11 ms·

Why Won’t Anyone Teach Her Math?

33 points by sebg 5y ago

zihotki 5y ago
Earlier submission - https://news.ycombinator.com/item?id=30328403 https://news.ycombinator.com/item?id=30328403 (Not much discussion though) Edit: formatting
graycat 5y ago
> Why Won’t Anyone Teach Her Math? Some people, a lot of people, will gladly "teach her math" and do a good job of it. E.g., I tried to, here: In the thread "Why won’t anyone teach me math?" at https://news.ycombinator.com/item?id=30302079 https://news.ycombinator.com/item?id=30302079 I posted "Part I" https://news.ycombinator.com/item?id=30307316 https://news.ycombinator.com/item?id=30307316 and "Part II" https://news.ycombinator.com/item?id=30307349 https://news.ycombinator.com/item?id=30307349 The two parts are needed because of length limits of HN posts. The OP (original post) "Why won’t anyone teach me math?" is about a coed at Princeton in a badly taught course in linear algebra. It turns out, I did really well in linear algebra, and "Part I" explains how well I did and how I did that. In "Part II" I give an outline of an introduction to linear algebra and matrix theory. For my background I've taught applied math and computer science at three well known research universities and have a Ph.D. in pure/applied math from a fourth. From how I learned math I have to say that there is a lot of having contempt for the students and dumping on them. This dumping on the students, treating them with contempt, is unnecessary, unjustified, inexcusable, and bad for the students, researchers, teachers, schools, math, and the US. The dumping isn't just in famous research universities: E.g., I went in grades 1-12 to the unique college prep school in the city. I got dumped on from the 4th grade on and maybe also in the first three grades but simply don't remember much about grades 1-3. I wanted to learn but got dumped on so much that I just gave up trying to please the teachers and did what I could with the books for the courses. Turns out, that was a good thing for me to do, especially for learning math. There were a lot of standardized tests, both aptitude and achievement, and apparently I did well on those, much better than how the teachers viewed me. Point: The opinions of teachers who dump on students can be highly inaccurate; some more objective measures are needed. Due to the objective measures, in the 9th grade I got sent to a math tournament and in the 11th grade, to an NSF math & physics summer program. Point: The objective measures helped. Turns out, that was true throughout my education. But for college I went to a private school that took lots of pride in doing well at teaching. Some of the teaching was quite good. Still, however, there was some dumping: E.g., the college got a new prof fresh from a famous research university, and he brought his dumping/contempt propensities with him. At one point I took a reading course from him from a then famous, advanced, notoriously difficult book in topology. So, for each chapter one week I gave a lecture to the prof on the math and the next week, on the exercises. I did well. Once another prof showed up. But even with that good self-teaching success, the prof at best only slightly relaxed his dumping/contempt mode. Point: In that reading course I was a spectacularly good student but the contempt still continued. My Summary View: I see no good reason or excuse for the dumping and contempt. I refused to do any such things in my teaching. Generally I told the students: The material is in the book. Class is to help you learn. So, I'm here to explain and answer questions. There is homework which is to work as many of the exercises as you need to to learn the material, in particular to get good at working the exercises. The tests are problems similar to the exercises -- if you are good on the exercises, you should be good on the tests. From the numerical scores on the tests, I rank the students, and the purpose is to simplify the assignment of letter grades: So, if student A does better in the ranking than student B, then student A will get the same or better letter grade than student B. But WHAT letter grades? My standards are, A means that know the material well; B, knows the material; C, knows some of the material; D, doesn't know much; F, doesn't know much and none of us want the student to get credit for the course. So, I look at the work on the tests, judge A-F and decide what final scores deserve what letter grades. Students are not in competition: E.g., I'm perfectly willing to assign As to all students who know the material well; would be pleased to do so; the situation would represent a big success. The department has no rules against my assigning As to everyone. I'm available in class, after class, and in office hours. Generally the office hours are not heavily used. The US colleges and universities have some really big heartburn about the comparative roles of teaching, applications, and research. Research: Can argue that academic research is by a wide margin the most powerful contributor to civilization, health, wealth, understanding, etc. So, with lots of research universities where the profs are required to publish in peer-reviewed journals of original research and hopefully get prizes for work they have done and grants for the work they are doing will, year by year we get some astounding results. Quite broadly the most respected research is theory based on math, theory that mathematizes the field. Applications and teaching are regarded as much less desirable. Applications. Schools of medicine take applications fully seriously -- that is, a lot of the teaching and research are done in research-teaching hospitals with patients at risk of dying. The field of medicine has a major and respected role for clinical, professional practice. The MD degree, to be a "doctor", is about practice, not research. In schools of engineering, there can be some significant attention to applications. Still, generally engineering schools do not try nearly as hard as medical schools to purse practice, be clinical or professional. Teaching. There usually is a lot of good teaching in colleges that emphasize teaching over research. But generally the research universities and their profs look down on teaching -- bad for the field, students, profs, schools, and the US. Generally there is a belief, attitude, assumption, expectation, tradition, etc. that school is to be a competition, pick winners and losers, be challenging, be a filter, have the students put up with being dumped on, get lessons in going without sleep, etc. As a prof, I refused to play that game -- it was in the interest of all my students to work together to learn, come to my office hours, confess what they didn't know, and get additional explanations, problem solutions, etc. My view now, from this thread and more, is that the US research universities are on thin ice, about ready for their "comeuppance". Via taxes, tuition, etc., the public is paying the bills and wants results -- contributions to health and wealth, national security, and especially good careers for the students. Bad teaching, dumping, contempt, generally hurting the students, are creating some really bad PR for the research. Next, for the teaching and a lot of what the customers want now is arriving via the Internet, e.g., YouTube. I did some teaching here in the "Part II" I wrote. A lot of that teaching is NOT good, but the best of it is getting good. When there is some really good teaching on the Internet for free or nearly so, bad teaching, hurting the students, etc. will come to hurt the universities, even the Ivy League. It's possible for a really good student, PBK, etc., brilliant, dedicated, to be so dumped on, treated with so much contempt, that their anxiety level gets really bad, they lose sleep, have physical symptoms, get depressed, clinically depressed, don't recover, and commit suicide. Some education. We're expected to pay for such abuse, via taxes, tuition, our health, our lives? Bad teaching, hurting the students -- NOT acceptable, grade F.
bradgranath 5y ago
Never took a math class that didn't provide a solution index for practice problems. University level students are expected to be able to self-regulate their study ethic and this sort of paternalist bullshit is turning undergraduate programs into trades learned by rote.
h2odragon 5y ago
I can't teach anyone anything. I have doubts that anyone else can do it, either; but can only speak to my own experience. I can provide lots of assistance to those who are trying to learn. We tell people "Edumacation" is going to happen to them whether they want it or not; and then they have to sign up for more "or you'll never have a good life" etc. It seems that we've lost the reason why we do these things. It's just empty ritual. Things are this bad in famous, expensive upper class schools; imagine how bad they are in poor to normal elementary schools. We got kids with failing grades because they never got a (theoretically school provided) chromebook, never got a login to "the homework sites", or can't get reliable connectivity from home or school. They may or may not know the material they were supposed to learn but who cares about that? As long as the attendance records are good the school gets paid.
- lbriner 5y ago
  An interesting take and, yes, in the west it is hard to instill in a student that it is up to them to earn their way to success by making the maximum use of the teaching resources and not to sit back and get fed what they need. In poorer countries, this is better understood, especially since many people do not go to school so the alternative to working hard is plain to see. Not sure how you fix it though, perhaps some out of the box ideas to reward those that work hard in a way that reinforces that hard works pays off. I don't know.
  - bernulli 5y ago
    That's got nothing to do with west vs. poor. Have you seen the 2-year French math requirements before you are even admitted to an engineering school? Have you seen German universities where there is zero advisement and where your two years worth of math courses in your engineering program are tested in a single final exam, as the very first feedback (no quizzes, no homework, no midterm, not split into 10 math micro courses, no projects, no extra credit, etc.)? It's sink or swim.
