

Mathematics Teaching No Longer Works - sanderjd
http://devlinsangle.blogspot.com/2015/01/your-fathers-mathematics-teaching-no.html

======
bazzargh
I tried to look up the original research for the table of what the Fortune 500
are after, and there's something odd there. The paper was _Cassel, R.N.;
Kolstad, R. (1998). "The critical job-skills requirements for the 21st
century: Living and working with people". Journal of Instructional Psychology
25 (3): 176–180._.

JoIP is
[http://www.projectinnovation.biz/journal_of_instructional_ps...](http://www.projectinnovation.biz/journal_of_instructional_psychology),
published by 'Project Innovation, Inc'. There appear to be no archives, and
patchy availability of paper abstracts online; so I checked the principal
author - he's Dr Russell N Cassel -
[http://library.csusm.edu/about/rooms/cassel.asp](http://library.csusm.edu/about/rooms/cassel.asp)
... who _retired_ in 1974 to found...Project Innovation Inc.

While Dr Cassel's bona fides are not in doubt, you have to wonder about the
level of peer review you get publishing in your own journal.

However the reason you'd need to see the original paper is that the Stanford
work and Devlin's article are predicated on the assumption that the Fortune
500's priorities have changed, but the Stanford paper shows no figures and no
confidence intervals from Cassel's paper, so was this just noise? Were the
1970 and 1998 studies even comparable?

Secondly, it's now 17 years since the second study - getting on for as much of
a difference as there were between the two studies. If priorities are supposed
to change so much over similar timescales, surely more recent evidence is
required?

~~~
analog31
One might also wonder about causality versus correlation. Do executives cite
"teamwork" today because they even know what it is, or because the buzzword
has been drilled into us every day for the past 30 years?

~~~
dalke
Interestingly, Google's n-gram viewer says that "teamwork" was at its lowest
from 1970-1980:
[https://books.google.com/ngrams/graph?content=teamwork&year_...](https://books.google.com/ngrams/graph?content=teamwork&year_start=1940&year_end=2008&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cteamwork%3B%2Cc0)
It didn't regain its 1950s peak until 1990.

That's also when "workplace collaboration" took off.

------
edtechdev
It's working exactly the way he has argued for in earlier writings: as a way
to weed out students and have them memorize meaningless procedures.

Two years ago he was arguing that "it's survival of the fittest; the process
has no respect for the individual, but overall is extremely effective."
[http://devlinsangle.blogspot.com/2012/12/the-
darwinization-o...](http://devlinsangle.blogspot.com/2012/12/the-
darwinization-of-higher-education.html)

And before that, he was arguing that math is basically just a meaningless
symbol game of memorizing: "more advanced parts of the subject are created and
learned as rule-specified, and often initially meaningless, "symbol games."
....must be learned in much the same way we learn to play chess: first merely
following the rules, with little comprehension..."
[https://plus.google.com/+DougHolton/posts/hJ35zfWYofF](https://plus.google.com/+DougHolton/posts/hJ35zfWYofF)

Luckily, a few colleges and instructors are trying to actually teach and
support student learning in these classes, instead of just acting as
gatekeepers who don't have a problem with high failure rates:
[http://blogs.kqed.org/mindshift/2014/12/intro-college-
scienc...](http://blogs.kqed.org/mindshift/2014/12/intro-college-science-
classes-that-enable-instead-of-weed/)

------
dalke
Quoting: any parent who opposes adoption of the CCSS is, in effect, saying, “I
do not want my child prepared for life in the Twenty-First Century.”

That's a bunch of baloney. The premise of the essay is that Fortune 500
companies are the best at deciding how our children should be educated, and
therefore whatever scheme is aligned with the needs of the largest businesses
- what's good for General Motors is good for America - is the one we should
pursue.

Just yesterday here on HN, account 'edward' posted a link to a 2012 Forbes
article titled "The Rise of the 1099 Economy: More Americans Are Becoming
Their Own Bosses". You'll notice that the 'Fortune 500 most valued skills'
doesn't include "independent thinking" in the list of top topics.

