Recently, Occupy Math looked at (and mocked) the idea that most students only need arithmetic in high school. This week’s post tries to provide an interesting look at compound interest which is one of these things, like toxicology or nuclear physics, where you are better off having a working knowledge of at least the major points. Its also an example of something beyond arithmetic that would be good to cover in high school. Strike that: substantial human misery could be curtailed if we covered this more completely in high school. Knowing enough to avoid abusing credit cards is a key skill that would not be that hard to teach, yet the subject is slighted in most schools! This issue is one of the key points supporting Occupy Math’s slogan that Math is the Right of all Free People.
Diffuse, inadequate treatment of finance in education endangers students.
Occupy Math went to Lawrence High School (go Lions!), in Lawrence, Kansas, where the math requirement for people not going on in the educational arena was “Business Math”. It used fake examples with business-sounding words and covered arithmetic through fractions. Compound interest was too hard. In present day Ontario, the math course for those not going on with anything using math is “Data Management” which has the potential to be a good course, but seems to have real problems with inadequate training and support for the front-line teachers. Financial literacy would be an excellent thing to teach. So: are we teaching it?
The short answer is “no”. The more nuanced answer is that we are acknowledging that it is important, but then burying the lead in a big way. In a 207 page document Ontario declares that it has introduced financial literacy across the curriculum. Word search the document: there are four mentions of credit cards, two of which are about protecting your online security and only one of which suggests that alternatives to credit purchases are worth examining. This at a time when easy credit and the resulting debt-trap are at epidemic levels – and frequently mentioned in the news.
How is training in safe credit card use not up front in bold caps?!?
Okay, what the heck is exponential growth and what does it have to do with Occupy Math ranting about credit cards? Exponential growth happens whenever the rate of growth (or decay) of something is in proportion to the amount of the stuff that is currently present. It covers growth of bacteria until they run out of space, decay of radioactive substances, and even the way drugs leave the body after you’re dosed. This means you need to understand exponential growth and decay to plan everything from heading off infection to making sensible decisions about medical or reactor waste. These are all topics that Occupy Math has covered in first-year university math courses. They also all have much less societal impact than the fact that credit card debt undergoes exponential growth if you don’t keep up your payments. The more you owe, the faster how much you owe grows. Said that way it sounds simple, but human psychology rears its ugly head here too.
It turns out that credit seems less real than cash and so impulse spending and unnecessary spending are much easier with credit cards. Additional perspective on credit-card spending appears in an article from Nerdwallet. Imagine this: the amount of your next payment needed to avoid additional debt is continuously displayed on the face of your credit card! We have the technology…
Some resources for teachers on financial literacy are available from Edutopia. Their front page advocates for making this kind of education about the students, an approach that Occupy Math endorses. Another resource, with lesson plans, is Financial Literacy for High School Students from InCharge. This one seems a bit abstract, but a good starting point.
Representing money in different ways changes behavior.
Occupy Math works on representation – how to represent problems to computers to make the computers able to solve them faster. He is co-developing a game to teach fractions and a big issue there is how to represent the factions. Three representations for one-fourth are 1/4, 0.25, and 25¢. A big question in the game’s design is which of these representations is better for teaching what? So: cash, credit cards, debit cards, and smart phones payment apps are all different representations of money. The articles cited above show that use of cash and credit lead to measurably different behaviors. How will phone payment apps change financial behavior? Nobody knows, but it is a question we should think about. At least your credit card does not actively nag you to make purchases while you’re trying to read the latest headlines.
Exponential growth, in the form of interest, can work for you. Occupy Math’s retirement account at his old employer is 8% money he put in, 16% money his employer put in, and 76% accumulated interest. Given all the excitement about the current American election, its interesting to note that “Super Business Man” Donald Trump would have far more money if he had kept his hands off his inheritance and just dropped it into the stock market in an index fund. Just avoiding interest on debt can keep you in good shape; actually saving can make you rich. In many places you can even get a tax-break on saving for retirement, making savings even more advantageous. That assumes, of course, that saving is possible at all.
Payday loans – getting rich off the poor.
A payday loan is a short term loan that, in theory, you repay out of your next paycheck. Typically the interest rate on these loans is close to the highest rate the law permits – and often it is over that limit by trickery. Used once in a long while to bridge an emergency these loans might be helpful, but mostly they are toxic. The high interest rates are justified by saying the loans are risky – but according to the sources Occupy Math found (including the linked article at the beginning of this paragraph) overall risk is not different from that on larger loans secured with property. When Occupy Math googles “payday loans” the first 25 hits – into the second page – were places that offer payday loans. This suggests that they are very profitable. Since only people living paycheck-to-paycheck need this sort of credit, its clear that the payday loan industry is horribly exploiting those on the lower margin of the economy.
Occupy Math doesn’t think financial education will directly help the people taking out payday loans – the people who take payday loans seem to do it because their other choice is losing their lodgings or not eating – not because they don’t know it is a dangerous course of action. That doesn’t mean there isn’t education to be done. If the general public had a better sense that payday loans create a poverty trap – one that lowers economic productivity, harms health, and potentially raises their own taxes – it might be easier to create alternatives or at least reduce the abuse.
Occupy Math has presented the case for financial math education and found some evidence that we are dropping the ball. Having designed a business math course for university, he is sure that an course that encourages financial literacy can also be a pretty good math class. Do you know of other places where a little math education might save a whole lot of money or, better yet, reduce human misery? Are other balls being dropped? As always, you are encouraged to comment or tweet.
I hope to see you here again,
University of Guelph,
Department of Mathematics and Statistics