Michael Eriksson's Blog

A Swede in Germany

Posts Tagged ‘education

Questions/exercises at the end of a chapter

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The questions and exercises* at the end of a chapter of school literature always annoyed me as a child. Even then they seemed like pointless busy work to me and they rarely made sense. To some part, this was my own laziness: if I liked the book, I wanted to read on; if I disliked it, I did not want the spend more time with it to answer some “stupid” questions. However, to a large part, my opinion was actually correct:

*I will typically stick to “question” below, for simplicity.

Recently, I have both revisited some of my old Swedish school-books during visits to Sweden and read a handful of college level texts from the softer sciences. I find that I still have a similar aversion, if one more nuanced and held for a better reason: Outside of the hard sciences, even in more advanced literature, these questions tend to focus too much on just repeating the stuff of the chapter, where true value would be found in making the students think about the material and to help them towards the areas and ways of thought that best help with a deeper understanding. In this, they are largely a waste of time, energy, and motivation. This especially because many questions can be unduly time consuming relative their value, should an honest attempt be made, as e.g with “find five other examples of X”, or even time-consuming and open-ended, e.g. “find as many examples of X as you can”. (That type of open ended question should be grounds for an immediate firing.) In contrast, a “Y is a similar example. Can the same arguments be made in that case?” would be a much better question/exercise—especially, when the answer is “no”. (The exact formulations used might need adjustment to the appropriate age bracket, both here and below.)

In contrast, the exercises* found in e.g. a math or a physics book actually force the student to use his head (or fail at answering)—here what has (ideally) been learned is actually tested, various ideas and approaches are often given new spins, the student is motivated to go back to the text to check what he might have missed that will help him solve a problem, etc. Importantly, mere learning, e.g. having memorized a formula, will rarely be enough if an understanding is not present. It is much harder, even if not impossible, to get through a math class without understanding than through a class from the softer sciences.

*Those with little exposure to math should note that these questions tend to have a very different character from the arithmetic tasks of the early years. They soon include solving problems and applying techniques, and even a first-year college text might ask for an own proof of a theorem. (At least for me in Sweden—with the continual dumbing down and whatnot, no guarantees can be made for the future or other countries.)

Many other fields are too different in character for this to always be possible and it is only rarely possible in the same manner—but why is the attempt so rarely made? Worse, when the attempt is made, it is often in a misguided or irrelevant direction, e.g. “How do you think that X felt, when […]”. In contrast, assuming that this question arose from a conflict,* a better question might focus on (a) exploring different perspectives of an issue, (b) learning that there are almost always different perspectives and that it is valuable to try to understand them, (c) approaching a question with reason and impartiality, e.g. in that a conflict is examined based on who has what ethical case (as opposed to e.g. who feels what). Another common error is a too great focus on personal opinion, e.g. “Who do you think was in the right?”, which is likely to result in an unreflected top-of-the-head answer from most younger students, usually based on emotions or identification—and will be seen as patronizing and unproductive by most older students (assuming that they do not still given an unreflected top-of-the-head answer). Here a better question would be e.g. “Who do you think was right and why?”. Better yet, leading to better thinking and removing the need to artificially side** with one party: “What arguments could X and Y make for their respective case?” This not followed by a “Who do think would be more convincing?” or similar.

*It need not have. I have seen similar questions asked e.g. relating to a happy event or an accidental misfortune.

**Which is unfortunate on at least two counts: Firstly, it can lead the student to lock himself into one position. Secondly, most realistic cases will cause good students to not side entirely with either party, and forcing such a choice is unproductive and/or forces a fake answer. A personal example of the latter: In one of my first school-years, we were supposed to name our respective personal idol. I did not have an idol. (It can be disputed whether I have ever truly had one, even now.) I just picked Björn Borg (or possibly Ingemar Stenmark), because he happened to be a very plausible answer for a Swedish boy at the time (1982?)—and I had to answer something.

Even my suggestions above are potentially too simplistic, unproductive, patronizing, whatnot. Much better questions are e.g. those involving a hypothetical, as “what if” Hitler had not invaded Poland*; those that cause the student to investigate commonly believed facts and assumptions; those that force a critical investigation of a line of reasoning; those that focus on abstracting and generalizing; those that point to the “why” of matter (e.g. why someone did something or why something did or did not work); etc.

*A scenario that I consider much more interesting that the more common the-Axis-won-WW2 scenarios. And, yes, this is a very open-ended question, but it is open ended in a different manner than “find as many […]”.

A downside of such questions is that they rarely have a short and definite answer, which make them fit poorly in e.g. the context of a typical answer/check-the answer workflow. But why should they—the point is not to have the right or wrong answer, but to think, to develop a better understanding, and, even, learning to ask the right questions for one-self. Moreover, such questions are not best asked at the end of a chapter—they should ideally be in the mind of the student while reading the chapter.

Excursion on repetition and filtering:
There are two aspects of typical questions that some might feel come up short with more productive questions.

Firstly, repetition. Here I counter that just reading a chapter once and then relying on questions for repetition is unproductive. It is better to read the chapter several times, preferably spaced out over a greater time interval. If need be, a short summary or a check-list is a better means of providing repetition. (As could more reader-centric work be, e.g. the reader writing an own summary.)

Secondly, knowing what is or is not important. Here I counter that such limits tend to be unproductive, because they cause the student to focus just on the “important” parts; that the opinion of what is important held by the book author need not be shared by the student (or his teacher); and that, again, a short summary or a check-list is a better means.

Excursion on other problems:
Generally, I often found various tasks, questions, whatnot, in school unnatural, unproductive, poorly thought-through, whatnot. This often because they were; often because no-one bothered with telling the students why the task was there. A telling example of both: In early English, we were given a set of questions to answer, with no further instruction. I promptly answered them in a reasonable manner, e.g. by “yes”, “no”, a name, …—and was promptly scolded by the teacher with the pseudo-argument “That is not how you would have answered those questions in Swedish!”. Yes, it bloody well was! In Swedish, I would have answered with “ja”, “nej”, a name, … While I am more verbose today, there is a wide range of questions that I would still answer in that manner, even as an adult and in any language. Very often, such a short answer is not only the most economical, but also the most natural and what benefits the asking party the most.

What the teacher did not do, was to explain the purpose of the exercise—to train active language skills. We were supposed to use formulations like “my name is […]”* in order to master such phrasings as a speaker/writer. Had she done that, I might** have been more receptive and/or improved my own study approach at an earlier date. Her approach is also a good illustration of how too many teachers behaved—instead of giving a good argument, all they had was usually pseudo-arguments or some variation of the “because I said so”/“because the book said so” theme.

