Frankly speaking: I am a computational chemist with a PhD working in academia, and have regular, though superficial intimate times with statistics, scientific visualization, programming and similar geeky staffs. Yet, I hardly ever use most of Math I learned in secondary education. I think it is a pretty safe assumption that 95% of the population has even less to do with Math in her everyday life. Yet, the public – including often even people with higher education in technology or physical sciences – can be pretty dumb in basic mathematics principles of everyday life.
How can it happen?
Deciding what is basic and what is advanced when a body of knowledge is taught is pretty subjective thing. My experience is that most teachers / professor use two guidelines to decide what is basic and what is important:
– “What did I studied first when I was a kid?” which is generally the same question as “What is the historical order of invention/discovery?” So everyone who studies Physics, will start with Classical Mechanics, who studies Chemistry, will go with the 150 years old test tube reactions, and people will study description of animals and similar if they venture in Biology.
– “What this kid will need if she/he will be a Physicist / Medical Doctor..” We often train with a profession in mind, and a specific role in mind both in lower and higher education. We rarely train black-box or user level knowledge, or if we do, it is generally just dumb memorization. There is no different Chemistry books for Biologists, who have a distinctly different view on Nature, or for Physicists.
So we train kids Math, we generally have some very well defined structure in mind that one will need if she/he wants to know all Mathematics, and generally we scale back like in primary and secondary education with the mind “OK, let’s teach her if we would train a XVIII. century Mathematician” kind of schedule.
Nice, but an average person will never ever in her life will use e.g. the sin function or complex numbers. On the other hand, the knowledge of exponential function would be something pretty useful: it helps very much understand how interests or loans operate. Yet, it is a reasonable guess that the majority of people has no gasp about how much money she/he pays when takes a 30-years loan with 5% annual interest compared without extensive play with an Excell spreadsheet (if she/he can calculate it at all). Similarly, a reasonably advanced overview on Probability Theory, and review of the main conclusions would be something that almost everyone can use, not only passionate gamblers. Is it more useful knowledge than the details of geometric construction using the Thales circles.
Do you agree? Do you disagree? If you have a little time, share your opinion in the comments!