Oh the irony of it all. Two days ago I post about two math books, at least one of which (if not both) I think everyone should read. This morning, reading my newsfeed, I see one of those “People Are Confused By This Math Problem” articles that pop up from time to time.
Often those are expressions without parentheses, so they require knowledge of operator precedence. (I think such “problems” are dumb. Precedence isn’t set in stone; always use parentheses.)
Some math problems do have a legitimately confusing aspect, but my mind is bit blown that anyone gets this one wrong.
According to the article, many people get the sum 5,000.
Which is off — that is to say: wrong — by a considerable amount (almost 22%).
As I look at that column of numbers, it’s hard to see how anyone could think it sums to 5,000. To me, that it can’t and doesn’t seems blindingly obvious.
But apparently what happens is that people sum it (in their heads) from top to bottom, so the running total they get is:
1000, 1040, 2040, 2070, 3070, 3090, 4090,…
And then it goes south when they add that final number, the 10. Somehow the rollover skips a zero and bumps the leading 4 to a 5.
That’s what happens when one’s mind has no feel for math because one has disdained or feared it, and I think that’s a major pity. No one should fear or dislike math — it’s far too crucial in our lives.
To me, the way people seem proud of being incompetent with math is shameful. It’s like taking pride in being illiterate. Math innumeracy is a form of illiteracy — it’s a lack of a key means of communicating about and understanding the world.
On YouTube, I’m struck by how many people find it important to comment about how poorly they understood some science or math video. They don’t add to the conversation in any way; they just announce their poverty. Are they begging for help or is it a weird form of reverse bragging?
When I look at that column of numbers, I see two groups. The four occurrences of 1,000 jump out immediately. Then one takes in the other four numbers, which are all small.
The four 1,000s immediately sum to 4,000.
The 10, 20, 30, 40 series is just 1, 2, 3, 4, multiplied by ten, which makes it 4! (four factorial) multiplied by ten, which is 100.
So the total sum is 4,100.
I read the article thinking there must be some weird trick I wasn’t seeing, but, no, it really is that simple.
It’s a glaring example of how innumerate too many people are.
Even worse in my eyes, they generally seem fine with that. As I say, to me that’s like being fine with being illiterate — it seems like going through life seriously impaired, and it makes me sad.
I really do believe that gaining some fluency with math leads to more clear and more logical thinking. A great deal of science and technology has evolved beyond the horizon of most people’s background or interest, but math fundamentals should be as common as reading and writing skills.
Recall that the original phrase was: Readin’, Writin’, and ‘Rithmatic. (The canonical three “R”s.) We’ve gotten well away from the last one, and I often wonder about the first and second — video involves neither.
But I suppose I’m just spittin’ in the ocean when it comes to math.
Oh, well, so it goes. It is what it is, I guess.
Stay summing sensibly, my friends!
November 22nd, 2020 at 11:13 am
One really nice thing about math is that it can’t be spun, and it’s hard to politicize. It’s even better than baseball that way when it comes to a refreshing escape from human bullshit.
November 22nd, 2020 at 11:43 am
I also wonder what the point of those “People Are Confused By This Math Problem” articles. What are they really about? Are they about how innumerate people are? Are they mocking? Is it stunned disbelief? Is it shared pain? Are people bonding over their innumeracy?
November 22nd, 2020 at 3:17 pm
I can proudly declare that I got the total 4,100… I was expecting that to be a typical wrong answer! I am one of these people that “struggles with maths and languages”. I realise it is a self-defeating mindset to simply accept this but it does feel like my brain just doesn’t grasp the way these things are generally taught – I struggled through high-school with these and I struggled to make progress in my own private studies of these subjects.
I do agree that such comments (as these, and) as you might read on Youtube that sound proud to “announce their poverty” don’t add anything constructive. The screaming of “I just don’t get it” is all too familiar. Rather, a way forward needs to be actively sought (perhaps by both students and teachers). “Why doesn’t a particular learning approach work?”, “What would work better?”, “What needs to be put in place to facilitate progress?”
