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I'm interested in school systems, and I have a question regarding the "college" level. (I have a French background).

When I look at college math or physics books, it seems to me that there is no big difference with what is taught at the high school level.

By comparison, in France, first year university math or physics books dramatically differ from high school books.

To put my question in a provocative way: what is the purpose of teaching at the college level what students already know from their high school courses? Or don't they? Or, is my vision of college contrary to actual facts?

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    The aim of educational systems can be quite different, hence the underlying expectations likewise will be different. I think about France where there's a sort of culling process. The American system attempts to accommodate and retain. As a result it seems in the latter the lines between early undergraduate and high school continues to blur, a general lowering of standards in one, not a raising in the other. – A rural reader May 9 at 0:07
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    Your Question would be improved if you explained the details of how your "first year university math or physics books dramatically differ from high school books" in France. – Basil Bourque May 9 at 5:44
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    "The American system attempts to accommodate and retain." Or, "no child left behind" becomes "no child allowed to get in front". – alephzero May 9 at 10:29
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    @Dirk: India has 23 official languages. Per the 2011 census, there were 259,678 people who spoke English as their first language, 83,125,221 second- and 45,993,066 third language speakers. Indians who post at StackExchange are a highly educated and nonrepresentative minority. – Stephan Kolassa May 10 at 6:56
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    @Mayou36 - or, instead of a citation, you could just live in the USA for the last 30 years and look around you. – davidbak May 11 at 0:09

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First of all, the US has no university system. It has somewhere around 1500 community colleges offering 2 year degrees and 3500 colleges and universities offering 4-year degrees, all of which run with more independence than an ordinary French university. (Keep in mind the federal government has established only a tiny handful of universities; public universities are nearly all set up by the individual states.)

Second, you should understand that there is no high-school leaving exam like the bac. Basically anyone who is willing to sit in the classroom and do a minimal amount of work can get a high school diploma. Harvard is incredibly selective and it's about as hard to be admitted to Harvard as it is to be admitted to the ENS. The top 100 or 200 of US universities are all selective, and the average student would not be admitted. However, most universities and all community colleges will allow anyone with a high school diploma to attend. (My university officially has admission requirements based on high school grades, but high school grades have been inflated to such an extent that these requirements are almost meaningless, and the admissions office routinely gives waivers to these requirements anyway.) About 85% of Americans earn a high school diploma and can attend community college. (Another several percent obtain a GED.) Only about 45% of French take and pass the baccalaureate general and can attend university.

At a community college, you should expect that many students do not actually know what you might think they should have learned from high school, and a significant number of students will have trouble with upper elementary material such as adding fractions. There will even be a few students who are functionally illiterate.

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    Note: GED = General Education Diploma (informally), a HS equivalent diploma earned by exams and mainly by adults who dropped out of school early. ged.com – Buffy May 8 at 21:50
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    For the foreign reader, public universities aren't all of our universities. Idk what % but universities are either state-run or private not federal. Most universities you've probably heard of are private (Stanford, Harvard, Princeton, NYU) – Azor Ahai -him- May 8 at 22:24
  • While the public Universities are run by the individual States, they all receive significant federal funds, which gives the federal government a significant say in how they are run. – Michael Richardson May 9 at 12:55
  • Comments are not for extended discussion; this conversation has been moved to chat. – cag51 May 12 at 3:42
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This is a US centric answer. Over the past 50 years there has been a vast change in what happens in HS. For example, when I was in school it was extremely uncommon for a HS student to take beginning Calculus. Now the better students do that pretty regularly through the Advanced Placement program which is an attempt to teach college courses in HS.

So, the course in Calc I and Calc II might look the same in an advanced placement course and in a first year college course, but those students who have done well in the advanced placement program (courses and exams) don't have to repeat those courses in college (ideally, anyway). They are able to start at a higher level and it then becomes easier for them to take higher level courses throughout.

