Lots of comments asking what is "Soviet/Russian Math" actually like, and how is it different.
I was lucky to get an education in three systems (Soviet Math, Romanian Math School (influenced by both French and Soviet Math school), and finally in a world top 40 university in North America.
I would summarize the Soviet/Russian Math/Physics approach like this:
- understanding of the mechanism/intuition behind the equations/methods is paramount
- teachers are astute at spotting students who memorize blindly, and will intervene to correct that
- while rigorous about notation, the mathematical representation always comes after understanding, not before
- the progression of teaching (order how material is introduced) is very well thought out
- the old soviet textbooks are generally less verbose than North American ones (less fancy), but high quality in their expression, typesetting, and ESPECIALLY (!!!) the quality of the exercises
- the Soviet Math textbook exercises are something to behold: they have funny/memorable setting (like jokes), they are short and easy to express, the numbers are chosen in such a way that the result will be a nice whole number, or pi, etc. Basically as a kid you can read one of those problems, lay down, close your eyes, and work on it in your head.
That being said, I did like some of the aspects from the so called "Western Math" (in my case Canadian university):
- teachers are more approachable, more friendly
- textbooks can be gorgeous (nice colorful plots, etc)
As an american who went through US-based curriculum in the 90s, this sounds FUCKING WONDERFUL.
Basically - it seems like the approach above treats math as a conceptual playground, where you should develop intuition and understanding.
Instead we seem to be going down the rote memorization route for most of our classes, where the goal was to apply an equation to some numbers and get the right answer, with little to no thought, and an emphasis on easy grading.
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Our physics education seems quite similar, though - and I loved that.
I have always liked math, but have never been great or very good at it. I graduated from a US public school gifted program, and a top 30 US university. The biggest problem I always had with math education is they didn’t teach the “why” nearly enough. I was lousy at memorizing formulas/methods (esp. in calculus), so I often found myself dead in the water during exams.
I used to suffer from the lack of "why" too until one day it dawned on me that there really isn't a why, or maybe, the why is always the same: for engineers doing classical physics solving problems by hand, it's convenient to define it that way. No more, no less.
When I was a math tutor in school, everyone would complain about lack of why. This was my approach to address the issue. I would describe a problem relevant to the class, say something like find the angle between two vectors, and ask them to think of a general way to do it. Usually this require some help from me but the solution was always "theirs". Then we would play with their solution: find corner cases, figure out which operations broke, develop a couple of theorems with it. Then I would show them the dot product, and a couple of its tricks (a.k.a. theorems), and they would get a good appreciation for why the dot product works the ways it does. And that's the why and the reason it stuck. It's useful way to solve a common problem. There is no magic or deep philosophical truth.
The problem is this teaching style works with a dialog to a few number of students. I am not sure how well it would work in a lecture setting. It was also not so easy on me as I would be the person who had to spot the problems in their definition, basically on the spot, and lead them to it on their own without revealing the answer. With basic things like a dot product it's pretty easy to know where to look (i.e. is their definition commutative, pretty much never) and finding issues and nudging them too it wasn't too hard. But it's likely hard to scale things like this on many metrics.
> I used to suffer from the lack of "why" too until one day it dawned on me that there really isn't a why, or maybe, the why is always the same: for engineers doing classical physics solving problems by hand, it's convenient to define it that way. No more, no less.
'Why' is shorthand for a description of the context of the operation or method being taught. My senior high-school experience was that my maths teacher just plowed through the curriculum from limits to derivatives to integrals and beyond without explaining what each was used for or why. I managed to scrape a pass in high-school calculus but never grew beyond the most rudimentary of understanding until I was taught by a university lecturer who invested time in explaining the why.
The backbone of my mental schema is narrative, so just throwing equations and processes at me does not cause the knowledge to "stick".
Teaching me that Gauss had a problem X that he tried to solve by Y, then showing me what he discovered process N, is invaluable to me because it aids my recall.
She passed her test on the first try, which was extremely rare at her school. She was taught in India, and became an American teacher as an older woman. She was an outlier. She graduated from a major public teaching program in our state of California (CSU Fullerton).
Most teachers fail their tests on the first try. This is not advanced calculus... this is elementary mathematics and reading.
The issue is that accolades in the education department do not translate to results. The state creates a monopoly on teaching via its certification process, with means education departments are guaranteed funding regardless of their results, given that once you have the credential, you're considered 'equal' to other teachers.
Despite my mother doing very well on her tests, she was fired and not granted tenure because she didn't follow her principal's teaching methodology. Even though her students were passing their own exams at higher rates and doing better (And of course my mother taught two boys who went on to make careers in science and mathematics), she was fired for not following the failing methodology.
This is what is wrong with American schooling. It's a race to the bottom and the teachers have no idea what's actual achievement because they've never achieved basic elementary schooling, much less seen it in others.