- JKCalhoun 5y ago
  No offense, but I think you're being a bit dismissive: if a students doesn't learn a thing it is because they didn't try. There is a middle road you are not calling out: if you make math (or any subject) approachable in your teaching style, you can get students to want to learn, try to learn. I'd say that is generally true for pretty much any subject. Why does someone try to learn history? Probably because they somehow became interested in it. A good teacher will try to make it interesting.
PaulHoule 5y ago
It's a structural problem in conventional physics classes (I'd think similar to math) that the median grade is awful (sometimes even like a 30) but it gets graded on a curve so that's considered a C, an acceptable grade. In a class like that students walk out with a passing grade but often a weak understanding of the subject. I was involved in teaching the PHYS 1101-1102 sequence at Cornell https://physics.cornell.edu/physics-health-careers https://physics.cornell.edu/physics-health-careers which is an auto-tutorial class where students are required to take each test multiple times until they get a grade that's high enough to indicate mastery. Some people find this course to be nervewracking, often they fail the test horribly two times, sit through debugging sessions with the tutors, come back and do pretty well on the last try and walk out with a B+ or A- grade. The course is unique in a lot of ways because it is focused on the needs of pre-meds to take the MCAT so it is heavy on fluid mechanics and all the tests are multiple-choice similar to the MCAT. Students who have less aptitude for the subject work harder in this class than a conventional physics class but they walk out with more mastery and they do much better on the physics part of the MCAT than students who take the conventional class that Cornell offers.
- deleted 5y ago
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- mattmcknight 5y ago
  This mastery based approach makes the most sense to me. The difference between grades and percentages is really weird. In some sense, we expect a 90% grade to mean you were able to solve problems on 90% of the material, or with a 10% error rate. However, in some of the higher level classes, the tests are not on whether you have learned and can apply the material, but whether you can solve new types of problems that you haven't seen before. I've always found these sort of tests to be quite bizarre, as you really can't study for them, and whether I would come up with the required insight in the time limit was an inconsistent indicator. They seem better suited as problem sets.
- electroly 5y ago
  That seems like a really interesting approach. I experienced exactly what you describe taking the introductory physics for engineers class. I got something like a 27% on the final exam, leaving entire problems blank because I did not even know how to begin. I clearly did not understand the material and would have dropped the class early if I was getting poor grades. But that didn't happen; with the curve, I received an AB in the class (halfway between A and B). They sent me on my way and to this day, I really only understand the physics that we learned in high school.
stuckinhell 5y ago
I relate to her quite a bit. What helped me understand math was realizing, Math was a language that required an lot of effort to read, understand, write. These days I find doing complex math with programming far far more understandable. I personally think my biggest blocker was the mathematical notation.
- nefitty 5y ago
  Same here! I've been studying the mathematical notation Wikipedia page, and being able to "pronounce" or verbalize symbols has made things much more comprehensible. My current internal tussle is squaring the declarative nature of math with the imperative nature of programming, which I find much easier to reason with. https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbo...
  - ramesh31 5y ago
    Studying the Greek alphabet was also massively helpful for me. In college I stuck a huge poster of all the Greek letters with their pronunciation above my computer monitor. It makes a huge difference reading an equation when you can say "omicron" or "tau" in your head instead of "weird squiggly thing".
uberman 5y ago
I'm kind of stunned by any defense of: "As a teacher I hand out problems people can work on but will not provide the solutions." That is completely BS and my degree is in Math and I labored through the same during my undergraduate degree. It is unacceptable in my opinion in any field and I hope that other fields like engineering and medicine don't take this elitist approach. Ever try or even see a "Leet-Code" style question that stated the problem without providing example results? Ever try to help someone with a problem on Stack Overflow who can state their problem but will not provide example data? How do you ever know you got the correct result? You don't. Perhaps worse, you are confident in a "solution" that includes an "off by 1" bug.
- lambic 5y ago
  It still amazes me that CS students are not allowed to google when working on their coding assignments.
  - uberman 5y ago
    Same here. I personally feel that ability of successfully google should be something we test for!
  - Scarblac 5y ago
    What about other subjects, physics, literature? Should they be allowed to Google too?
    - aqme28 5y ago
      Literature students are _definitely_ allowed to do research on their assignments. As a physics student, there were some exams where I was able to "google," but almost every exam I took allowed me to bring some notes.
    - lambic 5y ago
      Yep, open book exams should be the norm.
    - gilleain 5y ago
bannedbybros 5y ago
jorgeleo 5y ago
MY first class of calculus 1 we were about 80 to 90 students in the class, all ready to study and learn. The teacher walked in look at us and said: The department only allows me to pass 7 or 8 of you, so either you are a genius, or you are doing this class for the Nth time. At the end of the class, we pass 10, which makes it roughly a 10%. I talk to the teacher after the class about it and he told me that the department want it that way to filter out the people that does not make themselves responsible of their own learning. I did pass, and I don't agree with the brutality of the rule, but I do agree with the principle.
- caddemon 5y ago
  I could maybe see their point if it was just a really hard exam and only 10% happen to be able to pass it. But artificially restricting to 10% of the class is ridiculous. The goal should be to pass students that have the requisite knowledge, whatever the prof decides that should be. Judging only relative to peers is a lazy way for the prof to not have to make that distinction. It also creates a toxic environment.
- mysterydip 5y ago
  That doesn't make sense to me. In a group of 90 people there can be more than 9 of them who strive to learn. I get not making classes an "easy A", but making an intro class that difficult arbitrarily seems against the entire point of education.
  - JKCalhoun 5y ago
    Others might call it "gate keeping", but that implies an intent that I don't think is really there. I think instead that the math professors think everyone else is like them, learn like they did. I'm kind of dumb and so things as abstract as higher math have come to me with difficulty. I find I have to truly understand a thing before I can possibly expect to remember it or use it. And apparently I am not quick to understand things like differentiation, integration. I think I only grasped matrix multiplication, linear algebra when I tried to write a flight simulator from scratch (well, from a book actually, but it had you start from scratch with your own Bresenham algorithm for line drawing, write your own polygon clipping code, face culling, etc.). I have done pretty good (I must say) in helping my daughters get through high school math though since I do understand it (now). I think it helps that I probably approach teaching the concept as though it is to someone, like me, who is not going to make the mental leap to abstraction. I suspect many professional math teachers/majors don't suffer my shortcomings and don't teach from that vantage point.
fallingfrog 5y ago
“the mechanism is that the student works all the problems they can and then asks in office hours or review session about the problems they couldn’t do” Wait, really? You want all 150 students in all your classes to come to your office every time you give out a homework assignment? I never went to office hours unless there was some kind of highly unusual situation going on, like when I had a migraine with aura during an exam and couldn’t read the questions. Or when my wife had a life threatening accident and I had to tend to her and needed an extension on an assignment. Were other students just going in and out of there constantly?
- ameister14 5y ago
  >Were other students just going in and out of there constantly? YES. I didn't learn this until after college but apparently other people were going to office hours for all their classes whenever they could. It also helped them form deeper relationships with professors for recommendations.
  - notreallyserio 5y ago
    I never would have guessed people would spend much time with teachers/professors outside of class. If I had to schedule more than 1 or 2 sessions I'd drop the class; clearly I'm missing something and may need to retake prerequisites instead of wasting time failing.
  - tomcat27 5y ago
    ummm, a lot of it depends on scheduling conflicts. not that simple.
  - fallingfrog 5y ago
    I wish my profs had made that clear! I always felt like it was a big imposition to come in there and take up their time on what must have felt to them like a trivial problem. I would have been too embarrassed, I didn't want to be viewed as a needy or problematic student.
- yupyup54133 5y ago
deleted 5y ago
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lambic 5y ago