*Honestly, how often does this phrase actually occur among native speakers? Most often, I suspect, the speaker will just state his name; and the majority of the remaining cases will be some variation of “I am”. Similarly, “mitt namn är […]” (resp. “jag heter […]”) is not that common a phrase in Swedish, nor “mein name ist […]” in German.

**I make no guarantees, seeing that I could be extremely stubborn and disliked this type of exercise. However, the approach she actually used was a complete failure, almost by necessity, in terms of being convincing, and even if the improved version had also failed with me, it would likely have been more successful over a wide range of other students.

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Written by michaeleriksson

July 19, 2019 at 7:52 am

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Quotes on school and unschooling

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Going through some unread browser tabs, I encountered a page with “unschooling” quotes that I highly recommend. While I do not agree with everything there, much of it overlaps with my own observations and previous claims on school, schooling, education, etc.

This including (items are often overlapping):

The importance to think for one self, e.g in:

3. “The illiterate of the 21st century will not be those who cannot read and write, but those who cannot learn, unlearn and relearn.”

— Alvin Toffler

9. Believe nothing merely because you have been told it . . . or because it is tradition, or because you yourselves have imagined it. Do not believe what your teacher tells you merely out of respect for the teacher. But whatsoever, after due examination and analysis, you find to be conductive to the good, the benefit, the welfare of all beings — that doctrine believe and cling to, and take it as your guide.

— Gautama Buddha

That learning stems from the student, not the teacher, and/or that education and schooling are different things, e.g. in:

20. “Learning is not the product of teaching. Learning is the product of the activity of learners.”

— John Holt

38. Education is an admirable thing, but it is well to remember from time to time that nothing that is worth knowing can be taught.

— Oscar Wilde

42. “Self-education is, I firmly believe, the only kind of education there is.”

— Isaac Asimov

73. Schools have not necessarily much to do with education… they are mainly institutions of control where certain basic habits must be inculcated in the young. Education is quite different and has little place in school.

— Winston Churchill

The importance of curiosity and/or how school is troublesome through damaging curiosity, e.g in:

6. “Just as eating contrary to the inclination is injurious to the health, so study without desire spoils the memory, and it retains nothing that it takes in.”

— Leonardo da Vinci

Exposing the horrifyingly flawed claim that school is beneficial through socialization or through teaching social skills. Putting children together with other children, rather than adults, and expecting them to learn social skills is absurd:

11. “Nothing bothers me more than when people criticize my criticism of school by telling me that schools are not just places to learn maths and spelling, they are places where children learn a vaguely defined thing called socialization. I know. I think schools generally do an effective and terribly damaging job of teaching children to be infantile, dependent, intellectually dishonest, passive and disrespectful to their own developmental capacities.”

— Seymour Papert

The low practical relevance of school:

8. “There were no sex classes. No friendship classes. No classes on how to navigate a bureaucracy, build an organization, raise money, create a database, buy a house, love a child, spot a scam, talk someone out of suicide, or figure out what was important to me. Not knowing how to do these things is what messes people up in life, not whether they know algebra or can analyze literature.”

— William Upski Wimsatt

(I do not necessarily agree with the exact examples given in this quote, but I do agree with the principle.)

Disclaimer: I have not made any attempt to verify the attribution of these quotes, nor have I read them in the original contexts. I caution both that quotes are often misattributed and that a reading in context can change the implications considerably.

Note on typography, etc.: The original typography might have been changed in detail for technical reasons, but should be true in principle. The inconsistent use of quotation marks is present in the original. The numbers are taken directly from the original page. (In all cases, referring to the state at the time of my opening the page.)

Written by michaeleriksson

May 29, 2019 at 8:54 am

A few thoughts on educationrealist

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In December, I read large portions of the blog educationrealist.* I found it particularly gratifying that the author (henceforth “Ed”) verifies a great number of my opinions on schools and schooling with “from the trenches” information regarding current U.S. schools.**

*Already briefly mentioned during a recent blogroll update. I wrote most of the below a few weeks before publication, based on keywords and short descriptions gathered in December. Taking up writing again today, I can no longer recall much of what I had intended to write for the remaining keywords. This has led to some points being considerably more abbreviated than others. I was torn between throwing them out altogether and keeping the short version, but mostly opted for the short version. With hindsight, I should also have kept more links.

*My opinions are based on a mixture of my own experiences from Swedish schools in the 1980s and early 1990s, reasoning from principles (of e.g. human behavior and abilities), less detailed accounts by students or teachers, and discussions by (mostly) other outsiders. Correspondingly, there was a risk that the non-trivial changes over time or when moving from country to country had mislead me. This does not appear to be the case.

Among the interesting observations to be made:

  1. There is a strong component of innate ability to school success.

    This has corollaries, many contrary to what politicians tend to believe, like: It is not possible to teach everyone everything with a reasonable effort. A one-size-fits-all* school system will fail many students through under- or over-challenging them and through necessitating pedagogical compromises. Over-education is wasteful and unproductive at best. Ignoring group differences in “academic talent” is a recipe for failure.**

    *Ed usually discusses this in terms of (absence of) “tracking”, which is one way to make the school system “multi-sized”. I note that during my own school years more-or-less no such efforts of any kind took place. Cf. e.g. some discussion of skipping grades/being held back in [1]. No in-year acceleration or other differentiation, from which I could have benefited greatly, were available to the gifted. The first true differentiation took place in (the rough equivalent of) senior high-school, where students self-selected into more specialized programs based on interest, with some minor filtering based on previous grades when there were more applicants than places.

    **This especially with an eye on racial variety (which was almost a non-issue during my own school years, with an almost homogeneous population). Many posts deal with racial realism, the evils of various affirmative action measures, etc., approaching the statistics driven topics of “The Bell-Curve” from a more practical/personal/anecdotal angle. However, in the big picture, this is not limited to race—I note e.g. how German news-papers and politicians ever again complain about how the German system would hinder working-class children, without even considering the possibility that the differences in outcome could be partially caused by differences in (inherited) abilities that affect the respective probability of the parents being working-class and of the children doing poorly in school.

  2. The grade system is broken through rewarding effort, compliance, whatnot over actual ability and performance. Indeed, the picture painted is much bleaker than during my own school years, where there was a strong subjective component in the teacher’s evaluation, but where, at least, performance was measured through tests—not home work.

