Many Indian children can use math to solve market problems, but not school problems

by on September 8, 2017 at 2:06 am in Economics, Education | Permalink

The untapped math skills of working children in India: Evidence, possible explanations, and implications (with A. V. Banerjee, S. Bhattacharjee & R. Chattopadhyay)

It has been widely documented that many children in India lack basic arithmetic skills, as measured by their capacity to solve subtraction and division problems. We surveyed children working in informal markets in Kolkata, West Bengal, and confirmed that most were unable to solve arithmetic problems as typically presented in school. However, we also found that they were able to perform similar operations when framed as market transactions. This discrepancy was not explained by children’s ability to memorize prices and quantities in market transactions, assistance from others at their shops, reliance on calculation aids, or reading and writing skills. In fact, many children could solve hypothetical transactions of goods that they did not sell. Our results suggest that these children have arithmetic skills that are untapped by the school system.

Latest manuscript

Online appendix

Sourced here.

1 Steve Sailer September 8, 2017 at 2:12 am

Anthropologist Henry Harpending studied the Bushmen of southwest Africa. He noted that even though their language didn’t contain words for the number “four” or higher, they could tell when a shopkeeper tried to cheat them in making change.

2 Josh September 8, 2017 at 6:04 am

The bushmen use money? That’s a little disappointing.

3 aMichael September 8, 2017 at 12:09 pm

You could do a similar study on people’s math skills in games that they are really into that use numbers (like dominoes) vs. their math skills on standardized tests. I noticed in high school many students who were terrible at math (based on test scores and grades) but excelled at dominoes, making it seem as if those who were good at math couldn’t even count.

4 Matthew Young September 8, 2017 at 2:56 am

Pricing is a limited algebra.

Because of the basket system, cargos are containers within larger containers, thus container algebra is generally integer like and decomposable by integer ratios. The distribution of pricing quants is small, the S&L markets will discover a virtual denomination set, one that matches supply and demand queues properly. These are called the denominational algebra, as if your coinage denominations are virtually set to minimize making change. Your interest gains and losses are set according to how far off your purchase is relative to the virtual denomination algebra. Combinatorics and it is not time stationary.

5 Ricardo September 8, 2017 at 12:32 pm

So this is what America has become: intelligent answers to interesting questions.

(No, wait, wrong meme…)

6 msgkings September 8, 2017 at 1:00 pm

LOL nice.

7 Roger Barris September 8, 2017 at 3:15 am

This demonstrates something that I feel has always been missed in behavioral economics: it makes sense that people would be much better, and much more “rational,” in their real-life circumstances than in the type of hypothetical, zero-consequence tests that are used in studies of behavioral economics.

8 dan1111 September 8, 2017 at 7:27 am

There should be a behavioral economics study of this :).

9 Condorcet September 8, 2017 at 9:49 am

This has not been missed in behavioral economics; it has been the no. 1 criticism ever since the first economic experiments. Most of the phenomena which consistently show up in the field have been replicated in the field or have been demonstrated using real-world, observational data, though.
Behavioral finance for instance mostly uses real trading data and find that traders – in the market environments they are used – are subject to loss aversion, reference dependence, disposition effect, etc.

10 Adrian Ratnapala September 8, 2017 at 4:56 am

This sort of thing is plausible and oft reported: that people are better at concrete reasoning than abstract reasoning, even when they have the same mathmatical form. This one is interesting in that it applies to arithmetic (or more plausibily that it applies to the step just before the arithmetic where you digest the problem).

This is pedagocially useful for a vocational schools and such. E.g. a school that wants to train plumbers, turners & fitters and auto mechanics should also prepare them for doing their accounts. The right way then might not be to have a “maths” class with arithmetic, but to integrate the arithmetic into a “bookkeeping” class.

But I am very skeptical that this gives us tool for teaching mathematics qua mathematics. Advanced maths (even very slightly advanced maths) is all about separating form form subject matter. This skill does not come easily, and part of the education is to get around our natural preference for the concrete. Doubling down on the concrete stuff will only hold students back.

11 Axa September 8, 2017 at 7:46 am

The very precise definition of killing the good in the name of perfect.