> making nice prepared slides like the professors in all their non-math classes do, instead of just showing up and writing on the blackboard. I mostly agreed with the conclusions in this article, but this one stood out as something not so good. I much prefer a dynamic lecture to a boring slide presentation. My favourite teacher in high school was my biology teacher. His teaching style was to sit on his desk facing us, next to his overhead projector which had a reel of acetate on it, and just write and draw as he spoke. By the end of a typical lesson he'd have a few feet of acetate filled with notes and beautifully drawn diagrams (I always wondered if he kept them, should've asked). It was engaging, and his attention to detail showed how much he cared about the subject.
dcminter 5y ago
> the mechanism is that the student works all the problems they can and then asks in office hours or review session about the problems they couldn’t do As someone from outside that world this line strikes me as truly weird. Yes, if I struggle with a problem I may well be aware that I'm struggling. But what about the ones where I think I'm doing fine, but I in fact have the wrong answer? Short of bringing ALL solutions to be checked in office hours how would someone even know? Does it really mean that the answers are given but the working of the solution is not? That would seem more reasonable at least - is that what's meant here?
- Scarblac 5y ago
  I think much of the time, correctness of the answer can be checked easily. E.g., if you have to solve for x and find an answer, you can fill it in in the original equation and see if it works.
  - dc-programmer 5y ago
    This does not sound like a proof heavy class, but this approach unfortunately does not work as well for more advanced classes. Especially for problems where you can lose points for not writing the proof like a mathematician would even if you get the steps right (there was one prof in the math department who would deduct points for inelegant but otherwise correct proofs)
- hervature 5y ago
  See here for a list of problems from this exact course: https://www.math.princeton.edu/sites/default/files/2018-04/MAT202Sample%20Problems.pdf https://www.math.princeton.edu/sites/default/files/2018-04/M... These come with answers. It makes me wonder if "solutions" in the original article has been misinterpreted to mean "answers" in which case the complaints are much less warranted as you say. Regardless, from my experience, people who studied solutions often failed to learn the requisite verification skills necessary and ended up doing poorly on the exam. I believe the student from the original article would have performed the same relative to her peers if they were all given solutions. The only difference is that the exam would have decided everything. No additional learning would have occurred with the solutions. Unfortunately, students expect attendance to warrant an automatic A in the course. From my experience, the #1 predictor for a student's rating of a course was their perceived standing in the course and how much they perceived the instructor cared about their success. If you are an instructor today, put an additional 2 homeworks in the syllabus and then drop two of them over the course of the semester to accommodate you students' busy schedules and that should boost your ratings. Extra points for the theatrical democratic process during class.
mindcrime 5y ago
You hand out practice problems for an exam because you want students to do the problems, not because you want them to read the solutions; the mechanism is that the student works all the problems they can and then asks in office hours or review session about the problems they couldn’t do. That's so ridiculous it's hard to believe anybody could say that with a straight face. First of all, to a first approximation nobody goes to "office hours". I mean, this is Real Life we're talking about here - your instructor's "office hours" are basically never (ever) going to be at a time when it's actually possible for you to go even if you wanted to. And if you do go, is your instructor going to be capable of explaining things in a way that makes sense anyway? How many of us have known math teachers who are simultaneously A. perfectly competent to solve a problem and B. completely incapable of explaining how to solve the same problem to somebody else? Never mind that all of this requires that you find your instructor approachable / friendly / whatever enough that you'd feel comfortable going to their office and interacting with them individually in the first place. Basically, "office hours" are not a realistic solution to anybody's problem, with rare exceptions. Review sessions? Great, except for now the feedback loop between "do homework problem and get stuck" to "get explanation" is on the order of days. Yeah, that's effective. I don’t think it’s bad to include solutions, but I would never say that not doing so makes it “impossible to study.” That's because you're too myopic and unimaginative to consider that not everyone studies and learns the same way you do.
- deleted 5y ago
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- tzs 5y ago
  > I mean, this is Real Life we're talking about here - your instructor's "office hours" are basically never (ever) going to be at a time when it's actually possible for you to go even if you wanted to. Why would it be hard to go to office hours? These are schools where most students are full time students who live on or near campus and will have largely similar schedules. It is not hard for an instructor to have office hours at a time when most students in the class will be able to come. > And if you do go, is your instructor going to be capable of explaining things in a way that makes sense anyway? How many of us have known math teachers who are simultaneously A. perfectly competent to solve a problem and B. completely incapable of explaining how to solve the same problem to somebody else? If that is the case then how likely is it that it would have been helpful if the instructor had provided a written solution with the problem in the first place?
Scandiravian 5y ago
I think this illustrates a disconnect between what the teacher wants to accomplish and how the educational system works. At the end of the day, the goal of the students is to pass the exam, not to learn mathematics. If they have learned some by the end of the course, that's a bonus, but the way the system is structured this is inherently a side-effect. Some tests require that the students understand the topic in depth, but the map will never be the territory and I think framing this as "students and teachers need to work together to make better classes", misses the actual problem of exams being detrimental to learning.
- civilized 5y ago
  Exams may sometimes be disruptive to learning, but they exist for a compelling reason: they help ensure that students exiting the class have actually learned the material. All students want the credential of having passed the course, but not all students are willing and able to learn the material. If we care who learned the material, we have to verify who learned the material. To eliminate exams, we would have to either (1) change the world so it doesn't matter who actually learned what they earned credentials for in school, or (2) make all students so intrinsically motivated that they all reliably learn the course material without any need for verification. Does anyone think that either of these goals is realistic?
  - Tainnor 5y ago
    It's also conceivable (theoretically) to just decouple teaching from examination. Anyone may participate in any class (no entry requirements), but there's a certain bar for passing exams and getting a degree. To a certain extent, this possibility already exists with textbooks, openly accessible video lectures, etc., but there's also a lot of people who would still benefit from in-person teaching even if they'd never get to the same level of understanding as people who are going to earn a degree.
    - civilized 5y ago
      That's actually a very interesting idea. What if it changed the game so that instead of exams causing stress and discouraging learning, people were incentivized to learn at their own pace and eventually pass the exam? This situation already exists with many professional credentials, such as CPA, CFA, FSA, etc. They tell you what will be on the exam, provide practice problems, lots of study materials are available from different sources, and you take it when you're ready. There's also college exams that have a similar function (CLEP is the acronym I think?) but they're not really highlighted as a preferred path to students.
arch_btw 5y ago
awkward 5y ago
> And of course, most people taking Math 202 are not taking it for intellectual broadening, as Rabieh admirably was; they are taking it because somebody told me they had to. This is an unacceptable response as well. Why would the students get told that they had to if not for the purpose of intellectual broadening? In my college experience, symbolic logic served this purpose. It was taught by a clearly dismayed senior member of the Philosophy department, who used plenty of class time to berate the general idea of the "gifted computer whiz kid who doesn't do the work" while clearly running the material on autopilot from the publisher provided syllabus. It didn't make me less interested in philosophy, but it made me a lot less interested in formal philosophy as taught at that school.
lordnacho 5y ago
The office hours idea sounds crazy to me, and that is despite the fact that I actually had a professor's attention for an hour for each sheet. (2/3 on 1 tutorials). Some place doing mass lectures is going to inundate the professor's office, surely? Or perhaps in modern unis the students themselves share solutions on an online board? There's just so much self-learning involved it can be quite hard to narrow down your questions to where it can be discussed in an hour. That's especially if you actually tried to dig deeply into the concepts. You might have gotten stuck for days on a single problem, which is made much worse if there's no hints about how to find the solution. Another problem seems to be the opposite: you come in for the tutorial, you solve all the problems, and you're no wiser about the issues, despite having learned a mechanism for solving each problem on the sheet.
- tomcat27 5y ago
