Towards a Calculus of Education

Is there a Calculus of Education? What insight can we draw for education from what Newton called the fluxions or change? Calculus assists us to understand and study change. But it also thrives on continuity. It believes that change takes place smoothy. Everything is changing infinitesimally moment to moment. Like a movie, calculus divides reality into a series of snapshots and then recombines them, instant by instant, frame by frame, creating a seamless flow of the imperceptible changes. It has opened us to the secrets of nature as well enabled us to build our modern world.

Looking for a calculus of education may be also a study familiar to it. It is a study of change in education. Perhaps, we can take an analogy. Let’s say a dog is chasing a man. The man is running in a line at a constant speed v and dog takes a curve path and running closer to the man at the speed w. What could be the equation for the curve traced out by the dog? Let us say that the dog here stands for the student while the man stands the system of education. The equation that we are seeking is a differential equation.

A differential equation describes how a system changes its behavior as a result of ever-changing forces on it. All the pushes and pulls draw the system to be in some new condition or place, where the forces are different again. Thus, for instant, the system of education keeps changing and student has to constantly revise his/her directional heading. Calculus enables us to think about what is happening at an instant, in an infinitesimal unit of time. This means, we should be able to imagine the state or the ‘dynamic aiming’ of the student as consequence of the educational system at a instant. By solving the equation, we get the entire path that student has to follow, has followed or will follow (prediction). The whole trajectory is built of infinitesimal steps that the student takes or will take in pursuit of his education in a dynamically changing education system. We can see the journey of the student as a path of infinitesimal changes.

Isaac Newton tried to study the path of the planets around the sun by positing that they are moving under changing force of gravity. As they orbit the sun, they change the distance from it, which in turn changes the gravitational tug they feel, which then push them to a place in the next instant, where the force is again slightly different and so on. (Note the orbit of the planets is elliptical). Thus, solution for the motion of planet was contained in the differential equation. Thus, trying to solve what we might call chase problems, we may say that we are in the esteemed company of Newton.

Here, we have tried to convert the calculus of education for an individual student into a chase problem. It is challenging to think of growth or regress of the student in this way. The state of the student at any instance is different and the state of the system of education is also changing from moment to moment. We can trace ineffable patterns in time, place, as well as growth in knowledge in the life of the student. Thus, education and the growth journey of a student is a calculus of function of multiple variables. It can go up. It can go down and it can go up and down. We can see that change never stops in the field of education. To quantify growth in a gradual form, we use the power of functions like x square or x cube, in which the variable x is raised to some power. The simplest is a linear function where the dependent variable y grows in direct proportion to the variable x. The growth in education is complex may not be measured by relation of direct proportion. Growth in Education may be viewed as quadratic growth or exponential growth. Exponential growth feeds on itself and hence may be the best form to model the growth or decay in education.

This rate of change is given by what we call derivative in calculus. It specifies a rate of change as a specific time or point. It is symbolically represented as dy/dx. We can have the summation of the entire learning or growth curve by working the integral of the dy/dx. Growth journey of a student is mostly a non-linear function. In geometrical terms the graph of the function is a curve with the slope that changes from point to point. Parabola is a good example of this kind of a curve. The function can go up and go down and thus take the shape of geometric wave and we can calculate the derivative of an instant. We can see that the calculus of education is definitely complex can is different from student to student. One of the parallel of educational journey could be likened to a graph of a runner who 100 meters heats.

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