One of the topics that is underrepresented in the grade/middle/high school curriculum is finance / financial literacy. There is typically a “Home Economics” (HomeEc) course that is offered to students at some point in an effort to give some sense of finance. Beyond that, finance is not a part of most schools’ curriculum, though I do understand that there is a growing interest in making finance more prominent.

Amusingly there are two contradictory camps with respect to what should be taught in school. Go to Twitter and in the search type the following without the quotes “polynomials school house” and read some of the rant-esque tweets. The complaint basically is “why am I learning about polynomials when I really should learn about how to buy a car, a house, etc.”

<Sigh> What do polynomials have to do with this: $$P(t) = P_{0}\Big(1 + \frac{r}{n}\Big)^{nt}$$

Or this:
$$NPV = \sum_{i=1}^{N}\frac{CF_{i}}{(1 + r)^{i}}$$

In fact, the \(NPV\) (net present value) is often known (or is a given target) and the \(\{CF_{i}\}\) (cash flows) are given and the search is for \(r\) (related to the \(IRR\) (internal rate of return)) that solves the equation. But hey! That’s root finding for a polynomial of degree \(N\). Hmm, and if there were positive and negative cash flows, we could have more than one \(r\). Sounds like something that’s covered in Algebra 2, Precalculus, and Calculus. And why do we care about the \(NPV\) calculation? Well, let’s say you’re buying a house, or a car, or thinking about annuities.

So what would happen if we just taught finance without the requisite mathematics like some think can be done? Start beefing up those memorization skills. Well, actually this happens in college with undergraduate finance majors. Because, you know, when am I ever gonna use that math stuff?

You know what’s funny is that my first real job after getting my Bachelor’s in Electrical Engineering was in commercial real state finance working in a newly formed structured finance group. Why did they hire someone with an Electrical Engineering degree? The hiring manager later told me,

“We can teach you the finance, we can’t teach you the math.”

That’s called the “real world”, folks. And then in that job, it turned out that there was more math that was needed, so I went back to school for a PhD in Mathematics / Mathematical Finance.

But yeah, why do I gotta learn polynomials?

It’s easy to blame math education for not being relevant. Perhaps these folks would gain more traction in their cause if they asked, “Why do I gotta learn about Shakespeare when I should be learning how to buy a house, a car, etc.?” The truth is, we have applied math in subjects like finance, the engineering disciplines, the hard sciences, etc and that’s where the abstract concepts are made concrete. To me, the crankiness towards math by the “make math class relevant” crowd is valid, but misdirected. The question should be how can we integrate more math into other subjects than to overburden a math class with flimsy contextual problems in a shallow attempt to bring relevance. It’s almost better to work abstractly than to try to force context. Of course, a problem with working abstractly is more pedagogical than it is with mathematics. Here’s a different take on math misery.

It’s possible to weave math into just about every subject. After all, mathematics is an essential part of STEM and even STEAM, especially when Technology meets the Arts. However, I think it’s generally a mistake to try to disassemble math into discipline-specific math only. It will make math even more of a mystery. There is plenty of value in standalone math classes. Math can already be made more relevant if the hard sciences and engineering disciplines incorporated it more regularly. This happens in college. Hence why math is the filter for STEM v non-STEM.

Finance on the other hand, doesn’t really show up as a stand alone subject in grade/middle/high school, generally speaking (I know several schools that have strong finance programs that are more than just stock market competitions).

I started this with, “There are two contradictory camps …”; here’s the other camp.

Some people hold the notion that people will just learn what they need to learn when they need to learn it and school really is unnecessary. This line of thought has its problems just the same because people do need to learn about money management and the like, but somehow never do. School isn’t even “killing” the desire. In fact, school handsomely ignores finance.

So “school” is in a damned if you do, damned if you don’t position. If the topic isn’t taught, then the whining begins about how school isn’t teaching us things that we need. And if the topic is taught (polynomials, for example), then the whining begins about how school isn’t teaching us things that we need.