  > There's just so much self-learning involved it can be quite hard to narrow down your questions to where it can be discussed in an hour. I had this problem while taking grad courses. I needed time to produce follow up questions and office hours are just a misfit especially when I know there are a bunch of people waiting in line for time. What we ended up with is a Piazza where TAs mostly do the ritual. In popular areas, I wonder why I am paying when its no better than an internet forum, probably worse. I feel learning experience is just poorly structured. Teachers get away from the feedback received by invalidating it instead of introspecting it. I can't imagine any other field where feedback is just thrown out no matter how noisy it is.
mdip 5y ago
I have a lot of thoughts on this from my own personal experience and was honestly surprised to find that it was "Linear Algebra" that was the class being discussed -- I thought I was the only one who suffered through that! This was 20 years ago, for me, and my experience was nearly identical. I was not a great student in High School but ... now having to pay for my own classes ... did well in every class in college except for this one. I attended sessions with tutors offered through my class, I attended office hours, I failed ... hard. The pattern I kept running into was one of learning the material after the exams for each unit were returned to me. In fact, it was so ridiculous, I stopped going to class, resigned to the fact that I was going to fail and simply showed up for the exams. I re-took the class and managed a near-4.0 on the same material. The school I attended had a bad reputation among its math department as being ridiculously difficult staffed with professors who had a basic understanding of English. Of course, this came from students who had recently failed, and they'll have the loudest and often most defensive voices on the subject. None-the-less, out of the three professors, two were in the "avoid" category pretty quickly due to feedback I received about how difficult it was to understand the words they were speaking[0]. The third was a recent hire -- the rumor being that they picked someone from the US because of the frequent complaints about understanding the set of maths professors they currently employed. But I suspect a lot of people played the game of "pick the guy with the American sounding name" and found out the same thing that I did -- a deep south Alabama accent is much farther from English as it is spoken where I live than any ESL professor's native accent. I picked up about every fifth word coming out of this gentleman's mouth with his very thick drawl and unusual word choices and lousy grammar. In the north, we'd be surprised to find out that he's a maths professor, stereotyping him as a farmer I suspect, after reading this, that there was more to it than just my struggling to understand what was being said. My pattern was that despite all of the extra energy put into attending tutoring sessions and scheduling office hours, I found myself understanding the material just after we'd taken an exam on the portion we were studying. As this was too long ago, I don't remember if we were given solutions or not, but it fits with that pattern -- the tests were reviewed pretty thoroughly after they were taken and I could see what I did wrong -- it clicked. It clicked so much that despite getting a hard fail in the class, I ended up sailing through with -- I think -- a 4.0 or somewhere near the second time around, attending only on exam days -- with the same professor. The tutoring/office hours which are brought up as "the way you teach without the solution" were totally inadequate. The staff provided for assistance were not professors, or even particularly skilled tutors. They were advanced maths students who found the work being done to be easy and didn't know how to teach things that were very basic to them. Open office hours were difficult for me to get because I had a full-time job in the field I was seeking my degree in; they were always booked and by the time I knew I needed them, the earliest I could meet with the professor was after the exam. I ended up just scheduling them as soon as I was allowed and cancelling if I didn't need it. Many, many others did this -- it resulted in a group forming by the smallish meeting space that he reserved for these[1] in hopes that he'd finish early and grab the first student waiting. I never did this, but on days that I had a formal appointment, I'd noticed the waiting students would sit on the floor with their materials trying to help one another -- it was a blind-leading-the-blind scenario. And here's the worst of it: I'm not bad at math! This class made me fear every future maths course I had to take. I got through two Calculus classes many years later due to a desire to fill in the gaps I had learned from books -- they were easy by comparison. I think the way it was taught was specifically because it's a class that many fear; we were gently introduced to the concepts and they covered much less by comparison than linear algebra covered. They were also taught from a more practical standard -- while we were working with odd terms, functions, formulas and theory, they were often brought back to "and here's where it applies in engineering/life" which made it a lot more interesting. The problems we faced in linear algebra, despite having many interesting practical applications, were rushed through and were taught as though "this is just something that Maths majors learn so that they can fill whiteboards for use as props in movies and The Big Bang Theory to make the characters look smart". My experience in higher education was, in general, not a good one. I left this school a semester later and went elsewhere mostly because of this class, though the final nail in the coffin was an experience in my first programming class[2] where a test -- with very few answers -- responsible for half of the grade had a bug in it -- a failure to dereference a pointer ... a missing star, caused more than half of the answers to be "F - None of the above" or didn't have an answer. I chose to treat the unanswerable as "undefined behavior" (it was C, after all). Luckily, in an attempt to provide answers that might "look right", I found that if I pretended the function call didn't exist, I'd find an answer among the choices and explained to the professor that my fictional compiler optimized away the call since there wasn't an answer among the list that worked without it. I spent an hour arguing with the guy but he ended up re-scoring it to perfect. [0] One was Indian, the other was Pakistani and I know I would have done better with either of them given that I worked with folks from those regions regularly who had pretty thick accents; like anything, you learn to understand the phrasing and tempo and you stop hearing the accent pretty quickly. I suspect many of the younger students coming from American high schools struggled having encountered it for the first time. It's nothing on the professors or their country of origin, though. [1] I have never visited a professor for "Office Hours" outside of this class; I don't know if it was because this professor was on his first semester at my school or if this is common but no part of it had the scent of "open office hours" -- it was done in a conference room about the size of my kid's bedroom with a single round table and four chairs cramped under it, one of which couldn't be pulled out due to its proximity to the wall. The professor tended to explain things while searching for materials to help me ... that he didn't have on him that day, so he'd scribble on a piece of paper. [2] I agonized over this during the 45 minutes we had to finish the exam. Worse, it was proctored by a TA or assistant -- someone I'd never seen, before, and not someone who would know if it was a mistake on the professor's part or not. I'm also pretty sure the guy was playing Descent on the laptop he sat in front of while the test was being taken. It was pure luck that I found a way to answer the questions accurately which also could be defended when an accurate answer wasn't a choice. My concern was that by ignoring the bug, had the professor intended it, I'd have no defense that wouldn't sound like "I didn't notice it and now that I know I got it wrong, I'm trying to weasel my way to a better grade". It was still a tough hill to climb.
tzs 5y ago
BTW, if one wants to see more problems with worked out answers than their professor and/or textbook provides, there are books you can buy for this. For linear algebra for example you could get Schaum's Outline of Linear Algebra [1] for $13.44 which includes 612 practice problems with step-by-step solutions. There are such books for most of the major first and second year undergraduate STEM and STEM-adjacent courses. [1] https://www.amazon.com/Schaums-Outline-Linear-Algebra-Outlines/dp/1260011445 https://www.amazon.com/Schaums-Outline-Linear-Algebra-Outlin...
cottager2 5y ago
I’m surprised by the outrage to the teaching style, specifically people taking issue with the expectation that students take questions to office hours. Perhaps many who have studied math have forgotten, but “so and so is left as an exercise to the reader” is basically a trope at this point. I’d even go as far to say that you can’t really learn all the content in a math textbook without talking it over with someone. Math text books aren’t very dense, yet it can take a day or more to fully grasp a few pages. Simply adding more exercises, even with answers, isn’t necessarily going to deepen one’s intuition. Which brings me the specific class this article is about: linear algebra. LA has to been one of the worse taught classes, and that seems to be universal. Things like determinants and Eigen values are drilled in students’ heads without developing the intuition for the subject first. They’re given examples without context, which is what the girl described in the article seems to be struggling with. She probably still would struggle to learn LA even with answers to the examples.
dang 5y ago
Recent and related: Why won’t anyone teach me math? - https://news.ycombinator.com/item?id=30302079 https://news.ycombinator.com/item?id=30302079 - Feb 2022 (670 comments)