You'll also notice it doesn't include fine arts appreciation, history, ethics,
and the other ideals of a classically educated citizen, as compared to modern
educated worker.

~~~
sago
"You'll notice that the 'Fortune 500 most valued skills' doesn't include
"independent thinking" in the list of top topics."

Are you suggesting CCSS does a worse job of fostering independent thinking
than the curricula it replaced? Quite the opposite CCSS is completely infused
with helping children reason about unfamiliar problems in ways that allow them
to manipulate data and mathematical concepts. You're erecting a lovely
strawman there, but the fact if you want your children to be better
entrepreneurs then inquiry based learning is much better than sitting through
info-dump lectures and memorizing algorithms without context.

"You'll also notice it doesn't include fine arts appreciation"

Perhaps because it was an article about math education, written by a
mathematician, on a math blog, with math in the title.

If you're really interested in this stuff, then it is worth reading some
educational theory. There has been a lot of work on how the "classically
educated citizen" is a myth, only ever instantiated in a tiny elite. To argue
that all children should be educated in such a way is to argue that all
children should be part of a liberal elite. Which is not a bad argument, but
is not one, at its core, of education.

~~~
dalke
If the article is, as you say, only about math education, then it cannot
conclude "any parent who opposes adoption of the CCSS is, in effect, saying,
“I do not want my child prepared for life in the Twenty-First Century.”" At
best it can say that a parent who opposes adoption of the CCSS _for
mathematics_ , etc.

Since it makes a broad statement regarding CCSS, it cannot be, as you say,
restricted to math education standards. (There's also the technical
observation that CCSS is not the only way to achieve those underlying
aspirational goals. I see that Minnesota has decided to not use CCSS, and
assume a Minnesota parent may oppose CCSS for the honest belief that the
Minnesota standards are better for a 21st century life than CCSS.)

I brought up "classical educated citizen" precisely because it is a different
mythos. The essay only concerns itself with one specific goal - train the
workers of the top 500 companies of the 21st century. There are dozens of
often opposing goals for the education system[1], and to focus on only one is
a disservice. You suggest I should read some education theory, but omit that
the essay author is equally lacking; which was my point.

But since you bring up education theory, and elites, I feel it's useful to
point out your own strawmen. We've long had multiple education methods in
American schools. See
[http://cuip.uchicago.edu/~cac/nlu/fnd504/anyon.htm](http://cuip.uchicago.edu/~cac/nlu/fnd504/anyon.htm)
from the 1980s, on "Social Class and the Hidden Curriculum of Work". It points
out that:

\- "In the two working-class schools, work is following the steps of a
procedure. The procedure is usually mechanical, involving rote behavior and
very little decision making or choice"

\- "In the middle-class school, work is getting the right answer. If one
accumulates enough right answers, one gets a good grade. One must follow the
directions in order to get the right answers, but the directions often call
for some figuring, some choice, some decision making."

\- "In the affluent professional school, work is creative activity carried out
independently. The students are continually asked to express and apply ideas
and concepts. Work involves individual thought and expressiveness, expansion
and illustration of ideas, and choice of appropriate method and material."

\- "In the executive elite school, work is developing one's analytical
intellectual powers. Children are continually asked to reason through a
problem, to produce intellectual products that are both logically sound and of
top academic quality. A primary goal of thought is to conceptualize rules by
which elements may fit together in systems and then to apply these rules in
solving a problem. Schoolwork helps one to achieve, to excel, to prepare for
life."

To simply say that the options are "inquiry based learning" as compared to
some sort of "info-dump lectures and memorizing algorithms without context" is
ahistorical. It's like saying that before agile there was only waterfall.

You say my argument is "that all children should be part of a liberal elite.
Which is not a bad argument, but is not one, at its core, of education."