EDIT: in some ways america is doomed by its own success, in that, for those who can actually do math, reading, and writing, there are significantly more lucrative fields than teaching. Unfortunately, since teachers can't teach those skills, it's really a new aristocracy formed by parents who do know those skills passing them on to children.
So the haves spend money on education of their kids, and have-nots can't do that, relying on public schools which don't perform, and the possibilities gap is widening. Structural problem.
Yes they do. At minimum Mathematics have a why in that it is something that is arrived at logically, and provable. But when you learn mathematics, whether it be algebra or geometry and trigonometry or calculus or discrete, there is another why added, that of real life solutions. Why do we care about geometry? Well it ends up being useful in optics and physics. We like Trigonometry because it can help you build a building or bridge or shoot a cannon and take down said building or bridge. Calculus has innumerable uses in engineering and physics and finance and biology and everywhere.
I find this answer to be true, but misguided. In particular, this type of answer was the exact thing that turned me off of math for YEARS.
Maths DO have a why - We needed way to describe and model the world around us, and math was a requirement to do that.
Now - once the model and rules are put in place - Fine, you can bugger off and be as self-referential and contained as you'd like - "There is no why!"...
But lets be clear - there ABSOLUTELY is a why, and the second the world around you no longer matches the model of your maths, we start debating whether or not to throw the thing in the trash and make new rules (see set theory as the classic example...)
Programming languages do not have a why. The turing machine is an arbitrary model of computation, as is the lambda calculus, as is horn clauses. The 'why' is deciding which one is most convenient to solve a particular problem. Given that very good computer scientists come up with very different means of solving the same problem, it's clear there's no universal agreement upon which paradigm is better and that there's a lot of subjective reasoning as to why particular models are better.
Consider the natural numbers. There is no 'why' behind them. There are axioms behind them, and -- given those axioms -- there are statements about the natural numbers that can be logically reduced to the axioms, but the axioms have no why.
Moreover, it is provable the axioms have no why, because they cannot have a why, because the axioms cannot be proven except in relation to themselves. If you're so convinced the axioms have a why, please prove me and Godel wrong.
The 'why' behind natural numbers is a social one, and one of convenience. The natural numbers make it easy to solve and communicate about certain problems, but they are not the only way to solve those problem nor are they the only way to communicate about these problems.
For example, another way to deal with basic arithmetic, is to talk about numbers as sets. Now you can define certain operations on them, and completely ignore the axioms of the natural numbers. This model is way better than others for certain problems. However, you now have a new set of axioms.. and oh yeah, actually the most obvious ones are completely self-contradictory, so you'll need to choose Zermelo-Frankel or something else.
Or if you want to be even more general, you can simply talk about the lambda calculus, but good luck trying to 'prove' the lamba calculus theorems in itself, because you'll quickly hit the halting problem.
Of course you can then say... well let's get rid of that and use the typed lambda calculus, but then oh yeah you can't do anything interesting. Why are these choices made? Can the choices be justified in the systems themselves? No of course not. The idea that you can use 'logic' to derive these systems is also ridiculous because formal logic is itself a system with axiom (and a very controversial system at that).
But if you look at the lambda calculus, ZF set theory, and the natural numbers as simply models and systems that are sometimes useful, then it makes sense as to 'why'. But the 'why' exists independent of them and is not provable in them and is social and cultural in nature. It is certainly not mathematical as in order to 'do mathematics' (symbolic manipulations) you first need axioms.
Mathematics education in this country has been replaced by rote dogmatism which is why many Americans cannot handle this ambiguity.
What must be explained is that mathematics is a language and in order to communicate with other educated humans about these abstract concepts it behooves everyone to speak the same language. It is the same reason the word for 'dog' in English is taught as being spelled D-O-G. There is no why behind it. It's just the result of thousands of years of culture. Except mathematics is a more global language and more useful for different kinds of manipulations.
Again - correct but misguided in the general sense.
> It is the same reason the word for 'dog' in English is taught as being spelled D-O-G. There is no why behind it.
I agree with you completely, but I think you're guilty of speaking the wrong language in response to the question (and it would behoove you to consider it from the perspective of someone outside the field).
The question "Why" in maths almost always gets asked by someone new to the field, and they are not asking from a mathematical perspective - They are not asking you for a formal/provable "why", they're asking you what is the utility of learning this thing.
So lets go back to D-O-G. The utility is clear - I have this hairy, 4 legged animal that keeps licking me that I'd like to discuss with you. We can agree that D-O-G (or perro, or 개) refers to it.
But with math, SO MANY PEOPLE (especially those established in the field) jump right into the "Here are the rules of this system of math" without ever taking the time to talk about why someone might give a flying fuck.
It would be like me going and making up my own language and forcing you to learn it. No one else speaks it, it's got no books/literature/history, there are no works of art that reference it - it's literally the language this random person made up that serves ZERO purpose except for talking to that person.
No wonder so many kids don't like math!
