Many McGill Education Students Cannot Calculate an Average | Hacker News Reader

Many McGill Education Students Cannot Calculate an Average

stuartspencestuff.blogspot.com

289 pointsj2kun274 comments

I teach high school, and a colleague of mine went to an education conference a couple weeks ago. She was sitting at a table with three elementary school teachers. They were talking about how to gauge student progress when the students had taken a 100-question test, and a 50-question test. None of the three teachers realized that you had to scale the test scores before making a comparison between the two tests. These teachers thought you could just look at the number of questions the students got correct, and see if the students "score" went up.

My colleague pointed out that the questions on the 50-point test had twice as much weight as the questions on the 100-point test. One of the three other teachers realized their mistake - the other two just chuckled and said it didn't matter.

This isn't just frighteningly ignorant, it ends up having a devastating impact on many young people. One anecdote: I knew a bright young student who loved learning, but hated school. Why? He took algebra and french in 8th grade; he passed algebra and failed french. When he got to 9th grade he was placed in algebra again, and french 2. The school would not budge from its original placement; I don't know the rationale. He failed algebra because he refused to do any homework, and failed french because he couldn't make any sense of the class. I want smart teachers to take control of education so this s* doesn't happen nearly as often as it does.

Also, I've taught middle and high school math for 20 years now, mostly to students who struggle with math. I don't think I've had many groups of students who could come up with six different answers for a simple average problem.

Sounds like passing a student with 80% grade, only with 60%. It's like passing a student who didn't master 40% of the content, and compounding it over and over again with each grade level, until eventual nothingness.

That's what it means to pass a student with a B, C, or an F. This is not quite the same thing as mastery of the subject, but it's a good proxy. Even an A student will miss some stuff.

I had a conversation with a math teacher from another school not too long ago. Both of our schools require a minimum of two credits of math to graduate. My school allows students to spread this credit out developing a deeper understanding of basic math, and beginning algebra. His school requires everyone to receive a passing grade in the equivalent of Algebra 2. The lowest passing score at my school is a B-; at his school it's a D-.

We have a reputation for being an "easy" school, so I asked him what the value of earning a D- in Algebra 2. His response: "At least they've been exposed to higher math." That's such an elitist answer, and it does such a disservice to students.

The interesting part of the story is that he started to question the value of a D- when asked in this way. He stopped comparing basic algebra to Algebra 2, and started comparing a B- in Algebra 1 to a D- in Algebra 2. It's an interesting comparison.

Sounds like your school is suffering from grade inflation. The average grade used to be a C. (At my college, it still was.) If you tell the teachers that a C is a failing grade, they will not give a C grade to a student who's doing an OK job in their eyes.

It's not grade inflation. We're a small alternative high school, and it's easier for us to do the right thing for students, even if it means going against existing bureaucracy. The smallest unit of credit in our traditional high school is 0.5 credits; at our school it's 0.25 credits. We grant passing grades for the parts of a class students demonstrate an understanding of, and grant partial credit for a class. This mitigates some of the issues involved with averaging over the course of an entire semester.

Usually, when someone earns a B-, they do have a basic understanding of the material they were learning. A student who earns a D- with 0.5 credit at the traditional high school will usually earn a B- and 0.25 credits from us. At the traditional school, they're "done" with that class. At our school, they've got to do something to demonstrate further understanding. It's not a perfect system, but it's not as simple as grade inflation.

Is it more useful for your grade to tell you how much of the topic you know in relation to the other students in your class (C = the average grade) or for your grade to tell you how much of the topic you know (A = you understand everything that was taught, B = you understand most of what was taught, C = you understand some of what was taught...)

If you fit an entire class on a bell curve and give out 1 A, 2 B's, 4 C's, 2 D's and 1 F but the highest grade was actually a 32% would those grades be useful information? Sure, the A student knows more than the C student ... but none of the students really understand any of the material.

Edit: by "how much of the topic do you know" I actually mean "how much of what was taught of the topic do you know"

Ie, if the teacher taught you how to graph a linear equation and you can graph a linear equation, then you should get an A. If you can't graph a linear equation, you should get some grade less than an A. If nobody in the class can graph a linear equation, then what use is it to give an A to the person who can't graph a linear equation, but does it less wrong than everyone else?

How much of the topic I know? That would be vanishingly small for any grade before college, and barely a blip for classes in my major at the end of college. No, I don't think that's useful.

'We have a reputation for being an "easy" school, so I asked him what the value of earning a D- in Algebra 2. His response: "At least they've been exposed to higher math."'

When you say Algebra, I assume you mean what most of us learn in pre-college schools? As opposed to what a mathematics major in college would call "Algebra"? If so, that's hardly even "exposure" to higher math, that's more just a demonstration that there is a such thing other than raw numeric arithmetic.

> That's what it means to pass a student with a B, C, or an F. This is not quite the same thing as mastery of the subject, but it's a good proxy. Even an A student will miss some stuff.

Grade might be a proxy for mastery in some situations but it's likely not in the majority. Grade is more often than not a combination of mastery, ability to take tests, willingness to do homework and an accounting of how often you show up.

> I knew a bright young student who loved learning, but hated school.

Of course. Any bright student realizes that school has nothing to do with learning, and furthermore often interferes with it.

If schools existed to provide food instead of education, they'd start by lining up all the kids at the beginning of the week and doling out a single crumb to each. And if those crumbs happened to be rat turds instead of crumbs of bread, they'd never notice. Every once in awhile, the school stumbles across the rare child that is starving, absolutely ravenous.

How long do you think it'd be before that child started to hate school?

> want smart teachers to take control of education so this s* doesn't happen nearly as often as it does.

Teachers aren't in control. They're prisoners of the classroom every bit as much as any child is. Maybe more so, they can't hope to be expelled or to flunk out or to graduate. Teachers will never be in control again, if ever they were.

>bright student realizes that school has nothing to do with learning

Depends on the high school and teacher. My high school (and primary schools) had really great teachers and they motivated me to learn things I otherwise would not have. Young people often need a push to learn things that they don't immediately see as useful. Schooling does interfere with learning, but when the stakes are high (getting into a top college) we might as well make the most of it if the privileges are afforded to us.

> Depends on the high school and teacher.

In the US, each student will have between 20 and 40 teachers by the time they graduate highschool.

Thus, you can't just hope to play the public education lottery and get all good teachers for your kid. Even if things work out better than could possibly be imagined, that's what, 10 or 15 good teachers, quite a few more mediocre and 2 or 3 bad ones?

Sorry. The damage that a bad teacher can do outweighs much or all of the good that the good teachers can do.

If your kid would have 40 doctors throughout his life, only 2 or 3 of which were quacks, would that make you happy? Would you say "but the quacks will probably be the dermatologist anyway and not the surgeon, so it's ok"?

I wouldn't say that.

The only way for any of this to work out is for the impossible to happen, for nearly all of teachers everywhere across the nation to be good teachers. The distribution is pretty natural, the various colleges of education don't act as a filter, and schools are co-opted to do too many non-education tasks for that to ever be possible.

> Sorry. The damage that a bad teacher can do outweighs much or all of the good that the good teachers can do.

> If your kid would have 40 doctors throughout his life, only 2 or 3 of which were quacks, would that make you happy?

I don't think this analogy is quite right, nor is the conclusion you are using it to illustrate. A kid, especially a smart kid, knows when a bad teacher is bad and can just coast through the class (bad teachers nearly always err towards teaching too little and therefore being easy).

The worst case scenario in most subjects is they have a hole there, which in the case of non-STEM subjects is not catastrophic because they (English, history) are more about general principles rather than specific facts that nearly all adults forget. In STEM subjects, it can be worse because they build on one another.

I guess a truly bad teacher can deny evolution or something like that, but that typically only happens in controversial subjects where a student should have prior knowledge that there's a controversy. If they aren't, they will figure it out soon enough.

But really, a bad doctor can kill you. A bad teacher leaves a hole that a self-motivated person with natural curiosity can completely fill. Take programming (I'll assume you're a developer). If one of your CS profs had just not bothered to teach a specific course, would you be able to live through it? Of course, as attested by the many successful developers who are self-taught. When you grow up, you have to take responsibility for learning for yourself. If some students have to do it sooner than usual, that has pros and cons.

> A kid, especially a smart kid, knows when a bad teacher is bad and can just coast through the class (

There are many sorts of "bad". Sometimes they're simply ineffective or uninterested teachers. Other times they're borderline mentally ill and abusive.

How many times does the child need to be mocked or called names for lasting damage to happen? Can you judge this before the fact? "Oh my boy Timmy, he can be called names at least a dozen times with no ill effects, and you look like you'll only do that 8 times, Mrs. Kuntzenheimmer."

> guess a truly bad teacher can deny evolution

Or lock them in a closet. Or tell them "girls can't do math" so many times they believe it, and roll their eyes derisively if any of the 9 yr olds object. Or fail them out of spite... or have them expelled without true cause.

Oh man, there must be a 100 different kinds of bad. And few children have the life skills to mitigate that (few adults, if we're honest).

I have a different perspective on this. School, especially in the later part of K-12 is many different things. There is a lot of bullshit, academically speaking. I'd say about 2/3 of my highschool teachers were pretty mediocre. Then there were the good ones. I actually liked studying math in high school because I got placed in advanced classes, and in a grade above my own. It provided a challenge, but also the teachers did a good job of explaining what I might use this math for: becoming an engineer or a researcher. The 10th grade algebra teacher actually had us do labs that would normally be reserved for physics classes: let's measure the swing of the pendulum and show that it's a harmonic oscillator empirically.

So I wouldn't say "I hated school", but I would say I hated my gym, art, and health classes for sure (don't get me started on sex ed. and I grew up in a fairly liberal state).

I enjoyed the learning part of school, apart from classes I had no interest in, and was terrible at.

The alternative to school currently is homeschooling, and, I do not feel that I would be able to teach my children the range of topics covered at school, and ensure they understood them, even with a university education in a STEM subject.

My role therefore is to pique their curiosity about life in general and the universe, and allow them to explore questions, and show them why the world is so cool. This then enables them to use what they have learned in school to form bigger questions and answer them themselves.

"If schools existed to provide food instead of education, they'd start by lining up all the kids at the beginning of the week and doling out a single crumb to each. And if those crumbs happened to be rat turds instead of crumbs of bread, they'd never notice. Every once in awhile, the school stumbles across the rare child that is starving, absolutely ravenous.

"How long do you think it'd be before that child started to hate school?"

I just wanted to tell you that was the-truth-that-hurts so much it literally made my eyes well up. I just... it's... sadness. Sickness.

That is pretty sad.

Having gone through the Quebec education system and now reflecting over it, I can relate to that student. It seems to me (of course I'm biased but...) that french and history were always seen as more way more important than math classes and that is very unfortunate.

I was very lucky to be able to skim through french and math for most of high school. I didn't have an interest in french grammar and thought I was just horrible at math so I just skimmed through it and assumed it was normal. It wasn't until my first year of CEGEP where I had a very good math teacher and a great group of friends help me catch up and discover the beauty and usefulness of math. I would've never thought in high school that I would end up becoming an electrical engineer.

I'm sure I'm not the only one from Quebec with a similar story and from your experience, it doesn't seem like things are going in the right way.

I don't think you went to the right school. It was made very clear to my classes from sec 3 onwards that taking "higher level math" (436, 536) would open a lot more doors in CÉGEP and university.

On the same topic, I firmly believe that CÉGEP offers the best general education in the world for 17 to 19 year olds.

How can you say best education in the world? Have you studied all over the world to have a point of comparison?

I've been to three different cegeps and they all had their share of clueless teachers.

I'm pretty sure he's referring to the model, not the particular implementation.

I agree with you. I have a lot of friends in bot pre-uni (as myself) and in techniques and I find it awesome how a CÉGEP strikes a good balance between general education and specific classes.

> french and history were always seen as more way more important than math classes

Where I went we could chose advanced math classes in the last 3 secondary years.

Most of the students would not take french classes seriously and I think the CEGEP's french standardized exam has a high failure rate.

