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> I think these concepts are critical to basic citizenship.

In all my life this was never really something I considered important, but the whole pandemic thing gave an entirely new definition to ‘basic education’.

‘I learned all this stuff in high school, why do I have to explain these basic concepts?!’ Was a very common thought.

> Don't think algebra or exponential growth matter? I think these concepts are critical to basic citizenship. Real understanding of exponential growth helps you understand viscerally why, for instance, you should nip a viral outbreak in the bud, and reducing the spreadrate even slightly (R0) can make a huge impact later on, even if spread isn't totally stopped. This is all just gibberish if not learned in high school.

Indeed. I remember talking to a doctor who worked in the ER when the first wave of COVID (brutal in my country) was brewing. She said that it wouldn't be a big deal, they had like 50% of beds vacant (or something like that) so they would be able to handle it just fine. I said that by looking at the data, I thought they would run out of beds next week. Her expression was dismissive, like "this guy doesn't work in healthcare, hasn't set foot in an ER, what does he know?"

The next week, ERs were overloaded, of course. It was in plain sight from the straight line in log-scale graphs. But for most people (including most doctors) the interpretation was (and still is) "wow, this virus is rough, it comes in sudden waves out of nowhere!". Just because they don't understand exponential growth.

Do you really think doctors don't understand, or never learned, exponential growth? I knew a bioengineering student at Cal that was pretty smart and barely made it into med school. They had to go to a DO school instead of MD. So unless the bar for doctors used to be much lower than it is today, every doctor 'knows' what exponential growth is.

Whether they apply it to the real world is another thing.

I know people that don't think raising the minimum wage basically just causes inflation. They're just wondering why apartments in undesirable areas became 3x more expensive when minimum wage went from $5 to $15.

In my country most definitely don't. They take a little calculus in high school, but practically zero at university, unless they take an epidemiology elective or something like that. I know this well because my wife is also a doctor.

It probably varies a lot by country, like many things.

You certainly don't need calculus to understand exponential growth; you'd get a good sense of it from just looking at a chart.

The ability to apply learned theory to real life in cross-domain ways is not common and not so easily taught by rote. Teaching calculus to everyone won't solve this.

> I know people that don't think raising the minimum wage basically just causes inflation. They're just wondering why apartments in undesirable areas became 3x more expensive when minimum wage went from $5 to $15.

That's a pretty poor example though as there are many factors that contribute to property prices and there isn't just a mechanical link between wages and house prices.

Low interest rates probably have a much greater effect, given that most people aren’t buying houses with cash.

> Whether they apply it to the real world is another thing.

'Knowing' it but not applying it (and in what is literally a textbook circumstance, no less) is itself a failure of understanding.

I feel like calculus in high school can be so easily motivated but isn't. For what a high schooler is concerned, you can use it to model the depreciation of mobile devices, cost per day of upgrading devices or how much you save each day by waiting to buy (assuming used market), estimated lifetime revenue for each piece of social media content, the same parametrized on subscribers at time of upload, estimated lifetime additional subscribers per piece of content, etc.

My discrete math professor always made the problems involve food. Because college students are always interested in food, he said.

This assumes most people care about making optimal financial decisions. They don’t.

You're right! You know how you make them care? Demonstrating over and over again how important it is. At school. A place where we are supposed to equip people with the knowledge of how to function effectively in society. To give them the tools to live the best life they can.

School is a place where we indoctrinate all sorts of ideas into students, maybe we could spend a little more time highlighting financial decisions since it is so core to quality of life?

You know what they care less about? The complete abstract and being forced to learn a complex subject without a single morsel of motivation.

Like many, many people who understand exponential growth, I never took a calculus class.

The many, many people, including those in government, who clearly didn’t, prove that you’re an outlier.

That's certainly possible, even without self-learning. The topic is explained in precalc, typically. But it's important enough that I think going further is helpful.

So, I don't mean to force you into something you don't want, but do you think people who don't understand exponential growth are missing something relative to you? That they could benefit from the knowledge you have?

That's what I know having understood calculus to those who have bits and pieces of the concepts (exponential growth included) but don't have a big picture. If you have the time and ability to learn more, why limit yourself? Why allow yourself to be put at a disadvantage? And worse (not saying you are, it's hard to gauge from your comment) why would you be in favor of stiffing other people from being better?

