Do We Teach The Wrong Math?

I’ve been catching up with some older podcasts that I’ve been meaning to listen to lately, and one of them was a Freakonomics episode entitled “America’s Math Curriculum Doesn’t Add Up”

In it, Steve Levitt posits that the math we teach in high school is outdated, and unnecessary in today’s modern age of technology, and the kinds of skills people really need to navigate today’s world are not being taught at all unless you go to a college and major in those.

I’d highly recommend listening to the whole thing as there are multiple aspects to this and discussion points with various experts, but one of his big points was that we are still teaching people geometry and trigonometry when outside of some engineering disciplines, the vast majority of us would never use those skills, asking a computer to do it for us instead if we actually needed them, and we are not teaching people how to be data fluent.

I do agree with this, and it reminded me of something I wrote on my Child Abuse Survivor blog to try and help people make sense of mental health studies that seem to show constantly changing results. I’m going to borrow it here because it’s a completely made up example from the top of my head but one which can show us exactly how numbers can be manipulated to encourage us to believe certain things because we aren’t fluent with how the data gets created.

Let’s say that right now, the rate of people with super-human eyesight is 1 in 10,000.

A study was conducted to take a look at the health benefits of drinking apple juice. They took a look at 10,000 people who drank apple juice every day, and lo and behold, two of them had super-human eyesight.

Now, mathematically speaking, you could report that drinking apple juice makes you 100% more likely to have super-human eyesight. Awesome, I foresee a rush on apple juice purchases!

Again, technically speaking that is true, the rate is normally 1 in 10,000, it goes up to two in 10,000 for apple juice drinkers. That’s double the normal rate, or 100% higher.

But it’s also not the whole story.

One, we have no idea if drinking apple juice is the thing that got that one extra person to have super-human eyesight. It could just be a coincidence.

Two, and most importantly, for 9,999 people, drinking apple juice did nothing to change their lack of super-human eyesight.

Now, the problem when we are not data fluent is that when someone in the apple juice industry puts out a press release citing this study, and making the claim that you are 100% more likely to develop super human eyesight if you drink apple juice, many people will see that 100% figure, and turn that into an almost rock solid guarantee that apple juice is good for your eyesight. When, in fact, there is no actual evidence that is true. There’s also no evidence against it either. The study itself doesn’t even claim that. It simply claims that, for some unknown reason, in a group of 10,000 apple juice drinkers, there was one more person with super human eyesight than would normally be expected.

Now, is that something that the researchers want to look at further, and investigate a larger group, or try to repeat with a completely different group of 10,000 apple juice drinkers to confirm? Sure, it may very well be. Does it, by itself, prove anything about drinking apple juice in regards to eyesight? Not at all.

But, in today’s world, you are absolutely going to see a headline out there in the media, shared on social media, pumped up by apple growers, etc. claiming that “100% more likely” figure. That will, of course, be followed by various anecdotes from people who’ve been drinking apple juice their whole lives and never needed glasses, which in turn will end up with parents being shamed when their kids won’t drink apple juice, etc. because that’s the way we work in 2020.

And all of it will be because we never really understood what that claim meant and what the number represented. We read the headline, and never really looked into the numbers behind it, or even if we read the article and saw the numbers, we didn’t truly understand them. We don’t understand that these results will need to be looked at much more deeply, and have much more work done, before we can conclusively say anything about the effects of apple juice on our eyesight. In contrast, we also don’t understand the process and data enough to identify very early, inconclusive, results, compared to results from a much more thorough investigation that we really should be paying attention to.

Now, compare the number of stories like this you come across in a given day, week, or year to the number of times you’ve had to calculate cosine, or identify an isosceles triangle.

I think I can see where Levitt is coming from, can’t you?  Yes, there may be some folks out there who are doing advanced geometry as part of their work, but for most of us, that isn’t the case. All of us, on the other hand, are inundated with statistics every single day that we don’t understand, and make choices about our lives, our businesses, or careers, based on those same statistics. That’s a failure of education.

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