12 Nigel September 8, 2017 at 8:02 am

But I am very skeptical that this gives us tool for teaching mathematics qua mathematics. Advanced maths (even very slightly advanced maths) is all about separating form from subject matter. This skill does not come easily, and part of the education is to get around our natural preference for the concrete…

Or perhaps recognising that they are separate skills, and teaching them as such from an early age ?
Is mathematics the worst taught subject in schools.. ?

13 Maitreya September 8, 2017 at 5:37 am

India’s education system is truly pathetic. In PISA 2009, India (which nominated two of its best states for the test) stood 72 out of 73 nations. None of India’s universities figure in the top 150 institutes globally. Anyone who has worked with outsourced Indian IT engineers (who are from any engineering institute except the top 10) are just fit for repetitive support and programming jobs – jobs that could easily be replaced by robots and AI in 10 years for those who could afford it.

It is no surprise that the famed Indian IT industry (which is actually just the IT services industry) focuses largely on finding cheap ways to execute existing solutions. There’s innovation no doubt, but nothing compared to what other countries can’t do (but don’t due to lack of cheap labor).

Here is what is truly surprising. A vast number of engineers employees by Indian It companies fresh out of college do not have software engineering-related degrees at all. They are graduates in various other fields, such as Electrical, Electronics, Electronics and Telecommunication etc. The few-months’ training that the companies provide is considered enough to substitute for an entire 4 year degree. Such is the education system that after the training, the IT Engineering graduate is at par with the Electronics and Telecommunication Engineering graduate. This shows that the job is not difficult to do – ANY graduate will do it with a few months of training and hands on.

This may be contrasted with China, a country that Indians often like to compare themselves with. Shanghai stood first in the world in PISA 2009 and then again in 2012. The combined unit of Beijing-Shanghai-Jiangsu-Guangdong stood 10th in 2015. The plan is to nominate the entire country in 2018. Of course these results have their critics in the west – after all, the first instinct of a sore loser is to accuse the winning side of cheating. OECD officially responded to these allegations, castrating the haters in the process:

Whenever an American or European wins an Olympic gold medal, we cheer them as heroes. When a Chinese does, the first reflex seems to be that they must have been doping; or if that’s taking it too far, that it must have been the result of inhumane training.

There seem to be parallels to this in education. Only hours after results from the latest PISA assessment showed Shanghai’s school system leading the field, Time magazine concluded the Chinese must have been cheating. They didn’t bother to read the PISA 2012 Technical Background Annex, which shows there was no cheating, whatsoever, involved. Nor did they speak with the experts who had drawn the samples or with the international auditors who had carefully reviewed and validated the sample for Shanghai and those of other countries.

Only 2% of American 15-year-olds and 3% of European ones reach the highest level of math performance in PISA, demonstrating that they can conceptualise, generalise and use math based on their investigations and apply their knowledge in novel contexts. In Shanghai it is over 30%.

But most people – and almost all governments – know better; the UK recently started using translated Chinese math textbooks in some of its schools. China has multiple institutes in the top 100 globally. China filled 7 times more patents only in 2013 than India did in the last 67 years. Indian IT services companies – Infosys, TCS, Wipro etc. – are much touted abroad, but have utterly failed to take advantage of the recent revolutions in upcoming technologies such as AI, Cloud computing, 3D printing, Cashless transactions, face recognition, quantum computing, genomics, and so on. After all, the word “services” does come from the world “servant”.

14 Steve Sailer September 8, 2017 at 5:56 am

I wouldn’t be wholly trusting of raw PISA scores.

One obvious way to massage the scores upward is to not be all that assiduous in rounding up 15-year-old dropouts and lowlifes to take the PISA test. A recent PISA report said, for example, that Argentina’s terrible score shouldn’t be taken too seriously relative to some other countries because the Argentine authorities had diligently rounded up 80% of the 15-year-old population to take the test. That is a lot higher percentage than some other PISA participants (not to name names, but, ahem, Costa Rica, Vietnam, and Mexico).

15 Steve Sailer September 8, 2017 at 6:01 am

But, yeah, India’s trial run with giving the PISA in a few Indian states a number of years ago resulted in catastrophically low scores:

http://www.unz.com/isteve/pisa-scores-2-indian-states-flop/

India’s scores shouldn’t be this terrible. Islands with a lot Indian agricultural workers, like Mauritius and Trinidad, tend to score like Latin American rather than sub-Saharan countries.

