Michael Eriksson's Blog

A Swede in Germany

Posts Tagged ‘School

Follow-up: COVID-19 reactions doing more harm than good?

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Since my recent text on COVID-19 reactions, the stream with we-are-shutting-this-and-that-down, stock-exchanges-are-crashing, etc., has continued, now (if not earlier!) reaching ridiculous proportions. France, apparently, is trying to legally force people to remain in their homes absent non-postponable errands—a truly extreme measure. Denmark is blocking Swedes from entry. Etc. While the threat must be taken seriously, the vast majority of the damage until now has been caused by the reactions to the epidemic and by the fear of the epidemic—not the epidemic, it self. While the number of infected can grow much larger than today, I note that we are not dealing with the Spanish Flu or the Bubonic Plague, which posed a truly great risk of death to the infected. Moreover, again, that limiting the infected proportion of the population might well be doable with less extreme means.

We are rapidly approaching a point where even a worst-case scenario of the actual epidemic might cause less damage than fear and counter-measures.

To boot, recommended actions can have unexpected negative effects, be pointless, or see contradictory advice from other sources. For instance, today, I read on SVT’s video-text* that the Swedish police is urging schools to remain open for as long as possible, because the effect** on the police’s work would be too large otherwise. For instance, yesterday, someone noted that closing schools would be ineffective if the same students just met privately outside of school instead, and that students must also be kept at home.***

*The pages are short and not archived, and I have been unable to find a more detailed and linkable source on short notice. (This in part, because Swedish online news-papers are moving more and more towards pay-walling; in part, likely, because the video-text tends to react faster with news.)

**What effect is not specified, but I speculate that they fear having the cities overrun with restless children and teenagers. This especially, as the same page quotes or paraphrases the education minister (Anna Ekström): “Om skolor stängs måste barnomsorgen för dem med samhällskritiska jobb säkras” (“If schools are closed, the childcare for those with critical-for-society jobs must be secured.”) Both, incidentally, supports the school-skeptics claim that the role of school is too much “child storage” and too little education.

***I only partially agree: The claim would hold, if we truly had the same students meeting (and in similar or worse interactions as in school), but this is unlikely to be the case. Groups are likely to be smaller, interactions more restricted to certain “cliques”, and many will prefer to remain at home and/or physically alone anyway. (I certainly would have, at that age, and that was long before social media and smart phones moved social interactions away from personal meetings.) Nevertheless, this type of critical thinking is vital when dealing with far-going measures—and it seems to be missing among journalists and politicians.

Excursion on resistance:
An unfortunate side-effect of trying to avoid infections is that the overall human resistance to infections drops or fails to increase over time, making us less prepared for subsequent epidemics. This both regarding the training of the immune system of the individual (for sufficiently similar infections) and regarding evolutionary pressure. From this point of view, the current attempts to reduce exposure might well backfire in the long-term (assuming that future epidemics are handled similarly).

Excursion on “epidemic” vs. “pandemic”:
My choice of “epidemic” over “pandemic” in my first text was unconscious. However, I consciously stick with “epidemic” in the current text, because it is the more general word and much of what is said would apply equally without a global spread (e.g. assuming the same risks and reactions within an individual country).

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March 17, 2020 at 3:06 pm

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Comparative, superlative, and correct thinking

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During my visits to Sweden, I re-encountered some old grammar material, including the old bull-shit that a comparative compares two entities and a superlative three or more.

This is a good example of how undue dumbing-down* can hurt the students’ ability to think correctly and to gain a correct understanding of the matter:

*Or is the teacher or book author that lacking in own understanding?

The respective character of the comparative and superlative is quite different, and the above descriptions are outright contrary to accepted use:*

*I make some reservations for different situations in different languages, but this applies to at least Swedish, German, and English.

The comparative compares with no regard for numbers. For instance, all of the following are grammatically correct: “I am taller than Tom, Dick, and Harry.”, “I and Tom are taller than Dick and Harry.”, “I, Tom, and Dick are taller than Harry.” Equally correct is: “No-one among the four whose name begins with a ‘Q’ is taller than I am.”—even though there is no object to compare “I”/“me” with. Even dropping to comparing nothing to nothing is possible: “No woman taller than fifty feet is shorter than any man taller than sixty feet.”*

*There are neither women nor men of that size. Note that the paradoxical statement is actually truthful, not just grammatically correct, as long as at least one of the sets is empty.