But a student who hasn't done "AP" but wants to study math will start with those courses in college.

There are also a few exceptional secondary (HS) schools that teach quite advanced courses, such as multivariate calculus, advanced analysis, and a few others. But they are both difficult to get in to and hard to succeed in (as in lots and lots of work).

At the other end of the scale there are also secondary schools with insufficient trained staff to offer much in the way of math beyond Trigonometry and Analytic Geometry. But, 50 or so years ago, that was the standard for most US schools.

I'm quite certain, however that this model isn't practiced in very much of the rest of the English speaking world. It is quite different in UK, but so is the university system quite different there than here.

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    The fundamental difference is that the UK has a national curriculum for school education, and two levels of nationally standardized exams usually taken at the minimum school-leaving age (16) and two years later. Students aspiring to go to university would typically take 9 or 10 subjects in the first level exams, and 3 in the second level. University admission to study any subject requires a high enough grade in core subjects (e.g. English and math) at the first level, plus high enough grades in the second exams in the subjects relevant to the university course. – alephzero May 9 at 10:39
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    ... and the "9 or 10 subjects" examined at a national standard level means there are no mandatory "general education" component in university degree courses. – alephzero May 9 at 10:42
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    @alephzero The SAT, ACT, and SAT subject tests act as a de-facto nationwide entrance exam in the US. Opposite would be Japan which, despite recent attempts at standardization, still largely requires institution-specific exams, particularly at prestigious institutions. Also relevant is that the UK (and UK-derived systems) shift one year of college to high school, compared to the US. – user71659 May 10 at 1:32
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    @user71659: Community colleges do not have an SAT/ACT requirement, and most 4 year universities have one on paper but will basically admit anyone. Only a small minority of universities in the US are selective. Most are de facto open admissions. – Alexander Woo May 10 at 23:14
  • While a senior in high school I took college level courses through the high school and received college credit. – paulj May 11 at 17:35
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The other answers here are correct. Colleges and high schools across the US are so different (in my opinion the single biggest problem with US education) that it's almost meaningless to speak of how the average high school education compares to the average college education.

However, there is one difference between high school and college in the US that is more or less universal: instructional style. At the high school level, teachers are punished if students don't score sufficiently well on standardized yearly exams. This means that at most high schools, teachers employ a variety of strategies to make sure that as many students perform well on these exams as possible. The philosophy of high school level instruction is "if the students didn't learn it, the teacher failed (and should be punished)." By contrast, the philosophy of college level instruction is usually "if the students didn't learn it, the students failed (and should be punished, e.g. by failing the course)."

Because of this, in high school classrooms, instruction is typically varied and focused on remediation. The onus is on teachers to make sure that students learn. In college classrooms, instruction is typically synonymous with lecture. The onus is on students to learn what the course requires (indeed, even if the professor doesn't teach it).

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    Difference are good, because parents and students have different desires, needs and wants. I consider this aspect beautiful that a central authority does not have the power to force everyone to be molded to the whim of a central bureaucrat. – paulj May 11 at 17:38
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    @paulj The problem is that the tests are centralized and designed according to the whims of bureaucrats. What's odd is that when students fail to perform on these tests, the teachers usually shoulder the blame, not the bureaucrats who designed the tests. – Charles Hudgins May 11 at 19:30
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You already have very detailed answers on the U.S. system. Let me talk a little bit about how a French perspective creates distorted expectations.

In the French system, the curriculum is (essentially) set at the highest level by the Ministry of Education. Much of the nonsense passed as education in some countries (sometimes with sectarian affiliations) is simply illegal in France. The educational content you get in France is tightly controlled. In many other countries (including the U.S.), not so much. There are pros and cons.

Pro: at the time of writing, the French have competent or semi-competent government officials with a tolerance for logic and common sense. Meanwhile in some U.S. schools, Huckleberry Finn and To Kill a Mockingbird are banned.

