What if nobody is bad at maths?(theguardian.com)
theguardian.com
What if nobody is bad at maths?
https://www.theguardian.com/books/2023/may/29/what-if-nobody-is-bad-at-maths
13 comments
In the US k-12 math seems to be taught as a skill to pass tests and little else. Maybe if you're lucky you'll use some calculus or algebra in science classes.
And it's taught in a lock-step sequence. If you fall behind, it is generally impossible to catch up.
Lower division mathematics in universities seems to be taught either for math majors (the important people, selected based on whether they already know the course material), science and engineering majors (the plug and chug contingent), and everyone else (as a "weeder" course to discourage students from continuing in mathematics, science or engineering.) Instructors view the course as an exercise in effort minimization and student sorting.
A similar approach is often used in basic science and engineering courses as well.
The "weeder" course is a wonderful metaphor because it casts so many students in the role of "weeds" - harmful and worthless invaders who need to be pulled out by the roots, shredded and burned (or perhaps dumped into a compost heap, if the university is environmentally inclined.)
And it's taught in a lock-step sequence. If you fall behind, it is generally impossible to catch up.
Lower division mathematics in universities seems to be taught either for math majors (the important people, selected based on whether they already know the course material), science and engineering majors (the plug and chug contingent), and everyone else (as a "weeder" course to discourage students from continuing in mathematics, science or engineering.) Instructors view the course as an exercise in effort minimization and student sorting.
A similar approach is often used in basic science and engineering courses as well.
The "weeder" course is a wonderful metaphor because it casts so many students in the role of "weeds" - harmful and worthless invaders who need to be pulled out by the roots, shredded and burned (or perhaps dumped into a compost heap, if the university is environmentally inclined.)
I was considered bad at maths a long time ago, barely passed calculus in college. 20 years later, I wrote Geometry for Programmers.
Maths is a lot of things. Meticulous symbol crunching is one of them. I'm not good at that specific part, I'm constantly ending up with the wrong sign or losing variables doing even the simplest algebra. Luckily, maths is the other things too. For one, I get kicks from inventing things, and maths gives plenty of opportunity for that. I enjoy solving problems, I like experimenting, and there is a lot of that in maths too.
As for the symbolic computations, I acknowledge that there are people who enjoy them too, I'm just not one of these people, so I use a computer-aided algebra system. Makes math fun again: https://wordsandbuttons.online/sympy_makes_math_fun_again.ht...
Maths is a lot of things. Meticulous symbol crunching is one of them. I'm not good at that specific part, I'm constantly ending up with the wrong sign or losing variables doing even the simplest algebra. Luckily, maths is the other things too. For one, I get kicks from inventing things, and maths gives plenty of opportunity for that. I enjoy solving problems, I like experimenting, and there is a lot of that in maths too.
As for the symbolic computations, I acknowledge that there are people who enjoy them too, I'm just not one of these people, so I use a computer-aided algebra system. Makes math fun again: https://wordsandbuttons.online/sympy_makes_math_fun_again.ht...
I was put through all the way to Calculus in High School. Didn't do much for me, I didn't really ever end up using high level analysis in college. The math I did become interested in was set-theory, topology, logic, those sorts of things. I feel like its more important to teach kids those latter topics than analysis, since almost nobody uses analysis in their day to day lives, but operations of logic and abstract algebra and the like can always apply and also help you think about the world differently.
I would say: logic, set theory, algebra through elementary/middle school. Then introduce maybe some geometry and basic trigonometry in late middle early highschool. Then you can have different tracks for different areas of math: kids who really love analysis can do an analysis track, kids who think set theory is the shit can continue with advanced logic (maybe some philosophy of math?), geometry as well. And for Juniors and Seniors who are really, really into math, you can introduce advanced topics like analytical geometry or algebraic topology and the like (although I think those topics are probably more appropriate for a college level class).