In contrast, the superlative makes a statement about who in a certain set has a certain characteristic to the highest degree. For instance, “I am the tallest of us four.” says that “I” have the characteristic of being tall to a higher degree than any other element of this set of four. Again, this applies with no regard for numbers: “Out of Tom and Dick, Tom is the tallest.” implies a comparison between two entities—the alleged realm of the comparative. Indeed, even “Out of those among the four whose name begins with a ‘T’, Tom is the tallest.” is correct, despite an implied comparison involving just a single entity. In the same one-person set, Tom is obviously also the shortest, oldest, youngest, thinnest, fattest, best and worst educated, … (It could be argued, however, that the superlative fails on empty sets, due to the resulting weakness of formulation. If so, I would see it more as a matter of syntax than of logic, in that the concept extends to empty sets but is harder to formulate using e.g. English.)

From another perspective, it might* be sensible to view the comparative as comparing two** different sets and the superlative as discussing one single set. (In which case the “two vs. three” thinking is turned into “two vs. one”.) For instance, “I am taller than Tom, Dick, and Harry.” could be seen as “Everyone in set A is taller than everyone in set B, where set A consists of me and set B consists of Tom, Dick, and Harry.”. (And so on, for the other above examples.) The superlative formulation “I am the tallest of us four.”, in contrast, amounts to “In the set A, I am the tallest element, where set A consists of me, Tom, Dick, and Harry.”. Here we also see the futility of thinking in terms of the number of individual elements, as any of these sets could contain 0***, 1, 2, 3, or e.g. 534 elements.

*Reservations: (a) This might be a too abstract approach for people without prior exposure to set theory. (b) This is a spur-of-the-moment idea, which might have weaknesses that I am not yet aware of. (c) The implied use of “taller” on two levels of recursion in this paragraph should be understandable, but would be unsuitable for a formal definition.

**An extension to more than two might seem plausible in as far as e.g. “All elements of the set A are taller than all the elements of set B and C.” is an acceptable formulation. However, this is still better seen, I suspect, as a comparison between just two sets, one of them being the union of B and C.

***With the above reservation for the superlative and empty sets.

Written by michaeleriksson

September 16, 2019 at 11:36 am

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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Guns don’t kill people; people kill people

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For most of my life, I have considered “Guns don’t kill people; people kill people.” to be a cheap and pointless slogan. It is not without cleverness, but the main observation is so trivial as to be uninteresting and I detest argumentation by slogan instead of real arguments.

However, over the last few years, I have encountered several discussions of mass- and school-shootings—all followed by a call for greater gun-control. In light of these, I have slowly grown to understand that this slogan contains a truly profound insight into issues around guns and gun-control, or (more accurately) what is wrong with the debate on these issues:

If a teenage boy goes to his school and blasts away at students and teachers alike, how can questions like “Where did he get the gun?” and “How do we prevent others from getting a gun?” be the first to be asked?!? Is it not self-evident that the first questions should and must be “Why did he do it?” and “How do we prevent others from wanting to do the same?” in an exploration of actual motive, motivation, psychological problems, social situation, …?!? Is it not self-evident that a society (and/or school system) that brings about such events again and again has something much worse wrong with it than too little gun-control?!?

For that matter, would gun-control really even have helped? There are other ways to kill people than guns, e.g. by setting a fire, driving a car into a crowd, building a home-made bomb (instructions are available on the Internet), stabbing someone with a kitchen knife, poisoning a punch bowl, … True, guns might have enabled at least some shooters to kill more people than they otherwise could have, but if someone is driven to the point where these people have obviously been driven, I seriously doubt that a lack of guns would have stopped him.

Here is the rub, or at least a part of it: More gun-control is easy to come up with, easy to explain, easy to paint as (in a contextually unfortunate metaphor) a silver bullet, whatnot. Deeper analysis of what went wrong with the shooter, not just his guns, requires far more thinking and understanding, and might lead to answers that are unpopular. What if, as is my personal suspicion, it turns out that the school or school system carries a significant part of the burden? What if the consequence is that decades of ideas and reforms relating to school must be rolled back?

