Most children are taught the story of Sir Issac Newton sitting under the apple tree and being struck in the head by a falling apple and how the falling apple prompted him to discover gravity. However, what kids are not told is that same event prompted another Newton invention. Gravity is the force that describes how things are pulled down toward the center of the earth. In order to explain the concept of gravity and to make the new concept more useful, Newton invented a whole new branch of mathematics called calculus. I have an engineer’s training and have taken more mathematics classes than the vast majority of the population. Although teaching calculus to kids at an early age may be difficult, the basic concepts behind calculus are very simple, easy to illustrate and are vitally important in the teaching of financial education concepts.
Prior to the invention of calculus, it was very hard to make sense of many things in nature, because math was limited to snapshots. Algebra, geometry and trigonometry only make sense for the given data at a certain time. If you wanted to see how things behaved with time you needed to figure out the equation at a bunch of different points and draw the graph to see it. Calculus allowed us to see how things are changing at a given instant. It allowed us to see that if we are in our car and slam on the brakes, we can predict how far and how long it will take us to stop. It allowed us to see if we are spending money at a given rate and earning money at a smaller rate, how long will it be until we run out of money. These types of measurements weren’t easily performed prior to the invention of calculus.
When it comes to personal finance, each of us does calculus all the time, though we may not realize it. Calculus is used to measure the rate at which something is changing at that instant. Week-to-week, month-to-month, we adults always work the Net Income equation to make choices. Net income is simply total income minus expenses. The bulk of financial education is geared toward increasing the rate of change of the net income equation. When we work to be more frugal, we are making expenses smaller. When we invest, take on additional jobs or get wage raises, we are making the gross income side bigger. Both of these increase the rate at which the net income equation is changing.
By using the net income equation, we can make predictions about where we are going to be financially in the future. When will I be able to afford that new item? Will I have enough money to go buy groceries or go to the movies? Will I be able to pay my tuition bill? Will there be enough left over to continue to pay for other things? These are the questions that one can reasonably answer through the help of calculus.
I find it unfortunate that teachers in schools often tell about the first discovery the Newton made that day, but so often neglect to mention the latter. Kids need to know the concept behind calculus and rate of change at an early age. It will help them throughout life. If you think about it, you will find many ways to illustrate these concepts for your children in the car, on the playground and in the home.
This type of learning is important, because gravity tells us that, on earth, unless we do something about it, things fall. This applies to equally to checking account balances as it does to apples.