16 Kris September 8, 2017 at 7:57 am

India’s scores shouldn’t be this terrible. Islands with a lot Indian agricultural workers, like Mauritius and Trinidad, tend to score like Latin American rather than sub-Saharan countries.

Better childhood nutrition probably explains that.

17 Kris September 8, 2017 at 7:58 am

And better healthcare, and a better environment to live overall. India is rife with all sorts of pollution: air, water, noise….

18 shrikanthk September 8, 2017 at 10:18 am

Srinivasa Ramanujan had worse nutrition and healthcare than most of these “poor kids” today.

It’s about culture. Period. There simply isn’t a culture oriented towards learning in vast swathes of Indian society. Upper caste virtues haven’t percolated into the rest of the society. Despite affirmative action.

19 Just Another MR Commentor September 8, 2017 at 10:31 am

IQ is genetically determined. The “culture” argument is just the typical crap one hears from the left. Average Indian IQ hovers around 81 – even with the successful Indians in the US it will be reversion to the mean in the next generation or two.

20 shrikanthk September 8, 2017 at 10:35 am

If IQ is genetically determined, how do they improve over decades? (Flynn effect)

21 shrikanthk September 8, 2017 at 10:40 am

“even with the successful Indians in the US it will be reversion to the mean in the next generation or two”

That’s a little amusing. Indians are the second most affluent group in US (next to the Jews), with mean household income levels approaching six figures.

I would expect the mean Indian-American IQ to be around 115. And I don’t see why that would regress to 80 over a few generations. Indians in US are hardly ethnically (or culturally) representative of the average Indian.

22 Just Another MR Commentor September 8, 2017 at 10:42 am

I think the comments here will put things in better context for you
http://www.unz.com/isteve/pisa-scores-2-indian-states-flop/

23 Just Another MR Commentor September 8, 2017 at 10:47 am

Again, culture has nothing to do with IQ it’s generically determined with some environmental effects from childhood diet and pollution.

24 shrikanthk September 8, 2017 at 10:50 am

Seen. I don’t contest the 81 figure. I am contesting your view that Indians in US are around that figure, or will get there. That’s just being ignorant of the selection bias at work here.

Indians in US hardly representative of India. Not representative on any dimension

25 Just Another MR Commentor September 8, 2017 at 10:54 am

That’s true but they will in a few generations.

26 shrikanthk September 8, 2017 at 11:05 am

Unlikely. IQs are on the way up for the “successful” groups on account of greater assortative mating than in earlier generations

27 Just Another MR Commentor September 8, 2017 at 11:22 am

True but not for Indians, they only marry other Indians so they’ll revert to the mean Indian.

28 shrikanthk September 8, 2017 at 11:37 am

“they only marry other Indians”

There are many Indias. The one in US is not a random sample of India as a whole.

29 Just Another MR Commentor September 8, 2017 at 11:38 am

But it will become one, in the future.

30 blah September 8, 2017 at 11:47 am

@Kris: Regarding the childhood nutrition point you may want to see this:

http://www.epw.in/journal/2013/18/special-articles/does-india-really-suffer-worse-child-malnutrition-sub-saharan

I suspect Government schools + the fact that education is forced without much economic rationale on a lot of people who would rather be doing something else may be sufficient to explain the PISA debacle.

31 Reader September 9, 2017 at 6:35 am

This is not how regression to the mean works , @JustAnotherMR. If you select a group from a population and constrain themselves to mate within themselves, even after a large amount of time they will retain the founder effects so long as they don’t go back to the population as a whole. Regression to the mean only happens once. That’s why Ashkenazim remain smart after ages of deviating from the Middle East mean.

https://westhunt.wordpress.com/2013/06/07/the-breeders-equation/ explains it quite well.

32 RC AKA Darryl, Ron September 9, 2017 at 8:40 am

@Just Another MR Commentor September 8, 2017 at 10:31 am

“IQ is genetically determined.”

[The ceiling for IQ is genetically determined, but the floor is all environment.]

33 Hazel Meade September 8, 2017 at 12:19 pm

I wonder how India’s vegetarianism affects cognitive ability. Babies need a lot of iron to avoid becoming anemic in the first year of life, and iron-deficiency anemia can cause permanent mental impairment. So if vegetarian indians aren’t feeding their babies meat, or iron fortified foods, then that could easily lead to significant IQ impairments.