Now, I do not know what went wrong with the shooters or who/what is to blame, I do not know what the best way to prevent future shootings is, I do not know whether more gun-control would have helped. I do know this: The focus must be on the shooter—not the gun: Guns don’t kill people; people kill people…

Written by michaeleriksson

August 6, 2018 at 9:54 am

A paradoxical problem with school

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An interesting paradoxical effect of the current school system is that it simultaneously prevents children from being children and from developing into adults.

The resolution to this paradox is obviously that positive parts of “being children” are suppressed while the negative parts are enforced and prolonged. (Consider also the similar differentiation into child-like and child-ish human characteristics.)

Children in school are severely hindered in (sometimes even prevented from) just enjoying life, playing, walking around in nature, exercising the child’s curiosity, … At the same time, they are being taught just to do what they are told without thinking for themselves or to taking own initiatives, removed from any true responsibility, kept with other children instead of with adults*, … Play and similar activities, when they do occur, are often restricted and “organized fun”. The positive part of being a child is now curtailed around six or seven years of age; the negative is often prolonged into the “children’s” twenties, when they leave college** and get their first jobs—often even moving away from mother for the first time… In contrast, in other times, it was not at all unlikely for teenagers to already have formed families of their own, having children of their own, working at the same tasks as the rest of the adults, etc.***

*Cf. brief earlier discussions on what type of models and examples are presented to children.

**I stress that this is only partially due to the prolonging of studies per se: The more dangerous part is possibly the increasing treatment of college students as children. Cf. e.g. any number of online articles on the U.S. college system, or how Germany has increasingly switched to mandatory-presence lectures in the wake of the Bologna process. (The latter is doubly bad, because it not only reduces the need to take own responsibility, etc.—it also imposes an inefficient way of studying.)

***Indeed, I very, very strongly suspect that the explanation for many of the conflicts between teenagers and their parents are rooted in humans being built for this scenario, with the teenager having a biological drive to assume an adult role and the parent still seeing a little child. Similarly, that some teenagers (especially female ones) treat romantic failures as the end of the world is no wonder—once upon a time it could have been: Today, the boy-friend at age 15 will usually turn out to be a blip on the radar screen—in other times, he was quite likely to be the future (or even current…) father of her children. Similarly, starting over at 17 might have meant that “all the good ones are taken”.

If we compare two twenty-somethings that only* differ in that the one spent his whole life until now in school and the other went through some mix of home-schooling and early work-experience, not even going to college—who will be the more mature, have the better social skills, have more life experience, whatnot? Almost certainly the latter. Of course, the graduate will have other advantages, but it is not a given that they outweigh the disadvantages in the short** term. Why not try to combine the best of both worlds, with a mixture of studies (preferably more independent and stimulating studies) and work*** from an earlier age?

*This is a very important assumption, for the simple reason that if we just pick an average college graduate and an average non-graduate, there are likely to be systematic differences of other types, notably in I.Q. I am not suggesting that non-graduates are automatically superior to graduates.

**In the long term, the graduate will probably catch up—but would he be better off than someone who worked five years after high school and then went to college?

***Here we could run into trouble with child-labor laws. However, these should then possibly be re-evaluated: They are good in as far as they protect children from abuse, unwarranted exploitation, and health dangers; they are bad in as far as they hinder the child’s journey to an adult. I have also heard claimed (but have not investigated the correctness) that such laws had more to do with enabling schooling than they did with child-protection. To the degree that this holds true, they certainly become a part of the problem.

To boot, schooling often gives an incorrect impression of how the world works in terms of e.g. performance and reward. In school, do your work well and you get a reward (a gold star, an “A”, whatnot); in the work-force, things can be very, very different. Want to get a raise? Then ask for a raise—and give convincing arguments as to why you are worth it. The fact that you have done a good job is sometimes enough; however, most of the time, an employer will simply enjoy your work at the lowest salary he can get away with—why should he spend more money to get the same thing? Similarly, where a teacher will have access to test results and other semi-objective/semi-reliable explicit measures of accomplishment, such measures are rarely available to employers. For that matter, if your immediate superior knows that you do a good job, is he the one setting your pay? Chances are that the decision makers simply do not know whether you are doing a good job—unless you convince them.