Con: There are occasional missteps and missteps have huge consequences in France since they affect every student. An example is intolerance for the headscarf: a wonderful, avant-garde idea when it was implemented and almost certainly a huge national embarrassment a few years from now. I can already hear American T.V. networks making fun of the French.

Pro: new knowledge can be disseminated to every student in every part of the country. You don't have regional inequalities like you do in the U.S.. Sure Paris schools have better students on average, but a good student in a small French village will learn: in the U.S., redneck begets redneck.

Con: It takes forever for innovations to find their way into the curriculum as the ageing technocrats retire and are replaced by younger ones with a better grasp of the world around them. In the U.S. a school will not hesitate to teach the earth is a cuboid and if it is, they're ahead of their time, while the French will always lag behind.

Pro: Since bureaucrats at the Ministry of Education, not students nor their parents, set the curriculum, they can choose to emphasize math and technology, while de-emphasizing art and ancient Greek if they feel that's what will take the country forward. Meanwhile in the U.S., students and parents decide what the schools will teach them (schools adapt their curriculum to demand) and if that means teaching that the earth is flat and that the election was stolen, they will.

Con: In France centralization has created a system where it's nearly impossible to switch fields: If you took the literary stream (whatever it's called these days, they rename it every decade), you are unlikely to be able to study math and physics at "university" (I say university, but I include the classes prépas and grandes écoles of course). If you choose the wrong stream at the age of 12, you will pay for the rest of your life. Meanwhile in the U.S. you can major in "Poetry and Chemistry" or "Logic and Religion".

Edit (clarification): There is a great deal more diversity in the United States and other countries than there is in France. It's not just because of population size: Switzerland is also far more diverse than France. French centralization goes back a long way to the days when students who spoke their local dialects were severely punished (Louis the 14th and all that; see how widespread local dialects are today in, say, Spain and Italy compared to France). In France, if you took the "literary" stream, you're not very likely to attempt to take math/science/technology classes. Moreover math is (currently) unusually strong in France, by world standards, as a result of the early specialization. The U.S. system is far more flexible, mainly because it caters to student demands. So yes, many U.S. universities and colleges offer easy subjects, but if the students are willing to pay for it they must be getting something out of it.

That was too long for a comment.

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    Fun reading, if a tiny little bit polemical. Have my +1 to counterbalance all the downvotes you are sure to get. – Stephan Kolassa May 10 at 7:03
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    The US does have accreditation enforcing standards and requiring things that may be out-of-date, essentially acting as your French bureaucrats – Owen Reynolds May 10 at 21:47
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    @PatrickT "Redneck begets redneck?" Isn't it bigger than that, the poverty cycle and ed opps in the US? Parents beget children. Social stratification affects everyone. The "something" they get for their money is debt but for more job opps, not necessarily more education than a HS diploma. Mileage varies. – livresque May 11 at 1:10
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    @livresque. Sure, the sources of inequality and social stratification are complex, but educational institutions are typically expected to be a mitigating factor. This is no longer the case in the U.S.: education has become a "buyer's market". The probability of earning more than your parents is approximately 50% down from 90%. See, e.g. voxeu.org/article/trends-us-absolute-income-mobility-1940 . – PatrickT May 11 at 3:09
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    This is a minor point in your interesting answer, but I think it's worth noting that France is not the only country ( even in Europe) that considers headscarf as an issue when it is worn at school by teachers or by young students ( headscarf is allowed in universities in France). This religious sign is banned in public institutions in Turkey, for example. There are deep reasons for that, rooted in history. – Floridus Floridi May 15 at 6:57
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In my experience as an American student, the overlap depends heavily on 1. how good your high school is and 2. how good the college is. There is a huge range in the academic rigor of high schools and colleges. Public schools depending on region vary widely in how many advanced courses such as AP courses they offer, some only one or two, others 10+. Top level public high schools and good private high schools will already overlap with basic undergrad curriculum, and very good private schools already teach college level material. I went to a good public high school in a relatively wealthy area which had students who performed decently well at highschool olympiad type competitions and had one or two advanced classes taught by people who also taught at local colleges. Highly selective colleges will be much faster paced and expect much more math background, for example the first year undergrad math courses teaching set theory and combinatorics may already be more advanced than all of community college's math courses.

