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Math Problems for children from 5 to 15 (2004) [pdf]
- SeanLuke 5y agoFirst question: > 1. Masha was seven kopecks short to buy a first reading book, and Misha lacked one kopeck. They combined their money to buy one book to share, but even then they did not have enough. How much did the book cost? My goodness, that's an impressive 5 year old.
- noisy_boy 5y agoClearly you have not seen primary school math questions in Singapore's curriculum.
- natpalmer1776 5y agoHonestly this confused me at first read through. If I'm understanding it right, the book costs 7?
- SeanLuke 5y agoI figured it did.
- LeifCarrotson 5y agoI figured the same, but that's a curious definition for "combined their money". That means that Masha has no money, and Misha has six kopecks, so they combined 0 + 6 and are still short of 7. If the price was eight kopecks, they'd have one and seven each, and would have exactly enough. If it cost nine kopecks, they'd have 2 and 8, and would have more than enough. Eventually I concluded that the price must be between 7 and 8 kopecks, however, a kopeck is a fraction of a ruble, and Google tells me the exchange rate is currently something like 76 rubles per USD, and a kopeck is 1/100th of a ruble, so a tiny fraction of a penny, which is itself nearly worthless. Wikipedia says that hyperinflation in early Soviet Russia, inflation during the cold war, the 1998 redenomination of one new RUB ruble to 1000 RUR old rubles, and subsequent inflation in Russia all combine to mean that one kopeck in the early 90s is worth about 40,000 times less than one kopeck today. Similarly, my American son is sometimes confused why Mom and Dad pay for stuff at stores with dollar bills, but also have pennies, nickels, and dimes. Morris the Moose can buy a lemon drop for a penny, why does a small pack of lemon drops cost two dollars at the store? The last time you could subdivide a kopeck in half into a denga was around the 1917 revolution, so if the book cost 7 kopecks and one denga, Masha could have one denga and Misha could have 6 kopecks and one denga, and they could combine to get 7 kopecks but not have enough. The true answer is that if Masha and Misha have been collecting old kopecks forgotten between the couch cushions in their piggybanks, they'll be better off melting the coins for scrap metal, because they're not keeping up with inflation. You can barely buy a piece of paper for a ruble, much less a kopeck. Except the dengas, if they're in good condition, they should sell those to rare coin collectors for on the order of 100,000 kopecks, which is an awfully large number for a five-year-old to be dealing with.
- scotty79 5y ago> kopeck in half into a denga was around the 1917 revolution Really? I think I had 1/4 kopek coin somewhere when I was a kid (old foreign coin). I don't think it was this old.
- AlanYx 5y agoI wonder if there's an issue in translation. How could they "combine" their money if Masha had nothing to begin with? But if we assume quantities of money can be non-integers, then the problem is underconstrained.
- karamanolev 5y agoKopeck - "It is usually the smallest denomination within a currency system." I presume they used kopecks for a purpose and not rubles, dollars or another unit that can be subdivided. That forces the integerness of the amounts and thus the presence of a solution.
- Arnavion 5y agoThe solution to the second question requires half-kopeks.
- karamanolev 5y agoI looked at that problem after posting my original and was utterly confused. Would you trust yourself with an answer involving half-pennies? Seems like an error. As others pointed out, in #1, unless the kopecks are integer, the answer is underconstrained. #2 requires non-integer kopecks.
- deleted 5y ago[deleted]
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- watertom 5y agoThe problem is that the girls can't afford to buy a book singularly. Masha needs 7 kopecks to buy 1 book "Misha lacked one", which means to me as an native English speaker that Misha needed just one more Kopeck in order to purchase 1 book. When it's revealed that when they pool their money that they don't have enough to purchase just 1 book, I realized that the translation is faulty and stopped looking at the rest of the problems.
- bla3 5y agoHint: It's much easier if you don't know linear algebra.
- skyde 5y agoCan someone help me with this question. I tried wolframalpha but the question seem to make no sense. https://www.wolframalpha.com/input/?i=solve+for+y%2C+%5By+%3D+x%2B7%2Cy%3Dz%2B1%2C+y%3Ex%2Bz%2C+x%3E0%2C+z%3E0%2C+y%3E0%5D https://www.wolframalpha.com/input/?i=solve+for+y%2C+%5By+%3...