Here’s an articles which states that 70% of indian children under 5 had iron deficiency anemia.
https://www.hindawi.com/journals/anemia/2014/176182/

Anaemia is a major health problem in India. In the 2005-2006 National Family Health Survey (NFHS-3), a household survey aimed at having national and state representative data on population health and nutrition; the prevalence of anaemia was 70% in children aged 6–59 months, 55% in females aged 15–49 years, and 24% in males aged 15–49 years [4].

34 Hazel Meade September 8, 2017 at 12:26 pm

And another article discussing the effe ts of iron deficiency anemia.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4235202/

Among the cognitive impairments caused by iron deficiency, those referring to attention span, intelligence, and sensory perception functions are mainly cited, as well as those associated with emotions and behavior, often directly related to the presence of iron deficiency anemia. In addition, iron deficiency without anemia may cause cognitive disturbances. At present, the prevalence of iron deficiency and iron deficiency anemia is 2%–6% among European children.

Note the MUCH LOWER prevalence of iron deficiency in Europe as compared to India.

35 shrikanthk September 8, 2017 at 12:51 pm

60% of India eats meat. Vegetarian Indians are on an average richer with significantly higher education levels than meat eating Indians. Nothing causal of course. Just citing rhe correlation. You have it wrong

36 Hazel Meade September 8, 2017 at 1:36 pm

Ok, but, irregardless of why there is a lot of iron deficiency, there is a lot of iron deficiency, and it’s probably cause cognitive impairments.
It might not be vegetarianism, but it’s still happening.

37 blah September 9, 2017 at 1:08 am

@Hazel Meade: Interesting comment, though I too like Shrikanthk don’t find it correlated with vegetarianism (for the reasons he cites).

Perhaps it has to do with the fact that at least in India poor people eat *larger amounts* of rice/wheat and far smaller amounts of everything else – vegetables, fruits, lentils etc. If I remember it right, consumption of grains in India has plateaued for a while, whereas consumption of everything else has been increasing (including meat, which I am not happy about!).

38 space September 10, 2017 at 12:45 am

India’s space program, the engineers at least, all come from second-tier universities and towns, with significant female representation. The Brahmins from fancy colleges who would rather stay in India join Facebook and Google.

39 Kris September 8, 2017 at 7:54 am

India’s scores would likely increase dramatically if only private school kids were to take these tests. Government schools are truly abysmal. Teacher absenteeism (and lack of interest in teaching in general) is very high, and they can’t be fired because they are government employees.

40 Maitreya September 8, 2017 at 9:16 am

PISA includes private schools. There is no reason for assuming that India nominated only public schools and not private.

Moreover, even if the schools are private, the curriculum, textbooks, examination papers, evaluation criteria are all decided by the government.

If the Indian government really didn’t nominate private schools, then it seems the HRD ministry is more stupid than I gave them credit for. You never know with India: the then HRD minister Kapil Sibal went on television and dismissed the results, and his ministry claimed that the tests do not fit the “socio-cultural milieu” of Indian students.

http://archive.indianexpress.com/news/poor-pisa-score-govt-blames–disconnect–with-india/996890/

41 Kris September 8, 2017 at 10:01 am

I don’t know how to find that information. But the PISA scores presumably are averaged out over all the test takers, the majority of whom must have been educated in government schools.

There’s nothing seriously wrong with the curriculum, exams, etc. Pretty much all of my contemporaries got 800 or near-800 in the quantitative section of the GRE (I’m taking turn of the century) and it always astonished us how easy those questions were. Most of us used to struggle in the verbal section though, as English vocabulary was not very well-developed for most of us (excepting voracious readers.)

42 shrikanthk September 8, 2017 at 10:08 am

Kris – you’re probably referring to elite private schools in cities like Delhi and Bangalore (Eg : Delhi Public school, National Public school).

I studied in a government school – Kendriya Vidyalaya. And the standards are a LOT lower. The syllabus is great. The students at the top end (top 10%) are world class even in these KVs! But a good chunk of them are terrible. Especially in smaller towns.

43 Kris September 8, 2017 at 10:38 am

@shrikant,

Nope, it was Jamshedpur in the 90s. All schools there were pretty good, even govt ones (not in English though)

44 shrikanthk September 8, 2017 at 10:44 am

Jamshedpur is not a very typical Indian city. Perhaps even more atypical than Delhi or Bangalore!