    This is particularly interesting in light of an earlier text on admission criteria, where I oppose the suggestion to remove Högskoleprovet (“Swedish SATs”) for admissions to higher education in favor of a purely GPA based admission.* If we assume that the same trend is (or will be) followed in Sweden, the correct resolution would be to abolish GPA admission and rely solely on Högskoleprovet… (But just as Ed complains about the dumbing-down of the SATs, there is reason to fear that Högskoleprovet is suffering a similar faith. There certainly is a constant fiddling with it—notably, to ensure that boys do not outscore girls.)

    *Swedish admissions are centralized and use numerical criteria—not interviews, essays, extra-curriculars, …

  3. The negative effects of destructive students on others can be considerable.

    Interesting sub-items to consider is what type and degree of disciplinary measures should be allowed, and the benefit of splitting students into groups that are more homogeneous in terms of e.g. interest and behavior. (Yes, the latter might make it even worse for the trouble students, but they are not exactly thriving anyway—and doing so would improve the opportunities for everyone else.)

    I did some minor reading on this from other sources (but did not keep links), and found some stories that make even Ed’s experiences, already well beyond my own,* look harmless—including a female teacher writing about regularly crying with frustration in the evening…

    *To speculate on the difference, I note that I spent a fair bit of my school years in small classes, that anti-authority attitudes were not yet as wide-spread, and that Ed has taught many classes of a remedial nature. Racial factors might also play in, e.g. in that the cognitive differences in the class-room are greater in the U.S. or that many minority boys have a deliberate “tough” image. I know too little of his situation and experiences to say anything with certainty, however.

  4. Student motivation is highly important, and often something that the school system fails at (but which is often blamed on the student).

    This is the more depressing, seeing that a knee-jerk political reaction to school issues is to increase the time spent in school, which obviously will reduce motivation further even among the motivated, let alone the unmotivated. It also comes with other problems. Someone fails in school due to lack of motivation? Put him in summer school so that he will enter the following year already “school tired”. Let him repeat a year to prolong the torture. Let him take remedial classes to make his days longer. Etc.

    The correct solution is, obviously, to attack the lack of motivation (which is very often to blame on the school/teacher/school-system/… in the first place). If this problem cannot be fixed, other efforts are pointless or even harmful. If it can be fixed, the strong students will advance on their own, weaker will at least have a chance, and we have to have enough realism to be willing to part with the too weak students at an earlier time than “year twelve”.

  5. Politicians and education reformers are often very naive.
  6. There is a lot of trickery with re-classification of children, artificial passes of courses, and similar, for the purpose of making schools look good (or “not disastrously bad”?).

    A particularly interesting variation is the confusion of classes for/students in “English Language Learning/er” and special education: Apparently, many students who should be in special ed are put into ELL based on excuses, e.g. because the parents were first generation immigrants, while the child is a reasonably proficient native speaker who happens to do poorly in school. This way, the failure in school can no longer be blamed on the school (or, God forbid, the possibility that not all students are equally smart)—but on an alleged language handicap.

A point where his experiences (and some citations?) do not match my expectation is the competence level of teachers: He repeatedly expresses the view that the effect of increasing the subject* competence levels or minimum test-scores** of teachers has little effect on student outcomes. There is even some speculation on a negative effect on Black students, because they appear to do better with a Black teacher, and increasing the test-score limits would reduce the proportion of Black teachers. My own experiences with teacher competence are very different, but I could see a possible reconciliation in teachers affecting different students differently, e.g. in that a dumber teacher will bore/under-challenge/annoy/whatnot the bright students, while a brighter teacher might similarly over-challenge or have troubles with adapting to the dumber students—leaving the total effect on the student population roughly constant. (Similar explanations could include e.g. brighter teachers being stricter on dumber students when grading than dumber teachers are, resp. dumber teachers failing to appreciate good answers from brighter students.***) If this is so, we have an additional argument for segregation by ability (combined with corresponding choices of teachers); while ignoring teacher competence would be particularly bad for the brighter students.

*E.g. requiring better math knowledge in a math teacher. This in contrast to e.g. pedagogical training, where I am uncertain what his stance is—apart from a negative opinion of some of the training actually on offer.

**On some type of qualification test for teachers. Similar statements might or might not have been made concerning e.g. SAT scores or GPA.

***With several of my own less bright teachers, what I said sometimes went well over their heads. More generally, I have made the life-experience that stupid people often are under the misapprehension that someone brighter disagrees because he lacks insights that they have, while the true cause is typically the exact opposite—he has insights that they lack.

Looking at Ed, himself, he appears to do a great deal of experimentation and tries to improve his teaching over time. There are a few things that appear to work well for him and that could prove valuable elsewhere, including (big picture) running a hard line against students, treating students very differently depending on their behaviors/need/abilities/…, and attempts to motivate his students, as well as (on the detail level) many pedagogical tricks and techniques.

Unfortunately, there are a few other things that strike me as negative, even if some of them might be a result of external circumstances, e.g. that the school system leaves him with no good options or that he must make compromises between the interests of the students, his school, society, whatnot. This applies especially to his “D for effort” policy, which makes him a contributor to problems that he, himself, complains about, e.g. misleading grades and remedial students making it to college (while still being remedial). My take? It is never “D for effort”, it is never “E for effort”, it is absolutely never, ever “A for effort”: Unless actual accomplishment results from the effort, it must be “F for effort”. (Which, to boot, makes for a phonetically better saying.)

Another negative is a considerable mathematical naivete for a math teacher,* that is likely the cause of some weird ideas that are more likely to hinder than help his students, e.g. that higher order polynomials (or functions, depending on perspective) are arrived at by “multiplication” of lines** (i.e. first-degree relations like y = 5x + 3). Yes, this is a possible perspective, but it is just a small piece of the overall puzzle, and it strikes me as highly counter-intuitive and pedagogically unsound as an approach. (In my preliminary notes, I have a second example of “identifying numbers graphically only”, but I am not certain what I meant. It might have been something like requesting students to draw a graph and find the y-value from the x-value by measurement, instead of calculation, which would be pointless as an “only”, but could be acceptable as a preliminary step or to demonstrate the occasional need to use other methods than pure calculation.)

*In all fairness, he, unlike many others, understands and acknowledges that his understanding is superficial when he moves beyond the classes that he teaches.

**Generally, there is an extreme over-focus on geometry; however, I am not certain whether this is caused by Ed or the school (or the text-book publishers, politicians, whatnot). This includes e.g. viewing functions more-or-less solely as graphs, root learning of sine and cosine values, and similar.