- skyde 5y agoGot it: cost is 7 https://www.wolframalpha.com/input/?i=solve+for+y%2C+%5By+%3D+x%2B7%2Cy%3Dz%2B1%2C+y%3Ex%2Bz%2C+x%3E%3D0%2C+z%3E%3D0%2C+y%3E%3D0%5D https://www.wolframalpha.com/input/?i=solve+for+y%2C+%5By+%3...
- corpMaverick 5y agoPlease don't spoil it for the rest of us. @dang
- Arnavion 5y agoKnowing the answer is 7 isn't a spoiler. The point is to work it out. You'd have to click the URL and see the WA input to be spoiled about that.
- 09asdf0asdf 5y agoYou can constrain the result to whole numbers by adding "y mod 1 = 0" as an additional constraint. https://www.wolframalpha.com/input/?i=solve+for+y%2C+%5By+%3D+x%2B7%2Cy%3Dz%2B1%2C+y%3Ex%2Bz%2C+x%3E%3D0%2C+z%3E%3D0%2C+y%3E%3D0%2C+y+mod+1+%3D+0%5D https://www.wolframalpha.com/input/?i=solve+for+y%2C+%5By+%3...
- waynesonfire 5y agoneat trick, thanks.
- valbaca 5y agoYeah, this was confusing b/c to "be short" does imply that you have some money, otherwise you're 100% short of buying anything!
- rcoumet 5y ago> Vasya has 2 sisters more than he has brothers. How many daughters more than sons do Vasya’s parents have? In a world of gender and pronouns fluidity, does this even have an answer ?
- jMyles 5y agoIt is also nuclear-presumptive: it presumes that Vasya's parents have only daughters and sons with each other.
- culebron21 5y agoCuriously, Vasya (short for Vasiliy) can be a short form of girl's name Vasilisa (though it's rare). I can't recall any mention of divorce apart from school Literature course when I was in school in the 90s (most of material was inherited from the Soviet times). Knowing how Soviet editorial policies worked, I'm assured the editors considered mentioning divorces or non-married parents as seeding wrong attitudes and thus inappropriate for kids.
- dang 5y ago"Eschew flamebait. Avoid unrelated controversies and generic tangents." https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
- jMyles 5y agoAlthough I adore this guideline, I do want to step in to defend this comment. I think that many parents are trying to teach kids in this age range to take a wider view of the possibilities of family shapes and gender identities, and a question of this wording does indeed confound that.
- ordu 5y agoThe problem #13, mentioned in the introduction, is said to be really tough for academicians, but I'm not! Probably I'm just plain stupid.
- prvc 5y agoHe didn't specify the order (or/and script, if you prefer) in which the books were placed, so it's ambiguous.
- SamBam 5y agoThe same order a multi-volume set would be displayed in any bookstore or library in a left-to-right ordering country.
- ordu 5y agoTomes of Pushkin have a natural order ascending from left to right. It may be a cultural thing, but it would be obvious for any Russian child 5 years old or older. No tricks here. But, yeah, even knowing about the natural order of Pushkin on the shelf, I also gave it a thought. I was wrong and just wasted my time. It is an easy problem, without any tricks.
- imvetri 5y agoWhen child labour is illegal, Why shouldn't be child education. We are born with natural skills, mainstream education ruins originality.
- LeifCarrotson 5y agoThey're interesting to adults, too! Simple enough that it feels like you should be able to blurt out the answer, I'm more than twice the maximum recommended age and a professional engineer, but (at least for me) it takes some thought. The top recommended three: > 1. Masha was seven kopecks short to buy a first reading book, and Mishalacked one kopeck. They combined their money to buy one book to share, but even then they did not have enough. How much did the book cost? > 3. A brick weighs one pound and half the brick. How many pounds does the brick weigh? > 13. Two volumes of Pushkin, the first and the second, are side-by-side on a bookshelf. The pages of each volume are 2 cm thick, and the cover – front and back each – is 2 mm. A bookworm has gnawed through (perpendicular to the pages) from the first page of volume 1 to the last page of volume 2. How long is the bookworm’s track? I do take objection to the answer to question 13 - the author seems particularly set on one way of loading the bookshelves as correct.
