
Many McGill Education Students Cannot Calculate an Average - j2kun
http://stuartspencestuff.blogspot.com/2015/02/many-mcgill-education-students-cannot.html
======
japhyr
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.

~~~
NoMoreNicksLeft
> 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.

~~~
mehrzad
>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.

~~~
NoMoreNicksLeft
> 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.

~~~
xaa
> 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.

~~~
NoMoreNicksLeft
> 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).

------
sly010
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.

~~~
rogerbinns
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!

~~~
csours
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.

~~~
Dove
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.

~~~
worklogin
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?

~~~
Yhippa
> 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.

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

~~~
Yhippa
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.

------
jrells
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.

------
cs702
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...](http://www.smithsonianmag.com/people-places/Why-Are-Finlands-
Schools-Successful.html)

[2]
[http://www.mckinseyonsociety.com/downloads/reports/Education...](http://www.mckinseyonsociety.com/downloads/reports/Education/Closing_the_talent_gap.pdf)

~~~
strictnein
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.

~~~
Jtsummers
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.

~~~
hdctambien
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!

~~~
Jtsummers
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).

------
rayiner
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.

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

~~~
runeks
> 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.

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

~~~
bradleyjg
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.

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

------
jordigh
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.

~~~
danielweber
_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.

~~~
jessaustin
_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.

~~~
jerf
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.

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

------
fidotron
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-...](http://www.cbc.ca/news/canada/montreal/dismal-dropout-rates-among-
french-speaking-students-worry-minister-1.2771757)

"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."

~~~
Raphmedia
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.

~~~
japhyr
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?

~~~
Raphmedia
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.

------
t1m
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.

~~~
mod
[http://www.aaronsw.com/weblog/dweck](http://www.aaronsw.com/weblog/dweck)

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

------
pavel_lishin
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.

~~~
Raphmedia
An university.

~~~
strictnein
> An university.

Did you go to McGill?

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

------
3pt14159
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/s _s).

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.

~~~
jordigh
> McGill is not a great university

It still ranks pretty high:

[https://en.wikipedia.org/wiki/McGill_University#Rankings_and...](https://en.wikipedia.org/wiki/McGill_University#Rankings_and_reputation)

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

[https://glasgowuniversityabroad0910.wordpress.com/2009/10/16...](https://glasgowuniversityabroad0910.wordpress.com/2009/10/16/harvard-
americas-mcgill/)

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.

~~~
100timesthis
>"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...

~~~
jordigh
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](https://www.youtube.com/watch?v=29g57XTYgLE)

~~~
lotharbot
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.

~~~
100timesthis
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.

~~~
cafard
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?

------
ravitation
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.

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

~~~
j2kun
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.

------
bitL
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=-------

    
    
      C
    
    

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

------
klenwell
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.

~~~
cbgb
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?

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

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

------
sago
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.

------
grownseed
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.

~~~
j2kun
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.

~~~
grownseed
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.

------
tashoecraft
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.

------
Roboprog
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)

~~~
cafard
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.

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

------
pkulak
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.

------
keithpeter
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/](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.

~~~
madaxe_again
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.

~~~
keithpeter
_" 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)

------
aroman
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.

~~~
throwaway283719
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.

~~~
aroman
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.

------
relaytheurgency
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.

~~~
erroneousfunk
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.

------
growlix
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.

------
olssy
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](http://www.mcgill.ca/about/quickfacts/students)

~~~
poppet_
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.

------
geophile
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.

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

~~~
geophile
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.

------
acscott
Recommended reading: Innumeracy: Mathematical Illiteracy and its Consequences:
[http://en.wikipedia.org/wiki/Innumeracy_%28book%29](http://en.wikipedia.org/wiki/Innumeracy_%28book%29)

~~~
omegaham
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.

------
chm
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.

------
edtechdev
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...](https://www.cfa.harvard.edu/smgphp/mosart/video_archive_2.html)

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](http://www.learner.org/resources/series26.html)
and here:
[http://www.learner.org/resources/series28.html](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](https://www.youtube.com/watch?v=kO8x8eoU3L4)

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

------
Fando
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.

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

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

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

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

~~~
elros
Are you a manager? :-D

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

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

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

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

------
acjohnson55
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...](https://medium.com/precarious-physicist/enoughs-
enough-6c56afe36d00)

[2] [http://www.washingtonpost.com/blogs/answer-
sheet/wp/2013/05/...](http://www.washingtonpost.com/blogs/answer-
sheet/wp/2013/05/15/what-if-finlands-great-teachers-taught-in-u-s-schools-not-
what-you-think/)

~~~
omegaham
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.

~~~
acjohnson55
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.

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

------
volandovengo
Why is this #1 on the homepage?

~~~
acjohnson55
Because a largely highly learned subculture cares deeply about education,
evidently. Go figure!

------
PaulHoule
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.

~~~
SapphireSun
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.

------
VLM
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.

~~~
swalsh
[http://lmgtfy.com/?q=psychologists+near+me](http://lmgtfy.com/?q=psychologists+near+me)

