Turn on any cable TV news channel and the talking heads (eww…pundits) love to whine about the current state of American education, yet seem to be short on solutions-shocking, I know. Never fear, for not too long ago I have recommended overhauls to both philosophy and foreign language classes. Now it’s time to go over what needs to change about high school math class. As always, make sure you sharpen your pitchforks!
While probabilities are taught in high school math classes, this is often limited in scope. The classic examples used are coin flips, dice rolls, assorted jelly beans in a jar, messy sock drawers, et cetera. This is easy to see why; they are straight-forward, single variable problems that serve as a good introductory into the material. However, the world we live in is complex and problems we encounter are rarely ever of the single-variable variety out in the wild. Auto insurance companies are fantastic examples of calculating this. Their question is not simply what are the odds of this driver getting into a car crash? It is more what are the odds of this driver getting into a car crash based on how many miles they drive each day, their driving experience, age, zip code, et cetera? All of those variables impact the final answer. Online marketers use the same tactic in deciding who to market to. It’s not how likely are they to buy? but rather how likely are they to buy given their age, gender, race, income level, education level, et cetera? Even if the vast majority of students never become actuaries or marketers, they’ll at least develop an appreciation for data-mining, which is an ever-relevant topic today. The single-variable method of probabilistic thinking taught today leaves graduates unprepared for life in the 21st century.
Probabilities can be taught with another spin as well; career choices. This will be relevant to high school math students to help them conceptualize the actual odds of becoming an NBA player, a YouTuber with 10 million subscribers, a platinum recording artist, the President of the United States, or a Fortune 500 CEO. The career odds can also include options such as the odds of finishing medical school (starting as a college freshman in STEM) or becoming a Google’s top AI engineer. The aim isn’t to crush dreams per se, but to conceptualize that the students will have to embrace the grind as competition is fierce. Want to be an NBA point guard? Fine, then realize your rear-end needs to be shooting threes in the gymnasium every morning at 5am; if you don’t, forget about ever making it to the league.
However, my biggest gripe with high school math classes is that they don’t teach risk appropriately. Mathematically, this could be broken down as the probability of an event occurring multiplied by the impact of such an event occurring (this can be in financial cost). The teacher can tie this concept easily to businesses. The recent pandemic is a great example of risk management teaching. While the impact of a global pandemic that shuts down the entire economy is surely financially devastating, the odds were low enough to make this a negligible risk in 2019, hence that’s why so few companies had pandemic contingency plans. Allocating large amounts of capital towards something so unlikely is a poor return. The teacher could then pivot to another example; retailers de-icing sidewalks in front of their store. The odds of a slip-and-fall in the winter are high, and the impact of losing a negligence lawsuit are also high, hence many businesses allocate some funds to de-icing sidewalks. Probability multiplied by impact is a concept that engineers are taught (as they should be) however we need to introduce this to all student, for there is risk in every facet of life.
Risk mitigation is a concept that needs be taught as well. However, it has to be handled with some nuance from the teacher. By that, I mean the risk mitigation and not elimination; the former is being prudent, while the latter is a fool’s errand. Carrying a spare tire in the trunk of your car is a mitigation strategy against a flat tire preventing you from getting to work. However, carrying multiple spare tires is a poor financial bet; the odds are low that a driver would have two flat-tires at once yet carrying that second spare tire will surely impact the vehicles weight and hence its gas efficiency. Risk elimination for flat tires would be simply to not drive, which inherently cuts down on one’s career and social options. This is a high cost to pay for avoiding risk altogether. There are countless other examples that a savvy teacher can employ to drive this point home. Risk is to be mitigated against, if the probability and impact are both sufficiently high.
Game theory is another concept that absolutely needs to be taught in high school math classes. In a nutshell, it’s a way of using probabilities and minor algebraic calculations to quickly decide the best course of action. Entry level books on the topic exist, thus enabling students of all ability levels to join in on the lesson. Game theory, while imperfect (humans aren’t always rational!), has been used to deploy billions of dollars in R&D capital and soldiers onto the battlefield; the field has countless uses. A teacher with enough foresight and nuance can also weave into the lesson the difference between a zero-sum (strictly one winner and one loser) and non-zero-sum games, as well as how to tell them apart in real-time. As mentioned with single-variable probabilities, it is wise to teach students that not everything is a neatly calculable zero-sum game (along with that being a deeply cynical world view, but I’ll save that for philosophy class; we’re talking about math class here!). Students can be presented with various business, military, negotiation, or the classic Prisoners Dilemma to test their skills in game theory.
Opportunity cost is a common term that is thrown around on the internet, however the concept needs to be thrown around in a classroom; it currently isn’t. This will be useful for high school seniors; they can calculate the opportunity cost of attending college versus working in a clerical job directly after high school (as an example). This will help them to conceptualize that many decisions in life bear a cost, and the cost needs to be weighed against likely outcomes. However, it is important for the teacher to balance this out with some context; society cannot function on merely petroleum engineers alone.
Can these math-savvy teenagers now calculate the probability of an angry mob gathering on my doorstep?
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