HOME WORK IN MATHEMATICS EVERY DAY: IS IT A MUST?

The child comes home back from his long day in school.
The mother asks, “What did you do in school?”
Child: Mom! We had real fun today in PE lesson, you know! And, next week we are going for a field trip to Planetarium. And......”
Mother: Ok. Ok. What homework do you have today?
Child: I have to collect pictures for my Social Science class on “tools” ... we are going to do a project on it next week!
Mother: and in maths...?
Child: No homework...
Mother: oh..! No homework in maths? What type of teacher is she? Doesn’t know a child has to work on maths everyday... otherwise how will you get practice? Ok come... I will give you some problems ... You can work on them and practise...

This is a very common scenario in many houses. All parents expect the school to give lots of homework in almost all subjects, especially in mathematics. Due to the pressure from parents, the management of the schools also pressurises the mathematics teachers to give homework every day to their students, on any cost. Some schools even have a policy that students should have maths homework on their daily schedule while other subjects are allotted one or two days for homework. Is this necessary? Does giving homework as a routine process help develop mathematical skills for the children?
In those days, we did not have technology; we had to memorise most of the formulas and multiplication tables; so we needed practice on them. But now that the students do most of their work using computers, calculators, internets and software programmes, there is absolutely no need to memorise anything. It is only the concept that the students have to take into their minds. And that comes not through heavy homework, but through projects and participation in class.
It is the duty of teachers, of course, to make the students understand a concept exceptionally clear so much that he/she is able to approach it in multiple ways. For e.g., the concept of the slope of a line can be approached through geometry as well as calculus. A problem in profit and loss can be approached through algebra or arithmetic. Adding two or more fractions can be done in different ways – taking LCM, multiplying and dividing by a common number, changing the fractions into mixed fractions and adding them etc..in fact each teacher has his/her own way of doing this concept. Hence, if a topic is done in the class and the student is given a set of problems under that particular topic then, the student gets confined to solving those problems only with that concept; he will not be able to approach them in other methods. Instead, if those problems were given to the students after completing all the topics with which they can be solved, then the student will have an opportunity to think and choose the method. While giving homework, the teacher should not title it under one topic; rather leave it to the students to choose the topic under which the problems could be solved. This way, the student is trained the skill of “approaching a problem”, which is the first step in solving problems.
Instead of giving a bunch of exercise problems to be solved at home and submitted next day, the teacher can time her class such that in the last 5 minutes, she takes a challenging problem on the topic dealt just now, engages the class in some discussions and by the bell, she leaves it to the students to finish it at home and bring it back the next day for further discussions. This makes the student, take interest, to solve the problem, instead of grumbling over it, as most of them do when given any homework.
Giving homework every day makes the child dependent on the teacher and the homework. The child should also learn to have interest in the subject by himself, so that he takes up his books or other resources and start solving problems from them. This way, he /she is not doing his learning for others but for himself/herself, again which is the most important aspect in sitting an exam.
Homework is not the only way to make the student learn the concept. A teacher has hundreds of ways to check if the student has understood what he taught yesterday. He can, at random, put up a problem to the students, give some 10 minutes in the class and check how they are doing it by going round the class room. Just one problem is enough to check this. If this is done on regular basis, the students will automatically start listening and concentrating in the class; start solving some problems by themselves from their text books and other resources; start discussing the concepts with peers during their free lessons, all of which are healthy developments, towards the learning process.
There can be seminars conducted by students, which encourages them to do some own research and improves their presentation skills. This could help them more in understanding (as peer tutoring is very effective among the students) and gives them chance to discuss openly in class, which ultimately develops their problem solving skills.
Tests, of course, are another way of making students work on the problems. But, again, tests should not be a copy-paste of problems from the text books so that the students can memorise and reproduce the answers in their papers. Each test should be challenging, and again it should not be titled under one topic; rather it should cover any topic done until that time. This way, the students will be alert and keep themselves updated.
All these things can be done without following the “every – day - homework” rule. It is just that the students should be encouraged to do self-learning and research based learning. Parents also should understand this and check their children not for homework, but for their amount of participation in class and interest developed in the subject. It would be better if parents stop complaining about “mathematics and homework” and make a big fuss about it, because this attitude of parents develop an aversion in the minds of the children toward mathematics right from their childhood age. As they grow up, this aversion grows huge into a monster and it sticks to them so firmly that no one can put any sense into their minds.