33 points by sebg 5y ago

Earlier submission - https://news.ycombinator.com/item?id=30328403 https://news.ycombinator.com/item?id=30328403 (Not much discussion though) Edit: formatting

graycat 5y ago

> Why Won’t Anyone Teach Her Math? Some people, a lot of people, will gladly "teach her math" and do a good job of it. E.g., I tried to, here: In the thread "Why won’t anyone teach me math?" at https://news.ycombinator.com/item?id=30302079 https://news.ycombinator.com/item?id=30302079 I posted "Part I" https://news.ycombinator.com/item?id=30307316 https://news.ycombinator.com/item?id=30307316 and "Part II" https://news.ycombinator.com/item?id=30307349 https://news.ycombinator.com/item?id=30307349 The two parts are needed because of length limits of HN posts. The OP (original post) "Why won’t anyone teach me math?" is about a coed at Princeton in a badly taught course in linear algebra. It turns out, I did really well in linear algebra, and "Part I" explains how well I did and how I did that. In "Part II" I give an outline of an introduction to linear algebra and matrix theory. For my background I've taught applied math and computer science at three well known research universities and have a Ph.D. in pure/applied math from a fourth. From how I learned math I have to say that there is a lot of having contempt for the students and dumping on them. This dumping on the students, treating them with contempt, is unnecessary, unjustified, inexcusable, and bad for the students, researchers, teachers, schools, math, and the US. The dumping isn't just in famous research universities: E.g., I went in grades 1-12 to the unique college prep school in the city. I got dumped on from the 4th grade on and maybe also in the first three grades but simply don't remember much about grades 1-3. I wanted to learn but got dumped on so much that I just gave up trying to please the teachers and did what I could with the books for the courses. Turns out, that was a good thing for me to do, especially for learning math. There were a lot of standardized tests, both aptitude and achievement, and apparently I did well on those, much better than how the teachers viewed me. Point: The opinions of teachers who dump on students can be highly inaccurate; some more objective measures are needed. Due to the objective measures, in the 9th grade I got sent to a math tournament and in the 11th grade, to an NSF math & physics summer program. Point: The objective measures helped. Turns out, that was true throughout my education. But for college I went to a private school that took lots of pride in doing well at teaching. Some of the teaching was quite good. Still, however, there was some dumping: E.g., the college got a new prof fresh from a famous research university, and he brought his dumping/contempt propensities with him. At one point I took a reading course from him from a then famous, advanced, notoriously difficult book in topology. So, for each chapter one week I gave a lecture to the prof on the math and the next week, on the exercises. I did well. Once another prof showed up. But even with that good self-teaching success, the prof at best only slightly relaxed his dumping/contempt mode. Point: In that reading course I was a spectacularly good student but the contempt still continued. My Summary View: I see no good reason or excuse for the dumping and contempt. I refused to do any such things in my teaching. Generally I told the students: The material is in the book. Class is to help you learn. So, I'm here to explain and answer questions. There is homework which is to work as many of the exercises as you need to to learn the material, in particular to get good at working the exercises. The tests are problems similar to the exercises -- if you are good on the exercises, you should be good on the tests. From the numerical scores on the tests, I rank the students, and the purpose is to simplify the assignment of letter grades: So, if student A does better in the ranking than student B, then student A will get the same or better letter grade than student B. But WHAT letter grades? My standards are, A means that know the material well; B, knows the material; C, knows some of the material; D, doesn't know much; F, doesn't know much and none of us want the student to get credit for the course. So, I look at the work on the tests, judge A-F and decide what final scores deserve what letter grades. Students are not in competition: E.g., I'm perfectly willing to assign As to all students who know the material well; would be pleased to do so; the situation would represent a big success. The department has no rules against my assigning As to everyone. I'm available in class, after class, and in office hours. Generally the office hours are not heavily used. The US colleges and universities have some really big heartburn about the comparative roles of teaching, applications, and research. Research: Can argue that academic research is by a wide margin the most powerful contributor to civilization, health, wealth, understanding, etc. So, with lots of research universities where the profs are required to publish in peer-reviewed journals of original research and hopefully get prizes for work they have done and grants for the work they are doing will, year by year we get some astounding results. Quite broadly the most respected research is theory based on math, theory that mathematizes the field. Applications and teaching are regarded as much less desirable. Applications. Schools of medicine take applications fully seriously -- that is, a lot of the teaching and research are done in research-teaching hospitals with patients at risk of dying. The field of medicine has a major and respected role for clinical, professional practice. The MD degree, to be a "doctor", is about practice, not research. In schools of engineering, there can be some significant attention to applications. Still, generally engineering schools do not try nearly as hard as medical schools to purse practice, be clinical or professional. Teaching. There usually is a lot of good teaching in colleges that emphasize teaching over research. But generally the research universities and their profs look down on teaching -- bad for the field, students, profs, schools, and the US. Generally there is a belief, attitude, assumption, expectation, tradition, etc. that school is to be a competition, pick winners and losers, be challenging, be a filter, have the students put up with being dumped on, get lessons in going without sleep, etc. As a prof, I refused to play that game -- it was in the interest of all my students to work together to learn, come to my office hours, confess what they didn't know, and get additional explanations, problem solutions, etc. My view now, from this thread and more, is that the US research universities are on thin ice, about ready for their "comeuppance". Via taxes, tuition, etc., the public is paying the bills and wants results -- contributions to health and wealth, national security, and especially good careers for the students. Bad teaching, dumping, contempt, generally hurting the students, are creating some really bad PR for the research. Next, for the teaching and a lot of what the customers want now is arriving via the Internet, e.g., YouTube. I did some teaching here in the "Part II" I wrote. A lot of that teaching is NOT good, but the best of it is getting good. When there is some really good teaching on the Internet for free or nearly so, bad teaching, hurting the students, etc. will come to hurt the universities, even the Ivy League. It's possible for a really good student, PBK, etc., brilliant, dedicated, to be so dumped on, treated with so much contempt, that their anxiety level gets really bad, they lose sleep, have physical symptoms, get depressed, clinically depressed, don't recover, and commit suicide. Some education. We're expected to pay for such abuse, via taxes, tuition, our health, our lives? Bad teaching, hurting the students -- NOT acceptable, grade F.

bradgranath 5y ago

Never took a math class that didn't provide a solution index for practice problems. University level students are expected to be able to self-regulate their study ethic and this sort of paternalist bullshit is turning undergraduate programs into trades learned by rote.

h2odragon 5y ago

I can't teach anyone anything. I have doubts that anyone else can do it, either; but can only speak to my own experience. I can provide lots of assistance to those who are trying to learn. We tell people "Edumacation" is going to happen to them whether they want it or not; and then they have to sign up for more "or you'll never have a good life" etc. It seems that we've lost the reason why we do these things. It's just empty ritual. Things are this bad in famous, expensive upper class schools; imagine how bad they are in poor to normal elementary schools. We got kids with failing grades because they never got a (theoretically school provided) chromebook, never got a login to "the homework sites", or can't get reliable connectivity from home or school. They may or may not know the material they were supposed to learn but who cares about that? As long as the attendance records are good the school gets paid.

lbriner 5y ago
An interesting take and, yes, in the west it is hard to instill in a student that it is up to them to earn their way to success by making the maximum use of the teaching resources and not to sit back and get fed what they need. In poorer countries, this is better understood, especially since many people do not go to school so the alternative to working hard is plain to see. Not sure how you fix it though, perhaps some out of the box ideas to reward those that work hard in a way that reinforces that hard works pays off. I don't know.
- bernulli 5y ago
  That's got nothing to do with west vs. poor. Have you seen the 2-year French math requirements before you are even admitted to an engineering school? Have you seen German universities where there is zero advisement and where your two years worth of math courses in your engineering program are tested in a single final exam, as the very first feedback (no quizzes, no homework, no midterm, not split into 10 math micro courses, no projects, no extra credit, etc.)? It's sink or swim.
JKCalhoun 5y ago
No offense, but I think you're being a bit dismissive: if a students doesn't learn a thing it is because they didn't try. There is a middle road you are not calling out: if you make math (or any subject) approachable in your teaching style, you can get students to want to learn, try to learn. I'd say that is generally true for pretty much any subject. Why does someone try to learn history? Probably because they somehow became interested in it. A good teacher will try to make it interesting.