I find that odd because, sociologically speaking, your statement is that all
children should be part of the middle class or the professional class.
Consider this quote from
[http://www.academia.edu/2976656/Social_class_and_social_acti...](http://www.academia.edu/2976656/Social_class_and_social_action_The_middle-
class_bias_of_democratic_theory_in_education) :

> collaboration and teamwork have become increasingly central characteristics
> of middle-class life over the 20th century. Group success often requires
> managers and professionals to work closely with people they have no long-
> term relationship with. Each individual in these contexts is expected to
> independently contribute his or her own particular knowledge and skills to
> an often weakly defined common project. Collaboration in these groups is
> facilitated by the relatively abstract, elaborated discourse predominant in
> middle-class settings (Bernstein, 1971; Brown, 1995; Gee et al., 1996; von
> Trotha & Brown, 1982). For the rest of the article, I refer to this
> particularly middle-class form of joint action as discursive collaboration

Collaboration ("teamwork") is a middle-class value and has been for decades.
Why is promoting a middle-class value "at its core" part of education, where
so-called "liberal elite" goals are not?

Fussell back in 1983 in "Class: A Guide Through the American Status System"
also pointed out that teamwork was part of the middle class. I can't find a
direct reference online, though I found this summary: "Corporations hire [the
middle class] from second-tier colleges and teach them that being a team
player is the most important thing they can be." \-
[https://danielmiessler.com/study/class/](https://danielmiessler.com/study/class/)

A push for teamwork was solidly part of middle class consciousness already by
the 1980s, and likely much earlier. Part of my 'baloney' is to reject as
propaganda that idea that it's some new 21st century ideal.

[1] I would love a school system which educates more about the Participatory
Citizen and Justice-oriented Citizen described in
[http://www.mills.edu/academics/faculty/educ/jkahne/ps_educat...](http://www.mills.edu/academics/faculty/educ/jkahne/ps_educating_the_good_citizen.pdf)
. Otherwise, "Personal responsibility, voluntarism, and character education
must be considered in a broader social context or they risk advancing civility
or docility instead of democracy." You'll note that Fortune 500 companies are
not run as a democracy, and would prefer docile employees over justice-
oriented employees.

------
dubya
I think Devlin has useful things to say about math education sometimes, but
his argument here is terrible.

The big mistake is conflating the CCSS eight basic mathematical principles
with the actual curricula as implemented by the textbook publishers. There's a
lot of crap being adopted, as publishers tack common core reference numbers on
hasty edits of bad textbooks.

Then there are all of non sequiturs in the article. Eric Mazur has success
with IBL? Must be just the thing for first graders. Children in India with
access to a computer taught themselves all kinds of interesting things without
instruction? Sounds like a Common Core classroom to me.

------
citrin_ru
Fortune 500 most valued skills is a bit misleading. Reading skills not in list
for 1999. May be all candidates already has good reading skills. Or may be
fortune 500 companies want to hire candidates without reading skills?

------
tokenadult
To give the earlier comments posted here their due, I think Keith Devlin's
argument in the interesting article kindly submitted here is incoherent enough
that it is possible even for people who largely agree with Devlin's
conclusions to disagree with how he presented his argument. I really like to
talk about mathematics education here on Hacker News, because I am a (part-
time) mathematics teacher by occupation.[1] It's plain that mathematics
education is better if it is really _education_ ("drawing out," by word
origin) rather than teaching in the sense of speaking out words that maybe no
pupil is listening to. Mathematicians are fond of saying that mathematics is
like swimming--you can only learn it by doing.

I can cheerfully damn the Common Core State Standards in Mathematics with the
faint praise that they are generally better than the previously existing
curriculum frameworks in most states of the United States.[2] I have lived in
other countries, and I know that mathematics education can be done far better
than it is done in the United States.[3] Keith Devlin is certainly correct
that young mathematics learners must learn to work exploratively with
challenging problems that cause them to think and wonder about what they are
doing rather than merely memorizing thoughtless procedures.

It is also crucially important that elementary school teachers be trained and
equipped to teach mathematics well, as lousy mathematics instruction in early
childhood is an especially strong factor that keeps many American pupils
poor.[4] Right now many families are doomed to low incomes and thus low upward
social mobility by how their children are instructed in mathematics in
elementary school.

[1] The nonprofit organization that organizes the classes I teach provides
some details about the classes.