At the same time, we must not forget that “being children” is also potentially valuable to the children’s development—it is not just a question of having fun and being lazy. On the one hand, we have to consider the benefit of keeping e.g. curiosity alive and not killing it (as too often is the case in school); on the other, there is much for children to learn on their own (at least for those so inclined). As a child, I probably learned more from private reading and TV documentaries than I did in school even as it were—what if I had less school and more spare time? Chances are that I would have seen a net gain in my learning… I am not necessarily representative for children in general, but there are many others like me, and at a minimum this points to the problems with a “one size fits all” approach to school.

Or look specifically at play: An interesting aspect of play is that it is a preparation for adult life, and in some sense “play” equals “training”. It is true that the adult life of today is very different from in, say, the neolithic, but there are many aspects of this training that can still be relevant, including team work, cooperation, leadership, conflict resolution, …—not to mention the benefits of being in better shape through more exercise. These are all things that schools like to claim that they train, but either do not or do so while failing miserably. Chances are that play would do a better job—and even if it does not, it would approach the job differently and thereby still give a benefit. As an additional twist, I strongly suspect that the more active and physical “boy’s play” has suffered more than “girl’s play” in terms of availability, which could contribute to the problems boys and young men of today have. I have definitely read several independent articles claiming that the ADHD epidemic is better cured with more play and an understanding of boys’ needs than with Ritalin (and find the claim reasonable, seeing that ADHD, or an unnamed equivalent, was only a marginal phenomenon in the past).

Excursion on myself:
While I (born in 1975) pre-date the normal border for the “millennial” generation, I have seen a number of problems in my own upbringing and early personality that match common complaints* about millenials or even post-millenials—and for very similar reasons. For instance, I left high school without a clue about adult behavior, responsibilities, skills, …, having never been forced to confront these areas and having never been given much relevant instruction**, be it in school or at home. Once in college, this started to change, notably with regard to own responsibility, but not in every regard. Had I not left the country as an exchange student, thereby being forced to fend for myself in a number of new ways, I would almost certainly have entered the work-force in the state of preparation associated with the millenials. What I know about being an adult, I have mostly learned on my own with only marginal help from school and family***/****—and almost all of it since moving away from home at age nineteen… My sister, length of education excepted, followed an even more millennial path, with even less responsibility at home, a far longer time living with her mother, whatnot, and, as far as I can judge, still has not managed to shake the millennial way—at age forty. Making own decisions and living with the consequences, taking responsibility for oneself or others, not relying on parents to help, understanding from own experience that the world and its population is not perfect, …, these are all things that truly matter to personal development and ability to be an adult—and it is far better to gradually learn to cope from an early age than to be thrown out into the cold as a twenty-something.

*I stress that these complaints can be too generalizing and/or fail to consider the effects of being younger, in general, as opposed to specifically millennial; further, that the problems that do exist are not necessarily equally large everywhere.

**We did have variations on the “home economics” theme, but there was little or no content that I have found to be of relevance to my adult life. To boot, these classes came much too early, with many years going by between the point where (what little there were of) skills were taught and when they would have become relevant to my life—so early that I would still have had to re-learn the contents to gain a benefit. That home-economics teachers are pretty much the bottom of the barrel even among teachers certainly did not help.

***In all fairness, it is not a given that I, personally and specifically, would have been receptive had e.g. my mother tried to give me more advice than she did. This should not serve as an excuse for other parents, however. Other aspects, like having to fend more for myself at an earlier date would have been easily doable—even had I not enjoyed it at the time.

****Sadly, much of what I did pick up from my mother were things that I, in light of later own experiences, ended up disagreeing with, either because of different preferences or because it was not a good idea to begin with.

Written by michaeleriksson

December 22, 2017 at 7:38 pm

A critical look at PISA

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A few weeks ago, I downloaded a PDF with sample questions from the 2012 PISA math test*; today, finally got around to look at it.