Oh, the school/program I went to I was forced to take 436 and 536 (which is a good thing). However, just the general atmosphere was history and french is important, math, meh.

It's a bit sad IMO that in our current education culture, we portray the study of math and science as being somehow opposed to the study of history and culture.

I find the them inextricably linked. I'll never forget the human stories of mathematical discoveries from Erastosthenes to Newton, up to the present. And rigorous quantitative and symbolic reasoning is indispensable when discussing socio-cultural phenomena at all scales.

I wish math and science were taught with more historical narrative than they are, and likewise, that the humanities were taught with more mathematical/scientific rigor than they are.

I also think it would open up both to people who would otherwise have a hard time grasping them.

EDIT: added conclusion

I think it's the idea that math and science are the same regardless of their history. You can learn the history of them, but the answers don't change when you do. On the other hand, your answers about historic and cultural questions can change drastically depending on how informed you are.

Also, the level of rote memorization required vs. logic and analytic thinking. You think math and science could be improved via learning their history; I think history and culture can be improved by learning more about the reasoning behind individual things. Less focus on when and what and where; more focus on why and causes.

The very same thing happened in Portugal, where the Ministry of Education's guidelines for gauging teacher performance included taking the mean of a test graded in percentage points with another evaluation on a 1 to 5 scale.. by adding them and dividing by two!

Made even more embarrassing by the fact that the Minister is a mathematician.

He did what? Can you link a citation for that one please (pt is fine)?

If folks in Quebec can speak French, it should be pretty easy.

Having French as your native language doesn't mean French class is easy, and a sizable part of Québec's population doesn't speak French natively.

A sizable portion of Quebec's population east of Montreal doesn't speak English at all.

Imo, these results are not surprising (but sad regardless). There's similar studies in all fields. Economics is a prime example (with a couple of well publicized studies).

A little "closer to home"...I've listened to quite a few software developers who regularly A/B test and always implemented B if it had more whatever_unit than A. Significance be damned.

Statistics is pretty scary/best ignored on all levels I guess.

I was working in a nightclub during my college years and I've met many, many people who loved learning yet hated school and dropped. There is an immense pool of potential being wasted out there.

I'm one of the lucky few who did drop out of school yet found a job as a software engineer on AAA games; the job I wanted since I was a kid with my first NES. I don't think having a degree would've made much of a difference other than wasting more years of my life and putting me even more in debt.

What made me get the job as well as keep it and rise faster in the company than those with actual degrees is finding the discipline to learn on my own every day and trying to understand how things work and why. In school I always felt slowed down by the rest of the class or by bad teachers.

> I want smart teachers to take control of education so this s* doesn't happen nearly as often as it does.

This is the job of parents, not teachers. What does take control even mean? Public school teachers have no control.

> "What does take control even mean? Public school teachers have no control."

If they already had control, then they wouldn't need to take it, would they?

Good example of out of context quoting of even a short post. He said it's not the teachers' job to have the type of control that the original poster was saying that teachers should seize.

He responded to a proposal that it should be with, depending on how you interpret it:

1) An assertion that it is not currently the case. (Probably true, but completely missing the point of a proposal)

2) An unsupported assertion that it should not be the case. (An unsupported opinion in response to a thought out opinion isn't adding much to the conversation. He may as well simply respond "No, your opinion is wrong." A better comment would explain why he has that opinion.)

Many comments here are anecdotal. Quebec outperforms other Canadian provinces in most math rankings (Programme for International Student Assessment). Globe and Mail on the subject:

> But there’s also good news. Canada’s declining performance in math isn’t equally distributed across the country. When results are broken down by province, there are shocking differences. And at the top of the class is Quebec.

> While the math scores in most provinces were sliding over the past decade, Quebec’s already strong results held steady. Students in Quebec outperform their rest-of-Canada peers in every mathematical category. Quebec students ranked sixth in the world, tied with Japan and Macao, and ahead of the Netherlands.

> There is no single, silver-bullet solution to solving the problem of declining math scores in the rest of the country, but Quebec is clearly doing something right. Exactly what is more than a matter of opinion. The OECD’s assessment teases out what appears to be working in those countries that perform best in the PISA survey. Quebec’s education system has a lot in common with them.

http://www.theglobeandmail.com/globe-debate/editorials/quebe...

Oh well:- http://www.theguardian.com/education/2014/may/06/oecd-pisa-t...

> Quebec outperforms other Canadian provinces in most math rankings

Given what we have learned here today, I'm wondering if Quebec just has more questions on their exam :P

> They were talking about how to gauge student progress when the students had taken a 100-question test, and a 50-question test. None of the three teachers realized that you had to scale the test scores before making a comparison between the two tests.

That's not necessarily true at all. It's a function of the difficultly of each question. Possibly it could be generalized to the difficulty of each test -- where perhaps the questions on the 50-question test were twice as difficult as the questions on the 100-question test.

The best way to resolve your concern is to never assign a percentage per test -- just assigned points to each question based on difficulty. Then accumulate points and take an average only at the very end. But, short of that, taking a weighted average of the two tests is not necessarily any more correct than just taking the average of the percentages.

> My colleague pointed out that the questions on the 50-point test had twice as much weight as the questions on the 100-point test.

Actually there wouldn't necessarily be any correlation between the percentage of questions answered correctly and whether the students were making progress, and arguably that answer is even worse than just comparing the raw scores.

I've got a slightly subtler but similar story. I had a math teacher in high school who would curve her test scores to the lowest top score from any one class. In other words, if she taught three identical 10th grade Trig classes in a semester, for each test she would take the three top scores (one from each class), and curve the test to the lowest of those three scores. It's a reasonable enough idea, I suppose, since different classes will have different questions and thus spend slightly different amounts of time on various parts of the material.

The trouble was that she would not give over 100% to the people who earned a higher score on the test than the curve. Her tests were not weighted, meaning that Test-A curved to 85 points was actually worth less than Test-B curved to 90 points. (Supposedly, the then-new district-wide computer grading system couldn't handle such arithmetic complexities.)

At one point, I received a score above the curve. Let's say I got 90 of 100 points, and the curve was 85. Later, when I saw my grades, I asked why I was only given an 85/85 on that test. She explained that she didn't give "extra credit," and she wouldn't budge. She would say things like "you got 100% of the points, so there's no reason to complain." I asked, then, if I could at least be given a 90/90, and she very confidently explained to me that 100% of the points on the test is the same regardless of the total number of points. She would not entertain the notion that a 90/90 is better than an 85/85, much less that a 10th grader might be able to correct an arithmetic mistake of hers. I even presented the example of changing a 100/100 assignment to 1,000,000/1,000,000 and noting the affect on the total grade, but she would have none of it.

As you can probably tell, I'm still bitter about that test.

People often underestimate the bitterness that these experiences create in smart people. It's not a petty thing, either - it's life changing in many situations.

We need smart people to take control of schools.

The road of life is bumpy. I would not seek to smooth out the few remaining bumps in school. We are already in danger of creating fragile people who shatter at the first bump.

All this, even if the teacher's idea were quite wrong - but it's not. By "clipping" the score, the teacher created a hybrid between curved and uncurved grades. If curved and uncurved are acceptable, why not the hybrid?

Neither curved nor uncurved grades remove points that a student earned from the student's score. Uncurved grades obviously just give you what you earned, and traditional curved grades give you more than what you earned. This "hybrid" gave me *fewer( points than what I earned.

> and traditional curved grades give you more than what you earned.

Traditional curves (mapping grades onto a bell-shaped curve based on the class average) do potentially give lower scores than standard 10% brackets (90% = A, etc.)

There is a common thing used in some places (particularly secondary -- don't know that I've ever seen it higher ed) often called a curve which just takes the highest grade in the class or the grade at a certain percentile point and calls it 100% and renorms scores based on that, and that system never gives people lower than the pre-adjusted score. That may be what you are thinking of.

Yes, traditional curves do that, and that is a laughably preposterous practice.

Smoothing out bumps or making it "easy" and worrying about fragile stuff is totally unrelated to acting intelligent.

In early grades, I had amazing teachers. Plus they had "enrichment" where they pulled us out of less-useful classes, gave us a lab and a dedicated teacher who just said "hey, what are you interested in?" I excelled there.

After moving a few times, I unofficially dropped out of school in 7th grade (12 years old), after grilling my teacher and realizing she didn't really have a clue. Other teachers were worse.[1]

I attended for a few more years (partially coerced by illegal police force[1]), then at 15 dropped out for good by leaving the country.

Things turned out OK for me. But I lost a LOT by not getting a real education, not having a chance at college. Just the lack of maths alone takes a lot of effort to rectify. Yes, it's still my fault, but the system shouldn't be encouraging 12-15 year olds to make such mistakes.

Kids will have enough bumps with bullying and school life in general. Adding idiocy bumps that make a mockery of education and intelligence just make kids cynical and tune out.

(It also makes such graduates more OK with the idea of corruption, stupid bureaucracy, mediocrity, etc. - a shrug and a "that's how things work". Such things should be vigorously fought, not beaten into children.)

1: One "science" teacher: "Carbon-14 dating is a lie told by scientists that hate god."

2: Somehow there was enough of a "problem" to haul me in front of a judge who pre-emptively revoked my drivers licenses for 3 years. I told him I'd just get a pilot's license instead and enrolled in flight school the next month. I also found it hilarious how people in court used the term "infinite wisdom" when referring to the judge. Illegal part was that I am not a U.S. person so they didn't have jurisdiction for enforcing mandatory schooling any more than they'd have on any other B-2 visa'd tourist.

> Smoothing out bumps or making it "easy" and worrying about fragile stuff is totally unrelated to acting intelligent.

I stared at this sentence for a while and didn't quite decode it. Sounds like you've had your share of bumps. I don't know how old you are, but you may eventually decide you wouldn't change a thing.

But quite a few kids raised in good environments seem to have missed our on bullies (real, not cyber), and stupid, cruel authoritarian teachers.

This results in a naive and fragile person who is not equipped for the real world.

Have you read The Diamond Age? Neal Stephenson makes a similar point when the headmistress (really YT from Snow Crash) answers a complaint about a teacher.

Sorry, poorly written. I'm just making the point that there's a far cry from producing "fragile" people/overprotecting versus creating and defending a stupid system.

In the former case, it can be good to let kids have to get over some problems or deal with unfairness.

In the latter, encouraging or defending stupidity on the part of teachers or the school system only encourages cynicism or acceptance of such brokenness. School systems should try to encourage the ideals, teach people to stand up to bad things, not accept mediocrity, etc.

I'm 33 and have kids of my own, if that's relevant. I liked Snow Crash but don't remember those specifics.

Here is a story of something that happened to a friend of mine. This is from New Zealand.

He was taking 7th form Latin. Latin has enough students in the 3rd form but by the time you get to 7th form (The final year before university) there were only 20 or so students in the entire country taking the course. He was taking the course by correspondence because the school obviously wouldn't provide a teacher for a single student.

He scored 95% in the final exam. In NZ the end of year standardized tests are scaled to fit a curve across the entire country. He was scaled down to 43%. A failing grade.

Obviously in this case the only students that would bother taking Latin all the way up to 7th form are going to people who care enough about it to learn it well. The standard scaling method used doesn't make sense at all with this group of students.

He wrote a letter to the education minister of NZ complaining about this issue. Months later he got back a form letter explaining why test scores are scaled with no regard to the special circumstances.

Can you clarify what you mean? How does a curve cause a 95% to get scaled down to a 43% failing grade?

If you have 10 people who score:

    91%, 92%, 93%, 94%, 95%, 96%, 97%, 98% 99%, 100%

and scale the grades from 0-100, those students' curved grades are:

    0%, 11%, 22%, 33%, 44%, 55%, 66%, 77%, 88%, 100%

In other words, they turn the students' grades into their ranked percentile within their cohort. It's an absolutely brain-dead decision.

Oh, I see. Essentially curving from both ends, to fit a desired distribution.