Instead you need to explicitly start with the utility of math - ideally in ways that are entertaining and fun. Once a person has an application for some of the rules, they become SO MUCH MORE INTERESTING! Suddenly I care about why this rule might impact that rule over there, or why A and Z are related, or what sin/cos/tan mean.
Basically - sell me on the value proposition of your fucked up whacky language - That's what "why" is asking. Once you know those rules do something useful, it becomes a much more engaging field of study.
You are correct, but this explanation is cultural and sociological, not logical.
We must motivate math, absolutely. And to do so in my opinion starts with socratic questioning. You must convince the student that such an inquiry is even worthwhile.
One thing I'll point out is that we're not just seeing this in math. We see it in every field. More and more kids every year are insisting ( and their teachers are agreeing) that we can do away with inquiries into the English language and the humanities as well. There is a small, but continuing, effort to remove the knowledge of English masters like shakespeare and classic philosophers and treatises from the curriculum.
As a whole, American schooling fails to motivate learning of any kind. Math was the first victim, but the other subjects are also failing.
Sure, but we're in a thread talking about why some folks are choosing to send kids to "Russian" style maths teachers.
The whole discussion is from the perspective of the cultural and sociological.
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As an aside, I generally agree with you about american schooling. I think it's less a concerted effort, and more a sad reality of the fact that modern schools have essentially become federally funded child care in the US.
Indeed... As my mother was told by her principal in her inner city school for poor minority kids... "We're just here to watch them until they go to prison".
I could do calculus, in high school and college, but I wasn't very happy about it. Until I took a physics class in college which happened to be intended for the physics majors. Did the professor ever just present an equation and ask us to learn it? No! Every Single Physics Equation was explained from first principles, using calculus - a lot of integrals. Finally we were seeing a practical application, where calculus was just a tool to get you where you needed to be.
It was really helpful to me in highschool that the calculus teacher was also the physics teacher, and many students were enrolled in both classes simultaneously. You ended up learning both at the same time.
Teaching calculus through physics (and vice versa) actually makes a lot of sense.
Similarly, basic Linear Algebra and 3D graphics have great synergy. I took LinAlg and Computer Graphics the same semester in undergrad, and the first half of LinAlg led perfectly into the second half of CG. (The first half of CG was all 2D stuff, which didn't need any special math.)
I was a bit disappointed to see the differences between "algebra based physics" in high school and "Calc based physics" in college. It wasn't a whole lot more than "now rather than giving you formulas, do an integral to go from acceleration to speed, or speed to position".
It did feel good to see a practical use for the calculus I had learned, much more so than determining how much the surface area changed after adding a layer of paint 0.01" thick to a tank.
Also American, but was routed through, what was at the time, an experimental program called Integrated Math. Class was structured around word problems and the students were guided towards figuring out the formulas rather than rote memorization.
There was a ton of group work, which worked out really well for me, but if you didn't want to learn it was pretty easy to coast and let the group leader do most of the work / learning.
My British state education really did feel like "memorise just enough to jump through these arbitrary hoops which keep the government off our backs" sometimes. It's very exam-driven rather than learning for its own sake and apparently it's got even worse since schools started transitioning to academies and Gove's reforms took effect.
Normally the curriculum was split between knowledge and understanding, and problem solving. You could memorize the first part and not the second part. The problem solving sorted out who got the grades
As I was reading the summary, I was thinking "well, of course -- that makes sense. Any teaching curriculum has got to be like that so what is so special about Russian math curriculum?".
Then I read in other comments about US math curriculum and I was shocked to learn that not only they were NOT doing this, but they didn't have a better alternative. This is mind boggling. It seems almost idiotic.
My schooling was done in India. Our curriculum was quite well planned, but what is laid out here is the methodology of teaching in addition to the curriculum and textbooks. And that depended on teacher to teacher and school to school. But nonetheless, the textbooks were very well written so everyone got exposure to pretty much the same level of teaching styles, more or less.
When I came to US in college, I was surprised to learn that people didn't know basic techniques and tricks for algebraic manipulations. Of course, we were taught the basics and whys behind every trick but emphasis was also given to internalizing these tricks for quick computation by hand. This, in my opinion, is important because these tricks also become your mental models when thinking about math. And quick tricks would lead to quick thinking, roughly speaking.
It wouldn’t be an exaggeration to state that most Americans experience k-12 math as an exercise in memorization. Even relatively simple algebraic manipulation such as quadratic equations are drilled for factorization first.
Yep, it’s like teaching someone how to cook by quizzing them on recipes. I didn’t understand the purpose of calculus until grad school despite having “learned” it several times by that point.
This is significantly different style from Russian textbooks. If you want a nice one of those translated into English (albeit not the easiest to find a paper copy of), I like Piskunov’s book. https://archive.org/details/n.-piskunov-differential-and-int...
Which board was your school affiliated to, if you don't mind me asking? I went through my schooling in India too, and I had quite the opposite experience: concepts being taught with the only focus being on beating exams, rote learning prioritized instead of logical applications (in case of science), etc.