One important difference I noticed is that college gives much more independence in terms of homework. Most of my college classes had assignments given once a week and most professors did not care if you showed up to lecture or not. My college homework required much more independent thinking and persistence in solving problems, for example each math problem in one homework may take me anywhere from 0.25-10 hours of total time thinking and experimenting, while I would rarely spend any significant time on any one high school problem.

Some colleges let you "test out" of introductory courses if you have a certain score on the corresponding AP exam (usually a 5, the highest grade, sometimes a 4) or have credits from taking a course at a local college already. This varies widely depending on college and even between different majors at the same college. You might expect more selective colleges would be less accepting of AP credit, and this is true in some circumstances but doesn't hold in many others. My university, which is well known for its CS department and intro CS course, let students skip different levels of the intro CS course depending on if they got a 4 or 5. (They also had a placement test that I took to try to skip the intro class, but my personal gripe is that it wasn't written well with typos and it tested Java, for which I had no experience.) For some AP exams I got credit for the minimum major units but it didn't fulfill my major course requirements.

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  • I think I have heard that you can "test out" of entry-level college courses (I think by having high school advanced placement grades and/or performing well in admission tests); that is, if you are good enough you almost skip the first semester. Can you confirm that? That would be part of the overlap in course material the OP is observing. – Peter - Reinstate Monica May 12 at 0:17
  • @Peter-ReinstateMonica Yes. I added some detail to my answer. If you have any other questions I can try my best to give you my experience from applying and attending – qwr May 12 at 5:31
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They may use the same books, but college is about twice as fast as high-school. A year-long high school "AP computer science A" course tests out as a semester-long college computer programming-I. In practice, it's a little less (the high school version covers as many topics, but they write fewer program so are a bit weaker overall). I think high school chemistry is the same way.

The hours work out. The rule was that for a difficult college class you'd have 6-9 hours of homework each week, whereas -- I don't know this as well -- high school is a lot less.

It's understood that 1st year college classes can often be tested out of or handled with some sort of transfer credit. It was (probably still is) common to go to a nearby community college, transfer those credits, and come into college as a 2nd year student. That's when you get into the subjects that no one else teaches except a university.

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    AP Computer Science A may be a bad example. I've just looked at the 2021 curriculum, and it's still a joke. A typical Intro to Computer Science class at a university would cover that content in a couple months. There's a reason it's the only AP course that my university wouldn't give credit for. – Andrew Ray May 10 at 19:44
  • AP Computer Science once had an AB test which covered a little more material (stacks, pointers). However, AP CS AB enrollment fell, esp. among minority students -- so they changed AB->A to fight that decline: edweek.org/policy-politics/… In truth, this was a small change since "B" material was often covered in a few weeks. Your idea of a typical CS intro seems biased: top CS schools often use Structure and Interpretation of Computer Programming (little overlap w/AP CS) but that is not like the intro at most schools. – kurtosis May 10 at 20:35
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    @AndrewRay I suspected as much but my time reviewing transfers was before that course existed locally. To your point, going 1/3rd or 1/4th as fast makes it an even better example of my "HS may look the same, but it goes slower" thesis – Owen Reynolds May 10 at 20:35
  • @kurtosis You're right that it is secondarily true that aside from being very light on content, the AP CS A curriculum is spectacularly bad, with whole units on Java-specific concepts like ArrayList, immediately followed with a unit on 2D arrays, which I hope is all about how you should never use them in Java, though I doubt it. It even dips into ethics and intellectual property in the middle of the unit on iteration for some reason. However, while the AP CS A curriculum doesn't line up well with a real CS intro course, that just makes it even more of a joke. – Andrew Ray May 10 at 20:49
  • @kurtosis Hmmm...my read of that is that High Schools used to try to have a course that ran at the same speed as a college course, but it was cancelled for low attendance. Probably because it ran too fast. My understanding of the other half is that CS-Principles was created to get non-white males interested, and did that very well – Owen Reynolds May 10 at 21:09
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American "college" student here (I know that word has a different meaning in French). In my narrow experience, American college courses and books do indeed differ from high school courses and books, but there is a significant degree of overlap. For example, chapters 1-11 of Calculus: Early Transcendentals by James Stewart cover single-variable calculus, which I learned in high school (albeit with a different book), while chapters 12-17 cover multivariable calculus, which I learned in college. Furthermore, some students take both single-variable and multivariable calculus in high school, and some take both in college, so the same book may be used at both the high school and college level, but that does not mean that colleges reteach students what they learned in high school. More generally, most American colleges offer courses that are offered by most high schools, such as precalculus, and courses that are not offered by most high schools, such as abstract algebra and analysis. Furthermore, as others have pointed out, I think you will find a higher degree of overlap with high school material at a community college than you will at a four-year college, especially a more selective one.