I'm not getting the impression commenters are trying to limit others. Rather, there is a strange obsession with math most individuals will never need and doesn't satisfy them, in a world where one can learn so much else.

Even the exponential growth through calculus example is obsessively nitpicky: just draw a few graphs of y=x, y=2x, y=x*x and y=2^X. Most people will grasp the idea, and it's 30 minutes at most.

> most people will grasp the idea, and it's 30 minutes at most

I think we experienced very different pandemics. I could pick 100 people off the street and I guarantee you 9/10s of them aren't able to do a logarithmic change of base. If you can't do that can you say you grasp exponential growth?

> If you have the time and ability to learn more, why limit yourself? Why allow yourself to be put at a disadvantage?

So what is that advantage for everyday people? I see some people are making it a "citizenship requirement" but except for exponent, which is not a part of calculus anyway (OP original point), there seems to be little advantage to it.

You cannot really understand the nature of exponentiation if you do not understand calculus! Whoever is saying is likely ignorant or they have a shallow understanding, and when I say shallow, I really mean it, as in their knowledge is not sufficient. You cannot know a how dependence based on a power over a linear relationship is "stronger" without talking about rate of change, which is literally calculus. Perhaps you can have an intuitive notion of change, and that's fine, but the point of education often is to either refine intuition or correct it.

And that then leads me to my point above: if your knowledge is shallow, to the point that it limits you, then why clamor to limit yourself or further to limit others?

K12 math classes are not about understanding. It’s more like typing. The symbol manipulation rules you need to apply are few and straightforward. Just memorize where the keys are. Applying them is also simple. Just press. After that, the difference between an A and a C is all about hitting the keys in succession faster and with fewer mistakes. It’s a Zen thing; overthinking it will never get you there. Concepts like exponential growth and rates of change may be presented to you in lecture, but letting them in your head while doing problems is a classic blunder. Don’t think just do.

I am willing to bet that most educated people who walk around with gross misapprehensions of rates of change and exponential growth phenomena, have in fact drilled the computations just as well as anyone else.

Finance has calc all over the place as well. Marginal costs for instance.

>This is HW so one that comes to mind is programming.

> > Real understanding of exponential growth helps you understand viscerally why, for instance, you should nip a viral outbreak in the bud, and reducing the spreadrate even slightly (R0) can make a huge impact later on, even if spread isn't totally stopped. This is all just gibberish if not learned in high school.

I think programming/algorithm analysis and things like discrete simulations will give you a more durable notion of basic exponential growth for things like virus outbreaks than high-school calculus which is going to focus on things the derivative of the exponential function being similar to the function and stuff about Euler's number.

I hope you do realize "discrete simulations" is an application of calculus (analysis really). The "continuous" version of calculus is a special case. Sure though, this is a problem with the way calculus is taught (too much focus on symbolic differentiation and integration, although that becomes valuable somewhat if you become a physicist or engineer, primarily).

Yeah, discrete simulations that show things like exponential growth are basically just numerical calculus.

I think that how much calculus you get in highschool depends on which country you live in, I got 3 years (though the first one was minimal), I also got more in highschool physics classes.

But we also have national exams for entrance into Uni and no "general ed" requirement because we're expected to have met that minimum requirement in highschool

In all these cases learning the math is but one path to the understanding. Not a requirement.

Learning the math and the mathematical notation is probably the most powerful and straightforward way to fully understand the concept.

Did mathematicians before Newton not understand the concept of exponential growth?

Interestingly, the modern notation for exponents (including variable exponents and non-integer exponents) was developed by Euler after Newton's calculus. This modern, simple notation certainly makes it easier to explain the concept to the masses... And apply it in a spreadsheet or something.

Compound interest was understood earlier, too, of course. Thousands of years ago, in fact. But not with as clear and simple notation. It was often made illegal.

To reason with agility in a domain, one must have succinct language (verbal and symbolic) to express and manipulate ideas in that domain. Such domain-specific language facilitates both communication and understanding.

Symbolic mathematical notation was the breakthrough that most greatly increased the rate of mathematical breakthroughs thereafter.

Well said!

You don’t need calculus to teach exponential growth. 99% of the public doesn’t start plotting graphs whenever there is news of a viral outbreak.