I would say: logic, set theory, algebra through elementary/middle school. Then introduce maybe some geometry and basic trigonometry in late middle early highschool. Then you can have different tracks for different areas of math: kids who really love analysis can do an analysis track, kids who think set theory is the shit can continue with advanced logic (maybe some philosophy of math?), geometry as well. And for Juniors and Seniors who are really, really into math, you can introduce advanced topics like analytical geometry or algebraic topology and the like (although I think those topics are probably more appropriate for a college level class).
Interesting idea but the examples given are trivial mathematics. See art of problem solving for an actual problem solving based way to learn nathematics
People say they are bad at maths because they are being polite. It's like if they say they are bad at cleaning poopy toilets. It's because they can probably get someone else to do it for them.
I'm of the opinion that no one is bad at math.
But as the article says, math is challenging and precise, in ways other subjects aren't. There isn't always one and exactly one English answer: they have smoother correct/incorrect gradients.
What I think people actually hate about math is (a) having to practice/memorize to get up to the baseline, (b) being unsupported when they're not getting it ("dumb question" fear), & (c) as a consequence of being unsupported and never learning topics, future topics are impenetrable.
And naturally, instead of saying "I didn't invest enough time in practicing and/or ask my teachers enough questions," people in bad math learning situations default to "I'm bad at math."
No one to blame. Nothing to be done. Everyone forgiven.
But as the article says, math is challenging and precise, in ways other subjects aren't. There isn't always one and exactly one English answer: they have smoother correct/incorrect gradients.
What I think people actually hate about math is (a) having to practice/memorize to get up to the baseline, (b) being unsupported when they're not getting it ("dumb question" fear), & (c) as a consequence of being unsupported and never learning topics, future topics are impenetrable.
And naturally, instead of saying "I didn't invest enough time in practicing and/or ask my teachers enough questions," people in bad math learning situations default to "I'm bad at math."
No one to blame. Nothing to be done. Everyone forgiven.
I'm bad at math.
This doesn't mean I can't do math, but it means its 5x as hard for me as it is for you. I find math people actually wind up enjoying the puzzle and the mastery; I never did.
This isn't a problem. Most people find some things come easier to them or are more rewarding than others.
But it seems to me there's a line between helping people do stuff they're bad at and insisting that there's no such thing as being bad at them.
This doesn't mean I can't do math, but it means its 5x as hard for me as it is for you. I find math people actually wind up enjoying the puzzle and the mastery; I never did.
This isn't a problem. Most people find some things come easier to them or are more rewarding than others.
But it seems to me there's a line between helping people do stuff they're bad at and insisting that there's no such thing as being bad at them.
Do you remember the first time you found math "hard"? What was your teacher like? What was your experience like?
Honestly curious! (as someone who cried memorizing multiplication tables)
Honestly curious! (as someone who cried memorizing multiplication tables)
Huh, that's an interesting question. I'm not sure.
There was a moment when they broke out the honors tracks and I knew I should be in advanced history/english/science/everything except for math. I was doing fine at the regular pace, but would struggle to keep up with the kids who actually enjoyed the challenge and picked it up easy. But that tells me the split happened much earlier.
On the other hand, I know when I realized I was good at writing. I read constantly as a kid and started writing fiction by age 9.
And from that angle I can relate: I would help friends with writing in college. It's almost always possible to help someone who struggles to capture their thoughts clearly on paper or just approach a blank page, but that doesn't mean they're ever going to like the craft or develop a proclivity towards it.
There was a moment when they broke out the honors tracks and I knew I should be in advanced history/english/science/everything except for math. I was doing fine at the regular pace, but would struggle to keep up with the kids who actually enjoyed the challenge and picked it up easy. But that tells me the split happened much earlier.
On the other hand, I know when I realized I was good at writing. I read constantly as a kid and started writing fiction by age 9.
And from that angle I can relate: I would help friends with writing in college. It's almost always possible to help someone who struggles to capture their thoughts clearly on paper or just approach a blank page, but that doesn't mean they're ever going to like the craft or develop a proclivity towards it.
Further curiosity, did you do extra math at home before the honors split?
