Math is hard

[liv]

Having encouraged everybody else to post short posts with links to other cool stuff, I should follow my own advice! Here's four very interesting and different responses to XKCD's Forgot Algebra comic:

• helens78 talks about the fact that loads of people commented on the comic agreeing with the attitude it's supposed to be satirizing... I loved every second of math I took in high school and college, and I use algebra on a daily basis (Her post also contains a detailed text description of the comic, so I'm not going to repeat her transcription.)
  
• yvi (who lives and was educated in Germany) is annoyed by people who are smug about not being able to do maths: These are subjects that belong to "general education" and somehow, sciences beyond maybe grade 6 or 7 aren't
  
• petra observes that anti-intellectual attitudes to languages can be just as bad: Americans are not in the least bit shy about how much of their time they have spent learning skills that they do not presently use
  
• rho gives a great example of how maths is useful in real life: It isn't the specific knowledge that's useful; it's the way of looking at the world

All very much worth reading, including the comment discussions attached. There, how's that for a brief pointer rather than a long essay (which might never get posted)?

Comments

[jack]

Hm. I knew lots of people had a very negative experience with maths (in fact, compare to recent comments about how many people hate sports because of experiences at school). But I didn't realise they overlapped so much with people who liked xkcd...

[jack]

Oh, but I agree with making maths less negative :)

[jack]

Oh, and obviously I use maths in everyday life all the time, but to be honest, it probably would be more useful in general if we had less calculus and more compound interest.

[ajnabieh]

A++ agree on compound interest. Also statistics, which is, in math terms (as I understand it, having only a limited stats education myself) basically only multiplication a million times, but, in conceptual terms, is basic to understanding anything about the world. Says I, a social scientist.

[ptc24]

I wonder whether there's some validation going on, of the form "I struggled through this, resented it at the time, thought it would be useless to me... and I was right, dammit. Go me!"

[liv]

I think what happened with XKCD is that it got so popular that pretty much everybody on the internet reads it. And honestly Randall doesn't make that many maths jokes, these days. It's like how Beatles songs mess up music matching algorithms, cos basically everybody listens to the Beatles at some point, so it's almost entirely useless for predicting their other tastes!

[liv]

I largely agree with rho that maths is useful because it gives you a way of looking at things, more than because on a day-to-day basis you employ the specific manipulations you were taught in GCSE maths. I think just about the only thing from school I've ever used directly is changing the fuse in a plug (and even that isn't very useful any more, cos they made plugs non user modifiable). Well, that's a slight exaggeration, but only a slight one. But that doesn't mean everything I learned in school is "useless"! For example I learned a lot of meta-stuff about how to learn, and maths gives you a different subset of that from pretty much any other subject.

[liv]

I definitely agree that there should be more stats taught at a basic level. Whether it counts as part of maths is open to debate, but definitely worthwhile. Also probability, though again that may come under the heading of "stats" depending on your exact definitions.

I also really like the way that some continental schools (France is the example I'm most familiar with) teach everybody at least some elementary philosophy. Knowing exactly what Plato wrote is not particularly useful, but having some clue about the sorts of things philosophy can do would be a great help.

[liv]

I have a feeling that a lot of the problem here is to do with what people mean by using a particular school subject. Like, some of the pro-maths people are saying that they "use" maths to scale knitting patterns, or to decide what purchases are good value, whereas I'm sure all the maths resenters would say that what they're doing when they carry out those tasks isn't maths. Part of the problem is that maths contains a higher proportion than most other subjects of exercises that are designed to help you get a grip on concepts, and the exercises themselves are just a means to an end, but if that never gets explained to you properly, they seem like completely pointless make-work.

[siderea]

Yes, and further: "The people making me suffer justified doing so under the rubric that it would serve me in later life. They were wrong, and so they had no right to do what they did to me."

I think a lot of people feel that, but they don't dare come out and say it for some complicated psychological reasons.

[siderea]

whereas I'm sure all the maths resenters would say that what they're doing when they carry out those tasks isn't maths

I don't think they would. I think they would point out they don't do those things. Which in my experience most resenters don't, actually, do.

I think a lot of college-educated people, especially in STEM fields, greatly underestimate how math-free an existence it is possible to lead in our society. It's not a very lucrative existence, and it involves accepting occasional rip-offs and overdrafts, but there are a remarkable number of people whom that describes.

Part of the problem is that maths contains a higher proportion than most other subjects of exercises that are designed to help you get a grip on concepts, and the exercises themselves are just a means to an end, but if that never gets explained to you properly, they seem like completely pointless make-work.