What exactly is stopping someone from learning the material on their own? After all, that is the argument of the “just learn it when you need to” folks, right? Yet, the reality is that finance, a subject that is mostly not taught in school, is still something that the populous, as whole, doesn’t learn. Just look at household credit card debt in the US. CREDIT CARD! Where interest rates are an absurd 18-24.99%! Anyone with basic finance knowledge would shun this craziness. But people don’t have this knowledge and we come full circle to “Why do I gotta learn about polynomials when I should be learning to buy a house, etc.?”

Where else can someone learn about finance if not at school? Home is one place. The hard way in the real world is another. Or just on their own if they are able. Learning about finance the hard way is, well, hard. And often times it’s a lifetime of misery. Occasionally we hear of a cheery story of a couple who got rid of $150000 of debt in 5 years or something and then they write about how they did it. Kudos to them, they figured it out. But those folks are the exception than the rule. Most people are straddled with crushing debt for decades, which severely limits the other things they can do. Financial misery is much, much worse than math misery.

Learning about finance at home is also tricky. Without writing a book on this, in essence, the problem now becomes socio-economic. And I know I’m not doing justice to this topic, but broadly speaking, on average, which child will come out with better financial know-how: the one raised in relative affluence or the one raised in poverty? If I had to guess, parents who have a strong command of finance and money management will have a better chance of instilling those good financial values in their progeny, than parents who don’t. And further, it is probably safe to say, that those parents who don’t have a strong command of finance, don’t tend to be wealthy. As a consequence, the degree of financial knowledge stays clustered within socio-economic groups.

If done correctly, financial literacy education in school would be a great socio-economic equalizer.

Thus, there’s a need then to integrate finance into the school curriculum. So is there a way without major disruptions to the status quo?

For the next 1000 words or so, let me give a number of sample projects or research topics that can be incorporated into many of the “core” subjects, including Math. This is obviously not exhaustive, but a broad brainstorm.

Math

I know this subject the best, so I can detail it a bit more than the others.

• The lemonade stand — Hey! Now we actually get to ask how much it would cost to buy 200 lemons! (This is another joke/criticism about math word problems (“Only in math class do you have to buy 3000 cantaloupes”, sorry folks, small businesses think in these quantities (Oops, I didn’t mean to invoke “real world”.).).). (Yes, the punctuation is correct.) Now, at least the context isn’t forced. The purchase of lemons not withstanding, we can also discuss what it would take to have a profitable lemonade stand. We can compute relevant performance metrics and build a mathematical model to understand how the performance metrics change as a function of sales, wages, etc. This can all be done with arithmetic and a little Algebra. If we want to go nuts, we can bring some Calculus in.
• Buying a car or a house — Hey! That’s polynomials. We can compare different financing structures to see which one is the most cost effective. Some of this is already done in math texts.
• Analyzing foot traffic at a bagel shop — This can be a bit advanced or we can take a simplified approach. Given any local bagel store, from the hours of 6am to 5pm (typical hours for a bagel store) count how many people enter in fifteen minute intervals. What does it look like on Mondays? Tuesdays? What probability model can we fit to this data if we wanted to forecast for the following week? How many cashiers does the bagel store need at peak hours? By measuring foot traffic can we estimate the weekly revenue for the bagel store? Can we modify our lemonade stand model to apply it to the bagel store? This incorporates some time series analysis, probability theory, statistics, algebra, etc.
• Cooking or Going Out To Eat? — How much cheaper is it really to have taco night at home versus going out for tacos? Is it cheaper to make pizza at home or to go out for it? When grocery shopping how much of the purchased food just rots in the refrigerator? What does that do to implied cost of food? Is calories per dollar a good metric for evaluating how much value we get in our food purchases?
• Compound interest — What is it? How does it hurt you? How can it help you?
• Meta — What does it cost to run a school?