I went to a college prep school, and our math teacher from ~3-5 grades was excellent. (We were lucky and she moved up with our class every year)
But I had a sneaking suspicion that by the time the honors split happened (5th grade?), there was a substantial "home" work delta between future-advanced kids and everyone else.
I certainly didn't like math, but my father was dead-set on my learning it. So I know I completed every bit of school homework + a ton of extra practice problems + reviewed problems with him, before honors began.
I expect to everyone else it looked like I "got" math, but there was a lot of burning the candle, and it wouldn't have been my own choice. (That said, mostly grateful, as it did carry me through college math well)
I went to a college prep school, and our math teacher from ~3-5 grades was excellent. (We were lucky and she moved up with our class every year)
But I had a sneaking suspicion that by the time the honors split happened (5th grade?), there was a substantial "home" work delta between future-advanced kids and everyone else.
I certainly didn't like math, but my father was dead-set on my learning it. So I know I completed every bit of school homework + a ton of extra practice problems + reviewed problems with him, before honors began.
I expect to everyone else it looked like I "got" math, but there was a lot of burning the candle, and it wouldn't have been my own choice. (That said, mostly grateful, as it did carry me through college math well)
There are absolutely dumb questions. Such as sitting in class not paying attention and asking the teacher a question where the answer was mentioned 30seconds beforehand. 100+ times in a semester.
When said teacher has three of these students, the rest of the class suffers.
When said teacher has three of these students, the rest of the class suffers.
It’s all relative. In a class full of high iq (>150) people, many questions would be seen as dumb that wouldn’t be seen as dumb by a class full of people with learning disabilities.
The spectrum is wide. Everything alas is dumb. Never assume you’re the smartest person in the room.
The spectrum is wide. Everything alas is dumb. Never assume you’re the smartest person in the room.
There is no classroom full of students 3+ standard deviations above the norm. (15 is a standard deviation. 145 is 3 standard deviations).
And if there were, the reasons stupid questions would be asked is because kid#11 was not paying attention and nothing to do with their intelligence.
Which happens plenty of times with average students. These are subjects a decidedly average person can understand with effort and study. But if distracted by well... Life... Things happen.
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No joke, one of the smartest people I know was distracted in class because he won Jeopardy and the NDA / don't tell anybody was kinda stressing him out. That kinda thing.
Life finds a way to distract us, even the smartest of us.
And if there were, the reasons stupid questions would be asked is because kid#11 was not paying attention and nothing to do with their intelligence.
Which happens plenty of times with average students. These are subjects a decidedly average person can understand with effort and study. But if distracted by well... Life... Things happen.
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No joke, one of the smartest people I know was distracted in class because he won Jeopardy and the NDA / don't tell anybody was kinda stressing him out. That kinda thing.
Life finds a way to distract us, even the smartest of us.
> There is no classroom full of students 3+ standard deviations above the norm.
May be 145 is unrealistic, but 130 is not. It's only 1 in 44, which should be a pretty realistic figure. My own high school had a similar ratio of admission.
May be 145 is unrealistic, but 130 is not. It's only 1 in 44, which should be a pretty realistic figure. My own high school had a similar ratio of admission.
“was not paying attention and nothing to do with their intelligence”
You might be surprised to learn that people with an iq of 80 have a hard time paying attention to much of anything.
My point was not to quibble over the likelihood of a classroom of 150’s, but to illustrate a point, that what counts as a dumb question is largely a function of the average cognitive capacity of the reference group. You may disagree and find context doesn’t matter, and to some extent I can see where you are coming from: mistakes like not paying attention seem to be results of a slightly different thing than pure g intelligence. I see that, but suspect the correlation is so high that the distinction matters only a little.
You might be surprised to learn that people with an iq of 80 have a hard time paying attention to much of anything.