Let’s take towns like Varanasi, Kanchi, Dharwar…..more typical and representative of Indian demography

45 JWatts September 8, 2017 at 8:41 am

Somebody with a link to: https://indiaschinablog.blogspot.com/

is telling us that: “India’s education system is truly pathetic.” and that China’s system:

“This may be contrasted with China, ”

is awesome.

46 blah September 8, 2017 at 11:43 am

He is the Chinese Thiago Ribeiro.

47 Maitreya September 8, 2017 at 11:58 am

I’ve always said that MR is a blog where the comments make more sense than the actual post. Reading your comments however, I stand corrected.

48 blah September 9, 2017 at 1:02 am

Your comment merely reveals your deep narcissism and insulting-skill.

49 Hazel Meade September 8, 2017 at 12:12 pm

China does a ton of manipulation on it’s stats.

My brother worked in China for several years and he would report than many of the Chinese Engineers were basically trained in technical colleges, just to use a CAD program and little else. The Chinese government simply renamed the technical school a “University”.
Similarly there’s a ton of Chinese scientific journals that are just garbage. They exist only to project the image that Chinese science and technology research is on par with the rest of the world’s by publishing a lot of papers. They’re improving, but they’re really not on the level of Japan or South Korea yet.

India at least, publishes in English and is engaged with the real scientific community. They aren’t orchestrating a giant PR operation to make themselves look better than they really are.

50 Maitreya September 11, 2017 at 4:15 am

China is a large country with the largest population – and a developing country at that. Thus, compared to western countries, both genuine research and fraud are amplified. Of course, the western mainstream focuses largey on the fraud part of it.

I am not going to sit here and respond to the canard that somehow India is somehow better or even comparable to China in academic research and publishing. A simple school-child Google search would prove that there is no “race” between Indian and China – China has already won. Apparently, all global organizations and journals – who say that China is becoming a global leader in science and R&D (not withstanding the fraud cases) – are also in cahoots with the Chinese government in their PR campaign.

Remember folks – When other countries take initiatives to improve their scientific output, then that is absolutely genuine. But when China does it, then it is simply a PR operation!

51 anon September 9, 2017 at 4:00 am

All valid points by @Maitreya – and yes the Indian educational system is abysmal. But like anything else about India the range of variation is fairly wide. I have been noticing the steady flow of students from Indian Statistical Institute of Kolkata to Ph.D programs in the US, and then a smaller cohort of these students filtering to the Statistics departments (including top ones like Stanford and Berkeley) as faculty.

52 Anonymous Bosch September 8, 2017 at 6:32 am

Reminds me of the scenes in Roddy Doyle’s “A star called Henry” where Henry starts in school:

–Two and two? she said.
–Don’t know, I said. –Two and two what?
–Cows, she said.
–Four, I said (…)
–Twenty-seven and twenty-seven, she said
– What?
–Bottles.
–What’s in them?
–Porter.
–Fifty-four.
–Are you a genius, maybe?
–What’s a genius? I asked.
–A boy with a big brain, she said.
–More than likely, I said. (…)
She picked up a long piece of chalk and wrote 6 +6 +14 – 7 = on the blackboard. She did it without looking at the numbers; her eyes roved the classroom. Then, tapping the board under each number, she spoke.
–Now Henry, tell us all. If a man has six very valuable male dogs and six very valuable bitches and they have fourteen puppies but he has to sell seven of them because he’s been a bit slow with the rent and the landlord is threatening to evict him, how many dogs will he have left?
–Nineteen, I said.”

53 Bill Benzon September 8, 2017 at 7:05 am

I’ve not read the article, but off-hand I think work on the Wason selection task is germane. As the Wikipedia article says, “The test is of special interest because people have a hard time solving it in most scenarios but can usually solve it correctly in certain contexts. In particular, researchers have found that the puzzle is readily solved when the imagined context is policing a social rule.”

Well, arithmetic calculation is a bit different from the Wason selection task (which typically involves reason about the fronts and backs of four cards), but it is similarly abstract. But market transactions are social transactions. Here’s a preprint of a an evpsych article on it by Fiddick, Cosmides, and Tooby.