That idea has never made sense to me, at least if the class is using a system where having a score less than some specific percent implies failure.

Stack ranking does the same to employees in elite teams in real-world companies.

No it means the exam was way too easy. 90% of the questions were giveaways. If its ok to fail 400 out of 1000 students doing English, then its ok to fail 4 out of 10 doing Latin. Once you adjust for the easiness of the exam, he actually did not do too well.

Are you trolling? With a subject like Latin, the actual situation is that all the students are really good by the time you have only 20 students left in the whole country. The exam is probably not easy at all, and someone who didn't prepare well would get a much worse score.

You are assuming that it makes sense to make grading to a curve with a sample that is highly selective. It does not.

(I did not study Latin. Just as an item of curiosity, my country's public radio service YLE broadcasts regular radio news in Latin. You can listen and also read some of the stuff here: http://ohjelmaopas.yle.fi/1-1931339 )

In related news, the fifth-best player on an NBA team is a failing basketball player, because 80% of the starting players are better than he is.

You try to fit the marks to a normal distribution. It assumes that all classes/courses have the same distribution, with the same midpoint and that the only variation is that the test was too easy.

So, (simplistically) if the expected midpoint is 75, and everyone is in the 95-100 range, a grade of 97.5 would be shifted down to 75.

It does penalize students for having really smart friends and getting together to take a difficult course.

http://en.wikipedia.org/wiki/Grading_on_a_curve

Curving only makes sense when there's a normal distribution. Sounds like, at that point, the students were no longer in a normal distribution and therefore curving failed.

At the risk of sounding completely ignorant, what's wrong with what she did? In most classes I've been a part of, your total score was based on a weighted average of scores on particular tasks. The normalization here is a typical test curve -- a normalization that attempts to compensate for measurement error in one particular test, independent of the total class score. That's why she referred to "extra credit".

This was explicitly not the case in this class. A test curved to 85 points was worth less than another test curved to 90 points.

And honestly, even if each test was normalized to 100 points after the curve, I would still object (on ethical grounds, not mathematical) to not being given >100% when the test is curved to below my score.

Ah, I didn't catch that. That's... annoying.

Perhaps you might object mathematically too. I think of a curve as fitting the test scores to a specific distribution as a corrective to testing error. It's not the fitting that's the issue, it's how justified the target distribution is. If you truncate it, you have to justify doing that somehow (all prior test results had that distribution?). Of course, if the sample distribution squashes it enough, you might end up clustered at 100% anyway, but...

http://www.nytimes.com/2014/07/27/magazine/why-do-americans-...

I believe you might find this article very interesting. It is a discussion of how math education has changed over the years, and has strong words about the very problem you mentioned of the teachers being ignorant of math and passing that ignorance on to those they teach.

It's the simple stuff that kills me.

My friend's wife is an elementary school teacher and she's one of those really arrogant people who always has something more "intelligent" to say than everyone else.

She recently took over a project I was working on with her husband (my friend) so I've been emailing a fair amount with her. Her grammar is unbelievable for a school teacher. I mean, she doesn't know the difference between your/you're, their/there, then/than!

This is consistent with this review [0] I once read of a book [1] about mathematics teaching in elementary schools.

[0] http://www.ams.org/notices/199908/rev-howe.pdf

[1] Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States, by Liping Ma

Real story:

In Hungary students are rated from 1 to 5, where 5 is the best score and 1 is the worst. During the semester you have multiple tests (both verbal and on paper) each giving you a score between 1 and 5. Your final score is the average of these rounded to an integer. These final scores are the only important measure when you apply to study further, nothing else matters.

I had a [5,5,5] and had to take a verbal test which I didn't prepare for. My biology teacher decided to rate it as "three fourth" and logged it as "3/4". [despite being horribly wrong it was commonly understood that it actually means "between 3 and 4"]

However...

At the end of the semester she calculated my score as:

(5+5+5+3+4)/5 = 4.4 -> 4

instead of

(5+5+5+3.5)/4 = 4.6 -> 5

Imagine a 13 year old student arguing a 50 year old biology teacher in front of the whole class about how to calculate my score properly. I even tried to convince her to downgrade my "3/4" to a "3" and recalc my score (that would yield 4.5) She didn't listen, eventually I was thrown out of the classroom and finished the year with a 4, because of a math error.

Edit: This was long time ago, so I am almost sure the exact numbers are off, but I clearly remember the broken math and the result.

I had similar arguments with my university. They couldn't figure out how to weigh my grades. All grades are weighted by the amount of credit a course is worth, but they added it up wrongly. A Fucking university!

In my first year of university we had to do a maths module. My final score was 120%. Imagine just many different broken and non-mathematical things have to go into that!

I graduated High School with a 6.022 GPA[1]! Texas is Awesome!

1. Normal max is 4.0, school gave extra credit for Advanced Placement and college concurrent courses.

I was once told of a similar situation in a high school: AP classes were worth 6.0 in your GPA, while regular ones were worth 4.0. The valedictorian wound up being the person who realized this, took as many AP classes as possible, and as few regular classes as possible.

It is massively stupid and unfair -- but there is a part of me that sees that as preparation for real life, a great deal of which is run in stupid and unfair ways. While you'd like to change that, you also have to know how to respond to it when you can't change it.

Why is it unfair? The AP courses are more challenging, and therefore get more weight. Isn't the valedictorian (theoretically) the smartest kid in the school?

Somewhat unrelated, but AP courses can often be easier for brighter students as they generally keep disruptive clowns out and offer more engaging material instead of boring busywork. The classes are thus more like college classes and less like babysitting sessions.

> and as few regular classes as possible

I enjoyed band so I took it and they didn't have an honors or AP version. So for me to maximize my GPA would mean that I would have to forgo band all four years of my high school existence in order to min-max for GPA.

How is this min-max? Isn't this just straight maximization?

You are minimizing anything that hurts your GPA. If the highest grade you could get in a course is a 4.0 for a regular course and say a 5.0 for AP or Honors and band is a regular course you wouldn't want to take the hit from band.

If you have all your graduation requirements fulfilled, the system penalizes you for taking any further classes. You improve your GPA by taking a quarter of Nothing/Study Hall if you can't get another AP class.

And indeed, I believe the valedictorian did exactly that, for exactly that reason.

(Sorry I'm late to the party)

That is indeed exactly what happened -- the valedictorian was in all of the same advanced/AP classes as the rest of the top 10 students. But while each of us had additional classes like band, choir, or drama, she simply took the minimum number of credits, and as a result ended up with a slightly higher GPA. I actually ended up dropping all the way to fifth because I was taking math at a local college (multivariable calculus, linear algebra) which was treated as an ordinary course for GPA.

I am a high school senior taking two college math courses, but to discourage this practice (which costs the school money) the school counts my grade as a 4.0 max in my GPA (AP classes are 5.0, regular are 4.0).

The opposite happened when I went through high school. AP classes gave you a .75 bonus to your GPA, Honors classes gave a .5 bonus.

However, many of the AP classes were hard, to the point that the AP exam was laughable. The average grade in AP Biology was a C+, and more than 85% of the class got 5s on the exam. Same thing with calculus, physics, chemistry...

The valedictorian took AP Psychology, Statistics, Environmental Science, and US History, and then went down to the easiest Honors classes he could take. Just a .25 penalty on his GPA bonus... but he was getting 100s in the classes.

The kids who were looking for the hard classes to learn had much lower GPAs.

Can you be more specific? Curving and extra credit can go over 100, and extra credit can be common in a mandatory intro module.

I don't remember the exact details now, and this was at a British university that did neither extra credit nor curving. I think they weren't a particularly good teacher and just wanted everyone to get higher marks so things kept getting biased up for gratuitous reasons. And the result still called a percent.

Students are far less likely to complain about teachers, course work, etc the higher the grades they get, making this an easy cop out for the teacher.

Not quite a straight up math error but my high-school english class had a weekly 10 question spelling/definition quiz. Each question was worth "10%" if you got both the spelling and definition correct and "0%" if you got either wrong. I typically got all the definitions correct but very few of the spellings (a major weakness of mine) scored typically 20-30 "%". At the end of the semester these tests were weighted equally with the 2-3 essays and a aggregate reading comprehension score which I did very well on (typical grades of 98%). The result was me scoring "40%" in a class where I was one of the top participants. No amount of explanation from the principal, my family or me could change the teachers mind on the fairness of this.

Actually, this story makes me want to defend the teacher here.

Seems to me that this grading regime was explained beforehand and was a fair way of assessing your spelling and comprehension. Your complaint seems to be that you think the spelling should be a smaller proportion of the grade. While I agree with that, this appears to be a case of the teacher valuing skills differently not (as with so many other anecdotes being posted here) a case of the teacher not evaluating students fairly.

If comprehension and spelling were decoupled but still equally weighted then the aggregate score would've been significantly higher. Let's split the difference and say that 20-30% on the set of [all answers simultaneously spelled correctly AND comprehended] becomes a 25% on the "spells things correctly" axis. If we weight that equally against the "comprehension" axis then you get

  let R = 25   # reading
  let C = ?    # comprehension
  let M = 40   # reported mean

  (R  + C) / 2 == M
  (25 + C) / 2 == 40
  (25 + C)     == 80

  C == 55      # implied comprehension grade from a 40% average

If comprehension was any higher than 55% - which this anecdote certainly suggests - then the 40% aggregate score awarded is an ineffective assessment of the holistic learning picture.

This is the grade school equivalent of tossing out resumes over a single copy editing mistake.

Had a similar experience when I was in highschool with an answer on a physics test. She insisted that her math was correct, and pretty much the whole class got the answer incorrect. Despite us telling her why she was wrong, she refused to listen.

I took the problem to a technology teacher I had, who was known for being a extremely intelligent-abrasive-and-fair (was a nuclear engineer before changing career paths and genuinely enjoyed teaching). Explained the situation and gave him the problem to independently solve. He said he didn't want to overstep his bounds with the physics teacher, but the next day our scores had curiously changed to reflect the correct math.

Some people have too much pride to admit fault, especially to those they view as inferior.

I'm helping teach a math education course at an elite university. We should be teaching how to teach, but we actually teach elementary school math to education majors who struggle with the material. It blows my mind how difficult this course has been for the students. It seems that every week we are lowering our standards a little more. We have no real hope of finishing a significant amount of material in one semester (but that is all they will probably take). I doubt we would be able to just fail the whole class and keep our jobs. Our goal is to teach them one single concept, so they know what it feels like to really understand something, and then maybe they will chase that feeling later.

The author mentions that education students are generally chattier and less respectful during lectures. This is also true for our class, and we have had ridiculous problems getting students to arrive for scheduled meetings and stay on top of their responsibilities. On the plus side, most of them are highly energetic and charismatic, which are great for teachers.

I knew about these problems before this class, but I could have never possibly imagined they are as dire as I've seen.

In Finland, graduate schools of Education admit students only from the top 10% of college graduates.[1]

In the US, nearly half of all new teachers come from the bottom third of college graduates.[2]

Evidently, Canada is more like the US than Finland.

Depressing.

[1] http://www.smithsonianmag.com/people-places/Why-Are-Finlands...

[2] http://www.mckinseyonsociety.com/downloads/reports/Education...

How does that work? If you're so educated and skilled, can't you make loads more money in industry than teaching snot-nosed teenagers to solve linear equations? Or does making lots of money not matter as much in Finnish culture?

Finland both pays and respects its teachers. This is not so much the case in the US, where teaching is viewed as overpaid babysitting.

Also, prestige/symbolic capital is a powerful motivator. It seems to me that in the US, wealth is a major contributor to prestige, so they're often not dissociated in professional attainment.

Massachusetts is larger than Finland and has a better educational system. How does Europe fare when compared to the US?

> teaching is viewed as overpaid babysitting

I'd vehemently dispute that chartacterization. I've never once in my life run in to anyone who felt that way, with the possible exception of some politicians and union heads.