My point was not to quibble over the likelihood of a classroom of 150’s, but to illustrate a point, that what counts as a dumb question is largely a function of the average cognitive capacity of the reference group. You may disagree and find context doesn’t matter, and to some extent I can see where you are coming from: mistakes like not paying attention seem to be results of a slightly different thing than pure g intelligence. I see that, but suspect the correlation is so high that the distinction matters only a little.
> My point was not to quibble over the likelihood of a classroom of 150’s, but to illustrate a point, that what counts as a dumb question is largely a function of the average cognitive capacity of the reference group.
And in my experience, a "dumb question" is asked all the time by highly smart people who happened to have lost their attention span at that moment.
> I see that, but suspect the correlation is so high that the distinction matters only a little.
I was a very distracted student growing up. I made it a point to ask stupid questions, because it was more important to hold the class back and make sure I got my learning, than to otherwise pretend I was smarter than who I really was.
I get that teachers got pissed off at me for not paying attention. I also get that I was holding back the class. But alas, the name of the game is learning. You can't learn if you've missed the material. If you've missed the material, better ask the question right now (while you still remember), than wait later in the week when you've really forgotten everything.
And in my experience, a "dumb question" is asked all the time by highly smart people who happened to have lost their attention span at that moment.
> I see that, but suspect the correlation is so high that the distinction matters only a little.
I was a very distracted student growing up. I made it a point to ask stupid questions, because it was more important to hold the class back and make sure I got my learning, than to otherwise pretend I was smarter than who I really was.
I get that teachers got pissed off at me for not paying attention. I also get that I was holding back the class. But alas, the name of the game is learning. You can't learn if you've missed the material. If you've missed the material, better ask the question right now (while you still remember), than wait later in the week when you've really forgotten everything.
When I used to hear people ask those kinds of questions I just assumed they had learning disabilities of some sort. I never really felt “held back” by other students as much as by the curriculum or by ability grouping or the large class sizes.
I mean, I know this other guy who absolutely was mentally handicapped in my Calculus class.
He obviously could do calculus, but we all had to be careful how we talked and interacted, because his ability outside of math was almost nil.
Must have been one of those 'idiot-savants' or something.
He obviously could do calculus, but we all had to be careful how we talked and interacted, because his ability outside of math was almost nil.
Must have been one of those 'idiot-savants' or something.
This is why you can rewind video. What is the excuse for the desire for it to be like a theater play with the same actor/teacher reading the same script every year?
The irony is that it is the system that is stubborn, unable to learn from its mistakes, unable to just try things and fail, unable to comprehend why and when it fails.
When subjected to school I think I could have listed thousands of components of the formula that do not compute. Now I know the most significant and most outlandish mistakes are reasonably documented by sufficiently credible people. There are lots of much less obvious but hilarious and spectacular ideas and experiments.
A guy making a quality children TV program here said that teachers should have the highest salaries. Our smartest people should want to become teachers one day, as the ultimate career goal.
The irony is that it is the system that is stubborn, unable to learn from its mistakes, unable to just try things and fail, unable to comprehend why and when it fails.
When subjected to school I think I could have listed thousands of components of the formula that do not compute. Now I know the most significant and most outlandish mistakes are reasonably documented by sufficiently credible people. There are lots of much less obvious but hilarious and spectacular ideas and experiments.
A guy making a quality children TV program here said that teachers should have the highest salaries. Our smartest people should want to become teachers one day, as the ultimate career goal.
Indeed. I think the most cost, effective, and resource-efficient pedagogical method for undergrad would be {best video} + {played in a lecture all} + {with a TA breaking the video into chunks and asking for questions} + {TA session with smaller groups}.
Redoing 90% of the same lecture yearly, by faculty whose time could better be spent researching, is insane.
But any change in teaching upsets a lot of academia economics, which are tenuous as-is.
I expect it'd take a federal mandate to make the above shift (a la ACA and electronic health records).
Redoing 90% of the same lecture yearly, by faculty whose time could better be spent researching, is insane.
But any change in teaching upsets a lot of academia economics, which are tenuous as-is.
I expect it'd take a federal mandate to make the above shift (a la ACA and electronic health records).