CBSE followed similar methodology as described and was good too. But only select central schools were good at teaching it - the teachers there were well qualified, and some of them are a real gem too at teaching.
A Russian mathematics professor of mine in graduate school was a student under Kolmogorov. He taught information theory and algebraic combinatorics and helped develop a number of systems for the Soviets. He was extremely challenging, but he cared less about the grades and more that you were understanding the material.
He would say at the beginning of the semester: "You must learn to build the castles in your mind." The visualization of the constructions really helps to understand how to apply the concepts in different contexts.
The Polish professor would hand out chocolate to every student before every test, so that your mind was more relaxed.
That’s very insightful - when I switched to US high school, the approach to math was baffling - everyone had programmable graphing calculators, whereas I wasn’t allowed any calculator at all, and took a lot longer to solve the most basic problems. Most questions were answered by the teacher as “it’s a formula, you follow it and memorize it” (which sounded ridiculous to me for the exact reasons above - I was taught to understand the basis first, then the applications).
I never understood why graphing calculators were required for basic calculus or math courses. Always wondered if it was part of a marketing deal with the company that manufactured them. The course is said to require a particular make and model of graphing calculator.
It is more or less exactly this. Texas Instruments invests in extensive marketing aimed at teachers, school districts, and university math departments. They get a lot of free teacher training and materials centered around TI calculators, to induce them to require all new students to buy a $100+ Texas Instruments graphing calculator every year.
I believe it is more of a standardization of knowledge when picking the tool for mathematics. TI-83 calculator is common and easily to have all the students to use the same calculator and provides various approach of how to solve it. If one student is a outlier (like using HP calculator), then it could be an issue since the instructor only have the knowledge of using TI-83 (or its variants), the instructor couldn't help that student since HP and other graphic calculators have different inputs, layouts, etc.
And not everyone is good at solving math alone without the aid of the calculator. Some people simply can't solve mathematics at all, maybe up to multiplication/division level is the best they can do. I am not good with mathematics myself and struggles with some advanced algebra. It is not the matter of trying to solve, it is matter of memorization of mathematics formula and equations that US Education drilled down so hard which is ironic when they said that calculators are forbidden to use during the exam while they are encouraging to use the calculators in class and homework... Their pedagogy is fucked and hypocritical.
Sorry you had such an experience! There really is a lot to unpack here.
As the article describes, memorization of “formulas” doesn’t actually work for my students and leaves those that it “worked” disadvantaged in future learning.
My personal guess is the “not being good at math” originates from this, at least in part. It’s a confidence killer for sure that on one had you are being forced to do something unnatural (memorize weird looking formulas) and on the other give a somewhat easy, yet demeaning, way out by saying “it’s ok, you are just not good at math”.
The calculator to study and no calculator for the test is even more ridiculous - students are put in a high pressure situation without the very tool/crutch they came to rely upon. If anything, the inverse might make more sense - homework you have a lot more time and less pressure, so try working it out on paper. Test is timed, so it’s ok to use a calculator aid, so long as you show your work.
> My personal guess is the “not being good at math” originates from this, at least in part. It’s a confidence killer for sure that on one had you are being forced to do something unnatural (memorize weird looking formulas) and on the other give a somewhat easy, yet demeaning, way out by saying “it’s ok, you are just not good at math”.
Honestly, it is more direct at the instructors instead of the mathematics itself. I am not good with math because of the instructors' pedagogy. Honestly, I do like math and enjoy doing it (Khan's Academy helps a lot!). It is their approach with mathematics is the issue. Their pedagogy are not standardized enough to have consistency with each level of mathematics. There are instructors who dismissed their student's previous instructor because their former instructor gave them the shortcut or a shorter method while the new instructor are doing the same thing. Now you have a student who have a jumbled information of mathematics and that is difficult for the student to be able to relearn a new information while they can't erase/forget the previous method.
Also I am curious why it is difficult for instructor to explain HOW and WHY that solution is the correct answer? It is like they don't want to teach the concept of mathematics which is vital for critical thinking, IMO. When I asked the instructor of this question (this is in college), their answers is "It is the way I was taught in school" and I felt that is dismissive and hand-waving away the question.
Instructors are not entirely at fault because they also received the similar education in the past as we do. The mathematics pedagogy and the curriculum need a massive restructuring and cohesive way to teach the students to ensure that the students can use the previous knowledge to the next level of mathematics for consistency without changing or influencing the students to forget everything.
Like most things there probably is more than one cause, and I suspect a pretty big one is around compound effect of instructors having poor instruction themselves and then having to admit that they themselves don’t really know the subject.
Thankfully for me, my college Calculus professor(in USA) banned calculators for Calc 1 and 2(the two required Calc classes for a computer science degree at my public university).
He was heavily avoided by many and "special" for doing so. I found it easier to forego the calculator as it allowed us to focus on methods and how/why over just moving large numbers around.
That sounds pretty awesome actually! It also probably makes it a bit harder to prepare the materials, since you need to make sure it’s reasonably computable by hand.
