How can you teach a subject like calculus to kids? Asking them to by heart the formulae would be similar to asking an ant to lift a mountain. Calculus has immense applications in real life. Hence this branch of mathematics needs to be taught in a manner in which students can benefit in their future.
Calculus studies the effect of change. It studies how a function changes when a variable on which the function is dependent undergoes a change. Calculus is broadly divided into two – differential calculus and integral calculus – and is based on the idea of limits. Calculus is largely dependent on other branches of mathematics like trigonometry, geometry and algebra. Without a clear understanding of these three branches it is impossible to ‘learn’ calculus. Of course, there is the tried and tested method of by hearting formulas which in this case, might be a higher challenge thanks to the number of formulas involved in calculus.
When teaching calculus to kids, it is best to take small easy steps. Schedule the sessions in such a manner that there is a meaningful flow of the subject. Start with Limits. Limits are used to understand the value of a function when the variable on which the function is dependent approaches but is not equal to a particular value. Of course to understand this, the student should know the basic concepts like the dependent and independent variables, functions and variables, equations, degree of equations etc.
Once the concept of limits is explained and understood, gradually start the concept of derivatives. The process of finding derivatives is differentiation. Students often grab this concept pretty easily. Once they get to know how to find the first derivative of a function, teaching them to find the second, third, fourth… and nth derivatives will be more of a cakewalk.
After differentiation comes integration. Integration is the right opposite of differentiation. Also called as anti-differentiation, integration is quite confusing. Especially if the student is weak in trigonometry, integration is going to be the student’s worst nightmare. When differentiation finds how a function changes when there is a small change in the variable on which the function is dependent, integration attempts to sum up all these changes.
When teaching the concept of differentiation and integration to kids, care should be taken to include more of real-life applications. This will not only help the students in grasping the concepts but also reduce your workload. Well, you will obviously not need to explain the concepts again and again. Agreed that calculus is a difficult subject but, when learned the proper way calculus improves critical thinking in students. They learn to link real-life situations to mathematics. Not to forget the immense ways in which science and mankind has benefited from the different branches of mathematics.