I am not sure that this is true, if they are asking about some of the harder concepts even if someone thought they understood it at the time, repetition is key to learning. Repeating some of the harder things may make the rest of the students in the class better.
Nobody is, unless they're not 5. Brain plasticity is a thing, but the article doesn't mention it.
The article content and main thesis is actually very good: yes, we should improve math education, allow people to ask "stupid" questions, think about student's feelings and use more real-world examples to explain why different mathematical concepts are actually quite important.
However, I can't agree with the headline. While a lot of people are not actually bad at math and just need a better education, there's certainly a very large amount of people who are just really bad at abstract reasoning, and they will not be good at math or a lot of other tasks no matter how you teach them.
Ability is a combination of uprising and innate traits, and ignoring either one of this components for the sake of the other is a mistake.
However, I can't agree with the headline. While a lot of people are not actually bad at math and just need a better education, there's certainly a very large amount of people who are just really bad at abstract reasoning, and they will not be good at math or a lot of other tasks no matter how you teach them.
Ability is a combination of uprising and innate traits, and ignoring either one of this components for the sake of the other is a mistake.
The fundamental assumption of the headline is that human ability doesn't have a normal distribution. It's a kind of ironic error.
The problem with maths education is that it's often distant and unintuitive; there doesn't seem to be any connection between the manipulations and anything 'real' or 'visualizable'.
I don't know why we don't introduce elementary group theory at an earlier age. This is something quite intuitive; a bunch of things, and operations that convert between them, and gives a solid feeling for what the game is.
And although 'place numbers' are taught early, later we learn about 'bases' in a kind of fragmented way, whereas this is probably the time to introduce the whole elegant place-number system, showing places as exponents (including fractional exponents - ie 2^1/2 + 2^1/2 = 2^1 => x^1/2 is clearly the square root) in a coherent way, and toying with negative bases, base phi, ternary, etc.
'shut up and calculate' might work in some contexts, but it's not a good way to build understanding and intuition.
I don't know why we don't introduce elementary group theory at an earlier age. This is something quite intuitive; a bunch of things, and operations that convert between them, and gives a solid feeling for what the game is.
And although 'place numbers' are taught early, later we learn about 'bases' in a kind of fragmented way, whereas this is probably the time to introduce the whole elegant place-number system, showing places as exponents (including fractional exponents - ie 2^1/2 + 2^1/2 = 2^1 => x^1/2 is clearly the square root) in a coherent way, and toying with negative bases, base phi, ternary, etc.
'shut up and calculate' might work in some contexts, but it's not a good way to build understanding and intuition.
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>I don't know why we don't introduce elementary group theory at an earlier age.
Whenever someone says "we should teach X earlier", that necessarily means we have to teach some Y later, unless you want to add more hours to the schoolday. What would you evict from the curriculum, to make room for it?
Whenever someone says "we should teach X earlier", that necessarily means we have to teach some Y later, unless you want to add more hours to the schoolday. What would you evict from the curriculum, to make room for it?
Not necessarily; teaching some things earlier could make other things easier to understand.
But to answer directly, I don't see a particular need to teach long division/multiplication - they are just algorithms, and as long as the place-number system is understood thoroughly, there's really little use for them.
But to answer directly, I don't see a particular need to teach long division/multiplication - they are just algorithms, and as long as the place-number system is understood thoroughly, there's really little use for them.
See iconicmath.com for one perspective on this using iconic visual math, math that looks like what it means. Symbol processing aka calculation is better suited to computer science than the distinction/difference and indication of maths.
I don't think that being good or bad at something has as much of an impact as whether you're interested in it or motivated by it and therefore choose to do it in the first place.
When someone says they're bad at running, they typically don't mean that they would be bad if they went on a training regimen, they mean that their current state is untrained, bad.
When someone says they're bad at running, they typically don't mean that they would be bad if they went on a training regimen, they mean that their current state is untrained, bad.
A whole lot of "I think", "I believe," "I feel". No reference to existing educational research on what works and what doesn't.