- sokoloff 5y ago1. Depends on whether kopecks are divisible into a smaller monetary unit or not. If they are divisible into 100 units, I believe the answer is "anywhere between 7.00 and 7.99 kopecks". (Problem #2 requires kopecks to be divisible.)
- deleted 5y ago[deleted]
- ekster 5y agoA kopeck is like a cent (1/100th of a ruble).
- valbaca 5y agoThey're not. It's like a penny. Sure you may have parts of cents like with gas, but for girls buying books, it's the lowest currency value.
- Symbiote 5y agoLong ago, many currencies had more divisions than they do now. The penny of GBP came in quarter pennies (farthings) until 1950. Half US-cent coins were made until 1857.
- rdtsc 5y ago> The hypotenuse of a right-angled triangle (in a standard American examination) is 10 inches, the altitude dropped onto it is 6 inches. Find the area of the triangle. American school students had been coping successfully with this problem over a decade. But then Russian school students arrived from Moscow, and none of them was able to solve it as had their American peers (giving 30 square inches as the answer). Why? That's a good one. I know the answer but won't reveal it since it's a fun one to discover yourself.
- laszlokorte 5y agoFunny in germany we learn the formular for just that: Area_triangle = Base_triangle * Height_triangle / 2 /edit: fixed factor of two
- hereforphone 5y agolol?
- blagie 5y agoThere's a funny story. Before PISA, Finland looked up to the German school system, which was clearly considered superior by both sides. When PISA came out in 2000, Finland was surprised to come out on top for Europe. Germany's performance in math was abysmal -- behind the US even. People started flocking to see what Finland did, and stopped looking up to Germany. https://nces.ed.gov/pubs2002/2002116.pdf https://nces.ed.gov/pubs2002/2002116.pdf The German school system has since gradually improved -- it's no longer behind the US -- but it's far from world-leading.
- Someone 5y agoThat’s either a nice example of hemibel thinking (http://libertycorner.blogspot.com/2004/07/hemibel-thinking.html http://libertycorner.blogspot.com/2004/07/hemibel-thinking.h...), of your memory going away, or of an extremely lousy education. (You are of by a factor of 2)
- satchlj 5y ago
- kangnkodos 5y ago#18 is impossible. This margin is too small to provide the proof.
- blueplanet200 5y agospoiler for how to prove it: think of colors of chessboard (black/white alternating) and what colors a domino piece will always cover.
- SamBam 5y agoNice. I was confused by the L-shaped shading in the top-right corner of the diagram, though.
- eevilspock 5y agoblueplanet200's proof can fit in a sentence or two. So sounds like you came up with an entirely different strategy. I'm curious what it is (doesn't matter if it's not as elegant).
- waynesonfire 5y ago> 3. A brick weighs one pound and half the brick. How many pounds does the brick weigh? huh? Good luck 5 year old. This is how you get kids to hate math.
- haunter 5y agoVery classic problem but yeah maybe a bit overkill for 5 year olds http://jwilson.coe.uga.edu/EMT668/EMT668.Student.Folders/SeitzBrian/EMT669/brick.problem/halfbrick.html http://jwilson.coe.uga.edu/EMT668/EMT668.Student.Folders/Sei...
- SamBam 5y agoThat uses the wording "plus half a brick" instead of "plus half the brick." I think the "a brick" wording could be a little clearer for kids.
- jayrwren 5y agoI can't even read this as english. I feel these "problems" are more about poor grammar than they are math.
- mhh__ 5y agoI could parse it fine but if I were writing this I would include more redundancy e.g. "weighs one pound and half the weight of the [maybe use our to suggest to the reader it's the same one] brick". The well drilled student would be able to parse both but anyone who can struggle with getting the words into their head in the right order like me could struggle.