I think you need to expand your horizons. There are large portions of the US population that view our public schools as little more than glorified daycare. While I agree for the most part, I admit that there are exceptions where we do have really solid public schooling. The exceptions are for the rich kids in schools like New Trier, etc.. There is a nearly unlimited number of edu startups trying to address this very problem, they wouldn't exist if we had good schools.

Dispute it all you want. It's true. This plagues the lower echelons of society which you may be too distanced from to be aware of. Ask anyone from a school with a large population of students from poor families. When a kid's parents are illiterate and innumerate they tend to not rise above their station.

While you're correct in that teachers in better districts are respected, teachers in the inner city literally are babysitters (although I would argue that they earn every penny of their paychecks; they aren't overpaid). They spend so much time and effort keeping order that they can barely teach the classes. No parental involvement, kids with mental disorders who cannot be disciplined, insanely high class sizes, and an administration that shrugs and says, "Just keep us from getting closed."

Just get 'em to 18 (or earlier - a lot will drop out) and get 'em out the door. Someone else's problem now, probably the state penitentiary.

>teaching is viewed as overpaid babysitting.

I think it's also an example of the Dunning-Kruger effect, in which parents think that just because they have kids, it makes them experts at education.

This is ultimately harmful because it makes parents feel superior to educators in their respective field.

Many people also think they are experts in education, even if they don't have kids, but they've been to school.

Teachers in the US are paid more than teachers in Finland: http://graphics8.nytimes.com/images/2009/09/09/business/econ...

Adjust those for cost of living and the US would be even more competitive.

It's already adjusted for cost of living, the y axis is PPP.

A Finnish teacher at midcareer appears to make pretty much the average wage in Finland: http://www.oecd-ilibrary.org/education/teachers-salaries_tea... http://en.wikipedia.org/wiki/List_of_European_countries_by_a...

That said, 'Finland's teachers have high status, professional support, and good pay'[0], teaching 4 hours a day for 190 days a year. One can also presumably make that wage pretty much anywhere in the country, where the wage will go further than private wages that are likely mostly available in higher-cost areas.

So basically, it's a job with an average wage, but high respect and good working conditions.

[0] http://www.vox.com/2015/2/18/8063785/finland-schools-educati...

Earnest: how hard are they to fire?

Quite difficult. Generally, in Finland, firing a teacher requires an incidence of gross misconduct, such as violence towards pupils.

This is quite rare, though actual statistics are hard to come by. I know of one case in Helsinki area two years ago; this made headlines after a teacher physically removed a disruptive pupil from school cafeteria (generally, touching pupils is a no-no) and someone posted the scuffle in Youtube. The teacher was dismissed by headteacher, but it turned out that at least a partial reason was an earlier schism (perhaps political) between this teacher and the headteacher, and eventually the teacher was reinstated by the local school board.

Generally, firing a teacher is not very different compared to individual dismissals in other jobs in Finland; generally, processes for downsizing companies are not that complex while usually an individual dismissal is tricky.

Teacher salaries in Finland are not particularly good, but the profession is popular because pay in other university-trained professions is low (compared to US, or Germany, for instance) and therefore there are lots of applicants to teacher training. And the students can be assured that there are jobs, which is not the case for many other professions.

Does making teachers easier to fire draw better candidates into the profession?

Maybe. I'm sure the idea is that "I might be fired, better not get that job" is easy to imagine, as is people running away from the industry at high speed if they could be fired. Somehow most other professionals deal with the ability to be fired just fine.

But there are other forces at work that make less job lock good for workers.

First is coworkers. Education is a team activity, where your coworkers screw-up means more work for you. I've worked at places where management refused to fire people who needed fired, because of friendships or pain aversion. It was not fun fixing all their problems. Fortunately I quit and watched them circle the drain.

The biggest is the ease of entry and exit. If the only job available is one of a selected number where you have to wait for the current person holding it to retire, you have a situation like postdocs trying to get tenure track positions in American academia. On the other hand, if there is a flow of teachers moving around in job market -- including people new to teaching, and people stopping teaching to do something else -- there's plenty of room to find openings. It also makes it easy to move around: if your boss sucks, or your spouse wants to move elsewhere else in the country, you can find openings.

Well, if you make loads of money in Finland, the taxman will take a significant part of it. That decreases the incentives to work in industry.

And yes, making lots of money indeed matters less in this culture than (it seems, I don't know for sure) in America.

But I wouldn't say that teachers are paid that well in Finland. It's just that the expresssion (Finland.compare_compensation(teacher, engineer) > US.compare_compensation(teacher, engineer)) evals to 1.

Overall, the current Finnish political climate seems to be hostile to industry, and I see no signs of improvement. Elections in a few months, and everyone is a friend of the public sector employees, because they are such a significant part of the workforce and voting base.

For [1]: [2] disputes [1]. It states in [2] that it's the top 20% of _high school_ students on page 17. A very different stat. And [1] doesn't say college graduates, it just says graduates.

For [2] It's strange when I see these stats. Where I live in the US, 60-80% of high school teachers (depending on school) have advanced degrees (masters or higher). And that's also a weird stat to cite. What percentage of teachers with 5 years experience graduated in the bottom third? That would be a more important stat.

Their possession of advanced degrees says, sadly, little of their overall educational achievement.

> For [2] It's strange when I see these stats. Where I live in the US, 60-80% of high school teachers (depending on school) have advanced degrees (masters or higher). And that's also a weird stat to cite. What percentage of teachers with 5 years experience graduated in the bottom third? That would be a more important stat.

It's worth noting that the market for higher degrees for teachers is maybe not what people unfamiliar with it would expect. Plenty do get "real" higher degrees because they actually want to learn something, but there are strong incentives ($$$) for universities to offer fairly worthless higher degrees marketed toward working teachers, and many of them do.

Around here, at least, it's expected that a teacher will eventually get at least a master's. It's not expected that they'll choose a challenging program, or that they'll come out the other side substantially more knowledgable or capable at their job than they would have been without the course work. A master's from a top university puts you on the same pay scale as the guy or gal who went with State-U's-Cash-Cow-Teacher-Degree-Mill-Correspondence-Program—except that the school probably paid a much higher percentage of their costs than yours.

IME most school teachers with advanced degrees obtain them from pay-for-grade schools. Those degrees are essential for them to either move up the ranks in their programs or bump up their salary (here in GA a master's degree can be a $10k or more pay raise). It creates a strong financial motivation to get the degree, but they don't actually have time or desire to earn it. Same thing in military service (officer's in most branches were required to have graduate degrees by a certain rank, though at times this requirement has been dropped). Also federal civil service, many of my colleagues in a federal government job got their degrees from schools with lame graduate programs (observing their course work it was no harder than 3rd or 4th year undergraduate work at a second tier US university).

Advanced degrees are like bachelor's degrees used to be. Essential for jobs, so everyone's getting one. In 30 years all our children may be doctors just so they can flip burgers.

In 30 years all our children may be doctors just so they can flip burgers

This is a point that is often lost in these discussions. We've worked hard in the West to make higher education a commodity, but we haven't considered the unintended consequences. One of those is that if every millenial kid has an advanced degree, what makes them special snowflakes and differentiates them from the hoi polloi? Grade inflation and degree inflation mean that there's less incentive to get an advanced degree since ROI keeps decreasing while at the same time tuition keeps rising.

I doubt our PhD-holding children will be flipping burgers, though—the robots will do that.

I totally agree with everything you say. Here in Texas a Master's degree gets you about $1000 more a year. And that's still enough motivation to get the degree!

Hmm, I had to look it up once you said your number for TX. I don't think it's as big a raise here in GA at the state level as I was recalling. For a particular county I found, Houston County, the difference is $400/month for a teacher with 10 years of experience with a Master's versus a Bachelor's. A PhD offers almost $1k more than the master's alone. So by the time most teachers have it done they get around a $4k-5k pay raise (the difference increases with each year of experience).

A 20-year teacher with a PhD is making around $75k/year vs $55k for a teacher with only a bachelor's. If they're the sole earner for a household that's a strong incentive to finish up the degree and on the cheap/ease at a degree mill. Even if they're not, that extra $20k (or around $10-12k extra take home) is still more money that can be dumped into any retirement accounts or paying off the house before they retire (if they're financially savvy).

Indeed: [1] does not say and does not mean college graduates. What it appears to mean is that those admitted to Department of Teacher Education in Finnish universities come from the top 10 % of high school graduates. The teachers all take a master's degree.

(not disagreeing, just documenting)

The benefits of being a teacher in the US:

- Summers off (mainly a big deal because other professions have very little paid leave, not like the 4-7 weeks + holidays common in Europe)

- Very friendly to taking time off to start a family (thanks in large part to unionization. See previous item for why this is a big deal in the US)

- Health insurance usually good (Only matters because our healthcare system is so broken, see previous two items)

- Decent to good retirement, assuming politicians don't find a way to raid it.

- Consistent job market—most cities have about the same teacher/population ratio. i.e. you don't have to move to a certain place to find a job.

- You get to help kids learn (sort of, see last item below)

A lot of the appeal comes down to gaining European-like worker protections and services (effectively, though from the employer in this case), which is sort of funny. Something rarely considered when promoting mandatory vacation to all workers, universal healthcare, and protections for maternity/paternity leave: these would have a huge (negative) effect on the numbers of people going in to teaching, absent some substantial increases in pay or other perks. Not that that should discourage anyone from promoting those things.

The down side:

- Little respect/demonized by politicians. Relatedly, many benefits above under constant threat.

- Worse pay than a talented person, especially in STEM, could make elsewhere.

- Constant stupid pointless methodology churn that approaches the level experienced in programming, but to less purpose and possibly generating even greater stress.

- Maybe 75% of your work is basically secretarial, and a fair bit of that isn't directly helpful in the classroom (much of it's not helpful at all, to anyone—yay bureaucracy!) which can be discouraging if you went in to the profession because you wanted to teach.

Source: watched my wife go through an elementary ed. major and several years in the classroom, friends with lots of teachers.

Whoa - which U.S. state are you in? Most of those benefits are not really as good as you make them out to be.

My dad is a teacher and just announced his plan for early retirement this week. With the stripping of teachers' collective bargaining rights there have been severe drops in take home pay and changes to their benefits. He actually makes a little more money if he retires now than if he waits five years for some of the planned changes.

Right, hence:

- Decent to good retirement, assuming politicians don't find a way to raid it.

...

- Little respect/demonized by politicians. Relatedly, many benefits above under constant threat.

The benefits were a bit idealized, yes, but I think I qualified them fairly well.

[EDIT] And to be clear, I wasn't trying to paint a rosy picture of teaching as a profession.

Having a retirement plan already puts you well above average in terms of jobs in the U.S.

There are a lot more cultural issues at play that effect the education performance of the US compared to Finland.

The US has a far more heterogeneous population than Finland, so directly comparing them doesn't mean a lot.

It would be more appropriate to compare Finland to Quebec, given the two have similar racial demographic breakdowns.

There's a lot of immigrants in Quebec.

Racial mixture has Quebec being nearly 90% Caucasian.

That's definitely not the same thing as being 90% plus ethnic Finnish.

It's not.

But I said "racial background" not "ethnic background."

It is more complex than that. Teaching generally pays way better in Canada compared to the average salary than in the US (especially when pension benefits are included).

I have more experience with Ontario rather than Quebec. I would say in Ontario the teacher colleges are rather selective in who get to go, since the pay is so high, there's a lot of applicants. However math ability generally isn't part of the criteria.

Ontario right now has a massive glut of unemployed graduates from education faculties. I have always wondered why they didn't use math ability in picking new spots for teachers (right now it seems to be done by the whims of the principals).

Here are the stats: http://www.statcan.gc.ca/pub/81-604-x/2014001/t/tbld.2.1-eng...

Notice how the lower and maximum salaries are not very different, but how it takes much longer in Québec to get a decent salary.

Ex: after 10 years in Québec, you're still at 58,643 $CAD, but in Ontario after 10 years: 75,336 $CAD.

My daughter is in primary school. I find it seriously disturbing how underpaid the teachers are.