Perhaps, but the guy had been teaching these courses for at least 10 years so he really had it all down. I mean he taught almost completely from his brain.
Total math teacher too, his university email is so full if you email him it just bounces back.
My take on your list of advantages of soviet math/physics approach is mixed.
Fully agreed with you on the rigor regarding notation, really good progression of teaching (pacing and order in which the material is introduced), and soviet math textbook exercises being well thought-out and entertaining.
Very much disagreed on the rest, as my main personal gripe with learning math+physics in Russia was that there was zero emphasis placed on understanding of principles and logic and 100% on memorization. I spent 3 years taking physics classes there, and I learned effectively nothing, having to relearn it from scratch in the US. And that was the moment where I truly felt I understood what was going on, instead of treating physics as just another memorization exercise for a variety of random unrelated formulas. Similar with math, but to a lesser degree, because with math I was personally invested and was trying to understand the material rather than memorize, despite it hurting my grades in Russia greatly.
Overall both class and teachers didn’t like memorizers. On the other hand, it was possible to pass pretty well by memorizing. Sometimes teachers would put in random bits in tests to throw off memorizers. Sometimes it worked, sometimes it didn’t. All in all, memorizing and actual learning lived side by side.
The main difference from what West looks like, the Soviet-ish system was designed for failure. For me it looks very weird when lots and lots of people get best grades. I was raised that 10 (out of 10) is rare perfection. 9 is great. 7-8 is fine. Even 5-6 is ok if you ain’t interested in a given subject. Not everybody is super smart, not everybody is passing school with perfect grades. And that’s perfectly fine.
Unfortunately a couple decades later our education system is westernized and everybody DESERVES best grades. And the system is bending over.
>Overall both class and teachers didn’t like memorizers. On the other hand, it was possible to pass pretty well by memorizing. Sometimes teachers would put in random bits in tests to throw off memorizers. Sometimes it worked, sometimes it didn’t. All in all, memorizing and actual learning lived side by side.
I find it hard to believe, given my personal experiences and the fact that having to memorize a poem or a short story and then having to get up in front of the class to recite it word for word for a grade was an extremely common recurring homework assignment in literature classes in my Russian school (from elementary to high school).
Extra details about that type of a homework assignment for those curious: they cannot call up every student due to time constraints for each class period, so for every such assignment, only about half the students get called up (for some specific works that are "more important", they might call up everyone, but over 2 class periods; that was extremely rare though). But those assignments were so ubiquitous, you essentially got called up to the whiteboard to recite at least once every week or two.
We had those literature assignments as well. But in 12 years that happened a couple times most. Now don't get me started on literature writing assignment that are strongly advised to start in certain ways and it's best to just memorise the beginning off examples and just change few words....
Interesting to hear about an experience that's pretty much the same as mine, but rebalanced differently.
For us, writing was the same way as yours ("strongly advised to start in certain ways and it's best to just memorise the beginning off examples and just change few words"), but it only happened a few times at most, and more towards the latter years, while reciting stuff in lit classes was the norm the entire time.
And now I am starting to recall another type of assignments going until late middle school, where we had to write passages from textbooks in cursive in our "homework notebooks", mostly with small changes. Like "here is this 1000 word passage in the textbook written from the first perspective, rewrite it from the third perspective in pen". Made a typo? Well, restart, because while a couple of edits won't take much off your final score, any more than that makes a full restart a more worthy option (because it was required to use pen for those instead of a pencil; more diligent students who didn't wanna bet on getting it right on the first try, they did it first with a pencil and then traced it and erased the pencil). Another evening spent rewriting the same dull passage multiple times by hand in pen.
On the other hand, how do teach someone handwriting skills? Writing down a passage is better than random blabery IMO. I'll take the must dull passage any day over several pages of synthetic exercises.
>On the other hand, how do teach someone handwriting skills? Writing down a passage is better than random blabery IMO
I agree, however, doing it way past elementary school seems like a solid way of wasting time. When you are trying to learn writing or you are in elementary school, sure. But spending hours upon hours rewriting long passages multiple times due to random non-editable typos in late middle school felt mind-numbing and downright awful.
And of course, as you progressed in grades, less attention of graders was focused on the actual handwriting quality, with passages getting longer and more convoluted, so the handwriting tended to degrade the further you got in your elementary/middle/high school education. Not even mentioning what happened to it after high school, because by then (unless your handwriting was completely unreadable) no one cared.
And no, it didn't help in the long-term with handwriting at all. None of the adults tend to have textbook-good handwriting, it would barely even get a passing score in the best scenario (and that would be an exception). And just like in western countries, let's not even mention doctors' handwriting (but that's completely irrelevant to my point).
I've been in several provincial schools in 1990s, good and bad, and we've always had strong anti-memorizing sentiment in math classes, despite in literature classes memorizing was mandatory.
Both make perfect sense.
Now I heard it's turning more to the Western model, though.