- valbaca 5y agoExactly. It would read better as "The weight of a brick is equal to one pound plus the weight of half an equivalent brick" i.e. x = 1 + x/2
- satchlj 5y agoin this case, the line between grammar and math is fuzzy - english (or russian) and mathematical symbols are two different languages here which are each capable of describing the same thing. the challenge is to do the necessary translation and rearrangement
- agentultra 5y agoAnother interesting book in this vein if these problems tickle your fancy: https://www.amazon.ca/Math-Three-Seven-Mathematical-Preschoolers/dp/082186873X https://www.amazon.ca/Math-Three-Seven-Mathematical-Preschoo... Working on math problems together with your kids is a fun way to learn how they think and reason. It has led me to have a deeper emotional connection with my kids as I learn what they struggle with in school. I have slowly learned that some times framing the problem a certain way helps them to grasp what is being taught better than brute-forcing them through exercises and homework.
- grouphugs 5y agowe're doin' math alright one by one two by two then (tree n) by (tree n)
- gnull 5y agoFor Russian-speaking readers here who may want to challenge their children, here's the (original?) open book in Russian: http://ilib.mccme.ru/pdf/VIA-taskbook.pdf http://ilib.mccme.ru/pdf/VIA-taskbook.pdf
- coolspot 5y agoI suspect Russian-speaking readers of HN mostly have kids who can’t read/write Russian, unfortunately. Like my daughters, for example.
- gizmondo 5y agoHow actively did you try to teach them to do that?
- coolspot 5y agoThey did go into a Russian child care where they learned basic reading/writing. But after they went into US elementary school, we didn’t want to interfere with their English learning, so without practice they have lost reading/writing skills, but still can speak.
- gregsadetsky 5y agoThere are interesting Wikipedia articles on this topic: "Heritage language" https://en.wikipedia.org/wiki/Heritage_language https://en.wikipedia.org/wiki/Heritage_language https://en.wikipedia.org/wiki/Heritage_language_learning https://en.wikipedia.org/wiki/Heritage_language_learning
- amativos 5y agoThank you for that link! I can read Russian and that version is much clearer.
- xn 5y agoSunshine Math is a great set of math problems for grades K - 8. I couldn't find a publisher, but PDFs of scanned copies are available online.
- brightball 5y agoI try to make math fun in my house. A couple of things I’ve found that work: 1. Anytime there’s a “guess how many are in the jar” contest, I get my kids to use the appropriate formula for volume to see if they can guess the right answer. They usually get really close. 2. Show them how math helps them win at games. Monopoly is great for this where you can calculate the ROI for different properties on the board, how many houses are ideal, etc. you can go further with likelihood of landing on certain properties too. It works. The hardest thing about math motivation as a kid is “where will I use this?” Moneyball (movie) is a good one too.
- handrous 5y ago> It works. The hardest thing about math motivation as a kid is “where will I use this?” I struggle to motivate myself to brush up on or move farther in math as an adult, for similar reasons. Some recreational math is kinda fun, but mostly worthless except as a pastime.
- anyfoo 5y agoJust pick up (analog) electronics as a hobby, and it becomes relevant and necessary like nothing else. Add some light signal processing, and now you understand why you had those Algebra I and II courses in university.
- alexslobodnik 5y agoPlay Factorio [1] [1] https://www.factorio.com/ https://www.factorio.com/
- ffffwe3rq352y3 5y agoMoneyball is one of my favorite movies!
- domino24 5y agoIs there an answer list anywhere? It seems to me that some of these questions could have multiple answers depending on how you interprt the question. I know it is more about the thought exercise, but on some it would be nice to have the correct answer in order to learn how to find the solution.
- SamBam 5y agoI only worked through the first 13, but none of them seemed to me to have multiple solutions (with the exception of whether you can have less than one kopeck, which the author would assume the readers knew you couldn't).
- kangnkodos 5y ago#18 does not have any answer. It's impossible to cover the squares as requested.
- thaumasiotes 5y agoWhat do you mean? You just provided the answer. It's unique.
- thaumasiotes 5y ago> I only worked through the first 13 > (with the exception of whether you can have less than one kopeck, which the author would assume the readers knew you couldn't) You did notice that the cork in the second problem costs half a kopeck?
- purpmint008 5y agoThe only thing worse than being wrong is being wrong and not knowing that you're wrong. We really deserve an answer sheet here. Number 7 is boys+1 right?