*Linked to and discussed in some article somewhere. I do not remember the details.

I find myself being highly critical, with my main beef being the excessive amounts of irrelevant text, and the associated lack of abstraction and clarity. Consider e.g. the first problem group (“MEMORY STICK”) with formulations like:

Ivan has a memory stick that stores music and photos.

[…]

Ivan wants to transfer a photo album of 350 MB onto his memory stick

[…]

During the following weeks, Ivan deletes some photos and music, but also adds new files of photos and music.

[…]

His brother gives him a new memory stick with a capacity of 2GB (2000 MB), which is totally empty. Ivan transfers the content of his old memory stick onto the new one.

[…]

Not only are such formulations patronizing, more-or-less calling the test taker a child to his face, but they and the unduly concrete formulations distract from the actual math, hide the math, and introduce a too large aspect of reading comprehension*: A math test should test math ability—not reading comprehension**. This in particular when it comes to a test that could put students under time or other pressure, where the translation from text to math could prove to be a stress factor for many of them. To boot, there is at least a risk that the results are misleading through blending out the ability to handle abstract problems. “2 = 2 = ?” is a math problem; “Jack has two cookies and Jill has two cookies. How many cookies do they have in sum***?” is not.

*Likely also other irrelevant factors relating to the translation from text to math.

**I similarly recall once buying a book with mathematical and similar puzzles, likely by Martin Gardner, and ending up throwing it away: Not because the puzzles were to hard, but because I had to waste too much time wading through a sea of text to isolate the handful of data that actual was relevant to the respectively problem—boring and without an intellectual challenge. Only afterwards could I focus on solving the problem, which was what I wanted to do. This is very much like trying to watch a DVD and finding that the actual movie cannot be started before a number of copyright warnings, mandatory trailers, animated menus, …, have wasted several minutes of the viewer’s time.

***As an aside, I saw a similar formulation in a different context, for a younger audience, but using “[…] do they both have”. This is a good example of how incompetent question makers can ruin a question: The expected-by-the-question-maker answer would be four; the correct answer in the most reasonable textual interpretation is zero—there are no cookies that they both have.

Of course, there are many instances where a corresponding translation is needed in a practical situation; however, such translations are mostly not very hard and they tend to differ from the textual for at least two reasons: Firstly, in a practical situation the problem solver picks the relevant facts out of the practical situation—not out of a text by someone else describing the practical situation. To boot, the texts for “math” problems like these tend to not describe practical situations—just theoretical situations someone has translated into practical terms in a simplistic manner. Secondly, the view of a practical situation can often make aspects of the problem, thought errors*, unexpected complications, whatnot, obvious that are not so in a text.

*A good example of such obvious thought errors is one of the few problems I got wrong: “The ice-cream shop”, question 3. The question requires placing sets of chairs and tables within a shaded area, under a constraint regarding the walls of the surrounding room. Being in too much hurry, I just focused on the shaded area without considering that the walls did not coincide with its borders. This error would, admittedly, have been easy to avoid, had I taken my time—but it would have been virtually impossible to commit when standing in the physical room. This type of textual problem differs in quality from a real-life problems (to more than the roughest approximation), in a manner similar to how e.g. racing a car in a computer game differs from doing so in real life.

An added disadvantage of these text-heavy problems is “cultural loading [bias, whatnot]”*: The text introduces opportunities for such problems that would otherwise not be present, especially in light of potentially suboptimal translations (also cf. below).

*I am normally skeptical to complaints in this area, seeing that e.g. I.Q. tests tend to be abstract; that cultural knowledge tends to lower differences between groups, through adding an irrelevant factor; and that the cultural difference from test taker to test taker is usually comparatively low to begin with. Here we have a test intended for extensive global use, where little or no effort has been put in eliminating cultural variations, where there is an additional severe translation complication—and where the very point of the test is to compare and evaluate different countries! (Whereas e.g. I.Q. tests are conceived to compare and evaluate individuals.)

Some more specific criticisms:

  1. A few the items come with translation notes (the document being intended more for test makers and test administrators than test takers). However, there is typically no obvious reason why a specific point has a translation note and so many others do not. Worse, the translation notes are often highly specific, e.g. referring to translation into French (but not German or Swahili)*. To me, these notes mostly serve as a proof that the test is suboptimal.