Yet another is “lying to students” (see excursion), as demonstrated e.g. in a post on “The Evolution of Equals”. This post also shows some examples of enormous efforts being put in to teach the trivial to the dumber students, who might not belong in high school to begin with—at least a basic grasp of the equals sign should be present years earlier. Move them out of school or to some more practical course and use the freed teacher resources to teach those teachable… (Some other posts make a better job of displaying a great effort with little return, but this is the one post for which I kept the URL.)

Some other points could be seen as positive or negative depending on the details. For instance, he does some type of interactive/quizzing teaching that expects a “chorus answer” from the class. This might keep the students alert and force them to at least rote-learn some material—but it does not allow for much true thought and it does not demonstrate any deeper understanding among the students. I would certainly have found it annoying (or worse), had it been applied during my own school years.

Excursion on a generic solution to tracking, acceleration, etc.:
I have for some time considered taking a more “collegey” approach to school as a solution (sketch) to some problems. I see some support for this in the non-integrated approach taken to e.g. math in Ed’s descriptions.* What if the material to be covered, even in year one, is broken into rough packages of four quarter-semesters per semester and topic—and the students then go through these packages in whatever tempo they can manage? The strong students will soon move ahead of schedule, be it in general or in their favorite topics. Similarly, the student with an interest in a certain area, e.g. math, can move ahead in that area. The weaker students can take their time until they have mastered the matter sufficiently well. Etc. Exactly how to handle the teachers in this scenario is not yet clear to me, but it is clear that mere lecturing** to the class would have to be considerably reduced or combined with a division of people based on the package that they are currently involved with.

*Math was integrated through-out my own school years. While I do not see this as a pedagogical problem, it does limit flexibility.

**With some reservations for the first few years, I consider lecturing to be highly inefficient, often boring, and increasingly only suitable for weak students as we move up in grades. Strong students are able to learn mostly on their own and based on books. Cf. an earlier text on college material. In at least a U.S. context, it also helps with hiding the problem of sub-grade-level literacy—better to reveal and address the problem.

Excursion on memory:
A recurring issue is that Ed’s weaker students often actually do learn how to do something—but have forgotten it again by the next semester. This is likely partially caused by a too superficial understanding,* but it could also point to many simply having very weak long-term memories. Revisiting some past interactions with others, such a weak memory could explain quite a few incidents that I had hitherto considered rooted in e.g. an original pretended understanding or agreement,** willful non-compliance using pretended ignorance as an excuse, too great a stupidity to be able to make even a trivial generalization of a known fact, or similar. (Whether weak memory is the explanation I leave unstated, but it is something that I must consider in the future.) A twist is that I have partially not considered memory an issue, because I thought my own memory poor and rarely had such problems—but in comparison to some of Ed’s students, my memory is excellent…

*Understanding does not only help with recollection, but can also be used to fill in many “blanks”. Of course, in terms of school, it can require a teacher with the right attitude: I recall an oral examination (on the master level, no less) where the professor asked for a formula. I had not bothered to learn the formula, knowing that the derivation was very easy from first principles, and set about deriving the formula. He immediately interrupted me, stating that he was content with the formula and that the derivation was out of scope. Apparently, he expected students to blindly memorize the formula, while having no clue how it came about…

**Something that also occurs among some of Ed’s students, as might some of the other items mentioned.

Excursion on lying to students:
“Lying to students” roughly refers to giving them a simplified (or even outright incorrect) view, which is (perceived as) good enough for now and which they can easily understand—without telling them that it is a simplified view. The result of this is that those who do not progress in their studies believe things that are not true, while those who do progress have to unlearn and relearn things in a highly unnecessary manner. A particular complication is that it can be very hard to be certain what opinions/knowledge/whatnot, gathered over a prolonged time period, corresponds to what state of knowledge. In many cases, the simplifications can make something harder to understand for the bright students, because it simply does not make sense or because the non-simplified version is (in some sense) cleaner. A very good example is the theory of relativity taught on the premise that the speed of light in vacuum is fixed* vs the premise that there is an upper speed-limit on causality or information, which light reaches in vacuum—the latter is much easier to see as plausible, leads to more natural conclusions, etc.** To toy with a simpler example in Ed’s direction: Compare the teacher who says “It is not possible to subtract a larger number from a smaller number!” with the colleague who says “If one subtracts a larger number from a smaller number, the result is a negative number—but that is for next semester!”. Which of the two is more likely to have confused students the next semester? Possibly, to the point that other claims made are no longer seen as credible? Which is more likely to peak an interest into what negative numbers are? Possibly, to the point that ambitious students read ahead or ask for explanations in advance?

*In all fairness, this could be based less on a wish to (over-)simplify and more on historical development. Even so, it should not be the starting point today.

**Consider e.g. questions like “What is so special about light?!?”, “Why must it be the speed in vacuum?”, “What happens when light travels through a crystal at a lower speed?”, …

Written by michaeleriksson

January 14, 2019 at 10:42 am

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The status of practical learners

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In my earlier days in the Blogosphere, one of my comments* was answered with “So, you are a practical learner!”**. Knowing “practical learner” mostly as euphemism for those with some limited practical talent and a complete lack of intellectual accomplishment, I almost choked with the perceived insult and condescension.

*This was too long ago for me to remember the context and details.

**To paraphrase my main take-away. Here too, I do not remember the details, but the actual answer was likely a bit longer, and probably not intended to be insulting.

Since then, I have revised my opinion on practical learning considerably. For one thing, I have over the years increased my proportion of practical learning, e.g. in that I have so often found claims by others to be faulty that I often prefer to do my own informal experimentation/trial-and-error/whatnot (not just my own thinking). For another, practical learning (in the literal sense, which I will use throughout below) plays in well with my opinions on learning in general:

There are, somewhat over-simplified, two types of learners: Those who just gather knowledge provided by others and those who gain an understanding from the knowledge of others and/or create new knowledge of their own. A practical learner can to some degree be either; however, the weakest aside, the latter will likely dominate. Examples include anyone who observed an event and drew conclusions about how this event could be reproduced or avoided, what the positive and negative effects were, how the event could be utilized, … Consider a stone-age man who accidentally hits a piece of flint so that it can be used as a cutting implement, realizes that it is a potential cutting implement, tries to create new cutting implements by hitting other pieces of flint, and refines his technique based on further experiences—a practical learner who has done something most of his peers did not do and which helps the group to be more successful. Or consider a software developer who tries a certain approach to solve a problem, sees an unforeseen complication when the code is run, and modifies his approach thoughtfully* the next time around. I certainly suspect that many of the great inventors and researchers have drawn considerably on an aptitude for practical learning.