November 22nd, 2020 at 4:46 pm
I was the same way with the answer. It’s 4,100 obviously… but that must be wrong, right? Nope, it’s right and just an example of how some have a lack of facility with numbers.
I know a lot of people who I see as highly intelligent (in the intellectual sense, not just the consolation prize “emotionally intelligent” sense) who likewise genuinely struggle with math. I go back and forth on what to think about it.
Is it possible brains can be wired differently enough to matter? Is it a matter of learning styles?
I do wonder, but the science seems to suggest no in both cases. Any brain can do basic math (if it can function at all), and we’re learning that “learning styles” was a false idea.
What I think makes nearly all the difference is teaching styles, especially when it comes to science, and extra-especially when it comes to math (which is often taught in the worst possible ways by people with no feel or love for it). So I completely agree about teachers and students actively seeking better solutions. (In general I think our society needs a better outlook on teachers. They’re hugely responsible for our future.)
The other aspect I think is important is our cultural view of it. The “Math Sucks!” ethic isn’t viewed anything like a “History Sucks!” view, for example. We’re generally fine with innumeracy — it’s even seen as making one more human.
The first step in any subject is instilling curiosity about it and interest in it. That’s one reason I’m such a big fan of Grant Sanderson’s YouTube channel, 3Blue1Brown — he does amazing math videos. I’ve learned so much from him.
November 22nd, 2020 at 3:45 pm
I was mildly surprised that I got it right too. For me, I just counted the 1000s and added the two digit numbers separately, then added the results. That seemed too simple.
Having a background in Accounting, I can assure you that math can indeed be spun. And of course, “Lies, damned lies, and statistics” is a thing. Of course, that’s in applied math. The pure stuff is more, well, pure.
I think programming helps with logical thinking too. I often wish more philosophers did it, so they could see how much of a house of cards many of their arguments are.
November 22nd, 2020 at 4:51 pm
“I just counted the 1000s and added the two digit numbers separately”
Yep, exactly. Seeing the two groups makes it glaringly obvious.
“Having a background in Accounting, I can assure you that math can indeed be spun.”
Ha! Good point! 😀
(I might call that obfuscation more than spinning, but maybe it amounts to the same thing. Math certainly can obfuscate. Long ago I used to enjoy those “proofs” that 1=0 or other seeming math absurdities.)
“I think programming helps with logical thinking too.”
Absolutely, very much so. It’s a form of mathematics, after all! (So is logic itself, for that matter.)
November 23rd, 2020 at 1:44 am
I have a couple of degrees in mathematics (a first and a masters) and I got the answer WRONG! At school I was usually second highest in math (the top guy went on to read maths at Oxford). But my scores were usually in the high eighties or low nineties, which means that I often got answers to school maths problems WRONG, in examinations, when one is rushed. And this morning I saw this puzzle and rushed through it and thought yes, it is 5,000. I saw the four thousands, and then added us the 4, 3, 2 and 1 and got another round number, and my stupid primate brain told me that it was indeed 5,000. Only when I read on did I go back and check my working.
November 23rd, 2020 at 9:08 am
That’s really interesting. You spotted the separate groups and summed them separately, but then apparently lost track of the decimal point. That’s a different failure mode than suggested by the article I read. (Which I mentioned in the post — that people mess up adding the last 10.)
A friend said this reminded her of that puzzle that asks to count the number of “F”s in a paragraph, and just about everyone misses the one in the “OF” (because our brains tend to see it as a “V” sound). It’s looking less like a math-phobia problem and more like a brain-slip problem.
Given you got it wrong with your background, that seems the case. You don’t seem at all phobic about math. 🙂
December 20th, 2020 at 2:15 pm
Don’t mind me, just trying a LaTeX insert:
January 10th, 2021 at 7:13 pm
Here’s an interesting article about math anxiety.
I absolutely agree it is real, and I likewise agree it’s curable. However, I suspect, as with many ingrained phobias, curing it in adults is very difficult and requires considerable effort and commitment. I agree stopping it before it starts is key. We need good math teachers.