus, whether it be trigonometry or calculus or even geometry. So, although algebra as a topic has 13% weightage in the Board paper, its actual weight is much more, for its understanding becomes critical for many other mathematical areas.
The fact is that algebra was devised to provide simple solutions to complex problems which otherwise would have taken a lot more effort to solve. Let’s say that a car consumes Rs 300 worth of petrol a day, and if the question is about how many days will it take for a budget of Rs 5000 to be exhausted, then algebra comes in with the unknown quantity, ‘n’ days, which has to be found out. This is the case of a single variable. What if there are several variables involved? Let’s say that a combination of a car and a motor-cycle (Rs 50 per day) can be used, but there are specific days on which the motor-cycle is not available, and there are specific locations where the car will not go. This is getting a little complicated, and here is where algebra chips in by using multiple equations leading to possible solutions.
Often the real problem is with the way math has been taught in our schools. If math is taught as just math, in other words, as a set of abstract concepts, terms and operations, students lose interest, or begin to look at it only as a set of problem sums which must be solved only for the marks. Many a math teacher teaches algebra as sets of abstract terms. They start with linear equations in one variable and go on to two variables, and then multiple equations with multiple variables, mathematical progressions, and so on. Each topic is taught divorced from the real world applications where these concepts are applicable, thus separating learning from real life, and taking the relevance out of math. The right way to teach is to try and link everything that is taught to applications in our daily life. So arithmetic progressions could be about figuring out the taxi fare applicable for a certain number of kilometres of travel, and not just a(n)= b+(n-1)d.
One of the effective techniques to solve problems in algebra, or any other area of math, is to represent the problem in different ways in order to better visualise the problem. So an algebra problem can be represented algebraically in symbols or verbally in words, or numerically in tables, or visually in graphs, or geometrically in pictures. This multiple representation also helps students who have different learning styles. Those who are visually oriented may easily understand the expansion of (a+b)square when it is presented as a geometric figure:
We know that ‘(a + b)² = a² + b² + 2ab, but rather than having to treat this identity as something to be rote learned, try looking at it geometrically as in the following diagram.
When you look at it visually (see diagram), it’s very simple. The same type of representation can be used for (a + b + c) square or (a + b) x ((a - b) and so on. Explained well, or understood in simple terms, algebra need not be the terror it’s made out to be.
The writer is founder & director, Second School Smart Tuitions