- ksec 5y agoOn a related subject, here is a recent experience and I dont know how to deal with it. I have been helping my kids with their homework during the pandemic, I thought it would be easy since I got very good grade 25+ years ago. And then when I sat down doing it. I couldn't remember a thing. Not a single thing. All of a sudden, apart from basic algebra, all of the maths were gone. Zip, Zero. I couldn't remember how sin cos tan works any more. It was like a few years of memory in my brain went missing. For some people it may be funny and have a laugh about it. For me it was shocking, quite horrifying and depressing. I am thinking if I should relearn all those maths again. If so how do you go about it? Most of my friends aren't any good at maths so they thought not remembering any thing was not a problem. But for some strange reason all the basic for Physics, Chemistry and Biology were still there. At least half of it. It was just maths. I dont know if anyone else have similar experience.
- eidelweissflow 5y agoSame - I was a straight A student, loved solving math problems, but now I don’t remember a thing. I think it’s just how our brain works - it gets rid of knowledge that we don’t use any longer. Muscle memory like swimming or riding bicycle stays, but seems like language and math skills don’t retain unless they are being practiced.
- anyfoo 5y agoI don't think so. The feeling described here is familiar to me with certain areas of maths, ones that I definitely knew and have then forgotten seemingly entirely, but when I had to get back into them it was nowhere near having to relearn them. It's true that you forget without regular usage, but it seems the "concept" sticks around, and all you need is some refresher to be able to access it again.
- wrycoder 5y agoThe information isn't erased - it's just that the retrieval synapses haven't been reinforced. It is relatively easy to do that.
- bowmessage 5y ago> 12. A tide was in today at 12 noon. What time will it be in (at the same place) tomorrow? What is this, a maritime exam?
- SamBam 5y agoYeah, this one doesn't have anything to do with math, does it? Off the top of my head, I'd guess that tides lose about an hour per day, so the tide would be in at 1:00 pm. Ah, I guess the point of this is that the next tide is half way between those two, and so would be just after midnight. But to know this, you'd have to know that the tide's cycle is slightly longer than the day's cycle.
- simonebrunozzi 5y agoAt 1pm, considering that tides usually go with 6 hours and 15 minutes increments? (I hope my memory is right, took the RYA exam a while ago)
- deleted 5y ago[deleted]
- SamBam 5y agoBut what's noon plus 12 hours 30 minutes?
- maratc 5y agoConsidering the moon was at its highest today at 12:00, and will be at its highest again in ~29 days at 12:00, what time will the moon be at its highest tomorrow, which is 1/29 of its cycle? The question then turns into dividing 24 hours into 29 parts, or about 48 minutes per day, so 12:48. Bonus points (not in math) go to whoever knows that a tide can also come when the moon is at its lowest, or half that time, or 0:24 or so.
- agent008t 5y agoIt wouldn't be a Russian textbook without some completely unreasonable problems.
- Invictus0 5y ago> 12. A tide was in today at 12 noon. What time will it be in (at the same place) tomorrow? Am I a moron or is this a really bad problem?
- yakshaving_jgt 5y agoI had to look up the answer[0]. > Due to the Moon's orbital prograde motion, it takes a particular point on the Earth (on average) 24 hours and 50.5 minutes to rotate under the Moon, so the time between high lunar tides fluctuates between 12 and 13 hours, generally being 12 hours and 26 minutes. So, if the tide has affected the place at 6:00AM, then it would generally take around 12 hours and 26 minutes for the place to be affected by Ebb i.e 6:00 AM+12 hrs+26 mins=6:26 PM. Seems like a pretty tough question for a child? [0]: https://www.toppr.com/ask/en-my/question/if-a-place-is-affected-by-tide-at-600-am-monday-normally-at-what-time/ https://www.toppr.com/ask/en-my/question/if-a-place-is-affec...
- sethammons 5y agoI agree - I don't see how this could be answered outside of guessing without outside information.
- baldeagle 5y agoI assume that these are meant to be universally understood. If the tests were given in fishing villages, it may have been a much easier premise since much of their world is defined by the tides.