*Not to be confused with the “worst practice” of making random changes in the code until it appears to be running as intended.

Contrast this with someone who just mindlessly absorbs the contents of books, who can apply the algorithm of long division (see excursion), who knows in-what-year for a thousand events, who has absorbed but not understood the deep thoughts of others, … (In turn, not to be confused with the mindful reader. Cf. e.g. [1].)

Of course, the border between the practical learner and, e.g., the theorist can be hard to find—is our stone-age man still acting as a practical learner if he takes a thirty-minute break to just think his options through, during which he does not even touch a piece of flint? This, however, is only natural with an eye on how deeper learning works: Deeper learning, with an understanding of the matter involved, always comes from within, from own thought. External influences, be they practical observations, books read, statements heard by others, …, are food for thought—they are not thought it self. The source of this food matters less than what we do with the food. It is true that some sources provide more, more nourishing, or more easily digested food than others, but ultimately it is up to us to do the digesting.

In all fairness, it is likely true that the set of practical learners will contain a comparatively large sub-set of those not-very-bright (including the stereotypical “shop students”), compared to e.g. those who actually learn from e.g. books. However, there is no true reason to believe that the sub-set of the very bright would be smaller, even if those might engage in practical learning in other areas (e.g. experimental physics instead of auto mechanics)—and worth-while thinkers will almost certainly have several sources of food for their thoughts. Moreover, there are plenty of readers, likely an outright majority, who are not all that bright either—they read but do not truly learn. Similarly, many or most college* graduates have not truly learned—they have internalized some (possibly, a very considerable) amount of facts, methods, whatnots, but have failed to gain an understanding, cannot draw own conclusions, are bad at applying what they have internalized, etc.

*School and, increasingly, higher education have a strong tendency to favor the wrong type of learner. Too often, the mindless absorption is rewarded during tests, while understanding brings little or no additional benefit. In some cases, critical thought can be positively harmful to success, e.g. in fields like gender-studies.

Excursion on long-division:
I have never mastered it: In school it was presented as a set of mechanical steps, with no attempt to explain the “why”, which I imitated a few times to create the impression that I knew them. After that, I just winged the divisions that came up on tests (usually as comparatively easy steps within a longer calculation). In adult life, the divisions that I encounter are either so trivial that I can easily do them in my head (say, 231/11=21), so complicated that I would use a calculator* anyway, or from a context where I only need an approximate** value to begin with. In the unlikely event that I really need an algorithm, I understand division, the decimal system, etc. well enough that I could create it—which is far more valuable than memorizing a set of steps.

*I do not need long-division to solve e.g. 2319523/2344 using pen and paper, but a calculator removes an entirely unnecessary risk of an accidental error and is usually faster—be it compared to long-division or to an improvised calculation. This especially as the very few such calculations that are needed tend to carry a legal relevance, e.g. the extraction, for my tax declaration, of the VAT from an amount paid that includes VAT.

**That 2319523/2344 is a little short of 1000 will be enough in many contexts.

Excursion on men vs. women:
While the problem with a lacking understanding (etc.) is quite bad among men, it appears to be considerably worse among women (and is very often combined with the knee-jerk classification of everyone as intelligent who graduated from college). This could turn out to be a major future problem, if the trend of giving women artificial preference in e.g. hiring/promoting and politics is continued.

For an example, consider the relative likelihood of a homeopathic physician* being a man vs. being woman.

*As opposed to an uneducated user who might be forgiven for not seeing through the obvious quackery that homeopathy is. (But women appear to dominate there too.)

Remark on double posts:
Subscribers might have seen two incomplete postings of the above contents. This was caused by my failing to close the “tags” declaration for WordPress within the HTML code.

Written by michaeleriksson

December 9, 2018 at 1:58 pm

A potential revamping of college tuition

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With regards to college/university there is a subset of problems that could be partially resolved in a simple manner:

  1. In order to ensure a high degree of equality of opportunity and social mobility, it must be possible even for people with low income and little wealth (be it own or when looking at the parents) to gain degrees. (Assuming that they are intelligent and hard-working enough to succeed with the academic side of the equation—few misconceptions are more dangerous than the belief that college creates diamonds out of charcoal.)
  2. Colleges cost money to run, and it is not optimal to finance them through public funds. Not only is the use of “someone else’s” money a bad idea in general, but here those that do not go to college are disadvantaged in an unfair manner.

    Note that this affects the U.S. too, because of the considerable “financial aid” given. Notably, the financial aid is also a driving force behind tuition increases—when the economically weaker buyers of a uniform product are given more money, the sellers have strong incentives to raise prices. The price raise then hits everyone, while only the weaker where given aid, which increases the group that would benefit from aid. To boot, the original aid receivers do not benefit as much as intended, creating a wish for more aid per person. Here there is a risk of a vicious circle.

  3. Academically poor students tend to cost a lot more money than the better students, e.g. in that they require more support outside of lectures and that they are the main reason why the highly inefficient lecture system is still “needed”.
  4. There is a severe over-inflow of students not suitable for college, who force further dumbing down, weaken graduation criteria, etc.
  5. In tuition-heavy countries, colleges have an artificial incentive to let students graduate, pass, get good grades, or even be admitted, irrespective of whether they have actually earned it.
  6. Excessive income, as e.g. with some U.S. colleges, leads to waste, including an every growing administration.

    (As an overlapping special case, it could be argued that the U.S. campus system is an evil per se, and that the students would be better off paying directly for own and independent housing, as they do in e.g. Sweden and Germany, rather than to pay the colleges to provide housing. Certainly, my impression of the living environment, from U.S. fiction and general reputation, points to it being positively harmful to someone who actually wants to study, which would make it a doubly poor use of money.)

  7. If only partially relevant: Popular programs* often have to reject even qualified students.

    *I use “program” to mean something at least somewhat structured, with an at least somewhat separate admission, and similar. Due to the wide variety of systems in use, this word need not be suitable everywhere. Note that the word “major” would implicitly exclude e.g. master programs and med school, which makes it highly unsuitable, even other potential concerns aside.

Consider the following solution sketch*:

*It is highly unlikely that this sketch would be viable without modifications and there are details to clarify. Complications include what exact numbers to use, whether borders should be sharp or fuzzy, what criteria should determine who belongs where, whether percentages or absolute numbers are better, how many categories are reasonable, what conditions are best suited for what category, …

Colleges are by law forced to let the top 10 percent of students study for free, with costs covered by the colleges’ funds.* Students from 10 (exclusive) to 30 (inclusive) percent are charged approximately at cost**. Students from 30 (exclusive) to 60 (inclusive) percent are charged at cost + some reasonable*** markup. The remaining students can be charged whatever the college wants. There is no additional financial aid.