PaulHoule 5y ago

It's a structural problem in conventional physics classes (I'd think similar to math) that the median grade is awful (sometimes even like a 30) but it gets graded on a curve so that's considered a C, an acceptable grade. In a class like that students walk out with a passing grade but often a weak understanding of the subject. I was involved in teaching the PHYS 1101-1102 sequence at Cornell https://physics.cornell.edu/physics-health-careers https://physics.cornell.edu/physics-health-careers which is an auto-tutorial class where students are required to take each test multiple times until they get a grade that's high enough to indicate mastery. Some people find this course to be nervewracking, often they fail the test horribly two times, sit through debugging sessions with the tutors, come back and do pretty well on the last try and walk out with a B+ or A- grade. The course is unique in a lot of ways because it is focused on the needs of pre-meds to take the MCAT so it is heavy on fluid mechanics and all the tests are multiple-choice similar to the MCAT. Students who have less aptitude for the subject work harder in this class than a conventional physics class but they walk out with more mastery and they do much better on the physics part of the MCAT than students who take the conventional class that Cornell offers.

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mattmcknight 5y ago
This mastery based approach makes the most sense to me. The difference between grades and percentages is really weird. In some sense, we expect a 90% grade to mean you were able to solve problems on 90% of the material, or with a 10% error rate. However, in some of the higher level classes, the tests are not on whether you have learned and can apply the material, but whether you can solve new types of problems that you haven't seen before. I've always found these sort of tests to be quite bizarre, as you really can't study for them, and whether I would come up with the required insight in the time limit was an inconsistent indicator. They seem better suited as problem sets.
electroly 5y ago
That seems like a really interesting approach. I experienced exactly what you describe taking the introductory physics for engineers class. I got something like a 27% on the final exam, leaving entire problems blank because I did not even know how to begin. I clearly did not understand the material and would have dropped the class early if I was getting poor grades. But that didn't happen; with the curve, I received an AB in the class (halfway between A and B). They sent me on my way and to this day, I really only understand the physics that we learned in high school.

stuckinhell 5y ago

I relate to her quite a bit. What helped me understand math was realizing, Math was a language that required an lot of effort to read, understand, write. These days I find doing complex math with programming far far more understandable. I personally think my biggest blocker was the mathematical notation.

nefitty 5y ago
Same here! I've been studying the mathematical notation Wikipedia page, and being able to "pronounce" or verbalize symbols has made things much more comprehensible. My current internal tussle is squaring the declarative nature of math with the imperative nature of programming, which I find much easier to reason with. https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbo...
- ramesh31 5y ago
  Studying the Greek alphabet was also massively helpful for me. In college I stuck a huge poster of all the Greek letters with their pronunciation above my computer monitor. It makes a huge difference reading an equation when you can say "omicron" or "tau" in your head instead of "weird squiggly thing".

uberman 5y ago

I'm kind of stunned by any defense of: "As a teacher I hand out problems people can work on but will not provide the solutions." That is completely BS and my degree is in Math and I labored through the same during my undergraduate degree. It is unacceptable in my opinion in any field and I hope that other fields like engineering and medicine don't take this elitist approach. Ever try or even see a "Leet-Code" style question that stated the problem without providing example results? Ever try to help someone with a problem on Stack Overflow who can state their problem but will not provide example data? How do you ever know you got the correct result? You don't. Perhaps worse, you are confident in a "solution" that includes an "off by 1" bug.

lambic 5y ago
It still amazes me that CS students are not allowed to google when working on their coding assignments.
- uberman 5y ago
  Same here. I personally feel that ability of successfully google should be something we test for!
- Scarblac 5y ago
  What about other subjects, physics, literature? Should they be allowed to Google too?
  - aqme28 5y ago
    Literature students are _definitely_ allowed to do research on their assignments. As a physics student, there were some exams where I was able to "google," but almost every exam I took allowed me to bring some notes.
  - lambic 5y ago
    Yep, open book exams should be the norm.
  - gilleain 5y ago

bannedbybros 5y ago

jorgeleo 5y ago

MY first class of calculus 1 we were about 80 to 90 students in the class, all ready to study and learn. The teacher walked in look at us and said: The department only allows me to pass 7 or 8 of you, so either you are a genius, or you are doing this class for the Nth time. At the end of the class, we pass 10, which makes it roughly a 10%. I talk to the teacher after the class about it and he told me that the department want it that way to filter out the people that does not make themselves responsible of their own learning. I did pass, and I don't agree with the brutality of the rule, but I do agree with the principle.

caddemon 5y ago
I could maybe see their point if it was just a really hard exam and only 10% happen to be able to pass it. But artificially restricting to 10% of the class is ridiculous. The goal should be to pass students that have the requisite knowledge, whatever the prof decides that should be. Judging only relative to peers is a lazy way for the prof to not have to make that distinction. It also creates a toxic environment.
mysterydip 5y ago
That doesn't make sense to me. In a group of 90 people there can be more than 9 of them who strive to learn. I get not making classes an "easy A", but making an intro class that difficult arbitrarily seems against the entire point of education.
- JKCalhoun 5y ago
  Others might call it "gate keeping", but that implies an intent that I don't think is really there. I think instead that the math professors think everyone else is like them, learn like they did. I'm kind of dumb and so things as abstract as higher math have come to me with difficulty. I find I have to truly understand a thing before I can possibly expect to remember it or use it. And apparently I am not quick to understand things like differentiation, integration. I think I only grasped matrix multiplication, linear algebra when I tried to write a flight simulator from scratch (well, from a book actually, but it had you start from scratch with your own Bresenham algorithm for line drawing, write your own polygon clipping code, face culling, etc.). I have done pretty good (I must say) in helping my daughters get through high school math though since I do understand it (now). I think it helps that I probably approach teaching the concept as though it is to someone, like me, who is not going to make the mental leap to abstraction. I suspect many professional math teachers/majors don't suffer my shortcomings and don't teach from that vantage point.

fallingfrog 5y ago

“the mechanism is that the student works all the problems they can and then asks in office hours or review session about the problems they couldn’t do” Wait, really? You want all 150 students in all your classes to come to your office every time you give out a homework assignment? I never went to office hours unless there was some kind of highly unusual situation going on, like when I had a migraine with aura during an exam and couldn’t read the questions. Or when my wife had a life threatening accident and I had to tend to her and needed an extension on an assignment. Were other students just going in and out of there constantly?

ameister14 5y ago
>Were other students just going in and out of there constantly? YES. I didn't learn this until after college but apparently other people were going to office hours for all their classes whenever they could. It also helped them form deeper relationships with professors for recommendations.
- notreallyserio 5y ago
  I never would have guessed people would spend much time with teachers/professors outside of class. If I had to schedule more than 1 or 2 sessions I'd drop the class; clearly I'm missing something and may need to retake prerequisites instead of wasting time failing.
- tomcat27 5y ago
  ummm, a lot of it depends on scheduling conflicts. not that simple.
- fallingfrog 5y ago
  I wish my profs had made that clear! I always felt like it was a big imposition to come in there and take up their time on what must have felt to them like a trivial problem. I would have been too embarrassed, I didn't want to be viewed as a needy or problematic student.
yupyup54133 5y ago

deleted 5y ago

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lambic 5y ago

> making nice prepared slides like the professors in all their non-math classes do, instead of just showing up and writing on the blackboard. I mostly agreed with the conclusions in this article, but this one stood out as something not so good. I much prefer a dynamic lecture to a boring slide presentation. My favourite teacher in high school was my biology teacher. His teaching style was to sit on his desk facing us, next to his overhead projector which had a reel of acetate on it, and just write and draw as he spoke. By the end of a typical lesson he'd have a few feet of acetate filled with notes and beautifully drawn diagrams (I always wondered if he kept them, should've asked). It was engaging, and his attention to detail showed how much he cared about the subject.