- freshdonut 5y agoDamn I am dumb
- deleted 5y ago[deleted]
- syops 5y agoOne problem I give children aged 5 – 7 is the following. How old are you? (They answer X.) How many years did it take for you to become X years old? I've found that at 6 years old they start to relate their age with how many years it took to become that age. At 5 they usually can't make this connection.
- lhorie 5y agoCurious to see comments quipping that some of the math problems geared towards young kids are too hard. I'd recommend taking a look at Singapore Math[0] to get an idea of what kids in those age ranges are actually capable of doing, provided that adults shed preconceptions that children ought to be "sheltered from hard scary stuff", and instead encourage them. There are also great math-oriented games these days (I had some good success w/ prodigygame.com[1]). My youngest daughter is 6 and can solve simple multiplication and division problems. Sometimes she even surprises me. Some time ago, we were introducing ourselves to a new neighbor and the convo went somewhat along these lines: - my son: how old is your dog? - neighbor: she's 8 - son: she's so small, is she a puppy? - neighbor: oh no, she's grown up. 1 dog year is about 7 human years, so- - daughter [interrupting]: oh wow, so then she is 56! The other day, she came to me beaming to explain how she had just solved 38/2 (by doing 40/2, 2/2 and subtracting the results). Gotta say it's a joy to see a kid that enjoys math. [0] https://www.singaporemath.com/ https://www.singaporemath.com/ [1] https://www.prodigygame.com/main-en/ https://www.prodigygame.com/main-en/
- Koshkin 5y ago> 1 dog year is about 7 human years This is the average; the correspondence is not linear...
- inamiyar 5y agoProbably true, but the point was that the daughter was capable of quick multiplication, the age of the dog was..decidedly a minor detail.
- whimsicalism 5y agoClassic HN
- MontyCarloHall 5y agoParent comment belongs in the hall of fame right next to the classic "Dropbox is trivial—it’s just an FTP server under version control": https://news.ycombinator.com/item?id=8863 https://news.ycombinator.com/item?id=8863
- drdec 5y agoThis story needs a nerd-snipe warning
- coldblues 5y agoThe problem here is that most people won't use most of the math knowledge they gain (and then lose) in school. But for programmers, it's different. Math can be fairly common in programming, especially depending on what field you're working with, and you wouldn't want to lose the knowledge you gained in school, but, unfortunately, most people will lose it. What I propose is a better way to find math knowledge. In contrast to programming, math problems are harder to find solutions for, and the information available is quite sparse and hard to find online, from my personal experiences. When I try to tackle programming problems, most of the time I won't memorize code snippets or algorithms, instead I'll have a mental link pointing to the name of the algorithm or the specific page, that I can search up, find, and then implement. This is the total opposite of what school tries to do. They try to force memorization, which should come naturally. A better way to do it is to let the students have the equations and the necessary information that they need, then they can fit the puzzle pieces together to solve the problem. We live in the age where everything is becoming more and more documented, and we're still forcing memorization on people.
- juanjmanfredi 5y agoAnybody who has a credit card, mortgage, or retirement account needs to have a high-school level understanding of math.
- whimsicalism 5y agoDisagree - or maybe I just don't know what high-school level is.
- allochthon 5y agoKind of going in the same direction, I wonder whether it would be good to have children start out learning math in the context of accomplishing concrete, real-world tasks that require mathematical problem solving, and then only gradually abstracting from this concrete starting point if an individual seems to have an aptitude for math. Example: learning statistics in the context of gathering information about the health of people in a village.
- 5y ago
- marcodiego 5y agoA paper with interesting problems for children: http://toomandre.com/travel/sweden05/WP-SWEDEN-NEW.pdf http://toomandre.com/travel/sweden05/WP-SWEDEN-NEW.pdf
- anonymousDan 5y agoWhat I would like is a book of projects/real world problems/applied maths relevant to kids from age 5 on that could be used to motivate them better than rote memorization.
- orange_puff 5y agoI wonder if #27 is supposed to be proven without Fermat's Little Theorem. (The question is if p is an odd prime, then 2^{p-1} = pk + 1 for some integer k). Since p does not divide k, it follows from Fermat's Little Theorem that p | (2^{p-1} - 1).