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It's going to depend on which math and physics books you're looking at. There are typically several levels of 1st year college courses. First year calculus, physics, &c for liberal arts or business students are not the same courses as those intended for STEM majors. If you're looking at texts intended for the former, they probably do cover basically the same material that would be in the high school courses that students interested in math & science would take.

For example, looking at my local university's online catalog, there's "MATH 176 - Introductory Calculus for Business and Social Sciences" and "MATH 181 - Calculus I" for STEM students. Both of these require either passing some of the 20 or so basic math courses, or a sufficiently high score on college entrance exams. (ACT 28 or SAT 650.) Most people intending STEM studies will have taken those basic math courses in high school, and will have the necessary scores.

MATH 176 is a 1 semester course, and except for perhaps a statistic course, the last math course those business & social science students will take. MATH 181 leads to MATH 182 & 183 the next two semesters, then differential equations &c.

Likewise, we find General Physics I & II for non-majors, but Physics for Scientists & Engineers, General Chemistry vs Chemistry for Scientists & Engineers, and so on through all of the sciences.

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There are several differences between the two systems. It might be helpful to think of the first year of American colleges as weakly like the college preparatory courses in France. I say that because there is some attempt to even out the pretty substantial disparities among state educational systems. College in the US is one year longer than college in France.

For example, my cousin was from Louisiana when he went to college. Because they require both French and English, they do not require students to take four years of English. That can be an insurmountable barrier to a college that requires a student to have four years of English to be admitted unless they voluntarily took extra English. Some community colleges use that first year to teach deficiencies, although these are often "zero credit" courses.

Also, most, if not all colleges have a mission. It is usually a population they are designed to serve, but not always. We have local community colleges and tribal colleges that are designed to serve the college educational needs of the local population. They are a good choice for many students because they are adapted to the local education systems. They transition students from the local public school system to that which is expected from a person with a degree.

In addition, we have a system of private colleges and universities. They often have a different mission than the public colleges and universities. Quite often, they are as concerned with the intellectual and moral formation of the student as a reasoning adult as they are with conveying content. There are also private technical schools that provide narrow education and are focused on a single professional group such as engineers.

Intermixed with these are the research institutions. They are usually doctoral granting colleges and universities. They can be extremely rigorous and selective institutions or they can have a community college component where they transition students from the local educational system to research level education.

Also, although small in number, there are a number of military institutes and academies. They exist to train the future officer corps for both the state and national military systems. They are often elite institutions. The U.S. Naval Academy, based on post naval career outcomes, is probably the nation's number two or three school.