[http://ecae.net/math1/](http://ecae.net/math1/)

[http://ecae.net/math2/](http://ecae.net/math2/)

[http://ecae.net/math1/orientation/](http://ecae.net/math1/orientation/)

[2]
[http://educationnext.org/files/ednext_20123_Forum.pdf](http://educationnext.org/files/ednext_20123_Forum.pdf)

[3] "Good intentions are not enough" by Richard Askey

[http://www.math.wisc.edu/~askey/ask-
gian.pdf](http://www.math.wisc.edu/~askey/ask-gian.pdf)

Review by Roger Howe of _Knowing and Teaching Elementary Mathematics_ by
Liping Ma

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

"Word Problems in Russian and America" by Andrei Toom

[http://toomandre.com/travel/sweden05/WP-SWEDEN-
NEW.pdf](http://toomandre.com/travel/sweden05/WP-SWEDEN-NEW.pdf)

[4] "Racial Equity Requires Teaching Elementary School Teachers More
Mathematics" by Patricia Clark Kenschaft

[http://www.ams.org/notices/200502/fea-
kenschaft.pdf](http://www.ams.org/notices/200502/fea-kenschaft.pdf)

------
dusklight
Did it ever work?

------
Xcelerate
I am absolutely amazed at how much the debate centers around the content of
what is taught with Common Core. There was an article a few days ago on HN
about the mathematician who came up with the design for the math portion of
Common Core.

I think these people are completely missing the point. The focus should be on
_how to teach_ , not necessarily on _what_ is being taught. My sister is a
teacher. She has taught at some of the worst schools in the state
(1,000/1,100) and is just now beginning at one of the best schools. The
problem isn't the math itself; it is how the math is taught.

For some reason everyone in society feels compelled to voice their opinion on
how things should be done in education. This is absurd. Would the average
person dare tell a nuclear engineer how he should be designing his reactor?
Would they pretend to argue about the airflow over an aircraft wing? Would
they tell me I'm using the wrong Hamiltonian in my QM simulations? No, of
course not. They have absolutely no expertise and no experience in the field.
Similarly, the vast majority of _everyone_ has no experience whatsoever
teaching thousands of very different students from different backgrounds with
very different learning styles and needs. So why then does everyone feel like
they have the capacity to decide what the best education system is?

Most people recall going to school themselves when they were younger, and they
know what learning strategy worked best for them, and then they project this
learning style onto everyone else. That's not going to work. Does that
mathematician who helped designed the Common Core standards have any
experience working with a class where 97% of the students are on free lunches
and their parents are in jail and addicted to cocaine? Of course not; his
daughter goes to an upper-class school. Her situation is completely different.

~~~
rdtsc
> Would the average person dare tell a nuclear engineer how he should be
> designing his reactor?

If the average person were ocasionally or maybe even throughout their life
engaged in designing and building reactors, even just once, yes they would.

Let's say an engineer build one nuclear reactor during their lifetime. Would
you give their opinion any weight in nuclear reactor design? Well you should.
Especially if the reactor is still standing safely and producing electricity
(or you know, loads of Plutonium) [extrapolate to -- they are gainfully
employeed in a profession, not starving, or sleeping on the streets].

Unlike nuclear reactor or QM circuits building every adult is at some point
engaged in learning. Both as the one being taught (child, student) and the one
doing the teaching (parent, mentor, tutor).

> Does that mathematician who helped designed the Common Core standards have
> any experience working with a class where 97% of the students are on free
> lunches and their parents are in jail and addicted to cocaine? Of course not

Agreed. But then you take their datapoint as a singular data point, and with a
grain of salt that they came from a family of college professors, etc etc.
Instead of drug dealers.

Moreover, what the mathematician designing the Common Core should have done
was to look at what are some of the components in a country with better scores
and a more successful school system. I think we talked about about the school
system in Finland here (or was Reddit, can't remember anymore). The key was
that it wasn't just "better teacher" or "better worksheets" but a better
environment. Like you said, not being afraid of going home and getting beaten
by a drunk parent or worrying about not having a dinner that night. No ammount
of fancy new Worksheet and "shotcuts" will help that child.