That's why I posted my previous reply, despite me being in strong opposition of the "argue anecdata with your own anecdata" approach in discussions. But I couldn't resist replying, because all of my 9 years of experience in Russian educational system were the opposite of what OP claims in terms of memorization, and so were those of every single person I know in real life who went through that system (in other schools in Russia, not just from mine, obviously). Coworkers of mine (who went to Soviet schools a decade or two before I was even born) echoed the same sentiment in discussions on the topic, with the halfway sad "some things never change there, huh" sentiment.
Would have been less surprising if my school was doing poorly in rankings and such, but it was quite the opposite.
Of course, all my claims here are anecdata, but it just feels like something is off when the fantastic utopian description of how "soviet math" education works just runs counter to every single lived experience I had, as well as that of everyone I know in real life. Especially given that experiences of some of those people in real life I mention were separated from mine by both decades and geography (some did school in Moscow, others in smaller towns, some in soviet ukraine, etc.).
That sounds wonderful! As a product of Indian education (that prioritizes rote learning), I wish I had been subjected to such a school, maybe then I (and majority of other kids) wouldn't have fallen out of learning math like we did.
This is fascinating and I appreciate you linking it. I was mind-blown when I read page 8's claim that white supremacy manifests itself in mathematics education when "students are required to show their work in standardized, prescribed ways".
> The child of immigrants might have learned a
different way to solve a problem because that’s
how their parents were taught where they grew
up. If we just tell that student their way is the
wrong way, we risk turning them off to math for
life. If we take the opportunity to explore why
there are different ways to approach the same
problem, it can be a learning moment for the
entire class.
I certainly had this experience in school! I did many math problems mentally, using the method taught in schools today where a problem like 23 x 7 is split into ((10 * 7) * 2) + (3 * 7). As a result, showing my work was challenging, because the teachers of my time wanted us to write out the long multiplication and I didn't know writing the above expansion was an option.
Ah, yes. I was told to "show my work", but I didn't have any work to show. If they told me "For sake of illustration, show what the steps would be if you carried out the following algorithm", then perhaps I could have done that. But what they said was "show your work", and there was nothing to show.
Luckily, I had learned several years of the curriculum in advance anyway, and had contempt for what the teachers were doing, so it didn't change my opinion of math, only my opinion of school.
Part of schooling is learning and showing you can follow a specific set of instructions. As long as one was taught how to do long multiplication, I do not see the purpose of taking into account what every kids' parents taught them if the purpose of the exercise is to learn a certain method and then show that you learned that certain method by doing it.
Because in practice, that causes students to disengage from the learning process:
> If we just tell that student their way is the wrong way, we risk turning them off to math for life.
I certainly disengaged from some subjects in school due to frustration with "thou shalt" methods of teaching. I was even removed from an upper level English language class because I didn't draw the same conclusions as the teacher from the material.
was the wrong way, then that is harmful. But if the purpose of the test was to see if you can do long multiplication, and you were not able to do it because you did not want to or like to do it that way, then that is a personal problem.
The reality is that school (non university level schooling) is not purely about education or exploring the 18 million different ways something can be right or wrong. It is also an exercise in navigating one's way around other humans and their expectations and playing the game that you will have to for the rest of your life.
There is also the constraint of limited budgets and schools having to make do with perhaps not the most qualified educators. And there is certainly lots of improvement to be made, but this "racist math" stuff seems to be counter productive.
Additionally, mathematics uses standard notation and uniform rigorous standards for what is/isn't true. There is certainly some utility in teaching mental arithmetic skills, but the higher-level concepts are only accessible if one can formulate ideas in accordance with the rest of the body of research.
I had a chance to compare the systems, too but my conclusions are completely different. Teachers at the physics/math lyceum I studied at were emotionally unstable psychopaths with mood swings. They could switch from calm "kids, if you don't understand something, please, don't hesitate to ask" to the screaming at the top of their lungs of "are you a stupid imbecile? what a moron you're to ask that" just a minute later.
It was all about rote memorization. Rules, theorems, axioms. Not just the way to prove or principle behind, but the textual representation (to the teacher's liking) word-to-word. Of course, there was a division of students into multiple groups, and those with important parents had an easier time. Any of their bullshit was always graded as "A". But those actively disliked could get "F" for a perfect work. A dot at the end of the sentence is missing? "Go back to the kindergarten where you belong". Something is crossed? "What is it, a toilet paper? Go use it for wiping your ass" (they could tear it apart in front of you). So, the representation/look of the work always came first. A teacher was a lawyer, prosecutor, and a judge at the same time (just what some Americans wish to have as a state): you don't like something, go f___ yourself.
The textbooks. If you compare the best Soviet ones with some average American, you can come to the conclusion that Soviet are so good ("exercises are something to behold", "high quality in their expression", etc). But the best American books wouldn't give a single chance to the Soviet ones. In fact, even some Russian Empire textbooks so much better than Soviet (not to mention Russian), they are getting popular among parents for homeschooling (schools can't use books unauthorized by the ministry of education). The best American and pre-Soviet textbooks are born out of lectures, author's personal experience with students. Soviet authors are disinterested observers who don't care. Textbooks, apparently, were the product of central planning like process (so they were getting worse and worse, the further they went from Russian Empire epoch).