*It is of fundamental importance that the colleges’ money be used. If, e.g., government money was given to the colleges to cover the costs, the system would fail.

**Based on a reasonable estimate of how much each student costs with regard to what directly relates to the education, e.g. salaries to professors for the courses taken, but not e.g. the cost of running the administration or various sports programs.

***Possibly, 500 or 1000 EUR/semester (resp. the purchasing-power adjusted equivalent in local currency), or some percentage of the costs (on top of the costs themselves).

In such a set-up, worthy students will rarely have financial problems; colleges can still earn plenty of money (but with less issues of insane surpluses); a very wide admittance would be possible, but the academically less* fit would tend to disappear when they discover that they fail to score well enough to study cheaply, which increases the quality of the graduates; etc. Note especially that while colleges might still have incentives for over-admission and “over-passing”, the students so favored would still need to pay their fees, and these incentives will then be largely countered by incentives for said students to drop out**. To boot, the colleges only have incentives to keep the students on—not to give them better grades than they deserve or to let them graduate before they have reached a certain standard.

*Note that these need not be unfit when it comes to a competitive program. In such cases, the effect is not so much a removal of the unworthy as it is a filtering based on result, where today a filtering based on expectation of result takes place. For instance, instead of admitting those with a GPA of 4.0 and leaving the 3.9s lying, a program could admit the latter too, and then let the students filter themselves out based on actual performance over the first few semesters. (But there might still be some programs where this type of increase is not plausible.)

**From the given program at the given college. It is quite possible that studies are continued with more success in a different program and/or at a different college.

In countries where various forms of public funding pay for significant portions of the cost and tuition is kept very low, this scheme would allow the introduction of higher fees (without negative effects on worthy students) and a corresponding reduction of the cost to the public: Instead of effectively shelling out money to everyone who wants to study, the money is limited to the worthy—or even to no-one, because the worthy are already covered by the fees paid by the unworthy.

Also note that the restriction on costs includable in the two mid-categories give incentives to keep administration and other overhead down. For instance, if a professor is given a raise, ninety percent of students can be charged extra—but for an administrator, it is only the bottom forty. Ditto if the number of professors respectively administrators per student is increased.

Excursion on actual costs:
Keep in mind that the actual cost of a student is much, much lower than what some U.S. fees could make one believe—this especially when we look at a “marginal”* student or a student bright enough to learn from books (instead of lectures) and to solve problems through own thinking (instead of being led by the hand by TAs). As I have observed, it would sometimes be cheaper for a handful of students to pool their money to hire a dedicated, full-time professor than to go to a U.S. college.

*I.e. an additional student added to an existing class, who will typically add far less to the overall cost than could be assumed by calculating the average cost per student.

To exactly quantify costs is hard to impossible, when looking at e.g. differences in class sizes, salaries of professors, the type of equipment needed or not needed in different courses, what type of work* the students have to present, etc. However, for a good student taking non-wasteful courses, the marginal cost might be a few hundred Euro per semester, and a few thousand should be plenty in almost any setting and even on average.

*Compare e.g. a math course with one or two tests to a writing course with a handful of essays, all of which should be given insightful feedback. (Whether they are given such feedback, I leave unstated.)

Excursion on percentages:
When percentages are used, we can have situations like someone dropping out of the top 10 percent because others dropped out entirely.* Originally, I saw this as negative; however, on further thought, in might work out quite well, seeing that the limit will grow tougher in the more advanced years, stimulating competitiveness and keeping the level of those who graduate even higher. However, some type of fail-safe might be beneficial, e.g. that the percentages are converted to absolute numbers at the beginning of each semester. (If there were a hundred students to begin with, the ten best students are guaranteed top-level status, even if the class has shrunk to ninety at the end of the semester.)

*E.g. because he was the tenth best student in a class of one hundred, and is now the tenth best in a class of ninety.

Excursion on choice of college, program, whatnot:
A potentially positive side-effect is that strong students have new incentives to consider less popular colleges and programs. For instance, someone who could be accepted to Harvard, but with a considerable risk of having to pay, might prefer a college where he is almost guaranteed to be a top-10-percenter. Such decisions might in turn have effects like creating a downward pressure on tuition fees of expensive colleges, spreading talent more uniformly, reducing the “networking effect”* of top colleges, etc.

*According to some, the main benefit of going to e.g. Harvard is not the level of the education, but rather the career-boosting contacts made there. Also note that networking is often just a form of corruption—something that damages an employer and/or society for the benefit of the networker. Such damage can e.g. occur when someone is hired because of “whom he knows” rather than “what he knows”.

Excursion on the freedom of the colleges:
One negative effect is that it limits the freedom of colleges regarding pricing, which could have negative market implications and/or be ethically dubious. This complication should be seriously considered before an implementation is attempted.

A reconciliation might be to only put some categories of colleges under the suggested system, including all that are state owned/run, all that have received non-trivial public support within some number of years prior to the “now”, and all that have directly or indirectly benefited from financial aid to their students in the same time frame.

However, if push truly comes to shove, this is one area where even such a strong regulation would be acceptable to me—in light of the catastrophic decline of higher education over the last few decades and the great threat that an even further decline poses.

Excursion on living costs:
In a non-campus system, topics like rent might need additional attention. It might e.g. be necessary to allow some amount of financial aid, preferably in the form of loans, to cover such costs. However, importantly, this would be something between the government and the student—with the college having nothing to gain. Further, it is not a given that such aid would be necessary on a larger scale, especially as societies grow more affluent: For very many, living with the parents, monetary help from the parents, working summers, private loans based on expected future income, or similar, can provide a solution that does not use tax-payer’s money and does not have a major impact on success in college.

Remark concerning “Thoughts around social class”*:
This text is not strictly a part of that text series, but there is some overlap and the implied division of students into more and less worthy categories is highly compatible with an intended future installment.

*See e.g. the last installment published at the time of writing.

