Reflections on math education

Why is there such a big difference in math education between The Americas and (Europe and Asia) ? except for a few privileged who have the opportunity to access to math much earlier than the ordinary people.

The Question arises when in my first class in my topology class, my professor, who is russian, said that in Russia universities freshmen students take topology and geometry, measure theory and abstract algebra in their first semester. On the other hand, say in the US, most of students start taking calculus 1(with proofs removed) and a logic class on how to write proofs.

In third year when US undergrad math students are just learning the real math (topology, abstract algebra, and real analysis), Russian students are already taking courses such as algebraic geometry, differential topology, Category theory, Riemannian Geometry, etc.

Why is there such a brutal difference?

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For the United States and Canada, it is a consequence of relative lack of "streaming" in the school system. Streaming is not an unalloyed blessing. –  André Nicolas Dec 7 '13 at 6:59
This might help to focus a lot more the question, at least geographically. Apparently "The Americas" actually means the USA plus Canada while "Europe and Asia" means probably only Russia, or even the former USSR. Anyway, the conglomerate "Europe and Asia" is quite disparate in this context, with at least four or five subsets with different characteristics. –  Did Dec 7 '13 at 7:27
Can you explicitly mention examples of each of these subsets, and give us a flavor on each of their characteristics? thanks –  ILoveMath Dec 7 '13 at 7:31
Off the top of my head, the list of subsets should include (Western Europe) (and even that...), (Russia+former Soviet republics), (India), (China) and (Japan). Which leaves an awful lot on the side... // "give us a flavor on each of their characteristics" I might give one or two (mostly uninformed) hints but this would not lead us very far. A remark: I am a bit worried by your reaction to my former comment, which might indicate a thinly veiled desire to get rid of the message and/or the messenger at the lowest possible cost. So, let me repeat: the notion of a math educational system common... –  Did Dec 7 '13 at 11:52
@DonAnselmo: Did is simply saying that there is no single math educational system common to all of Europe and Asia. He’s right: there’s considerable diversity. –  Brian M. Scott Dec 8 '13 at 7:29

I don't think there is a single reason why the US lags behind Russia in math, but there are several possible explanations, each of which has its strengths and weaknesses. I will list them in the order of plausibility as it seems to me, and also pointing out their possible weaknesses.

1. The cultural atmosphere in the US does not look up to math and the sciences. Russian culture is more permeated with respect for these disciplines.

2. American society is materialistic. There is a certain amount of idealism involved in doing "pure science" like mathematics. A weakness of this argument is that Russian society is also apparently becoming increasingly materialistic. There is probably some truth to the claim that what you wrote applies more to the Soviet Union than to Russia today.

3. Mathematics is elitist. If you can do that integral, you are on top, and the fellow who can't feels like a failure. This goes against the grain of contemporary cultural attitudes in the US.

4. Mathematics is autoritarian: the teacher knows everything. Similar comments apply as in item (3).

5. The attitude of victimhood is common in the US. "I am a victim; who are you to tell me that 0.999... equals 1?" The weakness of this argument is that it applies only to certain groups within American society. However, the classroom atmosphere may well be dominated by such an issue. Note: one of the editors feels that this is a weak point. I concede that it is probably the most provocative of the six.

6. The US is characterized by a very high ratio of hours in front of TV/ipad per person. The effects of this have been felt since the 1950s when TV became a standard household feature, resulting in uniformly lower SAT scores for the generation entering TV-equipped homes.