>This isn’t a call to give up, though: instead, we should teach maths differently, in a way that doesn’t churn out mathophobes. When five-year-olds first encounter the subject, it’s as a creative, open-ended activity, involving play and exploration. They learn about numbers using colourful blocks that join up in different ways. They fit these shapes together and tell different stories with them. Just a year or two later, though, maths becomes a discipline with strict rules and a forbidding regime of right or wrong answers. Instead we should try to maintain that sense of exploration and open-endedness, of trying out different approaches to a problem and seeing what works. What’s important about times tables, for example, is not the answers, but the different possible relationships between numbers. What’s important about equations is not the solution, but the techniques we use to untangle a problem using logic. Some of these exercises could be presented more like a Sherlock Holmes mystery, where the focus is on how the clues are pieced together and not just on what the answer must be.
Where's the evidence that this would actually be a superior teaching method? The point of drills is to counteract the natural tendency to forget things. Fluency is gained through practice and repetition. People don't want to hear it, they think it's somehow regressive, but it's a fundamental fact about the brain. You can't get around it any more than you can build muscle without consistent training.
Think of an actual Sherlock Holmes mystery you've read before, months or years ago. Do remember the precise sequence of deductions made, leading from evidence to the killer? Probably not. Could you do what Holmes did, having read it? No, you couldn't. You remember enjoying the performance, you remember some quips and some characters, but not the critical details. It was fun, but you didn't learn anything! That's okay for passively enjoying fiction, but mathematics is supposed to be a thing you eventually do yourself, unsupervised. Getting the right answer will actually matter.
>One powerful way of maintaining interest is to link maths to whatever the children already care about, whether that’s food, singing, dancing, drawing, creative writing, sport, Lego, Minecraft or something else. Mathematical concepts can be related to the real world, rather than something abstract: commutativity, for example, might be presented as a dry numerical exercise along the lines of 5+2 = 2+5. Or we can bring it to life by talking about whether or not it makes any difference if tea is made by pouring hot water over tea leaves or by dropping tea leaves into hot water.
>These kinds of approaches will mean covering material more slowly. Some will argue that this is “dumbing down”. On the contrary, we will be teaching maths at a much deeper level, with the likelihood of these lessons being fully absorbed – rather than drilling students on a bunch of algorithms they’re able to grasp only superficially and will forget once they stop using them.
Hahah. She really thinks she's a revolutionary, doesn't she? She actually thinks nobody has thought of this before. They tried this exact thing in America in the 50s-60s, the "New Math". It was a resounding failure and roundly mocked:
https://www.youtube.com/watch?v=UIKGV2cTgqA
For my part, I understood perfectly well what I was doing when I learned algebra and calculus. "Find the root", "find the slope of the curve"; these are actually not difficult ideas. What is difficult is doing them consistently, quickly, without error. You can "know what you're doing" and still be totally unable to actually do it, in practical terms. Recognition ("I get it!") is fundamentally easier than recall ("I did it!"). The only way I got to fluency was by drilling hundreds of exercises. And don't just take my word for it; Alfred North Whitehead was fighting this "anti-actually-knowing-things-ism" crap a century ago.
>It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.
Her commutativity example doesn't make any sense. First, it's not clear that mixing water with tea leaves corresponds to addition. They are two different kinds of thing, and usually we can only add things of the same kind. Why can I "add" water and tea leaves, but I can't "add" apples and oranges? And what about subtraction? If water + leaves = tea, then surely tea - leaves = water. But if you take leaves out of tea, you still have tea, not the water you began with. Second, it does make a difference! There are slight chemical changes, and some people can tell from blind taste tests. Third, why tea? I could equally say that I "add" socks to my feet, and "add" shoes on top of those, but that's clearly non-commutative (but at least "subtraction" works, because I can take off the shoes and the socks and get my feet back!). Pedagogically the tea thing is a disaster -- it leaves you more confused than you started. I hated this kind of fake-explanation as a kid. It's sheer laziness on the part of the teacher.