And finally, a thing that really deeply touched me at a western University. A teacher when asked a question once said "I don't know, I have to check it". Holly f... Someone who openly admitted they don't know something, no freaking way! Back at the lyceum it would be "Shut your mouth with your stupid question, we don't have time for that". Then she would find the answer and during the next class say something like "now when we have a few minutes, I'll do you a favor, here is the answer... What a moron you're not to be able to conceive this yourself".
Math was boring as hell. Worse was only literature with essays.
Except that at lyceum we did have good teachers who could admit they didn't know, and the physics teacher did anti-test, where we could pose him a (correct) problem and if he couldn't find the answer, he added +1 to quarter mark, which was a great bonus.
I was about to reply with something like this, so thank you for posting it. I don't know where the top level grandparent comment comes from, but your experience matches mine almost 1:1 (except I went to school in russia between 2001-2010, so hardly soviet anymore, and then finished up high school+college in the US). Something to keep in mind: my school in Russia wasn't just a random school, but a physics+math focused gymnasium, one of the best public schools in the city. I am shuddering to even think what it was like at less well off schools.
Everything was about rote memorization, to the level i couldn't imagine in the US. Physics? Nope, memorize everything, you don't need to understand why or how formulas relate to each other or what they mean. Math? Nope, no need to understand logic behind anything, just memorize the formulas. Even with something like programming, we had to memorize bubble sort in TurboPascal, without the algorithm ever explained at a higher/pseudocode level (it was introduced in TurboPascal right off the bat and you had to memorize it line by line, I wish I was kidding; we were graded on how line-by-line it matched the given solution, not on whether the implementation actually worked/was valid). It was pain, I barely learned anything, and was convinced that I am destined to never do well in physics, thinking "this was just not for me, i am not smart enough to get it".
Then we moved to the US, and I felt like my eyes were opened. Physics were explained from bottom up, from actual phenomena and how they worked, and formulas were just a glue connecting those phenomena and their interactions together. There was zero actual need to waste time memorizing those formulas, despite formula sheets not being allowed on the exams, because they actually explained the logic/reasoning behind it all, so it was no issue at all to simply derive those formulas on your own during the exam.
Same happened with math and programming. I actually finally understood what I was doing, rather than robotically recalling appropriate strings to put on paper from memory.
In the russian school I went to, logic didn't matter, only correct answers. For a specific example, in every single physics course I ever took in the Russia, if you got the calculation wrong for one small part of the problem (which propagated to the final answer being incorrect), but you got the rest of it right, you get 0% for that problem. While in the US high school/college, I could even omit a small part of the problem that I didn't know how to solve, put a placeholder number there, and then solve the rest of the problem correctly, and I will get points for the parts I got right. Which makes sense, because if I forgot how to solve one out of many subproblems, but know the rest perfectly, or if I miscalculated a single variable, i just lose points for that portion. It isn't "all or nothing, the only thing that matters is the final answer." I get part of the reason the "all or nothing" system was done in my russian school, it makes grading much easier. But it also introduces tons of both false positives and false negatives. You know how to solve everything, but screwed up one small calculation? No points for the problem. Oh, you got the right answer at the end and wrote a bunch of gibberish to "get" to that answer (because you just copied the answer from someone else without knowing how to solve it at all)? Well, you got the answer right, so we will give you almost all the points. Cheating was off the charts. And that is at one of the most "prestigious" and highly ranked specialized gymnasium schools.
Of course, high school in the US still had plenty of memorization, but not even close to 100% like it was in Russia for me. And once US college hit me, it became even better.
>A teacher when asked a question once said "I don't know, I have to check it". Holly f... Someone who openly admitted they don't know something, no freaking way!
This, so much. Professors/teachers behaving like humans instead of "even if i was wrong, I am marking you down because you argued with the teacher, and the teacher is always right", that was incredible for me.
P.S. sorry for the long rant, but it bottled up, especially after seeing comments proclaiming the exact opposite of what I, and every single person I know in real life who went to high school/university in Russia, have experienced. Oh, and no comment on "Russian schools in the US" (as I feel like they could indeed be great, but the "russian" part of them is imo just a marketing trick), as that's a very different beast that I have zero experience with. I was talking only about Russian schools in Russia.
I've heard from many Russian immigrant friends who insist that Soviet education was one of the few areas that was done well in USSR. Particularly, mathematics, which, other than the obligatory Marx/Lenin quotes at the top of papers, tended to avoid ideological corruption.