Written by michaeleriksson

November 26, 2018 at 7:29 am

Adults say the darnedest things

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I just re-encountered the fiction (and real-life) cliche of the child–adult exchange “He started it!”–“That is no excuse!”. This is a good example of adults telling children things that simply do not make sense,* and that are likely to leave the children unconvinced: “He started it!” is not just an excuse—it is a perfectly legitimate reason. There might be situations where it can be pragmatically better to turn the other cheek, try to deescalate, find a more constructive solution than retaliation, whatnot; however, that has no impact on the ethics of the issue and expecting a child to understand such matters is highly optimistic.** Furthermore, there are many cases where retaliation in kind is the best solution, especially when boundary pushers and bullies are concerned (which will very often be the case with children): Both being exposed to consequences for inappropriate behavior and having to take a dose of one’s own medicine can have a great positive effect in limiting future inappropriate behavior.

*I suspect that this is partly due to the answer being dishonest, that the adult is motivated by something unstated. (“What” will depend on context, but a fear of negative consequences from e.g. fights between children could be high on the list, as could a wish to just keep some degree of peace and quit.)

**And arguments in that direction are usually absent to begin with.

Note how the “adult” reply makes no attempt at providing reasons or actually convincing, and how a discussion of pros and cons is entirely absent—it is just an (invalid) claim that the child is supposed to take at face value “because I said so”. No wonder that children are not more cooperative…

The “because I said so” is, of course, a good example in its own right—the effect of such argumentation is that the child’s rejection of a claim is complemented by a feeling that the adult is an unreasonable dictator. It might or might not create compliance in action, but compliance in thought is not to be expected. Worse, it could have a harmful long-term effect on the relationship. It is true that there might be a point where a child is too young or the situation too critical for a deeper discussion to beneficial; however, the uses that I have seen (be it in fiction or in real life) would usually have benefited from a motivation.* Consider** e.g. a child’s refusal do the dishes countered with “because I said so” vs. “we agreed that everyone should take a turn—and today is your day”; the adult’s refusal to play based on “because I said so” vs. “I am sorry, but I am dead tired and need to take a nap”; or even any discussion resulting in “because I said so” vs. “I pay the bills; I make the rules”. The last example might superficially seem to offer no real difference, but most children (above a certain age) will at least be able to see the adult perspective of the bill payer and the hypothetical alternative of buying greater freedom through going hungry and homeless—but not of the more power-based “because I said so”. (Also note that “I am the parent; I make the rules” is closer to the dictator than to the bill payer.) At the same time, I advice against reasonable sounding arguments that do not make sense on closer inspection or that could back-fire.***

*Generally, even among adults, I recommend that any rule and whatnot be given some form of motivation, so that those affected know why something should or should not be done. This to increase the chance of compliance, to make more informed choices possible (e.g. when dealing with interpretation and special cases), and to allow a critique of the rule with an eye on future improvement.

**I stress that I do not consider the alternative arguments to be silver-bullets—dealing with children is hard and often amounts to a “damned if you do; damned if you don’t” situation. They are, however, improvements.

***E.g. “That is no excuse!” above. A more interesting example stems from my own childhood (pre-VCR): My mother argued that she should watch the news on the bigger color-TV and I a simultaneously broadcast movie on the smaller black-and-white one, because she had not seen the news in a week (due to a study absence). From my perspective, the negative effects of the inferior device on a movie were larger than on the news, and it might be years (not a week) before another opportunity to watch that movie arose. The result? I was left with not only an implicit “because I said so”—but also with the feeling that my mother was dishonest… (Adult me is open to the alternative that she simply had not thought the matter through.)

A sometime reasonable, but more often misguided, argument is “And if your friends all jumped off a bridge, would you follow them?!?” (with many variations). The analogy involved is usually inappropriate (notably regarding dangers) and/or too subtle (the “lemming” aspect). Normally, the only justification is that it came as a response to a weak argument from the (typically?) teenager, e.g. “but all my friends are going”. Here, however, such “smart ass” answers are not helpful. Better would be to evaluate the suggestion (e.g. going to a certain party) on its merits, factoring in both the fact that “all my friends” can seem like a strong argument to the teenager (even when it is not), and that there are at least some cases where the argument has merit through its impact on teenage life* or through giving a different perspective**.

*The degree to which adults should be concerned about this is limited, but it is not something to ignore entirely. There are aspects of popularity and networking that might be largely alien to an adult (and to some teens, including my younger self); however, they are there and showing them some consideration is not wrong.

**Notably, that something is wide-spread and tolerated by other parents could point to a too restrictive own attitude.

Generally, I caution against giving “smart ass” answers to children, and recommend using only factual arguments. For instance, my school class would sometimes be asked to explain/solve/perform/… something that had simply never been taught (especially when teachers changed). Typically, someone would reply with the idiomatic “det har vi inte fått lära oss”, which carries the clear intent of “that has not been taught” (and an implicit “so you cannot fairly require us to know”). Unfortunately, this phrase is vulnerable to the deliberate misinterpretation of “we have not been allowed to learn this” and the answer was invariably along the lines of “Who has forbidden it?”. The results on the class were never positive… To boot, this answer is doubly unfair in that (a) the students cannot be expected to guess what the next teacher considers “must haves” when the previous teacher saw things differently, and (b) traditional schooling severely limits the time, energy, and (often) interest available for own learning in addition to the official curriculum. (Note that both, even taken singly, invalidate the potentially valid angle that this answer does have—that learning should not be limited to school and that teachers usually indicate the minimum to learn.)

In a bigger picture, adults often impose constraints or obligations on children that make little sense. For instance, what is the point of a child making his own bed, should he not see a benefit for himself in doing so? There is no automatic advantage in a made bed and if no-one else is hurt by it… Indeed, apart from when I receive visitors (actual reason) or change the sheets (trivial extra effort), it might be more than twenty years since I, as an adult, made my bed.

Excursion on women as perpetrators:
While errors like those above are by no means limited to women, they do appear to be considerably more likely from women. It is conceivable that at least some of the problem stems from an arbitrary imposition of some irrational values that often occur among women (e.g. that any and all violence no matter the reason is evil, or a wish for orderliness-for-the-sake-of-orderliness).

Excursion on fairness:
Much of the above is related to the feeling of being unfairly treated. A fair treatment is by no means a guarantee for a happy and well-behaved child; however, the opposite will make things worse. Where fair treatment might be important to most adults (at least when on the receiving end…); it is paramount to most children.

Written by michaeleriksson

November 13, 2018 at 2:08 am

A few thoughts on role-models

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Disclaimer: The below borders on free association, even by my standards.

In a recent text on math and “college material”, I mentioned the Feminist fallacy of demanding specifically female role-models for young women in various fields, especially the STEM ones—is it not better to pick someone worthy of admiration, while ignoring sex?