    *For instance, `Translation Note: In French, “penguin” is “manchot”.’ Do they consider specifically French translators to be idiots? Is there some (unmentioned) odd complication around penguins in French? (If so, are there really no other language with the same problem?) Of course, if the questions had been made abstract, there would be no need to mention penguins in any language…

  2. There are quite a few unfortunate formulations that could lead to unnecessary errors—and one where the formulation is outright incorrect: “Question 4: MP3 PLAYERS” states “The normal selling price of the MP3 items includes a profit of 37.5%.”, which would normally mean that 37.5% of the overall price is the profit. However, what is actually meant is that the price includes a mark-up, not a profit, of 37.5%. It is true that a later sentence claims “The profit is calculated as a percentage of the wholesale price.”, referring to the same profit; however, in combination, this is an extremely non-standard usage and in order to take this into consideration, the reader basically has to ignore the fact that he has a clear claim. A reasonably analogy would be a question claiming “a gin-and-tonic includes 37.5% gin” and then slapping on a “the percentage is relative the amount of tonic”. To boot, even a careful reader would not necessarily make the corresponding modification, because it would be equally conceivable that the several uses of “profit” referred to different concepts*. (This was another question I got “wrong”; however, unlike with the “ice-cream shop”, I put the blame on the test makers.)

    *E.g. in a scenario of “Given the profit (as a percentage of the selling price), give the profit (as a percentage of the wholesale price).”, incidentally showing that it would be better to use “profit” for the amount only, and otherwise speak of e.g. “profit margin”.

  3. “CHARTS” uses a poorly structured and hard-to-read diagram* as data input. Coloring, spacing, and lining contribute to introducing an entirely unnecessary complication; it can even be disputed whether this type of diagram was suitable for the data at hand**. Being able to read a diagram is a valuable skill, but here it is not just a matter of understanding how to read data from the diagram in principle—there is also an optical complication that made my eyes water.

    *Generally, the examples using some type of excel-style diagrams give an argument that such diagrams are more-often-than-not inferior to a table with the same data: Save diagrams for complex data where the visual can truly help in detecting trends and connections—do not throw them together willy-nilly because “diagrams are cool”.

    **A bar chart; a line chart would would likely have been more appropriate. It can also be disputed whether it really made sense to combine all four entities in one chart, or whether one chart per entity would have been better. (Assuming that we do not use a proper table to begin with…)

  4. At least question 5 of “CHARTS” is ambiguous through the talk of a “trend” that “continues”: When we speak of a continuation, it is the question what continues. Here we deal with diminishing CD sales, and in a real-life scenario, it would be highly likely that a continuing trend would be measured by a percentage (e.g. sales diminishing by twenty percent per month) or otherwise be measured relative the remaining sales; however, looking at the previous data, from which the extrapolation must be made, it appears to be more of a fix drop. (The instructions for the test administrator do indeed speak of a “linear trend”.) When extrapolating a trend, however, a model is needed, and it is highly simplistic to just assume e.g. a linear trend—even when a handful of data points point towards an approximately linear relationship. There are other models that might match the data, especially when factoring in the risk of a diagram distorting the data ever so slightly.*

    *Indeed, using my original numerical approach, with approximate read-outs, I repeatedly landed above 400 (compared to 370 as the allegedly correct answer), on at least one occasion close to 500. (Note that this is still close enough that I would have picked the right option from the multiple-choice entries.) Only after using a knife to approximate a straight line from A to B did I find 370 acceptable. However, even this is approximate, because I had to guess where the crossing line for July was… (Note: I am unaware of the equipment available to the test takers. If graded rulers are allowed, better “measurements” are possible, and correspondingly better outputs are to be expected—but at a cost of boring detail work that would have been unnecessary, had the test makers had the common sense to use a table of data instead of a diagram…