- gnicholas 5y agoI'm looking at the first question and wondering: • What is the intended path the student is supposed to go through to figure this out? Guess and check? Some thing more specific? • What would you say is the generalizable lesson for the student? How does solving this problem, which is an edge case, help you think about other problems in the future?
- agent008t 5y agoIf Misha is 1p short, and combined with Masha's fund still cannot afford a book, how much money could Masha have possibly had?
- teekert 5y agoI printed this, will try them all, then translate to my language and try with my kids. I love this stuff.
- France_is_bacon 5y agoThis whole thing does not make sense. Math is racist and this post should be deleted: This is actually a claim that is being made often these days: the sciences in general, and math in particular, are racist. The latest comes from Oregon: The Oregon Department of Education (ODE) recently encouraged teachers to register for training that encourages “ethnomathematics” and argues, among other things, that White supremacy manifests itself in the focus on finding the right answer. Part of the toolkit includes a list of ways “white supremacy culture” allegedly “infiltrates math classrooms.” Those include “the focus is on getting the ‘right’ answer,” students being “required to ‘show their work,'” and other alleged manifestations. “The concept of mathematics being purely objective is unequivocally false, and teaching it is even much less so,” the document for the “Equitable Math” toolkit reads. “Upholding the idea that there are always right and wrong answers perpetuate objectivity as well as fear of open conflict.” ODE Communications Director Marc Siegel also defended the “Equitable Math” educational program. . The first sentence is mine. And I'm letting the sarcasm-impaired know that it actually is sarcasm on my side. The rest of it is real, though, I didn't write it.
- someelephant 5y agoThese people are entitled to their opinion. Pushing back is likely to make them stronger. Better to focus on the positives like finding the right answer brings a sense of accomplishment and showing one's work teaches the process of deduction. Those are some useful skills to learn with math while white supremacy culture can be learned about in other settings. We don't force people to do math in English class, it doesn't seem right to learn about white supremacy in math class.
- ZoomerCretin 5y agoCan you not inject culture warfare where it doesn't belong?
- deleted 5y ago[deleted]
- userbinator 5y ago
- cycomanic 5y agoOn the subject of teaching math to kids I found two books quite fun (and my daughters have been enjoying them as well). 1. Moebius Noodles 2. Avoid hard work! Both of these take a playful approach to teach quite advanced mathematical concepts. What I particularly liked was a focus away from calculations and numbers. The argument given in one of the books is that starting to teach math by counting and then calculation is like only starting to read books after children learned the alphabet. Children are very capable to figure out more advanced maths concepts even without being able to calculate fluently yet.
- gnicholas 5y agoThose books look cool, and it appears they are available for download on a name-your-price basis (literally says "Type the amount (from zero to infinity)"). What a generous and cool idea!
- scotty79 5y agoDerivation of answer to the problem #16 here: https://datagenetics.com/blog/may32013/index.html https://datagenetics.com/blog/may32013/index.html
- walshemj 5y agoSome of those are not even Grammatical "A brick weighs one pound and half the brick. How many pounds does the brick weigh?"
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- eevilspock 5y agoA lot of comments complaining that many of the problems don't have definitive answers, e.g. #12 (tides) and #13 (bookworms). I think the point for some problems is not finding the answer so much as developing logical, analytic and critical thinking skills; to learn the value of looking at a problem from different perspectives and the necessity to sometimes think outside of the box; and to be able to find the holes and ambiguities -- sometime to even reject the question outright.
- misterprime 5y agoThe struggle is real. Someone help me out here please: >5. Two old ladies left from A to B and from B to A at dawn heading to-wards one another (along the same road). They met at noon, but did not stop, and each of them carried on walking with the same speed. The first lady came (to B) at 4pm, and the second (to A) at 9pm. What time was the dawn that day? I think dawn was at 6am. This assumes that Old Lady A travels the full distance in 10 hours and Old Lady B takes 15 hours to travel the same distance. I don't know how I arrived at that answer other than some sort of trial and error. I don't like it. Any advice?