54 Epictetus September 8, 2017 at 7:44 am

When I ran a consulting business, some of the employees loved to argue vehemently why it was a bad idea to try an quantity a problem, rather than just trying and proving their case. All of those employees claimed to be weak a maths, if pressed, but they were all expert at working out if payroll had made a small error in their paycheck, and at any maths supporting their claim for more pay. So what? As other research has found, incentives matter.

55 Li Zhi September 8, 2017 at 8:44 am

I doubt that math (“maths” for those ahem who prefer longer and less rational abbreviations) as taught in elementary school is anywhere near as effective and useful as it could and should be. While you’d think after many centuries of practicing the art of education that we’d know what we’re doing, we don’t seem to. Although, given the variety of human experience, I doubt that a single approach is optimal. While I know parents are a large part of the problem, as are the astoundingly low standards and low pay of teachers, I suspect the largest problem is separating math as if it is divorced from the rest of the world. I’m sure if we relegated language to the same “learn how to use it during the instructional class, and use it no where else during the day” that the kids would be nearly illiterate coming out of school. Oh, wait; in many cases that’s what we do. I know a prize winning high school math teacher who taught imaginary numbers but had NO idea where they’re actually used in everyday life. And she had been teaching for over a decade. Divorcing the teaching of any subject from the use of that subject, whether it be arithmetic, Riemannian Geometry, statistics, logic, science, history, language arts, or even economics and the other almost objective (soft) sciences is just pathetically stupid.

56 Attila Smith September 8, 2017 at 3:21 pm

@ Li-Zhi: I have taught the hypercohomology of complexes of coherent sheaves on non-reduced complex analytic spaces (or on more general locally ringed spaces), with no regard whatsoever to “history, language arts or the other almost objective (soft) sciences”. I’m curious to hear how you would have taught the subject differently from my “pathetically stupid” way. By the way, since you seem to be an expert on Riemannian Geometry, can you remind me if there exists a riemannian structure on real affine n-space that makes it geodesically complete? (You may use history or economics in your answer, of course.)

57 Jeff R September 8, 2017 at 8:46 am

David Simon got there first:

Wallace: Damn Cyril look! Close your eyes. You workin’ a ground stash. 20 tall pinks. Two fiends come up at you and ask for two each, another one cops three. Then Bodie hands you off ten more. But some white guy rolls up in a car, waves you down and pays for eight. How many vials you got left?

Wallace’s Little Brother: Fifteen?

Wallace: How the **** you able to keep the count right and you not be able to do the book problem then?

Wallace’s Little Brother: Count be wrong they **** you up.

58 Giorgio September 8, 2017 at 9:20 am

Ugh you beat me to it

59 JFA September 8, 2017 at 9:03 am

There’s a great scene in the wire (I think season 4) in which a math teacher is posing some question about fractions (or some other concept) using balls or pie as the object and the kids look on him with incredibly blank stares. He changes the question to use money instead and the kids can solve the problem with no issues. He switches back to the balls and they are again stumped by the question.

I’m glad professors from MIT are finally catching up with David Simon.

60 Dave September 8, 2017 at 9:41 am

Ha! My same thought! I didn’t see season 4, but (I think) in season 1 there is a scene where an older brother is helping his younger siblings with math homework. They are stupefied until he restates the problem in terms of the drug packages moving in and out of stash spots!

61 derek September 8, 2017 at 9:32 am

And Canada, with a wonderful education system produces children who passed math classes but don’t know how to make change.

62 Just Another MR Commentor September 8, 2017 at 11:27 am

Canada has a lot of immigrants from India. It’s going to have a lot of problems in 30 years with the much lower IQ second generation.

63 Stuart September 8, 2017 at 10:32 am

I taught maths to a girl who had exactly the characteristic in the article. But she also confounded me with this (I was trying to teach the class how negative numbers work):
Vicky, What happens if you subtract 1 from 1?
– You get minus 1
– No, think of it this way: I give you a banana, and then I take it away from you. What have you got?
– I’m minus a banana.

64 peri September 8, 2017 at 10:49 am

I hope that anecdote is true, because I love it.

Everything is relative, and I guess nothing is too.

65 Stuart September 8, 2017 at 12:06 pm

Gospel. As in the original piece, to get her to do subtraction I had to pose the problem in terms of “How much change would you give if….”.