  5. “Question 2: PENGUINS” is extremely naively modeled and/or poorly formulated, to the point that a bright* student could** get caught up in time-consuming speculation about the correct-yet-unrealistic assumptions to make. The hitch lies in “By the end of the year 20% of all the penguins (adults and chicks) will die.”: The eventually needed model assumes that the deaths will all occur at the end of the year (or at least after the other main event of the year, the raising of a chick), which is entirely unrealistic. In reality, deaths will occur through-out the year. Had the formulation been “At the end of the year […]” this would have been OK—unrealistic, but without ambiguity. However, this is not the formulation used. Now, the formulation used is inconsistent and ambiguous, and the “at” interpretation is a quite reasonable way to resolve the issue—but it is not the only way: The resolution could equally be “[…] will have died.”, which is consistent with a more realistic model and is what would be expected, were we dealing with a real-life penguin situation. Unfortunately, with this resolution the problem becomes under-determined…

    *The less bright tend not to see such complications, which can be to their advantage when it comes to simplistic tests—but to their disadvantage (and science’s…) when they try to become scientists.

    **As was I, but I had the leisure of not being under time pressure; and have enough knowledge of poor test questions to come to the “right” conclusion fairly fast.

  6. “SAILING SHIPS” deals with a technology that seems dubious and/or where weird fictional data have been used to describe a real technology. The inclusion of an apparently actual trademark (“by skysails”) makes it outright shady—is this a commercial plug?

    Notably, the intention is to use a sail attached to a ship by a line, hovering considerably higher up than a regular sail, because “the wind speed is approximately 25% higher than down on the deck of the ship”. Now, this would probably imply a maximum of 1.25 * 1.25 = 1.5625 gain in “push” (both the number of air molecules hitting the sail and the average momentum of individual molecules increases by a factor of 1.25), but with a minimum that could be considerably lower, because the faster the ship goes the lesser the net air speed and the lesser the advantage. At the same time, one example seems to aim for a 45 degree angle, which would divide the force into components, with a proportion of 1/sqrt(2) going horizontally and the same (uselessly) vertically. We then have a maximum gain of 1.5625/sqrt(2) ~ 1.1: The 25% higher wind speed has resulted in a 10% improvement… Barring other advantages (e.g. the possibility to use greater sails) this is hardly worth the trouble. True, the 25% higher wind speed could still give a higher overall speed by more than 10%, because the positive force will only cease after the ship hits the wind speed; however, firstly a higher ship speed means a greater loss in terms of water and air resistance, secondly this technology is not intended for pure sailing ships, but as a help for diesel ships. If the data provided are realistic, I am puzzled as to what the actual point would be.

    Or take specifically question 4: A sail is here alleged to cost 2 500 000 zeds*, while diesel costs 0.42 zeds per liter, which implies (with some other assumptions made in the text) that the sail will pay for it self after 8.5 years! Compare this to the reasonably to be expected costs for regular sails and consider the risk that the sail has failed and needed replacement or extensive repairs before 8.5 years. Sigh… An online source gives the current price of diesel as “1-Dec-2017: The average price of diesel around the world is 0.99 U.S. Dollar per liter.”, from which we can give a rough Dollar estimate of the sail price as 5.9 million**—what the fuck?!?!

    *A fictional currency used for several examples.

    **2 500 000 zed * 0.99 dollars/liter / (0.42 zed/liter)

    (If I were to analyze the technology more thoroughly, as opposed to a test dealing with the technology, I would have additional objections and/or points needing clarification. How, e.g. is the sail handled during a storm without having to cut it loose, to a horrifying loss of money?)

I probably had more objections when going through the questions the first time around (with the purpose of solving the problems), but I have lost my energy here, being about half-way through on my second iteration (with the purpose of writing this post). There was definitely at least one case of “faster speed” or something in the same family, showing a conceptual confusion that no mathematician should underlie: A vehicle can be fast or slow, but its speed cannot; an item for sale can be cheap or expensive, but its price cannot; etc.

As a final note: There was a third question that I failed, namely “Question 2: REVOLVING DOOR” (i.e. the penultimate question). Lacking in concentration, I calculated (I hope, correctly) the linear width of the opening, but the question actually asked for the “arc length”. I take some comfort in the arc length being easier to calculate, but would of course still, correctly, have been marked down.

Written by michaeleriksson

December 17, 2017 at 12:40 am