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I like this answer. I need, though, a little more explanation regarding number $3$. For instace, what do you mean by "contemporary cultural attitudes in U.S." ? –  ILoveMath Dec 10 '13 at 14:26
Also, and sorry for bothering you again, but I would like to make an opinion regarding number $3$. I believe Mathematics should not be elitist. We should blame the people who do Math regarding this issue since some of them create divisions among students, and hence creating an elite. For instance, as an example, I remember once having a professor who, in class, he would say things like: "you either get it or you don't get it", etc. I think this kind of behaviour creates divisions. What is your opinion on this issue? –  ILoveMath Dec 10 '13 at 14:42
Oh, and I forgot, thanks for taking your time to answering my question! –  ILoveMath Dec 10 '13 at 14:46
I think this is not a good answer. Every single one of the six points is a classic platitude, generally publicly held conventional wisdoms that 'sound true', but are actually difficult to verify, if not totally based on myth. Sociologists would immediately disagree with the bombastic "...resulting in uniformly lower SAT scores for the generation entering TV-equipped homes". Are you seriously going to claim that as the dominant cause-effect relationship? The argument of victimhood, point 5, is perhaps the most irrelevant of them all. –  Newb Dec 10 '13 at 16:30
(Addendum) As further illustration of my complaint, take the statement in point 1, "Russian culture is more permeated with respect for these disciplines." You would have to present a very strong and detailed sociological as well as historical argument to have even a foothold making that claim convincing. Finally, there's the problem of the proposition itself: we're accepting the idea that the US is 'lagging behind' Russia in Math. This is not necessarily true in and of itself: this claim should be subject to rigorous examination before jumping to nearly nonsensical pseudo-explanations. –  Newb Dec 10 '13 at 16:33

Your professor, who is Russian, likely grew up and did and his undergraduate maths education in the Soviet Union. What your professor said may have been true then, though I don't think it is still the case today: if it were true, graduate departments everywhere would be filled with Russian students. In either case, it sounds like your professor made a strongly exaggerated statement.

However, during the days of the Soviet Union, it was recognized that the USSR was producing quite capable young mathematicians. Without delving into too much history, the most compelling explanation for this (that I've read) was that the USSR was doing poorly economically, and education in the more applied fields is expensive, requiring field-excursions, experiments, etc. By contrast, all that you need to do math is a pencil. Moreover, mathematics has extremely useful general applications at the more advanced levels. They wanted great technological progress at the lowest possible financial cost. From a governing point of view, it was obvious to focus education on pure mathematics.

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I think the first part of your comment on user72694's answer also applies to this answer. –  anderstood Oct 18 '14 at 22:27

Being multilingual helps a lot. It really does not matter which languages one has, though.

What this does is to help the mind realise that words like 'always' actually is several different ideas, and that one can not effotlessly jump from one to another. In maths, you see infinity as meaning 'anything that is unbounded', where the Indians had no fewer than five, and in my researches, I use a good number of different infinities too. They do not become equal by way of the word: many have different names (class infinity, cascade infinities, teelic infinities, horogonal infinities).

Here in Australia, they bring on the heavy mathematics at senior (Years 11, 12). You can chose to do 'Maths A', or 'Maths A' and 'Maths B' in the electives. Maths B introduces you to a series of four modules where you do things like Matrices and Vectors, etc.

At university, they expect people entering particular streams to have A and B, but because these are a subsection of all of the modules available for high schools for making the Maths A/B courses, the idea is that they can cover the whole material rather fast, since you ought be familiar with half of it.

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I've heard in Europe and in Russia especially that people have their future education mapped out from about the time they're in middle school. This means people who will specialize in mathematics in university know so very early on and the focus of their studies shifts accordingly. This produces a very biased sample of mathematically inclined students entering into mathematics oriented universities. In contrast in the U.S. people enter college without even knowing their major and many universities are tailored so as to give mathematics education for the common man in the way that most technical fields require (the basics at least).

To me it seems we're comparing apples and oranges in the way these systems go about teaching people mathematics. One system knows "real" mathematics and emphasizes this from the get go, but does so to a preselected audience of future mathematicians. The other teaches mathematics to people who need to use mathematics but who aren't necessarily future mathematicians.

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This may not be entirely accurate. Societies in Singapore, South Korea, Japan, Russia, and many European countries produce high school graduates with a vastly superior level of mathematics preparation than in the US, even before any "streaming" takes place. Many of those societies emphasize the virtues of delayed gratification. –  user72694 Dec 22 '13 at 15:30

I agree with RR and would just add that students in Europe who have been identified early-on for a math/science education might also take 2 or even 3 math subjects per year in high school and subsequently would not be bothered with requirements covering much history, social studies, health, etc. So they may learn more math in one year than the average American student has even heard of, especially as they approach the end of a one year beginning Calculus sequence. But this ability to focus comes at the expense of other subjects and a less well-rounded education.

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