dcminter 5y ago

> the mechanism is that the student works all the problems they can and then asks in office hours or review session about the problems they couldn’t do As someone from outside that world this line strikes me as truly weird. Yes, if I struggle with a problem I may well be aware that I'm struggling. But what about the ones where I think I'm doing fine, but I in fact have the wrong answer? Short of bringing ALL solutions to be checked in office hours how would someone even know? Does it really mean that the answers are given but the working of the solution is not? That would seem more reasonable at least - is that what's meant here?

Scarblac 5y ago
I think much of the time, correctness of the answer can be checked easily. E.g., if you have to solve for x and find an answer, you can fill it in in the original equation and see if it works.
- dc-programmer 5y ago
  This does not sound like a proof heavy class, but this approach unfortunately does not work as well for more advanced classes. Especially for problems where you can lose points for not writing the proof like a mathematician would even if you get the steps right (there was one prof in the math department who would deduct points for inelegant but otherwise correct proofs)
hervature 5y ago
See here for a list of problems from this exact course: https://www.math.princeton.edu/sites/default/files/2018-04/MAT202Sample%20Problems.pdf https://www.math.princeton.edu/sites/default/files/2018-04/M... These come with answers. It makes me wonder if "solutions" in the original article has been misinterpreted to mean "answers" in which case the complaints are much less warranted as you say. Regardless, from my experience, people who studied solutions often failed to learn the requisite verification skills necessary and ended up doing poorly on the exam. I believe the student from the original article would have performed the same relative to her peers if they were all given solutions. The only difference is that the exam would have decided everything. No additional learning would have occurred with the solutions. Unfortunately, students expect attendance to warrant an automatic A in the course. From my experience, the #1 predictor for a student's rating of a course was their perceived standing in the course and how much they perceived the instructor cared about their success. If you are an instructor today, put an additional 2 homeworks in the syllabus and then drop two of them over the course of the semester to accommodate you students' busy schedules and that should boost your ratings. Extra points for the theatrical democratic process during class.

mindcrime 5y ago

You hand out practice problems for an exam because you want students to do the problems, not because you want them to read the solutions; the mechanism is that the student works all the problems they can and then asks in office hours or review session about the problems they couldn’t do. That's so ridiculous it's hard to believe anybody could say that with a straight face. First of all, to a first approximation nobody goes to "office hours". I mean, this is Real Life we're talking about here - your instructor's "office hours" are basically never (ever) going to be at a time when it's actually possible for you to go even if you wanted to. And if you do go, is your instructor going to be capable of explaining things in a way that makes sense anyway? How many of us have known math teachers who are simultaneously A. perfectly competent to solve a problem and B. completely incapable of explaining how to solve the same problem to somebody else? Never mind that all of this requires that you find your instructor approachable / friendly / whatever enough that you'd feel comfortable going to their office and interacting with them individually in the first place. Basically, "office hours" are not a realistic solution to anybody's problem, with rare exceptions. Review sessions? Great, except for now the feedback loop between "do homework problem and get stuck" to "get explanation" is on the order of days. Yeah, that's effective. I don’t think it’s bad to include solutions, but I would never say that not doing so makes it “impossible to study.” That's because you're too myopic and unimaginative to consider that not everyone studies and learns the same way you do.

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tzs 5y ago
> I mean, this is Real Life we're talking about here - your instructor's "office hours" are basically never (ever) going to be at a time when it's actually possible for you to go even if you wanted to. Why would it be hard to go to office hours? These are schools where most students are full time students who live on or near campus and will have largely similar schedules. It is not hard for an instructor to have office hours at a time when most students in the class will be able to come. > And if you do go, is your instructor going to be capable of explaining things in a way that makes sense anyway? How many of us have known math teachers who are simultaneously A. perfectly competent to solve a problem and B. completely incapable of explaining how to solve the same problem to somebody else? If that is the case then how likely is it that it would have been helpful if the instructor had provided a written solution with the problem in the first place?

Scandiravian 5y ago

I think this illustrates a disconnect between what the teacher wants to accomplish and how the educational system works. At the end of the day, the goal of the students is to pass the exam, not to learn mathematics. If they have learned some by the end of the course, that's a bonus, but the way the system is structured this is inherently a side-effect. Some tests require that the students understand the topic in depth, but the map will never be the territory and I think framing this as "students and teachers need to work together to make better classes", misses the actual problem of exams being detrimental to learning.

civilized 5y ago
Exams may sometimes be disruptive to learning, but they exist for a compelling reason: they help ensure that students exiting the class have actually learned the material. All students want the credential of having passed the course, but not all students are willing and able to learn the material. If we care who learned the material, we have to verify who learned the material. To eliminate exams, we would have to either (1) change the world so it doesn't matter who actually learned what they earned credentials for in school, or (2) make all students so intrinsically motivated that they all reliably learn the course material without any need for verification. Does anyone think that either of these goals is realistic?
- Tainnor 5y ago
  It's also conceivable (theoretically) to just decouple teaching from examination. Anyone may participate in any class (no entry requirements), but there's a certain bar for passing exams and getting a degree. To a certain extent, this possibility already exists with textbooks, openly accessible video lectures, etc., but there's also a lot of people who would still benefit from in-person teaching even if they'd never get to the same level of understanding as people who are going to earn a degree.
  - civilized 5y ago
    That's actually a very interesting idea. What if it changed the game so that instead of exams causing stress and discouraging learning, people were incentivized to learn at their own pace and eventually pass the exam? This situation already exists with many professional credentials, such as CPA, CFA, FSA, etc. They tell you what will be on the exam, provide practice problems, lots of study materials are available from different sources, and you take it when you're ready. There's also college exams that have a similar function (CLEP is the acronym I think?) but they're not really highlighted as a preferred path to students.

arch_btw 5y ago

awkward 5y ago

> And of course, most people taking Math 202 are not taking it for intellectual broadening, as Rabieh admirably was; they are taking it because somebody told me they had to. This is an unacceptable response as well. Why would the students get told that they had to if not for the purpose of intellectual broadening? In my college experience, symbolic logic served this purpose. It was taught by a clearly dismayed senior member of the Philosophy department, who used plenty of class time to berate the general idea of the "gifted computer whiz kid who doesn't do the work" while clearly running the material on autopilot from the publisher provided syllabus. It didn't make me less interested in philosophy, but it made me a lot less interested in formal philosophy as taught at that school.

lordnacho 5y ago

The office hours idea sounds crazy to me, and that is despite the fact that I actually had a professor's attention for an hour for each sheet. (2/3 on 1 tutorials). Some place doing mass lectures is going to inundate the professor's office, surely? Or perhaps in modern unis the students themselves share solutions on an online board? There's just so much self-learning involved it can be quite hard to narrow down your questions to where it can be discussed in an hour. That's especially if you actually tried to dig deeply into the concepts. You might have gotten stuck for days on a single problem, which is made much worse if there's no hints about how to find the solution. Another problem seems to be the opposite: you come in for the tutorial, you solve all the problems, and you're no wiser about the issues, despite having learned a mechanism for solving each problem on the sheet.