With the current exchange rate, that is pretty good pay, compared to U.S. teachers. Anecdotally, my mother has 27 years of experience and a masters, and only makes roughly the Quebec figure.

I think that your [1] Smithsonian mag is painting a bit too rosy picture. I live close to the place, Kirkkojärvi, where the interviewed teachers work, and not everyone is quite as happy as that. I know someone who moved away from the area to another school district just because he said he wanted his kids to learn Finnish at school, instead of teaching schoolmates to speak and write.

The Smithsonian piece was published after Finland scored high in the 2009 PISA rankings. In 2012 rankings, Finland had dropped quite a lot: 12th place in maths, 5th in science, 6th in reading. That's not very bad either, but it's far from the top, now occupied by Shanghai, China.

Did the quality of Finnish teachers drop in three years so much that the academic achievement of pupils fell sharply? Of course not. It's the same teachers, largely similar population, achieving similar results, but the PISA ranking was weighted slightly differently, and the results changed immediately.

This shows how things are perhaps more sensitive to how you measure them, not how they actually change.

I think this is the biggest problem:

> Some of their answers, like 16 and 18, were lower than any value in our sample.

> Some of their answers, like 120, were higher than any value in our sample.

It suggests that people not only don't know how to compute the average, they don't have a solid grasp of what the concept even means.

Not necessarily. The respondents may have just applied a mechanical procedure and did not do any kind of sanity check.

> The respondents may have just applied a mechanical procedure and did not do any kind of sanity check.

That's exactly what rayiner is saying: they don't understand what they're doing, they're just applying some formula, because they've been told to apply that formula.

I'm saying you can understand the concept and still fail to do a sanity check using that knowledge.

It's the difference between understanding in some abstract way and internalizing.

Once you've internalized a concept something that is so far out of whack would immediately look wrong. For example:

23894739 x 23894739 = 2

I would expect anyone who has internalized the rules of multiplication to immediately and intuitively reject that. Not that they could tell you what the correct answer is, but know that can't be it at a glance.

The claim is that the concept that the arithmetic mean is going to be somewhere between the extreme values in a list is simple and fundamental enough that it should have been similarly internalized by university students.

That doesn't look wrong to me, it just looks like multiplication mod n...

If you really understand the concept, the sanity check should be almost subconscious. You should see the nonsense answer and be uncomfortable with it, even if you're not explicitly going through a "compare with an estimate" step.

Or have trouble with reading comprehension.

>Not necessarily

necessarily! Applying a mechanical procedure is the very definition of not understanding.

Especially if they can't even apply it right

> means

Pun intended

As a McGill math grad, I must say that it was a running joke in the math department how the Education students didn't really need to know any math (some B. Ed. students shared classes with us during the first year or two). The B. Ed. students freely accepted this joke and were quite self-deprecating about their mathematical skills. Several of them even felt cheated for taking our "advanced" math classes which were, in their opinion, far beyond anything they would ever have to teach in high school or CEGEP.[1]

I guess these jokes had some basis in reality.

[1] Québec has a somewhat outdated education system where the last year of rough equivalents of high school and first year of university in US are done in a somewhat "vocational" college called a CEGEP which is an intermediate step between high school and university. The original purpose of this was to help bring more students into university.

This notion that you only need to know as much math as you're going to teach is ridiculous. The more your students struggle in math, the deeper your understanding of the subject needs to be. It takes a fair bit of skill and understanding to accurately diagnose and address misunderstandings.

Knowing higher level math also lets you help younger students learn things in a way that sets them up for success later on. Students can learn "advanced" concepts at a young age if presented at the right time, in the right way. But you can't introduce those concepts if you don't know them, and recognize when it's appropriate to introduce them.

This is an excellent couple of points. A math teacher doesn't just have to be able to know how to do the problem himself; he also has to be able to figure out where the student's misunderstanding is and how to correct it. Not only that, he needs to be able to do this for dozens of different students, all of whom have their own difficulties and misunderstandings.

I'm sure that there are people with only high school math understanding who can do this... but it just seems to me that the kind of personality traits that would make someone learn how to teach math like this would also make that person extremely passionate about learning it to the best of his ability and potential. I can't imagine a passionate history teacher who isn't also passionate about learning more history. Same thing with an English teacher who only reads John Grisham books (not that there's anything wrong with John Grisham).

Several of them even felt cheated for taking our "advanced" math classes which were, in their opinion, far beyond anything they would ever have to teach in high school or CEGEP.

Are you saying that people would go to school to be math teachers and say "teach me the math I need to teach my students"?

That's nuts.

I can't imagine a Spanish teacher who only knows the Spanish in the textbook. Or a woodshop teacher who only knows how to make napkin holders. Or an English literature teacher who's who's only read two of Shakespeare's plays. Or a computer programming teacher who only knows one language.

My dad taught civics and American history. I could ask him anything about those topics and he would answer, and love answering. My attention span would run out way before his knowledge and passion ever did.

I can't imagine a Spanish teacher who only knows the Spanish in the textbook.

I don't need to imagine her; she taught me for three years in high school.

danielweber ought to damn well be able to imagine it too because I guarantee beyond a shadow of a doubt that he had teachers that worked like that too.

It's easy to miss when we're kids and we still have that presumption that the teachers must know so much more, but what little left of that illusion I had was shattered when I got to college and on a whim started examining the curricula of the teaching degrees. No, they do not necessarily know more than they are teaching. They may. They can. They may even know a lot more because they really love it. But there are plenty who do not.

True, I had some teachers who were just reading from the book, like my health teacher.

Mine was a French "teacher". Fortunately only for one year. She normally smelled of stale beer.

Are you saying that people would go to school to be math teachers and say "teach me the math I need to teach my students"?

This is how teachers in Ontario (who avearge around $75k/year) learn how to teach math.

As long as everyone has equal access to education, there isn't a problem here.

I just spoke to a family member who's also a McGill grad and was told the education program is "the worst by a mile".

It seems a little disingenuous to lump the education program in with the rest of McGill.

It demonstrates how little the administration cares to maintain an acceptable standard of education in one department. Where else are they dropping the ball?

Underneath this is the simple fact that educational standards in Quebec are disgracefully bad. A frightening proportion of kids never graduate high school either, and making it into McGill is near the upper reaches of achievement for those that do.

This is going to provoke a lot of kneejerk "but it's worse in [x]". No, in the developed world it's probably not. There are lots of dynamics unique to the Quebec situation which allow this to perpetuate.

Edit to add a useful reference: http://www.cbc.ca/news/canada/montreal/dismal-dropout-rates-...

"Last year alone, only 40.6 per cent of the boys followed in the 2007 cohort at the French-language Commission scolaire de Montréal graduated in five years."

That. Growing up in Quebec, I can honestly say that my mathematical education was really, really bad.

I remember spending a whole year where we had no math teacher, so instead we had one of the french language teacher teach the class. We did mostly math related crosswords.

All the kids were failing the class, so they simply made us all pass. Great job, school.

I still have a lot of issues because of this. Hard to learn advanced concepts when your basics were screwed up.

That being said, one of the beautiful reason that not many Quebecers don't make it to university is the fact that the CEGEP can throw you into the work force for a low price and a short amount of time. I wouldn't want this part to change. High school however? The whole program is a mess.

What makes it so hard to find a math teacher in Quebec?

I've traveled through Quebec a number of times, including a bicycle trip that went through Chibougamau - as a visitor, I love the province. I can understand that some remote areas of Quebec are hard to staff effectively. Is this more than a rural/ urban issue?

Note that the stat I pulled out is from a school board in Montreal.

We have a lot of underfunded school. The particular school I am talking about is next to a train track and a metal foundry (everything was covered with yellow dust and there was smog all over) and uses a parking space as a recreation area (hey, you can play hockey on it during winter...). In 2009, one of the wall/window fell during winter and the kids had to wear their coats indoor for a month, since plastic garbage bags and duct tape was all that was covering the hole.

As for what happened to the math teacher in question, I believe that she had left the school because she had to teach multiple groups (can't remember how many groups, but it was without a doubt too many) that were too bigs and filled with kids that shouldn't have been there in the first place. Learning disabilities, violent teens, etc. all crammed in a small room, groups of... I think it was 35 students.

The public French school boards tend to have lower passing rates in maths and sciences then the public English boards though, chalk it up to the shit-show you need to be allowed to learn in English or whatever else might be at play. But the math and science reforms that Quebec implemented 8 years torpedoed basic math and science proficiency across the board.

> No, in the developed world it's probably not.

You could even argue about developing world. Children usually have a strong motivation to learn, and unless there is civil war, they do.

Well to be fair, we don't know that the 6 students called were from Quebec. McGill is a fairly popular school for kids from Ontario and the Maritimes provinces too.

And Americans. It's a cheaper (or was given recent international tuition increase) option for those who can't afford even in state tuition in some states.

As anything else, the situation is more nuanced. Quebec schools as a whole are pretty good: http://www.theglobeandmail.com/globe-debate/editorials/quebe...

The problem is that good students are mostly in private schools and specialized programs (international programs) so "regular classes" in public schools contain a lot of low performing students and students with disabilities.

My gf is a public high school teacher in Montreal and they do miracles everyday with the low amount of resources that they have to work with. She has a M.Sc. in her specialization (history), but do mostly special education tasks since the student level are so low.

So if 60% of the 80% condemned to use the public school system are failing to achieve the already lowered standards this is mere nuance?

What you have in Quebec is an elite (both english and french speaking) that gifts their children a private bilingual education with actual competition while they actively deny those rights to the rest of the public. Poor monolingual french speakers are actively screwed from birth to such a degree that they don't even notice how bad it is.

I'm just saying that we must be careful citing CSDM numbers because they represent a special situation. The CSDM have a lot of first generation immigrants, poor students, students with learning disabilities, etc. The middle class students are in good schools in the suburbs or in private schools.

The CSDM in Montreal has such a bad reputation that if you're not accepted in a specialized program (let say, international baccalaureate), you go to a private school if you can afford it (4k$/year). And don't let me start about union rules for new teachers...

On the other hand, if you're a special ed teacher, CSDM is hiring like crazy. Not so much for math, social science, french, English teachers though.

The CSDM is not a special situation at all. You can go to the townships, Lanaudiere, through every Montreal suburb and find the same phenomenon at work.

The root problem is Quebec's monolingual french speakers have been force fed a diet of anti-intellectual nonsense for so long they no longer see the value of education. Hockey is seen as the way out, but failing that the government will always be guilt tripped into paying welfare for them.

This. But this is not because "good students are mostly in private school", it is because public school is just bad.

I am a Quebec resident and I have been, for most of my high school, in a private school. I went one year to a public school: the level of education was SO poor and the students' motivation was the lowest I had ever seen.

There is an huge disrepency between public/private sector and people are trying to cut down private school funding[1].

I've seen both, and public school is a disgrace, no kid should have to go through this. I've seen teachers insulting students (and vice versa), teachers being hangover on a class day and telling the students to read their book, teachers raging against students (and vice versa) and just classes being generally content-less.

[FR] [1] http://www.lapresse.ca/le-soleil/opinions/editoriaux/201407/...

EDIT: Not saying we should abolish public school, but it HAS to improve. My experience (and what I have seen of people going into higher eduction) was horrible. Private school has good students because it has (majorly) good teachers (and some selection, I admit), whereas public school has a dominance of bad teachers.

This is not surprising. My grade 4 kid's teacher told me that our kid "just might not be good at math, and that's OK". This is a shocking attitude, but one I find commonly held: that basic math is some kind of optional, specialized skill.

http://www.aaronsw.com/weblog/dweck

She's also exhbiting a static mindset. She of all people should believe in the growth mindset.

Yeah, it's perfectly fine not to have a good grasp of calculus. But basic math? We use it every single day. Someone who is innumerate is at just as much of a disadvantage as someone who is illiterate.

For those of us who are not from Canada, can someone explain what McGill is? I feel like I'm missing a lot of context.

edit: apparently it's a very prestigious university. I was assuming that it was a remedial high school program. Holy crap.

An university.

One of the most prestigious universities in Canada!