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- orange_puff 5y agoLet C be the point where they meet in the middle and s be dawn. It takes Lady 1 `12 - s` time to walk AC and 4 time to walk BC. It takes Lady 2 `12 - s` time to walk BC and 9 time to walk AC. Let's find the ratio of time it takes Lady1 to walk a distance to time it takes Lady2 to walk a distance. The ratio should be the same for all distances since their speed doesn't change. Thus, (12-s)/9 = 4/(12-s) <=> s^2 -24s + 108 = 0. The quadratic formula gives us s = 6, 18. Since 0 <= s < 12, s = 6.
- Koshkin 5y agoSimply translate the words into equations: (16 - t)v = d (21 - t)w = d (12 - t)(v + w) = d Then, if you substitute v and w in the third line, it turns out that d cancels, and you are left with a quadratic formula of t, one of the two solutions being 6 (and the other one making less sense).
- areyousure 5y agoAfter their noon rendezvous: One lady traveled some distance in 9 hours, and the other lady traveled some other distance in 4 hours. Before their noon rendezvous: you switch both the distances and the ladies. If x is the number of hours before noon that they traveled, you thus get that the ratio of 9 to x (what the first lady covered in 9 hours, the second covered in x) is that of x to 4 (what the first lady covered in x hours, the second covered in 4). Thus x is the geometric mean of 9 and 4, or in other words, x=6 and sunrise was 6 hours before noon at 6am.
- purpmint008 5y agoWell, where are the answers?
- datatrash 5y agoSome of the first "problems" have multiple answers. I don't think that is how anything should be taught. First problem depends on whether or not smaller coins exist, fourth problem depends on the actual fill volume of glass and barrel. Those questions do not have an answer. Didn't read further than that.
- datatrash 5y agoOnly read the first 4 problems. 1 and 4 have no answer and I doubt teaching math by utilizing logic fallacies does any good. First depends on potential subdivision. Fourth depends on the fill level of the vessels. Don't think that is the right way to teach anything.
- z2trillion 5y agoI don't think the answer to 4 depends on the fill level of the vessels. All that matters is that the volumes of the liquids in the barrel and the glass are unchanged, so that volumes of the foreign liquids will be equal.
- chki 5y ago> Fourth depends on the fill level of the vessels. I don't think it does.
- fserb 5y ago1 has an answer
- a0-prw 5y agoThese problems are very simple and surprisingly fun to work with. Their purpose is to develop "thinking culture" (Arnold says this in the intro). He also writes that "the worst at solving these simple problems are Nobel and Fields prize winners" :) Now, I think that's Russian hyperbole or poetic licence, if you will, but it does illustrate an issue I run into nearly daily teaching maths to 13 - 15 year olds: Some of the kids think in ways I have a hard time understanding and often solve problems in ways which are difficult for me to grok because they are not using mathematical language to explain what they're doing. This happens especially with kids who generally perform poorly in maths. They solve problems similar to these in ways I have a lot of trouble understanding because it's like we are speaking two different languages. These problems are trivially easy if you translate them into simple equations (the ones I've done, anyway). The problem is I don't think that's what Arnold means when he says "Thinking culture", so I suspect I might be cheating ;) Edit: Nr. 13 is wonderful :)
- foxes 5y agoNot commenting about the difficulty, but some of the later questions definitely require a bit more specialised knowledge. #74-77, "uniform, dense, smooth map, open set". Basically some topology questions. Some other questions are just weird, #54- just plot a parametric equation? Also a few integrals? I think anyone (kids included) could go pick up this stuff fine, but doesn't quite match with the blurb given (why not define some of these things in the questions and work through it that way). I imagine then what this could be good for is if you use these questions as a bit of a teaching guide/goal. Maybe work your way through the concepts/problem with the end goal being the question, but then introducing stuff as necessary, rather than just throwing the entire question out there.
- snicker7 5y agoI met one of Vladimir Arnold's grandchildren at a high school math summer camp. One of the things that stood out to me was his insistence that his proofs were as simple and understandable as possible. Unlike other students, he would intentionally avoid using sophisticated techniques. He would brag that a "third grader" could understand it. His preference for simplicity and elegance was clearly inherited from his grandfather.
- nazrulmum10 5y agoHelpful items
- account_created 5y agoNo offense, but Masha is broke af
- mynameismon 5y agoAny idea where to find the answers? These are extremely intriguing to do, even now.