I think it's telling that she describes herself as a mathematician, and relates no personal experience of teaching mathematics. People far out on the right side of the ability distribution tend to have trouble imagining how average people think. And grownups in general tend to forget how hard it was as a kid to learn things the first time, because they can't shed the mental framework they built up and see things with untrained eyes again.
EDIT lol of course, she's a category theorist. that explains everything.
>This isn’t a call to give up, though: instead, we should teach maths differently, in a way that doesn’t churn out mathophobes. When five-year-olds first encounter the subject, it’s as a creative, open-ended activity, involving play and exploration. They learn about numbers using colourful blocks that join up in different ways. They fit these shapes together and tell different stories with them. Just a year or two later, though, maths becomes a discipline with strict rules and a forbidding regime of right or wrong answers. Instead we should try to maintain that sense of exploration and open-endedness, of trying out different approaches to a problem and seeing what works. What’s important about times tables, for example, is not the answers, but the different possible relationships between numbers. What’s important about equations is not the solution, but the techniques we use to untangle a problem using logic. Some of these exercises could be presented more like a Sherlock Holmes mystery, where the focus is on how the clues are pieced together and not just on what the answer must be.
Where's the evidence that this would actually be a superior teaching method? The point of drills is to counteract the natural tendency to forget things. Fluency is gained through practice and repetition. People don't want to hear it, they think it's somehow regressive, but it's a fundamental fact about the brain. You can't get around it any more than you can build muscle without consistent training.
Think of an actual Sherlock Holmes mystery you've read before, months or years ago. Do remember the precise sequence of deductions made, leading from evidence to the killer? Probably not. Could you do what Holmes did, having read it? No, you couldn't. You remember enjoying the performance, you remember some quips and some characters, but not the critical details. It was fun, but you didn't learn anything! That's okay for passively enjoying fiction, but mathematics is supposed to be a thing you eventually do yourself, unsupervised. Getting the right answer will actually matter.
>One powerful way of maintaining interest is to link maths to whatever the children already care about, whether that’s food, singing, dancing, drawing, creative writing, sport, Lego, Minecraft or something else. Mathematical concepts can be related to the real world, rather than something abstract: commutativity, for example, might be presented as a dry numerical exercise along the lines of 5+2 = 2+5. Or we can bring it to life by talking about whether or not it makes any difference if tea is made by pouring hot water over tea leaves or by dropping tea leaves into hot water.
>These kinds of approaches will mean covering material more slowly. Some will argue that this is “dumbing down”. On the contrary, we will be teaching maths at a much deeper level, with the likelihood of these lessons being fully absorbed – rather than drilling students on a bunch of algorithms they’re able to grasp only superficially and will forget once they stop using them.
Hahah. She really thinks she's a revolutionary, doesn't she? She actually thinks nobody has thought of this before. They tried this exact thing in America in the 50s-60s, the "New Math". It was a resounding failure and roundly mocked:
https://www.youtube.com/watch?v=UIKGV2cTgqA
But in the new approach, as you know, the important thing is to understand what you're doing, rather than to get the right answer.
....
(And you know why four plus minus one
Plus ten is fourteen minus one?
'Cause addition is commutative, right!)
For my part, I understood perfectly well what I was doing when I learned algebra and calculus. "Find the root", "find the slope of the curve"; these are actually not difficult ideas. What is difficult is doing them consistently, quickly, without error. You can "know what you're doing" and still be totally unable to actually do it, in practical terms. Recognition ("I get it!") is fundamentally easier than recall ("I did it!"). The only way I got to fluency was by drilling hundreds of exercises. And don't just take my word for it; Alfred North Whitehead was fighting this "anti-actually-knowing-things-ism" crap a century ago.
>It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.