Sure, but if those ends were ever reached, wouldn't they be self-evidently useful? If they were useful? I mean, I'm in favor of math and think it's keen and useful. But if one manages to get to adulthood with at least and average intelligence, yet see no personal utility in math, then whose fault is that?

One of the unfortunate facts I learned in school reform was that there are rather a huge number of primary school math teachers who never studied math or the teaching of math -- their specialization was in other topics -- and rather hate and fear math themselves. At one point in the 1980s, I heard the figure that 90% of math teachers in California hadn't had any specialist training in math instruction, and might not have beyond an elementary school level of math attainment themselves.

Have you ever read John Holt's How Children Fail? I really can't recommend it highly enough. It's about how children become estranged from their good mathematical sense by schooling, and the effect that has on them. (Also, Holt writes like an angel; he's one of my English-language heros.)

[naath]

I don't think they would. I think they would point out they don't do those things. Which in my experience most resenters don't, actually, do.


My experience of knitters is certainly that many will raise the cry of "ugh, math" if it is suggested they do ... well, any arithmetic at all. The sock I just finished knitting required (something like) take the number you just reached and subtract 10 mod 22; the pattern provided full hand-holding (is your number less than 10? if so add 22)... and also an apology for the maths.

[liv]

I've been mulling on this comment all week, but prioritizing last-minute wedding prep over DW discussions. Thanks for all this info and food for thought, though!

they would point out they don't do those things
That could well be, and I hadn't given enough consideration to that possibility.

a lot of college-educated people, especially in STEM fields
Yes well. Even before I went to an elite college to read [major in] a numerate science, and blagged my way into maths for chemists to learn advanced calculus, because maths for biochemists was boringly trivial, I've always been absurdly good at maths. This is definitely a problem for me in drawing conclusions about maths education, because the subject came so naturally to me that it really wouldn't have mattered much how bad my educational experience was.

Still, I think Randall is probably talking about the sort of people he socializes with and the sort of people who read XKCD, who I guess are mostly "people like me", if not specifically college graduates then people who are generally quite successful in academic type pursuits. So they're not people who leave school absolutely innumerate, they're likely people who are basically able to do maths but resent the kind of exercises that school used to teach them those skills. Don't know, I'm speculating, but that would be my interpretation of the cartoon. And from personal experience, I have medical students who have gone through their lives with outstanding academic success, yet balk at anything that looks like maths even though they can perfectly well do the kind of manipulation involved if you express it in a way that doesn't look too mathsy.

how math-free an existence it is possible to lead in our society
Fair point, definitely. I'm an idealist about universal education, though. You can get by without using any maths, and you can most certainly get by without knowing anything about history or literature or speaking any other language than your native one, but I don't think people should have to, even if they don't particularly enjoy or excel in those subjects while at school.

there are rather a huge number of primary school math teachers who never studied math or the teaching of math
That is unquestionably part of the problem. I think it's not quite so bad over here; I don't believe you can qualify as a primary school teacher here without at least some training in maths teaching and at least GCSE maths (which is a school-leaving qualification for 16-year-olds, certainly more than elementary school). But it is a profession that tends to attract people who are less strong on the maths side, and that definitely does get passed on to kids.

I've also come across some scary research that children who are (told they are) "good at" maths are much more likely to think of themselves as intelligent and capable and able to master new academic topics than children who are (told they are) "bad at" maths. Specifically maths, I think partly because of the issue of primary school teachers being weak in that area anyway. And partly because maths (at least at elementary level) is the type of skill where you either can do a particular problem or you can't, and if you don't have a good teacher who is skilled at dealing with this, it's easy to feel that there's just something fundamentally wrong with your brain, in contrast to other subjects where it's more likely that you'll feel that if you practice more you'll gradually get better.

Have you ever read John Holt's How Children Fail?
Nope, thanks for the rec!

[liv]

Really nobody should be made to suffer at any point in their education, that's just awful pedagogy! But I do think people should be "made to" persevere with subjects they're weaker in. I do think it's often true that teachers have a better idea what skills are useful in real life than children or teenagers, but it's the responsibility of the teacher to demonstrate the usefulness, not just assert it!

It's sort of bleakly amusing that my circle are also currently discussing a recent report about girls being put off sport by poor PE teaching in schools. I can't link you to the most detailed commentary on this because it's in a locked post, but seriously, take a group of people who are not only college-educated but most of whom have graduate and professional degrees, and watch them talk about how they spent years resenting how they were treated at school when they didn't excel at sport, and how as a result they never did any exercise at all once it stopped being compulsory. Going through your life never doing any physical exercise is much worse, and much more impoverished, than going through your life never doing any maths! Yet bad teaching combined with a lack of talent can destroy the confidence of even quite high-achieving individuals.