66 Floccina September 8, 2017 at 10:38 am

It amazes me how early children start to understand money.

67 peri September 8, 2017 at 11:17 am

This reminded me of once having the task of getting the slow table of a first grade classroom through their math work. I too thought children would naturally arrive at school understanding money as a matter of their own interest. Asked to figure which coins were needed to pay for candy or whatever, this one little boy refused to attend to the problem. Didn’t seem to know the values of coins, or pretended not to. He insouciantly insisted that he would simply “write a check” for the candy.

It was torture to be paired with him one-on-one, under the threat of an assignment, whether of the math or abc’s or cutting-and-pasting variety – but the manner in which he resisted classroom mores almost seemed to reflect a kind of sly cleverness at times.

His inability to focus, remain seated, not annoy his classmates, etc., led the teacher to persuade his mother to medicate him, and he went from being a problem, but also one of the more interesting people in the room, to being a sort of cipher in the remainder of his time at the school.

68 Hazel Meade September 8, 2017 at 12:00 pm

Math is a language, so my guess is this is a distinction between being able to speak a language and being able to read/write in that language.
That is, the kids can go math in their heads, but if you write an equation saying x+2 = 4, they will have no idea what those symbols represent.

69 Slugger September 8, 2017 at 12:29 pm

I think that there is more than one way to process a mathematical problem. One way is the formal scholastic way that we are taught in school, and another way is an informal rapid way that might be hardwired in our brains. My schooling emphasized the “show your work” approach. I would often read a problem, “get” the answer very quickly, and then laboriously construct the long method to get the right answer that my teachers wanted to see. I think that many of us can do a lot of math with the informal method, but we let this skill erode away by not using it. The existence of a nonscholastic way of getting mathematical results is dramatized by savants that do fantastic calculations while actually having little/no classroom exposure.
Plato thought that learning to read would impair the powers of the mind to memorize. Perhaps the classroom impairs our mind’s power to calculate as well.

70 education realist September 9, 2017 at 12:30 am

I wrote about this in my own cflassroom–it’s not at all unusual to find kids who can’t think abstractly but have excellent arithmetic skills.

1. Kid who had to verbalize math problems to solve them. He couldn’t isolate x in 3x=15 but if you asked him what times 3 = 15, he’d say “5”. He could get three or four operations deep, too. https://educationrealist.wordpress.com/2012/10/06/teaching-students-with-utilitarian-spectacles/

2. Kid with a measured IQ well below 85 who knew all his math facts cold, could do math in his head beautifully, but could not comprehend what a line meant–the slope, the intercepts, whatever. Tre in this story: https://educationrealist.wordpress.com/2013/10/31/noahpinion-on-iq-or-maybe-just-no-knowledge/

71 peri September 9, 2017 at 11:51 am

#2 was the first of your posts I read, I believe – perhaps you linked to it here.

I realize he’s a young man and younger then, but Noah Smith’s position was so strange. He clearly felt he was Standing Up for All, despite his use of the label “dumber than a box of rocks” – yet the hinge on which he would award people their humanity, really seemed to be: whether they could be trained to manipulate algebraic equations.

72 education realist September 9, 2017 at 3:42 pm

Exactly. He’d talk casually about IQ and “dumb”, while arguing that anyone can learn algebra. He’s never gone back to that well, from what I can tell, so perhaps he understands how foolish he was.

73 JK Brown September 9, 2017 at 12:52 pm

So they’ve got the opposite of “school helplessness”. Keep the bloody “educators” away from these kids or they’ll be ruined.

“In spite of the fact that schools exist for the sake of education, there is many a school whose pupils show a peculiar “school helplessness”; that is, they are capable of less initiative in connection with their school tasks than they commonly exhibit in the accomplishment of other tasks. ”

–How to Study and Teaching How to Study (1909) by F. M. McMurry, Professor of Elementary Education, Teachers College, Columbia University

74 byomtov September 9, 2017 at 2:18 pm

Utterly unsurprising.

Long division is boring. Batting averages are fun.

Addition is boring. Figuring out what you can buy with the five dollars your uncle gave you is fun.

etc.

75 Manu September 11, 2017 at 12:40 pm

Reminded me of this scene from the first season of The Wire: https://www.youtube.com/watch?v=-of-FsuPCj4

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