A friend who lives in a wealthy suburb of Boston posted this update on Facebook:
Parent/Student/Teacher night at school. Each child was assigned to teach the parents what they were learning. My son was demonstrating adding fractions. Several of the parents could not do it – 2nd grade math.
Coincidentally, as he was posting that I was in the middle of a couple of hours of recurrent training for instrument flying. A jet pilot friend who is a CFII graciously went up with me in a Cirrus SR20 and watched for other airplanes and monitored my performance while I wore a hood that restricted my view to just the instruments. It is a well-known phenomenon that pilots get rusty and there are embarrassment-free opportunities for refresher training. In fact, given that FAA regulations require at least some refresher training every two years, even the sharpest pilots can do a bit of training without anyone asking “How come?”
The Facebook posting above shows that most folks don’t remember everything that they learned in elementary school. But where can one get refresher training on fractions, state capitals, and the rest of the 1st-5th grade curriculum? The obvious answer would seem to be Khan Academy, but https://www.khanacademy.org/math/arithmetic/fractions seems to be geared at first-time learners and those who want to develop an exhaustive knowledge of a subject, not at those who just want some dusty neural pathways touched. A quick Google search turned up Homework for Grown-ups: Everything You Learned at School and Promptly Forgot
Is there a weekend course that grown-ups could take every 10 years?
Have kids, spread out every few years, then continue with grandkids 🙂
Based on my experience as a volunteer math tutor at the local community college there are a fair number of people who have never really understood or learned how to manipulate fractions – it’s not just that they forgot.
I’ve worked with people for whom 6+4=10 and 6+5=11 seem to be unrelated facts.
I think a refresher course needs to be necessarily specialized, and you need to look for them. So there are many remedial classes anyone can take at Community colleges or classes for older people at YMCA’s, Jewish centers, etc… but you have to look for them and know that you need it. A pilot refreshing very specialized knowledge is a kind of special case of learning within his career to keep up with safety which hopefully he is always conscious of.
For most people fractions is the kind of general knowledge they’re not conscious of, they either use it or they don’t and if they have a problem figuring out the number of eggs in a cake recipe they don’t think they need to buckle down and go over fractions for two hours with a teacher.
I think its worthwhile to ask, “why are we still teaching kids fractions?”. If 99% parents can function without fractions in their careers, why bother teaching fractions to kids? Fractions are shortcut created to make approximate calculations easier to perform manually. But with calculator apps doing exact decimal calculations for us, fractions are obsolete.
Yes, fractions are used to teach concepts like ratio and scale, but why not teach those concepts directly and skip over obfuscated fractions?
And while I’m ranting: when was the last time in your daily life that you manually factored a polynomial? Or applied a trig identity? Even in professions where systems of polynomial equations are used, they are never manipulated analytically, they only are solved by numerical approximations that give a “good enough” answer (source: I used to write oil reservoir simulators).
dg –
I had to factor and add simple rational expressions (polynomial fraction of z-transforms) last week. I was at a customer worksite and needed to redesign a digital filter quickly. The customer (a Fortune 500 company) fired all their receptionists and none of the engineers knew how to get me an internet connection. A ‘Virtuall Receptionist’ over video conference from the Philippines gave me a password to a WiFi connection that did not exist at that building I was at. So, I could not check out a Matlab license from my company’s license pool. I could not download an app for my iphone to do the design for me because I had slow internet from the tower and again, no wifi. Piece of scrap paper from a junk fax message and a pencil and I made the customer and my employer happy.
Its true that you don’t need to know math to get along in your daily life but there is a price to be paid for innumeracy. On the micro level, you get worse deals at the supermarket because you can’t figure out unit costs – on the macro level, you can’t compare mortgages or compute the value of an IRA.
To some extent a feedback loop exists. The average person is ignorant so all the systems of daily life are written to accommodate ignorance. A small increase in average capability in math and science might pay big dividends. Think Singapore.
Another question is: why are we not teaching children the skills they will need in life? How to calculate how much it will cost to buy and run a car. How to cook nutritious meals. How and why to save for retirement. How to apply for a job and how to handle a job interview. Which over-the-counter drugs are worth buying and which are not. How to avoid a fistfight, and if unavoidable, how to win and how to lose. How to deal with questioning by the police when you are innocent, and how to deal with questioning by the police when you are not innocent. How to handle a monetary windfall. How to keep a job, and how long to stay in a job before moving on. How to take care of your little brothers and sisters. How to take care of your children. How to take care of your parents.
Tony Randall, when asked why he is so smart, replied, “all you had to do to make people think you are smart is remember everything you learned in school up through 9th Grade.”
Interesting that you ask. I’ve been trying to refresh my recollection of some of the calculus I took in college, and while my fractions are fine, my Algebra is nowhere near up to snuff anymore. (Interestingly, because of a lot of time doing financial computing, my arithmetic is actually better than it was when I was a kid)
Let me know when you find out!