Consistently one of the best ranked universities in Canada. It also has the largest endowment and highest endowment/student in the country.

> An university.

Did you go to McGill?

Yes, yes, I get the downvotes. But, come on, everyone was thinking it.

It's the #1 ranked university in Canada.

It is one of the top-ranked universities in Canada (roughly equivalent to an Ivy League university in the US, or Oxbridge in the UK).

The flagship public university in Quebec. If not the most prestigious university in Canada, certainly close to it.

Whatever this means: http://www.topuniversities.com/university-rankings/world-uni...

I just talked to a a family member who wen't to McGill's business school and according to her the education program is "the worst one by a mile", and is pretty much separate from all the other programs. Courses in the education school wouldn't even count as electives towards her degree.

McGill is not a great university, but it isn't poor either. It doesn't have the pride that Waterloo (our MIT) or Toronto (our... Columbia? Dartmouth? We don't have a Harvard or Yale) has, but it's solidly mid-tier.

And this does not surprise me one bit.

I've met engineers failing out during first year at Waterloo that didn't know the second law of thermodynamics ("why don't we put wind turbines on top of electric cars?") I've met engineers failing out during first year that didn't understand basic units (ie, velocity (m/s) times time(s) equals meters (m = m/ss).

Fuck, I even went to a private school and when a teacher went on maternity leave a history teacher had to teach grade 11 math. After a week I told her I would do it (and I did it) because she couldn't even handle basic, basic y = mx + b stuff, let alone hyperbolas.

The worst part of the whole thing is that Canadian students know* our system is fucked. We have so many immigrants from countries like India and their kids are years ahead of us, but nobody cares! I was screaming about how I hadn't learned anything in math between grade 4 and 8. Nothing. Think about that. We did fraction math for four and a half years. The whole system rewards minimizing absolute failures until around grade 10 or 11. Then people can finally split up into different achievement levels.

It is insane. Also, we underpay our teachers and we don't pay more for math teachers. So for someone like me, I can either earn $200k running a tech company with my Applied Science Bachelors or I can go back to school to get an education degree and earn less than what I earned coming out of university.

> McGill is not a great university

It still ranks pretty high:

https://en.wikipedia.org/wiki/McGill_University#Rankings_and...

and they still sell those "Harvard: The McGill of America" sweatshirts every year.

https://glasgowuniversityabroad0910.wordpress.com/2009/10/16...

That B. Ed. students are coming so unprepared from McGill is quite sad.

Its liberal arts programme is also much bigger than Waterloo's, but comparable to UofT's.

>"Harvard: The McGill of America"

mmm and they didn't realize that McGill is in America too? May be the parent post has a point...

As a Mexican, I don't like it much either, but I'm also tired of trying to convince the world that America isn't the US.

Here is some consolation:

https://www.youtube.com/watch?v=29g57XTYgLE

There are three [0] "America"s -- North, South, and United States of. Clarification is only required when context is inadequate to distinguish between them.

Similarly, "star" can refer to a shape, a celestial body, or a talented/lead performer or athlete. You wouldn't interrupt a conversation about sports to say "stars aren't just guys like LeBron James; Aldebaran is also a star." That would be asinine and obnoxious.

So please, out of respect for everyone's time and sanity, learn how to use contextual clues and stop trying to argue that "America isn't the US".

[0] OK, there are actually even more "America"s -- a band, multiple cities, ships, movies, etc. But the contextual clues in this post suggested we had "large regions of land" in mind, so I left the other forms of "America" for the footnote.

> "America isn't the US".

Depends whom I'm talking to. When I talk to you and others like you, I'll be careful to note that unqualified "America" to you almost always means "the United States". It never meant that to me growing up, nor to a bunch of other people. However, due to the global influence of the US, most of the world considers "America" to be the "US".

It's not really about context or anything that could be called objective. It just means different things to different people. And because for me "America" has very emotional meanings (such as for example, Morelos' proclamation that "... so Americans may only be distinguished by vice or virtue"[1] or Luis Miguel's song "América"[2], or Las Águilas del América [3]), I will never personally accept the meaning of "US" for "America".

You may have other emotional attachments to the meaning of "America", so I will try to respect those when I use the word around you or others like you.

[1] https://en.wikipedia.org/wiki/Sentimientos_de_la_Naci%C3%B3n

[2] https://www.youtube.com/watch?v=SL3u7qU_09w

[3] note their logo: https://en.wikipedia.org/wiki/Club_Am%C3%A9rica

> "It's not really about context ... [it] means different things to different people."

The identities of the speaker and audience are part of context. As you correctly inferred, if I'm speaking, an unqualified "America" probably means "the United States". If you're speaking, it probably means "the largest landmass in the western hemisphere". If we're quoting Obama speaking to the Senate, or Morelos during the revolution, we can infer what they mean by "America".

Accept the meaning the speaker intends, when it's communicated clearly enough that you can infer it. That's how communication works.

> The identities of the speaker and audience are part of context.

I cannot in general assume that information on the internet.

Depends on which part of the internet. (The context of the context ;) )

that's not context, that's because USA is the biggest power in the Americas, so powerful that it overshadows all the other regions/countries, and that's why some people living in the Americas feel belittled by that.

I know you were not replying to my post directly, but to clarify my position: I'm european, I don't particularly care about the distinction, I just found that it was a very depressing message to put on a university t-shirt from outside USA.

Ah, and please, out of respect for everyone's time and sanity, stop patronizing other people.

Please don't mistake confidently arguing for patronizing.

"The USA is the biggest power" is a form of context. "The speaker is from [country X]" is a form of context (Churchill, definitely not from the USA, once famously said "You can always count on Americans to do the right thing - after they've tried everything else.") There was adequate context for the original t-shirt to make it clear what "America" was referring to.

Which makes the "not just the US" argument come across as similar to if you argued that "LeBron isn't the only star, Aldebaran is also a star". Virtually everybody knows there are multiple meanings of the word "America"; we don't need to be told that every time we use it to refer to the US. The appropriate standard for word usage is "the same republican principles as American civil and ecclesiastical constitutions" [Noah Webster], that is, popular usage. And in popular usage, "America" can be used to refer to the US, or to the landmass as a whole; arguing against that is like arguing that we should stop calling famous actors "stars" because they're not luminous spheres of plasma. It's incorrect, and also annoying.

There is also the point that the United States of America was the first state to incorporate "America" in its name. It was an independent state when the rest of the Americas were at least nominally colonized by European powers. Much of the rest of the world got used to calling the USA "America".

For that matter, the official title of Mexico included "United States"--should I apologize when using "United States" or disambiguate in case somebody wants to mention the United Mexican States?

I was depressed mostly by the very lame message, I just find it sad.

Rankings and reputation are interrelated, but not the same thing. For example, rankings punish large class sizes, but well known professors like Larry Smith command 500+ person classes; simultaneously reducing rankings while improving reputation.

I would argue that McGill hits the right numbers, and certainly has a great law program, but it is middle of the road in terms of reputation.

Somewhat unrelated, but if you had to pick an American school that Toronto would be 'our version of', Harvard is probably a better bet than Columbia:

> from 2000 to 2004 U of T professors produced more publications in the fields indexed by Thomson Scientific than faculty at any other public research university worldwide... the University of Toronto stands second only to Harvard in publications among all private and public universities.

(The numbers are a bit out of date, but Toronto's relative place among Canadian universities is probably unchanged).

McGill is a great university for a lot of the more "classical" fields.

However, you're right, McGill is far from being the top engineering university in Quebec.

I was screaming about how I hadn't learned anything in math between grade 4 and 8. Nothing. Think about that. We did fraction math for four and a half years

I ended up being taught the same thing many times in math classes, but I noticed that my classmates -- even in honors classes -- had completely forgotten the last time we had learned this. They insisted they had never seen it before. The teachers had been through this many times so they weren't surprised.

I don't know why I could remember it when other students cannot. A tiny part of me says that those kids hated math and shoved it out of their brain as soon as they could. I'm not sure that's fair of me. My wife says it isn't and that I'm the unusual one with the math brain.

I think a surprising number of people simply can't math.

This seems incredible if you're one of the people who can math.

But really, I've known otherwise bright people whose brains fall apart at the first hint of abstraction.

Basic arithmetic is fine, but you can forget about trying to teach them anything more complicated.

Simple equations? Trig? Basic stats? They just can't do them, no matter how many times you repeat the explanations, or how many different ways you try to present them.

So I think it's not unlikely that an aptitude for math and symbolic abstraction is unusual, and not something you're going to find in most of the population.

Remember, by the time you get to a university you're in the top 20% of the population anyway. (More like 10% for STEM.)

So it's maybe not so realistic to assume that's how most people are.

There are two theses I have, not sure which is right:

1. Those people biologically can't math. (Alternatively, we are the mutants who can math.)

2. Culture has given them math anxiety, which causes panic when being asked to do math.

I think it just that Math requires abstraction and abstraction is genuinely hard. Because it is hard and highly desired skill very few teachers are good at it

There's an awful lot of people who think they are bad at math but they never really tried it because they find arithmetic difficult/tiresome/whatever.

Ask them how long it will take to drive somewhere, no problem, they can calculate it.

Ask them to solve an algebra equation with 1 variable? No way, they don't know how to do that.

TL;DR I am currently taking an adult who "can't math" through Khan Academy from K-2nd on up and she's "mathing" wonderfully now that we're comprehensively filling in the understanding gaps. Too bad she still doesn't like it. :P

I know someone in that class of people that "can't math". Initially I tutored her in algebra and she did alright when we were working together, but as soon as I turned her loose or she went in to take a test she couldn't remember or apply the techniques. She was allowed to go into Pre-calculus (she wants to be a Chem Major). But without extensive help on each section she would fail spectacularly. And after a while it became obvious why. She could think logically and when explained clearly or relating to other concepts she's recently learned it all made sense, but she had so many deficiencies in basic math that nothing past that would really stick. As an example I taught her the formula for computing the area of a square multiple times, but she would swear this was the first time each time because there was no foundation to hang that new knowledge on.

Now I but I have her working through Khan Academy from the ground up (K-2nd) and now that she's up to 5th grade and I've explained how basic concepts relate together, like multiplication and area or fractions and division she's actually starting to "get it".

She just lost the thread of "mathing" around 3rd grade and never found it again. Now that she can go through it at her pace and has someone that can patiently explain it from multiple angles it makes sense and she's doing things on her own that I was afraid she's never "get".

That said without Khan academy and a detailed list of sub-topics in math (45 individual skills for dealing with fractions for example) I'd have never been able to cover all the small things that add up to a detailed understanding of arithmetic. I'd have covered fractions from maybe a handful of angles and called it good knowing that it wasn't enough practice without having an answer for how to practice more without stupid rote repetition of the same kinds of problem.

I think for a lot of people the problem is that they don't know there is a map (a lot of mathematics fits together quite nicely).

I also think that a lot of instruction is pushed at people that are missing some fundamental bit or another, so even though the concept is close within their reach, it doesn't end up sinking in.

It's another example of how we humans arrange things so that the winners keep on winning (that is, people who are caught up end up actually learning the new stuff, people who are behind waste the time).

when a teacher went on maternity leave a history teacher had to teach grade 11 math

Likewise, in grade 11 the trigonometry teacher had to leave and the wrestling coach had to fill in. The students had to teach him the material.

From what I've heard McGill is very dependent by program, and education is by all accounts by far the worst program they offer.

Look, I understand that this should be a topic of conversation. I have no problem with that. If Québécois feel like the education they are receiving is sub-par then there definitely should be a discussion about it.

But! What I also think is distressing is that, based on this article (and its author) alone, there is also an extreme lack of understanding of statistics. The evidence presented is purely anecdotal. I read the entire article waiting for the author to cite some study or personal research, but that never happened. So, unless there is more compelling evidence out there, maybe the author, McGill students, McGill faculty members, or Québécois (or Canadians in general) should start by gathering some more information before discussing solutions.

It's just a student expressing outrage at his classmates ignorance of basic math. Especially future teachers.