tomcat27 5y ago
> There's just so much self-learning involved it can be quite hard to narrow down your questions to where it can be discussed in an hour. I had this problem while taking grad courses. I needed time to produce follow up questions and office hours are just a misfit especially when I know there are a bunch of people waiting in line for time. What we ended up with is a Piazza where TAs mostly do the ritual. In popular areas, I wonder why I am paying when its no better than an internet forum, probably worse. I feel learning experience is just poorly structured. Teachers get away from the feedback received by invalidating it instead of introspecting it. I can't imagine any other field where feedback is just thrown out no matter how noisy it is.

mdip 5y ago

I have a lot of thoughts on this from my own personal experience and was honestly surprised to find that it was "Linear Algebra" that was the class being discussed -- I thought I was the only one who suffered through that! This was 20 years ago, for me, and my experience was nearly identical. I was not a great student in High School but ... now having to pay for my own classes ... did well in every class in college except for this one. I attended sessions with tutors offered through my class, I attended office hours, I failed ... hard. The pattern I kept running into was one of learning the material after the exams for each unit were returned to me. In fact, it was so ridiculous, I stopped going to class, resigned to the fact that I was going to fail and simply showed up for the exams. I re-took the class and managed a near-4.0 on the same material. The school I attended had a bad reputation among its math department as being ridiculously difficult staffed with professors who had a basic understanding of English. Of course, this came from students who had recently failed, and they'll have the loudest and often most defensive voices on the subject. None-the-less, out of the three professors, two were in the "avoid" category pretty quickly due to feedback I received about how difficult it was to understand the words they were speaking[0]. The third was a recent hire -- the rumor being that they picked someone from the US because of the frequent complaints about understanding the set of maths professors they currently employed. But I suspect a lot of people played the game of "pick the guy with the American sounding name" and found out the same thing that I did -- a deep south Alabama accent is much farther from English as it is spoken where I live than any ESL professor's native accent. I picked up about every fifth word coming out of this gentleman's mouth with his very thick drawl and unusual word choices and lousy grammar. In the north, we'd be surprised to find out that he's a maths professor, stereotyping him as a farmer I suspect, after reading this, that there was more to it than just my struggling to understand what was being said. My pattern was that despite all of the extra energy put into attending tutoring sessions and scheduling office hours, I found myself understanding the material just after we'd taken an exam on the portion we were studying. As this was too long ago, I don't remember if we were given solutions or not, but it fits with that pattern -- the tests were reviewed pretty thoroughly after they were taken and I could see what I did wrong -- it clicked. It clicked so much that despite getting a hard fail in the class, I ended up sailing through with -- I think -- a 4.0 or somewhere near the second time around, attending only on exam days -- with the same professor. The tutoring/office hours which are brought up as "the way you teach without the solution" were totally inadequate. The staff provided for assistance were not professors, or even particularly skilled tutors. They were advanced maths students who found the work being done to be easy and didn't know how to teach things that were very basic to them. Open office hours were difficult for me to get because I had a full-time job in the field I was seeking my degree in; they were always booked and by the time I knew I needed them, the earliest I could meet with the professor was after the exam. I ended up just scheduling them as soon as I was allowed and cancelling if I didn't need it. Many, many others did this -- it resulted in a group forming by the smallish meeting space that he reserved for these[1] in hopes that he'd finish early and grab the first student waiting. I never did this, but on days that I had a formal appointment, I'd noticed the waiting students would sit on the floor with their materials trying to help one another -- it was a blind-leading-the-blind scenario. And here's the worst of it: I'm not bad at math! This class made me fear every future maths course I had to take. I got through two Calculus classes many years later due to a desire to fill in the gaps I had learned from books -- they were easy by comparison. I think the way it was taught was specifically because it's a class that many fear; we were gently introduced to the concepts and they covered much less by comparison than linear algebra covered. They were also taught from a more practical standard -- while we were working with odd terms, functions, formulas and theory, they were often brought back to "and here's where it applies in engineering/life" which made it a lot more interesting. The problems we faced in linear algebra, despite having many interesting practical applications, were rushed through and were taught as though "this is just something that Maths majors learn so that they can fill whiteboards for use as props in movies and The Big Bang Theory to make the characters look smart". My experience in higher education was, in general, not a good one. I left this school a semester later and went elsewhere mostly because of this class, though the final nail in the coffin was an experience in my first programming class[2] where a test -- with very few answers -- responsible for half of the grade had a bug in it -- a failure to dereference a pointer ... a missing star, caused more than half of the answers to be "F - None of the above" or didn't have an answer. I chose to treat the unanswerable as "undefined behavior" (it was C, after all). Luckily, in an attempt to provide answers that might "look right", I found that if I pretended the function call didn't exist, I'd find an answer among the choices and explained to the professor that my fictional compiler optimized away the call since there wasn't an answer among the list that worked without it. I spent an hour arguing with the guy but he ended up re-scoring it to perfect. [0] One was Indian, the other was Pakistani and I know I would have done better with either of them given that I worked with folks from those regions regularly who had pretty thick accents; like anything, you learn to understand the phrasing and tempo and you stop hearing the accent pretty quickly. I suspect many of the younger students coming from American high schools struggled having encountered it for the first time. It's nothing on the professors or their country of origin, though. [1] I have never visited a professor for "Office Hours" outside of this class; I don't know if it was because this professor was on his first semester at my school or if this is common but no part of it had the scent of "open office hours" -- it was done in a conference room about the size of my kid's bedroom with a single round table and four chairs cramped under it, one of which couldn't be pulled out due to its proximity to the wall. The professor tended to explain things while searching for materials to help me ... that he didn't have on him that day, so he'd scribble on a piece of paper. [2] I agonized over this during the 45 minutes we had to finish the exam. Worse, it was proctored by a TA or assistant -- someone I'd never seen, before, and not someone who would know if it was a mistake on the professor's part or not. I'm also pretty sure the guy was playing Descent on the laptop he sat in front of while the test was being taken. It was pure luck that I found a way to answer the questions accurately which also could be defended when an accurate answer wasn't a choice. My concern was that by ignoring the bug, had the professor intended it, I'd have no defense that wouldn't sound like "I didn't notice it and now that I know I got it wrong, I'm trying to weasel my way to a better grade". It was still a tough hill to climb.

tzs 5y ago

BTW, if one wants to see more problems with worked out answers than their professor and/or textbook provides, there are books you can buy for this. For linear algebra for example you could get Schaum's Outline of Linear Algebra [1] for $13.44 which includes 612 practice problems with step-by-step solutions. There are such books for most of the major first and second year undergraduate STEM and STEM-adjacent courses. [1] https://www.amazon.com/Schaums-Outline-Linear-Algebra-Outlines/dp/1260011445 https://www.amazon.com/Schaums-Outline-Linear-Algebra-Outlin...

cottager2 5y ago

I’m surprised by the outrage to the teaching style, specifically people taking issue with the expectation that students take questions to office hours. Perhaps many who have studied math have forgotten, but “so and so is left as an exercise to the reader” is basically a trope at this point. I’d even go as far to say that you can’t really learn all the content in a math textbook without talking it over with someone. Math text books aren’t very dense, yet it can take a day or more to fully grasp a few pages. Simply adding more exercises, even with answers, isn’t necessarily going to deepen one’s intuition. Which brings me the specific class this article is about: linear algebra. LA has to been one of the worse taught classes, and that seems to be universal. Things like determinants and Eigen values are drilled in students’ heads without developing the intuition for the subject first. They’re given examples without context, which is what the girl described in the article seems to be struggling with. She probably still would struggle to learn LA even with answers to the examples.

dang 5y ago

Recent and related: Why won’t anyone teach me math? - https://news.ycombinator.com/item?id=30302079 https://news.ycombinator.com/item?id=30302079 - Feb 2022 (670 comments)