Finally, there are the Ivy's and the Public Ivy's. They are the place where the children of the wealthy who are at least slightly talented meet the nation's best and brightest. About a third of the students are "legacies," the children of alumni. They get in because their parents or grandparents or great grandparents got in. Admission is a combination of wealth and talent.

Another factor is the difference in the goals of the French and American educational systems. Except for technical education in American high schools, the goal is to teach a little of everything. The education is general and only focused if the student chooses to focus it.

So, to try and answer your question as to why some college textbooks are similar to high school textbooks, the books fill a need. Some students enter college with two semesters of calculus, an extra year of chemistry, an advanced English composition course, and an advanced biology course. Others are struggling with math, English, and the sciences.

America is very uneven and very unfair to be born in. Without being here, it cannot really be explained because of the size and political differences. There are places in the United States without running water, sanitation systems, or electricity. There are states that still rely on "one-room schoolhouses," where all grades are taught at the same time by one teacher. That teacher is teaching first grade and twelfth grade in the same room. There are places where the teacher does not speak the same language as the students. There are schools in the US that don't have books because they cost too much.

Sometimes in the same town, there will be a public school where students are required to turn in their science lessons in virtual reality modeling language. Some schools have robotics programs. Some high schools offer college classes in their building alongside high school courses.

American colleges are the last chance for the students who have the greatest disadvantages to be given the opportunity to catch up with the most privileged.

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    I find your third-to-last paragraph a little hard to swallow. I'm sure there are cabins in the woods without water and electricity in both the US and France, and I fail to see what they have to do with education. I would be surprised if there are schools where the same teacher is teaching first and twelfth grade in the same room (and if that happens in some faraway place in Palau, I would expect similar in some French DOM/TOM), much more if entire states still "relied" on this, suggesting a widespread policy. Can you add a few links? – Stephan Kolassa May 10 at 7:09
  • @Stephan Kolassa: OTOH, having grown up in a place that approaches the (rather exaggerated) extreme of that paragraph, I pity kids forced to grow up in urban areas. – jamesqf May 10 at 15:24
  • @StephanKolassa I live in Montana. We have a huge number of one room, one teacher schoolhouses. We also have a large number, certainly in the tens of thousands, without access to running water, sanitation or electricity. As to where they exist, here is a link. billingsgazette.com/… The article says there are over sixty, but I was reading a report that said there were still 88 although that was five years ago. – Dave Harris May 10 at 22:03
  • @StephanKolassa As to housing quality, I have another from Montana, although you can also get the same in the American southeast and on many reservations. greatfallstribune.com/story/news/local/2016/03/31/… – Dave Harris May 10 at 22:05
  • @StephanKolassa I think the paragraph is a fair enough description. The U.S. is probably more diverse than even the E.U. Add to that the fact that schools are substantially funded by local property taxes, and the discrepancy between the good and bad places leads to a big overlap between elite high schools and sub-par colleges. – Peter - Reinstate Monica May 12 at 0:32
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The content doesn't differ between advanced high school courses and college courses, but the pedagogy and evaluation techniques do.

For example, when I took AP biology and calculus in high school, they were taught over the course of 2 or 3 semesters, and the grades were based roughly 80% on attendance, homework, and regular quizzes, and 20% on mid-term and final examinations. Classes were mostly lecture, but also included in-class work, where students could get familiar with the content and receive help from the teacher. The teacher was concerned with each student succeeding.

In college, the classes which teach this same content are taught over the course of a single semester, with the evaluation criteria basically flipped: Grades were based roughly 80% on mid-term and final exams, and 20% on homework. Classes were completely lecture, and while the instructor wants you to succeed, the burden is on the student to ask for help when they need it. Another difference is that these classes were often accompanied by companion "classes", such as twice weekly recitations (where a graduate student would help a 20-30 person subset of the lecture class, without a separate grade), or labs (focused on experiments, graded separately).

*This is an anecdotal answer based on my experience as a millennial growing up in the US, going to public schools and a public R1 university.

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