You may not even need to imagine this situation as it has been a reality for many students sitting in a math course. You’re staring at the blackboard while the teacher reviews in excruciating detail how many fish will be left in an imaginary pond after a month’s time. Really, you know that this is an attempt to make something as boring as algebra into some sort of real-life application. Then the thought hits: “Why do I need to know this?”
Well, I can sympathize. You don’t need to know how many fish will be left in the pond at the end of the month. You don’t need to know how many years older Sally is than John. The river is flowing at three miles per hour – who cares?
It is a common misconception that math is about numbers and answers cours particuliers maths. Math is not merely a “move this here and that there” subject of study. Math is the study of balance, flow, and freedom of logic. The key to solving any math problem is to never change anything. We only move things. For example, you may remember problems like this:
John is nine years old. In three years, John will be exactly half the age of Sally. How old is Sally?
Don’t worry; I’ll spare you the work. Sally is 21 years old. In case you are wondering, in three years John will be 12. At this time, Sally will be 24 because John will be half her age. Well, that’s what their ages will be three years from now – so, today, Sally is 21. Does it really matter what their ages are? No. Who are John and Sally, anyway?
The point is that by solving the problem you needed to put your head in a mindset of juggling multiple pieces of information. You had to move numbers around and look three years into the future. You had to try things and experiment. You had to check that all your numbers were in line and all the pieces fit together. Believe it or not – you had to use your imagination. The important part of learning math is not the answer – it is the process your mind uses and the creative ways in which we juggle information. The answer to that problem will always be “21 years old”. That never changes. The way that we present the information may change and that, my friends, is the magic of learning math.