Also something that competent mathematicians interested in education have been discussing for many years. It's interesting how we choose to call anecdotes "writing on the wall" when it turns out to be correct and "unsubstantiated by data" in other scenarios.

That reminds me when I took one business class during university studies and during the final exam I wrote a formula like:

  A * B

D=-------

Well, this was rejected by the teacher stating that C should be under B and not A. Oh...

Could they figure out how to do it in less than 5 minutes if the stakes really mattered? I agree calculating averages is a pretty basic skill that I find has many day-to-day applications. But this also smells like a lighter version of the trick interview question.

Which is to say, I'm sure there are people out there who would smirk at me when they found out I didn't know how to tie a square knot off the top of my head.

IMHO, calculating an average is something every teacher should have to do many times throughout their career (at the very least for calculating how well individual students performed on a test relative to their peers).

Calculating an average is the statistical equivalent of 2 + 2. Who could respect a teacher who had to look up the algorithm for 2 + 2 every time they were asked to compute it?

I would hope most teachers stopped calculating averages by hand a long time ago.

You still need to know the algorithm though to understand it's limitations.

Similar to another comment, how can you evaluate the correctness of the computed value if you don't know how the computation is done?

But understanding what an average represents is obviously important.

> But this also smells like a lighter version of the trick interview question.

It would be bad if we were talking about children forgetting it after one year. Since this is university students we are talking about, that's horrendous.

If they can't do averages, one wonders what else their basic education lacks. And how they even got there. And what they are worth to potential employers.

Somehow basic math like addition, mutliplication, fractions, mean, median, and mode, is in no way similar to tying square knots. Especially for future teachers.

I sit on the board of governors of a public school in Wales, which has decided it needs to focus on math after bad PISA results.

We had an official from the local government come in to tell us that she'd gone through our testing scores and divided schools into quartiles, so she could focus her efforts. Good, I thought.

Then she said, because of how she'd done the calculation, she had ended up with three quartiles. And she hoped most of the schools in the middle quartile (like us) would be able to reach the upper quartile for math next year.

I tried gamely to point out she was an imbecile, along with a reference to Lake Wobegon, but most of the rest of the governing body seemed to think this was entirely reasonable.

This is abysmal and unfortunately, it is far more widespread than people like to believe, particularly in supposedly advanced countries.

I've worked with programmers who could not do proportions, compounded with designers, managers etc. who were in the same boat, I'd hear conversations along the lines of:

"This is terrible, X is 3/4 of Y!" "I don't think you got it right, I got 75%, which isn't that bad"

The conversations and quarrels would go on forever, no joke.

Sadly, basic Maths isn't the only thing an alarming proportion of people do not seem to understand properly. I constantly see people with Masters, PhDs and whatnot, in various subjects (from Sciences to Journalism, Economics, etc.), who can't read and write properly. Not only do I wonder how they got where they are in the first place, but what worries me most is that there's clearly no fundamental understanding of the underlying, simple logic. Not meaning to offend anyone here, but simply looking at the comments on HN, a lot of people are guilty of bad spelling and questionable grammar, and I'd argue most people here are supposedly more educated than the average person.

I see schools competing on how they're teaching four year old kids additional languages, ten year olds how to make mobile apps, and the list goes on, but I'm yet to see a single school that advocates teaching simple logic. For instance, how about teaching grammar again? Most of my friends can't tell the difference between a noun, a proverb, a verb and so on. Not that the nomenclature matters, but I do think the intrinsic logic of a sentence does.

I'm not blaming anyone in particular, I'm really putting everyone at fault here. School systems largely aim to satisfy stats as opposed to humanely helping students, supported by politicians who like to give out numbers, whatever they mean, so that disgruntled parents may assign blame where they see fit (which is very rarely themselves), and on and on. Add to that a toxic culture of anti-intellectualism and the cycle repeats itself.

People like touting the Education system for all, but I doubt that the huge machinery we created really works for anybody, or at least everybody.

While I agree with you in general, HN comments should (and do) have lower standards for grammar, spelling, and logical reasoning. If I spent as much time on my HN comments as I do on research papers I probably wouldn't get more than one comment per month.

I completely agree with your sentiment and I'm definitely not asking for research paper quality in comments (be it HN or other places), but I do think getting the basics right goes a long way towards better comprehension and credibility.

I believe these problems extend beyond Canada and into the U.S. I know several of my peers who have started, or are applying to get their masters in Education/teaching to become teachers. I have heard them willing admit that they are very poor in Math like it is something to brag about. I've seen them struggle to compete basic arithmetic, and yet somehow they believe this is totally ok and that they are qualified to teach. Math needs to be elevated and respected, and it is going to take a restructuring of the curriculum in order for it to happen.

Before we get too smug, don't let the education majors challenge you to a writing contest :-)

A few years after I finished my BS in Comp Sci, I took both the GRE and the CBEST (California teaching test). The percentile ranking skew between the two populations was interesting.

A 98th percentile ranking in "verbal" in the engineering group only put me at the 50th percentile ranking in writing in the teaching group.

(OTOH, I was at the 99th percentile in math in the teaching group, but I had a reasonably high score at math in the GRE as well)

Engineering majors score higher than education majors on the verbal section of the GRE: http://www.ncsu.edu/chass/philo/GRE%20Scores%20by%20Intended...

The verbal portion of the GRE didn't used to involve writing--I haven't taken it in a long time. But some of what I see written by and for teachers makes me wonder how good they are at writing, and at distinguishing good writing from bad.

True: the GRE verbal was multiple choice, not actually writing. Closest proxy I could come up with to compare the writing results.

May experience is different. During a masters program in education a TA confided that when grading our papers he found that the writing from those with math and science degrees was OK, but they all were competent in their subject matter. The writing quality for English/History majors was all over the place - some of the best and worst. We concluded it was because it is easier to objectively test math and science proficiency. Profs are OK with failing you even if your work really hard.

It's much better to be 98/99 or 80/99 percentile than 99/50. Engineers at least understand writing enough not to make facepalm-inducing mistakes like miscalculating the average.

Writing exams are subjectively graded. If you're a liberal arts major you've been indoctrinated into the same system as your graders and are trained to write in a style that they are biased toward. Adding essay questions to standardized entrance exams was a huge mistake I'm glad to have missed.

And teachers make a lot more in Canada than they do in the United States. If you're good enough at math or science to do anything else, why would you be a teacher? It's a harsh way to look at it, but it's true.

In the US, states have their own teacher certification exams. They are pretty much just testing your understanding of 8th-grade math and science. I know a lot of teachers and I don't think any of them passed it the first time. It's like passing the bar in the world of teaching. People take it up to a dozen times. After they have gone through two years of graduate school.

UK has tests in Mathematics and in English for anyone who wants to take teacher training for schools (not needed for 'post compulsory' or pre-school yet).

http://sta.education.gov.uk/

Might be fun to try the practice tests out on colleagues...

Helping managers to aggregate pass rates per class into an overall pass rate used to be a fun thing to do many years ago. They are better at data management now because of our focus on targets in the UK. Not so good for holistic education but managers can certainly hack their stats.

I'm in the UK, and I don't think it's fair to be singling out teachers on this.

I work with retailers - we make eCommerce systems - and I never cease to be staggered at how many CFOs/finance people/buyers/business owners don't:

- Know the difference between "gross" and "net" when talking about prices, tax, or margin. - Know how to calculate a percentage. What's 10% off £90? No idea. - Virtually all fall for the "mark it down by 10%, then mark it up by 10%... same price!" fallacy. - Completely fail to grasp statistics. "Me" is not a statistically significant sample size.

So long as Western society treats mathematical literacy with contempt, this will only get worse - and treat it with contempt we do, for if you are able to figure out the average of two single digit numbers in your head, you are a "braniac" or a "geek", which is fucking incomprehensible.

"Virtually all fall for the "mark it down by 10%, then mark it up by 10%... same price!" fallacy."

That is a classic GCSE Foundation Maths exam question: and I have to say most of the teenagers I teach can explain why you won't get back to the same price!

I wasn't singling out teachers myself but the OA looks as if it was. There is an honest desire to improve things over the next 10 years in the UK and all main parties agree about the general policy if not the detail so I am slightly optimistic (but teachers have to be)

Oh my god — I can't believe it.

A professor of mine in college (I'm currently a freshman — this happened a few months ago) told me a story _exactly_ like this — just at the University of Pittsburgh Masters in Education program and wherein nobody knew (or cared) that 1 was not a prime number.

I may be more dumbfounded now than I was sitting in his office during office hours... one is an anecdote, two is pattern.

In fairness, thinking that 1 is a prime number (or just not knowing that it isn't) is in quite a different league to not knowing how to calculate the average of a list of numbers.

See my comment to the other reply. Ordinarily I'd agree, but these were all graduated undergrad math majors in a course about how to teach math (specifically prime numbers) to high schoolers.

I think knowing if 1 is prime is almost trivia compared to knowing how to calculate an average. The latter is incomprehensible to me. What age are the students in this anecdote?

From what my professor told me, they were almost exclusively in their mid-20s, having just finished undergrad degrees in math.

You're right — knowing if 1 is prime is kind of a trivial point, but this was a course for would-be math teachers specifically about how to teach _math_ to high schoolers. In fact, the specific context of the story was an in-class presentation about teaching kids about primes.

I definitely should have mentioned that in the OP.

I tried to make this comment a reply to a separate comment but it errored out. I had a funny thing happen to me in college that ruined my one chance at a 4.0 semester. I had just begun my physics major but had some electives to take as well.

I was taking the introductory microeconomics course. At the end of the semester I had received a B and I was relatively certain that I had achieved better, so I went to the professor's office and asked to see how my grade had been calculated. As he started showing me the scores, I realized that none of them had been mine! In the end he had mixed my scores with another student who had the same last name (a very common name, in the professor's defense). I was very happy at that point because I was really thinking I would receive an A! Sadly, the professor shook his head and said that I would still only get a B.

I was a bit shocked so I asked what the final calculation had given and he said a 0.8994. There were not 10,000 points possible and final grades had to be a two-digit representation of the semester's work, so I was unsure why this kept me from an A. I explained to him that the last digit was not significant since there was no "point" to represent the digit, basically trying to explain significant figures to him. I then stated that since the grade had to be either an 89% or a 90%, surely it was more appropriate to receive a 90%.

He shook his head again and said to me what was probably one of the most infuriating and condescending things I'd ever heard from a moron with PhD. He said that economics as a field was likely much more difficult than my primary coursework and that I should not take it too hard that his course was my lowest grade that semester. Now I do not really buy into the perceived/nearly mythical reputation of difficulty that physics has gained, but I do know that we at least put our dependent variable on the appropriate axis. I am not an exceptionally gifted student, so I never did have another chance to receive a 4.0 semester in my math and physics coursework. I have always held a grudge against that professor.

EDIT: I realize I forgot to mention the part that was really infuriating, as I see that it is really not that frustrating as told. The thing that angered me the most, and the reason I went on about significant figures, is that the professor himself was not against rounding! He said that had I received an 0.8995 I would get the A! His entire grading framework was hinged on a poor understanding of math.

Don't get me wrong, I'd also be frustrated. However, if you view the grades as cutoffs rather than rounded percentages, I think the professor's view makes sense. The cutoff for an A- is .90 Therefore, if the score was 0.8994, then you did not make the cutoff, and your percentage grade of 89% would be more appropriate.

I TA'd a capstone neuroscience seminar at McGill for multiple years, and you'd be amazed at how much difficulty many of the students had at expressing themselves in writing. And I'm talking about those who spoke English as a first language. These are final year university students who got into a very competitive program.

It is worth noting that McGill has over 60% of students coming from outside of Quebec so this doesn't have much to do with Quebec's education system. http://www.mcgill.ca/about/quickfacts/students

But the article is about creating good educators, the problem is't the students coming in, it's the ones coming out of that education program, who will eventually become teachers. The problem is the program.