Her commutativity example doesn't make any sense. First, it's not clear that mixing water with tea leaves corresponds to addition. They are two different kinds of thing, and usually we can only add things of the same kind. Why can I "add" water and tea leaves, but I can't "add" apples and oranges? And what about subtraction? If water + leaves = tea, then surely tea - leaves = water. But if you take leaves out of tea, you still have tea, not the water you began with. Second, it does make a difference! There are slight chemical changes, and some people can tell from blind taste tests. Third, why tea? I could equally say that I "add" socks to my feet, and "add" shoes on top of those, but that's clearly non-commutative (but at least "subtraction" works, because I can take off the shoes and the socks and get my feet back!). Pedagogically the tea thing is a disaster -- it leaves you more confused than you started. I hated this kind of fake-explanation as a kid. It's sheer laziness on the part of the teacher.
I think it's telling that she describes herself as a mathematician, and relates no personal experience of teaching mathematics. People far out on the right side of the ability distribution tend to have trouble imagining how average people think. And grownups in general tend to forget how hard it was as a kid to learn things the first time, because they can't shed the mental framework they built up and see things with untrained eyes again.
EDIT lol of course, she's a category theorist. that explains everything.
I'm dyscalculic (with a formal diagnosis) and the "nobody is bad at math, just try harder!" attitude drove me into deep depression during my school years. I still have nightmares about it.
It's surprising since dyslexia is so common and accepted. We understand and accommodate their disability.
It's surprising since dyslexia is so common and accepted. We understand and accommodate their disability.
The title is mathematically equivalent to “what is nobody is good at maths?”
This currently-prevailing attitude that humans are interchangeable cogs with no individual talent or personality would be hilarious if it wasn’t so destructive.
This currently-prevailing attitude that humans are interchangeable cogs with no individual talent or personality would be hilarious if it wasn’t so destructive.
Not at all. Just because no one is bad doesn’t imply everyone is equally good at math, unless you think there are only 2 discrete levels of math aptitude. Good and bad.
You can mince words, but the concept of being "bad" is relative to the whole. A person bad at maths today would have been good by 1800s standards.
Also there isn't anything wrong with being bad at something. If you enjoy it, do it anyway. If you don't enjoy it, do something else.
I was a solid "low A student in STEM and barely passed English (haha as a lot of us are). I couldn't care less. I scraped through, and absolutely didn't go into the field of literature. Nothing wrong with that.
Also there isn't anything wrong with being bad at something. If you enjoy it, do it anyway. If you don't enjoy it, do something else.
I was a solid "low A student in STEM and barely passed English (haha as a lot of us are). I couldn't care less. I scraped through, and absolutely didn't go into the field of literature. Nothing wrong with that.
The article starts with “Here’s how to stop maths-phobia setting in” but does not focus on how to overcome ingrained maths-fobia in adults.
What attitude towards math would have prevented your depression and trauma?
I think that if “anyone can do math” implies “equally well”, or “any kind of math”, this is going to hit a lot of people hard.
I found the math that I was good at very late in life.
What attitude towards math would have prevented your depression and trauma?
I think that if “anyone can do math” implies “equally well”, or “any kind of math”, this is going to hit a lot of people hard.
I found the math that I was good at very late in life.
I half-jokingly refer to myself as a recovering math-phobic. What did wonders for my relationship with the subject was to have an actual, concrete problem I wanted to solve, and to experience first hand the joy of understanding its mathematical solution for the first time. It’s the same joy I experienced as a young programmer: the thrill of success, mixed with wonderment at how something could be so simple and yet so magical.
I am convinced that accomplishment breeds passion, and that the way to get over a fear of math is the same as any other phobia; confront it in small increments until you’re able to get a few “wins”.
I am convinced that accomplishment breeds passion, and that the way to get over a fear of math is the same as any other phobia; confront it in small increments until you’re able to get a few “wins”.
Math is taught so poorly in school. It is taught as rote memorization of formulas with no context and no questions about WHY we are doing what we are doing.
I've been on a personal quest to help rehabilitate people who self identify as "bad at math" because I'm convinced that most of them have been doing some sort of trauma induced avoidance for their whole lives and don't deserve to have this math shame hanging around their necks.