Since then, I have spent some time thinking on role-models*, both with regard e.g. to Feminist calls for 50–50 representation of the sexes in math books and to my own experiences:

*Used in an approximate sense on two counts: Firstly, I have mostly seen such calls in Sweden (“förebild”) and Germany (“Vorbild”), and I am not certain what the ideal translation in context is. Secondly, the words in all three languages are unnecessarily strong and imply more than is warranted in context. (This, however, is not unusual with everyday use of these words.)

Let us start with a question: If sex requires such special treatment, why then not e.g. height and hair color?

In a Feminist world-view, which almost invariable denies significant inborn differences between the sexes, these three criteria make comparably little sense.

On the other hand, for those of us who believe that there are inborn differences, e.g. that men tend to be naturally more interested in STEM topics or that they tend to dominate the high (and low) extreme of I.Q., there might be some justification—that young women see that there actually are opportunities for women, should they have the interest, the ability, and the dedication needed. In this manner, the role-models could serve as a counter-weight to the other young women in their circles who show no sign of interest or ability; the female relatives who have trouble telling the difference between Internet Explorer, Google, and the Web; etc.*

*Note that if the feminist world view was correct, such a counter-weight would not be needed, implying that this argument does not apply in their case.

However, here specific examples of (true or faked) great women in the STEM fields give the wrong impression and group statistics would be much more helpful, e.g. what (true) percentage of professionals in a certain field are women. This way, a more correct impression is created and better choices can be made than if e.g. a math text book is arbitrarily filled with 50 % male and 50 % female mathematicians.* Women should know that there are opportunities (subject to the aforementioned constraints) and that they are not carbon copies of other women, but not be led to believe that the field is naturally 50–50, and certainly not led to believe that anyone who has a degree in X is actually good at X**.

*Even such problems aside as smart young women seeing that the women are included on lesser merits or being aware of the debate (bright young women have been known to read the news papers…) that led to the 50–50 proportions—either would not only defeat the purpose, but could actually back-fire though the impression that women are only included through “affirmative action”, never through actually being worthy. More generally, many Feminist, PC, Leftist, whatnot groups appear to be working under the assumption that people are so stupid that they must be manipulated into having the “right” opinion; however, whatever might or might not hold in the overall population, people lacking in intelligence and the ability to think for themselves have no place in e.g. math. Simply put: Someone susceptible to or “benefiting” from such manipulation is unlikely to be a good candidate for the STEM fields in the first place…

**Another common fallacy—and a much worse one at that: A degree is worth little more than the paper it is printed on, should the the right understanding, the right abilities, or the right brain be absent. More often than not, at least with today’s graduates, they are absent… (And, yes, that applies to the men too.)

More: Too much discussion of e.g. top mathematicians can create a very wrong impression and lead to great disappointments, faulty expectations, or undue pressure for members of either sex.* The simple truth is that the likes of Leibniz, Newton, Gödel, or (to pick the likely strongest female candidate) Noether are very rare birds. The chances are overwhelming that no-one, male or female, in this AP math class, this Calculus 101, or this graduate course on Riemann geometry will be comparable to Leibniz et al. Such perceptions of standards was one** of the reasons why I, myself, did not pursue math/academics beyond the master level—I saw what these rare birds had accomplished, measured success against them, and feared that I would fail to make a truly noteworthy contribution, e.g. founding a new field, solving one of the major open problems, or finding a theorem of fundamental importance.*** Today, I realize that even a more modest (and realistic) career as a metaphorical made-the-NFL-but-not-the-Hall-of-Fame mathematician would have been an accomplishment to be proud of.

*But likely especially for women, who are often exposed to a simplistic message of great success being inevitable (at least, unless the “Patriarchy” interferes), despite such success being a rarity and requiring at least one, more often two, and even more often three out of great ability, hard work, and luck.

**Others include my time as an exchange student and a wish to remain in Germany afterwards, a wish to make a bit of money, and having become over-satiated with math the first few years of college: I am not telling a sob story about how someone would have been an NFL Hall-of-Famer, had it not been for that knee injury the last year of high school—I merely caution that we should avoid knee injuries…

***In high school and the first one or two years of college, I did well enough that such aspirations originally seemed plausible to me. A little more detail is present in some sections of an older text on issues relating to education ([1]).

Excursion on other issues:
In a more complete analysis of the calls for female role-models (this text is more geared at the issue of impressions caused by role-models vs. reality) other arguments can be relevant, including the inherent unfairness towards the people featured in math books (deserving men “quota-ed” out; undeserving women “quota-ed” in) and the myth of sex being irrelevant gaining a greater foothold in the overall population.

Excursion on differences:
A common problem in discussions like these is misrepresentation or, conceivably, misunderstanding of opinion by e.g. Feminists, notably in the form of statements about groups being distorted to exceptionless statements about individuals. (The equivalent of “every single man is taller than every single woman”.) Here I stress the importance of understanding the difference between the individual and the group, individual and group characteristics, and individual and group outcomes. This especially when areas with a high selectivity, including elites, is concerned. Cf. e.g. parts of [2] (search for/scroll to “Thoughts on comparisons and the effects of variation:”).

Excursion on fear of failure:
One of the negative things ingrained in me through school was a fear of failure, sometimes even a fear of not being perfect*, that I have only overcome through time. This fear of failure was not an obstacle** as long as I succeeded with ease, but when things got tougher it could be a problem. During my college years, my “brute force” approach (cf. [1]) eventually brought me a few unnecessary failures, I learned that I had limits, and I caught enough of the history of math to understand that the best-of-the-best had often already made major contributions*** at my age. To some degree, I fell victim to a “if I do not try, I cannot fail” thinking. (But, again, this was only one of the reasons for my not pursuing a math career.)

*Not to be confused with a tendency towards perfectionism, although there might be some causal overlap.

**But it did lead to e.g. some cases of undue test anxiety and the odd nightmare in the extended why-was-I-not-told-that-we-have-a-test-today family. On the positive side, I have never had a I-forgot-to-put-on-my-pants-before-going-to-school nightmare.

***In all fairness, they had often been helped by having less mandatory schooling, giving them more time for an actual education and for their own thinking.

Interestingly, this type of thinking is one those sometimes alleged special problems of strong female students, especially when society is too be blamed for women’s problems—and, as usual, this “female” aspect is flawed. It might or might not be more common among female students (group differences again), but in reality, it appears to be a reasonably common problem among strong students (strong performers generally?) of either sex. A notable “named” example of a similar type is the “impostor syndrome”, originally alleged as a problem of accomplished women, but which has less to do with being a woman and more to do with being accomplished.

Written by michaeleriksson

November 5, 2018 at 3:52 pm