I met some education majors in the 70s, when I was in college and grad school, (at McGill, coincidentally). It was clear, even then, that many of them were aiming to become grade school teachers because they could not do math beyond the grade school level. My encounters with my kids' teachers over the years have only reinforced that impression.

Two examples:

1) A 4th grade teacher who gave assignments in which presentation counted for 80%, and content for 20%.

2) A middle school math teacher who claimed the answer to the question "Flipping a coin, what are the odds of getting heads or tails?" was 50%. She really meant to be asking two questions, one about heads and one about tails. She completely missed the significance of the word "or" in questions about statistics.

This article does not surprise me at all.

I think your point 2) is unjustifiably harsh. It may have been misinterpreted. I think it's an honest mistake.

I talked to the teacher, and she was definitely confused. If not by the math concepts, then by the common English phrases used in talking about probability.

Recommended reading: Innumeracy: Mathematical Illiteracy and its Consequences: http://en.wikipedia.org/wiki/Innumeracy_%28book%29

Just re-read that book a little while ago. It's dated in a couple of its examples, but it's still pretty powerful and easy to read.

Purely anecdotal and IMO a bit disingenuous. Most McGill students are not from Québec for starters. I could comb through the requirements set by the government concerning secondary education and easily find many supposedly acquired skills that the author either forgot or never learned.

Write the same story about how a lot of anglophone students do not learn to speak/write/read French properly as they simply do not care and you will be overwhelmed by responses in their defense.

I've seen this thing quite often. There's a famous video clip of MIT graduates, in cap and gown, who can't make a bulb light when given a battery and wire. I disagree with the blog author's interpretation that this is about the students being "stupid." I posted the comment below.

I wouldn't interpret this as "education majors are stupid." I would interpret it as, all of us, even the best of us, are stupid in certain contexts with certain topics and certain time pressures. This is partly due to how we are taught and how we learn in school. Our knowledge is inert (inaccessible in other contexts) because it is often taught without context. The technical term for this is "transfer" - our learning often doesn't transfer. An older term for this is "encoding specificity" - our learning is "locked" to the context in which it is encoded. For example the myth that if you are drunk while studying you should be drunk when you take the test.

Here is a dramatic example that had a huge influence on reforming science education. On the bottom right of this page is a video clip of MIT graduates, in cap and gown, who, given a battery, bulb, and wire, can't make the bulb light. There's also a clip of Harvard students. https://www.cfa.harvard.edu/smgphp/mosart/video_archive_2.ht...

The full videos that go into why this is happening (because of how they are taught) and how we can address it (contextualized and constructivist instruction techniques like problem-based learning, simulations, etc.) are "Minds of Our Own" and "A Private Universe", which can be viewed online here: http://www.learner.org/resources/series26.html and here: http://www.learner.org/resources/series28.html

Another brilliant example comes from comedian Father Guido Sarducci's routine on the "Five Minute University" - how he can teach in 5 minutes what you remember 5 years after college: https://www.youtube.com/watch?v=kO8x8eoU3L4

From the headline I assumed McGill would be a grade school/middle school or maybe worse, a high school. But it's a university?

On Canada's education: I came from Belarus when I was 10 and was put into 5th grade. Until I got to 9th grade, there was no new math taught to me. I didn't know about the unit circle until 10th grade, however, my friends from home learned about it in 7th grade. This is only one example. Maybe Canada's university education is at par, I don't know, but the years leading up to it are mostly wasted, to say the least. Since grade 1 we sat attentively and quietly at desks listening to the teacher, they commanded our respect and their classrooms were always well organized for learning. Compare that with Ontario, when I was placed in 5th grade. We were never encouraged to read out-loud to the class, come to the front of the class to answer questions, solve math problems on the board or to memorize and tell a poem. We did not read classic authors, or poets and learn their works. Our reading speed was not measured, we were not assigned reading, writing or math homework beyond simple "spelling sheets" and "fill in the blank math sheets". We were not taught to keep an organized student planner, or keep an organized notebook. Our homework was not graded, our grades were not tracked and were never revealed to us. We were never told what we needed to improve. We never had to write short, well formatted and grammatically correct paragraphs and short pieces. We never wrote dictations, we never actually wrote anything beyond single worded "fill-in-the-blank" worksheets. Our penmanship was not judged, proper grammar was not encouraged or judged. All these things were taught to us in Belarus from grade 1 to 5. I was shocked to come to Canada and learn that in fifth grade, students had to sit on the floor for parts of the day as the teacher read to them, like kindergarten. Knowing this I often reflect on how much obvious potential is wasted and opportunity missed by Canadian elementary education systems. I visited Belarus when I was in 9th grade, my friends there were writing essays in English and Spanish as weekly homework. Compare that with French language education in Canada, by 9th grade, after 5 years of elementary school French, I could count to a hundred and read a little. I did not know proper grammar or how to write sentences. Anyway, there are many examples in other subjects as well. Each time I reflect on this, I cannot help but feel how pathetic the education is. It's not serious. It then comes as no surprise that there are teachers at conferences who are not able to comprehend weighted averages, as japhyr mentioned. I wish elementary education in Canada were reformed completely.

In my country was a politician who was outraged by the fact that 50% of people earn below the national average.

You should look up median and how it is different to the average.

Technically, average is ambiguous. Usually refers to mean, but also median and mode.

The solution is obvious don't allow outside observers into education classes. /s

Are you a manager? :-D

The private schools in QC are a bit better... at least in my experience. It's too bad, the public system is so broken.

If true, this is horrifying. I went to McGill and the Education students didn't seem this incompetent.

Isn't this story just about a single anecdote? To me that makes it nearly meaningless.

My takeaway: I had no idea the ‽ character was a thing. Hooray!

This is alarming but not particularly surprising to me, if the culture of education is similar between the US and Canada. Judging by this piece and one I read hear a few days back [1], there may be more similarities than I'd thought.

Ed school for far too many is a compelling choice for people who want a relatively easy college degree. I don't want to diss the countless teachers who choose that route out of genuine passion and love for education and knowledge, but we don't do a whole lot to filter for these people.

And it's an incredible shame, because my brief two year teaching career convinced me that it's one of the most demanding career paths a person could choose. I'm a lead engineer today and was once a startup founder, and neither job comes close to the stress, the emotional demands, the direspect, the time demands, the politics, the motivational skills, and the relationship building teaching required of me.

We act like it's such a big mystery why we have such problems in education. To me it's pretty simple:

1. It's an extremely demanding job that's only becoming more demanding with the constant shifting of accountability (i.e. blame) onto the teachers.

2. Teacher prep is largely horrible. Many ed schools will take anyone with a heartbeat, and highly selective alternative prep programs like Teach For America (of which I am an alum) give people minimal training in comparison.

3. Segregation, poverty, and policy create a situation where the students in the greatest need are the worst-served. This is what really kills our system, because students of privilege often have enough advantages to make out okay even in spite of the first two issues.

No amount of draconian accountability standards, school privatization, or winner-take-all compensation schemes are going to fix these things.

There is some hope though, if we're willing to reach for it. We have a lot of human capital in our education system, but I think we're applying it poorly. Instead of feebly demanding that everyone suddenly become an 10x teacher, we should find better ways to utilize the competent (if not universally brilliant) people we do have. Reduce teaching load and scale back the job to something people can excel at without having to be a martyr.

[1] https://medium.com/precarious-physicist/enoughs-enough-6c56a...

[2] http://www.washingtonpost.com/blogs/answer-sheet/wp/2013/05/...

One thing that I've become a firm believer in is that teaching isn't the problem; administration is. A good administrator or group of administrators will make the entire school into a team that can excel. They set a clear vision for what teachers need to know and do. They set clear standards for discipline, which are practiced in a fair, evenhanded, rational fashion. They uphold high standards and remove the non-hackers who can't do the job. They respond quickly to concerns and show that they legitimately care.

Incidentally, one of the biggest reasons why private schools do so much better is that their administrations tend to be better. When a kid is acting up in class, he gets punished. When a teacher sucks, he gets fired. When concerns come up, they are addressed quickly and promptly. These things are so important that teachers willingly and happily take a pay cut just so that they can be in this environment.

In contrast, a large number of public schools have horrifyingly incompetent administrators. The school then becomes a muddled mess where individual sparks are snuffed out by the chaos. Who would teach in such a place?

One of my favorite models of people's performance is the "10-80-10" distribution. 10% are heroes, who will do an amazing job no matter how bad things get. 10% are shitbags, to be extirpated with prejudice. The remaining 80% will go with the flow. If your school is awesome, they'll approach the heroes. If it's garbage, they'll approach the shitbags. Administration is what decides where the 80% will go.

One of the few jobs I want even less than my old teaching job is my old principal's job. The role has insane expectations. The collective administration has to be capable of management, budgeting, academic master planning, public relations, recruitment (of staff and teachers), HR, scheduling, event planning, behavior management, and the list goes on practically forever. The principal has to build a team that can cover all of these bases with no gaps, and in a school district like the one I taught in, they have to do it with a very limited number of people and typically on a very difficult time scale.

In a rough school district, turnover is rampant. Few sane people want to take this role or honestly feel qualified to do it, so it tends to attract manic people, with the assortment of negative personality traits that tends to correlate with. You name it: manipulativeness, sleaziness, narcissism, capriciousness, etc.

I have yet to see a private school that effectively serves the neediest communities with a model that is actually replicable. Even the best charters tend to weed out the neediest students, in their messaging, their admissions or through high daily expectations with lack of support. The lack of support undercuts high expectations at all levels of the educational system.

Thank you for this perspective. As a public school teacher who did leave a higher paying, more glamorous career to work with youth these threads can swing between white knuckles and tears.

We've got a lot of talent inside and outside the education space - but we're not creating a system that will retain (or home grow) that talent. I'm hopeful we will start to see better tools to provide strong resources and modeling to young teachers + valuable feedback/fresh ideas to veterans. We can't just churn through the smart, young ones two-years-at-a-time and squeeze out those with deep experience.

For those of us out of the loop: What is McGill?

Why is this #1 on the homepage?

Partly because it's important to society.

Partly because programmers love to talk shit about their peers who studied non-STEM subjects and had a lot more fun in college.

blame the algorithm

Because a largely highly learned subculture cares deeply about education, evidently. Go figure!

Because hacking education is an interesting problem and a good portion of HN is shade tree mechanic discussion about interesting problems.

There's nothing wrong with shade tree mechanic discussions. They are an interesting diversion when you are trying to waste some time while drinking your coffee at the start of the workday.

Because its average score was high enough.

I dunno, in elementary schools in the U.S. they start teaching the median by grade 2.

The mean is good when you want an actual expectation value (i.e. how much fast do I lose money when I play this slot machine) but the mean is not the tool to use for characterizing and unknown probability distrbution.

Well, CLT does guarantee that most means will follow a gaussian distribution if you repeatedly sample from the same distribution. Also, if you're relying on a single statistic to characterize a distribution, you've got another thing coming buddy. ;) Always report first and second moments, range and/or outliers. Histograms are even better tho binning is tricky. You're right to fear distortion, but changing your one statistic isn't gonna save you.

The funniest part of the story is the article got the formula for average wrong.

The article listed all this "add them all up and divide by how many" but thats totally wrong.

The real way averages are calculated is you write a script for an actor wearing a lab coat to sell more toothpaste, and some liberal arts grad picks a number that rolls off the tongue and sounds good. Sometimes politicians use "average" as a verbal filler. like "like" or "um", it doesn't mean anything numerical it just sounds good and fills space.

So the kids that wrote 18 or 120 are the only kids who got it right. You put your nose in the air and sniff what someone wants to hear about a conclusion they've already drawn, and if higher or lower is better, well, thats what the answer is.

The answer to "whats the average of one 100 and nine 20s" is NOT, repeat, NOT 28. Thats never going to sell toothpaste in TV commercials, sounds terrible.

If you have a system of commerce built entirely on lies and deceit and asymmetric unfair marketplaces, some weird rant about mathematical truth is like asking how many angels dance on the head of a pin.

http://lmgtfy.com/?q=psychologists+near+me

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