The Ontario government is again thinking that somebody needs to do something about math education. In the near future, many people will ask me whether they really need to know math to learn about the real estate business. Enough people think that numbers are not important in business because success seems to depend on getting things done, on communication, on personal relationships and so on.
This post is about how numbers, plus more advanced forms of mathematics, are important because solving problems is fun and useful. For nearly everybody, the real goal of learning math should be to become comfortable with it.
Accountants say that numbers are the language of business. In other words, get used to it since saying “I am bad at math” will not get you promoted. People should learn to see numbers (fractions, percentages, …) as an another form of communication: both as the person sending the message and as the person who needs to correctly interpret the information being sent by others.
Story-telling is important but can only get you so far. Think of the numbers in a financial statement as a photograph. Running a business day-to-day requires understanding the dynamics: in other words, the photograph is one bit of a movie. Understanding change is why everybody should want to understand functions, formulas and algebra. Everybody uses functions and symbols all of the time: e.g. “profits depend on how much we sell” (a.k.a. π= f(Q)) or “cash flow will vary over time because government policy and market conditions vary over time” (a.k.a. CF= f(t, GP(t))).
As an undergraduate, I remember taking one class on actuarial math. The symbols made little sense and the manipulation seemed to be an odd bit of memorization. In reality, it was an advanced form of what I learned in high school and the answers affected whether somebody retired comfortably. In a business such as real estate, which worries about cash flow over decades, people struggle with concepts such as the time value of money and its computational counterpart (net present value). Being comfortable with math means that you can ask that high-priced consultant whether their surprisingly-precise computer model makes any sense.
Calculus is a flash point. In my conversations with students and their parents, I notice a common confusion. If the calculus class was intended to teach the rules of calculus only then I could tell a business student to memorize all of the important ones in about 10 minutes. Sir Isaac Newton (or Leibnitz?) invented calculus to solve a problem. Therefore, most of the class time is spent understanding those rules well enough to apply them to a wide range of What If questions or optimal decision puzzles, which add insight to mechanical calculations and something more creative than a boring number.
Many employers are disappointed at the poor problem solving skills of many applicants. Good math classes explore problems by starting with few preconceptions about what the answer “should be”. The restrictions imposed by the rules of algebra and the rules of calculus are not arbitrary: they exist for a reason and you ignore those reasons at your peril. People who really like to solve problems know that math can be fun.
I cannot offer good advice on the best way to teach math. I do not know which comes first: puzzles or techniques. In the end, people need to know the techniques and how to see puzzles.