The Business of the Hard Sciences and Engineering

• What does it cost to mine the precious metals in our electronics?
• What does it cost to ship these precious metals to a processing plant? To a manufacturing facility?
• How much do we really save by installing solar panels?
• What does it cost to produce a solar panel?
• How green are solar panels?
• What are financial risks / rewards for the research and development of a new drug (pharamceuticals)? What does the research development cycle look like?
• How do we locate oil? How do we know where to drill? What math is required for that? What are the costs associated with drilling for oil? How much oil has to be sold in order for there to be profit in the venture? How do tax subsidies change the profitability equation? Is it worth paying a lobbyist?
• What are the lawsuit risks for a faulty product that could injure someone? How much do you invest in quality control? This easily leads to, “what is quality control?”, which leads to statistics.
• Is it cheaper for communities to have locally grown food in the supermarkets or for the food to be imported? (Consider how much food rots just in transport. Balance this against an economy of scale that large food producers have versus the local farmer.)
• What does it cost, from start to finish to make a cell phone? (Pick a specific cell phone.)

History

With history, we can be everywhere and everywhen and we can merge with the hard sciences and dabble into economics theory.

• What was Tulip mania? How did it start? How did it end? What were the long term consequences? How did it destroy an empire? From this we can explore other market crashes and understand the national and global financial impact. What happened in the Great Depression? How was it similar to Tulip mania? How is it different? What other manias have happened? What was Glass-Steagall? Studying manias / crazes gets us into psychology, which can get us into mass marketing.
• How did Alexander the Great finance his campaigns? How did Caesar? How did Genghis Khan? How did Napoleon? How did the US in World War II? Vietnam? The Gulf War?
• How did the economy of Rome change from the peak of the Holy Roman Empire to its decline? What did their imports / exports look like?
• What is a barter system? How did it work before the advent of money? Can bartering work on a global scale or only on a small community scale? Does the internet make a barter economy viable?
• How has the tax code changed? Why do we have a tax code? How many accountants will go out of business if the US simplified its tax code and went to a flat tax rate like some politicians have suggested? Where will the US government raise money if it abolished personal income tax?
• What is the economy of a government? What is a banana republic?
• What is a utility function? What is supply and demand? How do we price the lemonade at our lemonade stand?
• Read and discuss “The Wealth of Nations” by Adam Smith.
• Did there really exist an Ancient World Bank? What was its purpose? Why did it not succeed?
• What was the cost of a knight’s armor? How did a knight acquire it?
• How much did an arrow cost? How important (cost wise) was it to have trained archers versus a bunch of men with a lot of arrows being fired haphazardly? What battlefield tactics existed to goad the enemy into firing a volley of arrows so that the arrows could be fired back at the enemy?
• How did people earn a living during the US Civil War?
• Once women entered the work force what did it do to household income? expenses? What was the effect on the national economy? What are the (financial) benefits / drawbacks in financial planning in a single-income household? In a double-income household? How does raising a child change if one person is a stay-at-home parent versus both parents earning an income / having a career?
• What did the local / national / global economies look like before the introduction of consumer credit cards?

The Arts

• What does it cost to produce your school’s version of Romeo & Juliet?
• Inline with the idea of supply and demand, how does an artist not starve?
• How does one make a living being a musician? How much is that living?
• What does it cost to produce an album / book / work of art? To distribute it? To market it? When does an album / book / work of art become profitable? What are royalties? How do they work?
• Does the color red really make one more hungry? How do sales at a restaurant change based on the color scheme?
• What does it cost to make the color purple? What did it cost in ancient times? Why was purple a color of royalty in Ancient Rome?

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Notice that personal finance is just the tip of the iceberg into financial literacy. In each of the topics, we can always integrate personal finance. For example, we can look at the earnings prospects within each field. From this we can budget and develop a plan for saving enough money to purchase a home. Is it cheaper in the long run to buy a house or to rent an apartment? Why? How? What are the assumptions? Is it cheaper to buy a new car for $25000 or to just take a cab always? After how many miles of driving does a cab become more expensive? 100000 miles? 200000 miles? Remember to factor in periodic maintenance, insurance, etc when purchasing a car! How much do kids cost to raise? How much does the first child cost? How much does the second child cost? All of this requires math that’s beyond basic arithmetic.

Anyway, this is just a start. Get in touch with me if you’d like for me to provide training for weaving in some financial literacy lessons. I continue to work in finance while maintaining a foot in education. And I can tell you that the complaint about polynomials is bogus.