Mathematical Equations - What are they?

Usually, people are always scared of the word mathematics, especially ‘mathematical equations’. Equations always have variables and this is the main reason for the fear.
Variables are unknown quantities. They are either in terms of y or x, normally. Sometimes, variables can also be in z, r, θ and so on. Basically a mathematician represents any unknown quantity using a small alphabet. Some alphabets like a, b, c or p, q etc. will be used as constants. The basic difference between a constant and a variable is clearly seen from their literal meanings. Constants can be assigned only one value (fixed) where as variables can be assigned different (varying) values. These variables along with some constants and numbers make an equation.
An equation is simply a relation between two variables. If one variable (say, y) changes its values as a result of change of values of another variable (say, x), then y is called a depended variable, depending on x and since x takes its own values, it is called an independent variable. A formula which connects y and x, defining the relation between them is called ‘an equation’.
The simplest equation would be y = x, which says that y takes the values of x as it is. If we have an equation like y = 2x then, it means that y takes double the values of x. There can be more such equations like this, e.g., y = 3x + 4, y = 5x – 2 etc. These are simpler equations which give a direct relation between x and y and ultimately forms a straight line on a graph sheet.
More complex equations are also possible. The dependent variable y can vary inversely with x, ( y = 1/x), vary as the square of x ( y = x2), vary as the square root of x (y = √x) etc. These equations are called polynomial equations. y = sin(x), y = cos (x) etc are called trigonometric equations since the variables are related by trigonometric functions. The other equations are logarithmic( y = log(x)), exponential (y=ex), hyperbolic (y = sinh(x)) etc.
Though equations are scary, they play a very major role in almost every industry and technology. Without equations, it is impossible to even think about anything ranging from driving a car to sending a rocket to space. Even making a bicycle wheel needs an equation. Making a coca-cola bottle is done basically using mathematical equations.
The mathematical equations are not only used in mathematical concepts but also in other subject areas like chemistry, physics, biology and even literature and sports. All chemical equations are basically mathematical. Physics involves majority of mathematical equations for e.g. E = mc2. Literature sometimes needs mathematical calculations as to the relation to the number of pages written per hour/day. Of course, the motion of a football is a wonderful mathematical equation called quadratic or projectile. In biology, mathematical equations play a very important role. They are used in finding the pH values, in determining the location of genes, finding the growth rate of organisms etc. The common types of equations used in bio-technology are logarithmic, exponential, simple linear simultaneous, differential etc.
If one can understand that equations are nothing but simple relations between two quantities involved in a discussion, then there is no need to dread this concept. It starts with our basic everyday life activity. One can make lots of equations every day. For e.g. a mathematical equation can be formed between the days and the temperature. Every industry needs equations to chart their progress and profit/loss. There is no business without mathematical equations involved. Even for cooking, in every house hold, one needs to interpret the ingredients to his requirements using an equation in some way or the other.
All equations can be graphed for better understanding. Graphing an equation gives a good perception of the equation, same like a bar graph or pie chart in statistics gives a better understanding than a table of values. Usually the dependent variable is taken on the y-axis and the independent variable is taken on the x- axis. For example, a biologist draws the graph of an equation relating to the growth rate of particular bacteria in an organism. It will be easy for him to interpret the results and their consequences through the graph than just by looking into the equation. A steeper curve will be more alarming to the biologist
Presently, many softwares have been developed to interpret the data and make an appropriate equation which will satisfy the given data. This is very helpful, since sometimes it is humanly impossible to interpret certain data like distances of planets from the sun etc.
Hence, mathematical equations form part of our life and it should be taken as an interesting and essential concept, and not as a frightening, evil spirit. Smarter people can solve any problems in life if they can interpret the situation and make an equation out of it. Though solving equations is another major concept in mathematics, making an equation by itself is considered as a very first step to solve many problems. Making equations from a given data is usually called ‘modelling’ in mathematical terms. Henceforth, we can call an equation, a model, if it gives less terror!