What's funny is that the differences in pedagogy is probably a result of that "ideological corruption". Going through the American education system, it's clear to both professors and students alike that the system was designed on the assumption that there should be winners and losers, and that meaningful education is an afterthought. My math professors complained that the way the system worked made it impossible for a student to have continuity in their learning experience, and if you measure the number of A-students in one course who get an A in immedate next course, it's random. They weren't talking about courses that have large conceptual leaps between them. They were talking about first semester calculus vs second semester calculus.
I studied in 1988-1999, and these stories may be true for Soviet elite education, but not for average Ivan. I personally studied at a school with advanced Physics and English (our teachers after graduating from uni went to Minneapolis for a year of practice). But maths had nothing close to what's described in the article or comments here. No witty simple problems, just boring theorems, then simple tasks to solve.
I did see those witty nice problems in journals and special math tasks books, but that never appeared in our lessons. That was boring like hell. Well, ...at least it wasn't dumb, we did take logarithms, derivatives etc.
But if you take an average Russian, they can't solve a simple proportion problem: say, income tax is 15%, you paid $450 of tax, how much net salary did you get? The answer is easy: 450/.15*.85 (then do it on calculator), but when I did this calculation with accountants from vocational college, they were stunned and didn't get how I did it. I'm not exaggerating a bit.
So those people were either from elites, or nostalgic.
On other courses in Soviet/Post-Soviet school.
Russian language focused mostly on orthography, punctuation and participles. Like if British school focused on spelling "coloUr" or "emphasiSe". The examples of good style were only 19th century literature, especially Tolstoi's suffocating long sentences.
Literature course is similar to what Paul Graham wrote about in his essays: old, boring and already unimportant literature, plus writing essays that must imitate literature critics. I think this was the most hated task at school, and it lasted all the way from 5th to 11th grade. Such essay writing is still obligatory till today in 2021, and I see consequences of it while teaching in a university: students write in unnatural high style, but have difficulties conveying their thoughts or selecting proper evidence (few can distinguish between facts and theories). And that's in a good university -- I'm scared to think what less smart people write. This is not a "degradation" of modern ages, it's almost unchanged since Soviet times.
History course conveyed a Communist narrative, cherry picked facts and asked you not to analyze anything but to remember dates/years. E.g. a textbook on medieval history (6th grade), a paragraph on knights and their armor started with exactly this phrase: "It was not easy for peasants to fight even one feudal lord." (then it described the armor). The entire country of Grand Duchy of Lithuania (at the time it was also called Lithuanian Russia) was omitted, except for being shown on a map. Because it was embarassing to compare that country with Russia under Ivan the Terrible (who became an icon in Stalin's age).
Geography was interesting to me, but when I got to Wikipedia in 2004 and started reading on languages and nations, I saw how much was missing from there.
Biology was a simple and rather boring literature, and the home work was to read a paragraph and be ready to retell it. Most students would simply learn them.
(Actually, with mediocre English teachers that was the case as well: read a text, called "topic" and retell -- and the teacher saw students telling the text learned by heard, but didn't care.)
So, to conclude, math in Soviet elite education was good. Other courses were probably reasonably good, because those elite schools for talented also attracted good teachers. But the average school was of much lower quality.
Friend from Bulgaria was telling me about the annual recruits for the required conscription into the army. Most were illiterate peasants. There ancestors had been illiterate since time immemorial.
Many of the Soviet-era textbooks (mainly by Mir Publishers) are now published by low-cost Indian publishers and available on Amazon.in. Just search Amazon.in for Piskunov, Irodov, Vygodsky etc.
Anecdotal, but still: What you have described might have been the case in a handful of top schools, mostly at metropolitan areas. The key difference for the "rest of us" was a high school theacher who would pick top 1-2 pupils after couple of lessons and teach at their pace for the rest of the year. This is my case and the story that was confirmed by dozens of people in my university.
This is probably a dumb question, but I'm guessing all the textbooks are in Russian?
I really would be interested in seeing this:
> - the old soviet textbooks are generally less verbose than North American ones (less fancy), but high quality in their expression, typesetting, and ESPECIALLY (!!!) the quality of the exercises
but sadly it would be no use to me if it's not in English
I also had a similar experience both on the US and Polish side. The US math exercises that I experienced through my niece were really much more focused on reading comprehension, but almost hoping that the student trips up. Maybe its because I am not a native speaker, but this seemed to be not constructive to the task at hand.
A book that appeared previously on Hackernews is Lev Tarasov's "The world is built on probability". This is not striclty a textbook, but it is translated in English in a way that preserves a lot of the feel of the original:
https://archive.org/details/TheWorldIsBuiltOnProbability
There are plenty of books in Western literature where exercises are also very good, and not only in math, but other fields too. One that comes to mind is Jon Bentley's "Programming Pearls", which has very well chosen exercises.
I was lucky to get an education in three systems (Soviet Math, Romanian Math School (influenced by both French and Soviet Math school), and finally in a world top 40 university in North America.
I would summarize the Soviet/Russian Math/Physics approach like this:
That being said, I did like some of the aspects from the so called "Western Math" (in my case Canadian university):