Mathematics Teaching No Longer Works
devlinsangle.blogspot.com
devlinsangle.blogspot.com
JoIP is http://www.projectinnovation.biz/journal_of_instructional_ps..., 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 ... 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?
That's also when "workplace collaboration" took off.
Why don't we just call a spade a spade and call Devlin out for working backward from a preconceived text?
You start with the conclusion and gather the evidence that supports it.
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...
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
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...
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.
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.
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 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... :
> 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/
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... . 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.
There's the increasing desire to run schools as a business, rather than as a public good. There's the increasing push for removing union protections. I think it's funded partially by a way for for-profit companies to make money off of all of the education dollars, hid behind the religion of free market.
That said, none of these are new factors. It's all a difference in weighting factors over the last century or two. One of those reweightings is Bill Gates, whose foundations funded nearly $250 million towards Common Core. That buys a lot of influence if done right.
It's not worth my time to educate you when you don't know the basics and would rather ask unanswerable questions than research it yourself.
I do strongly agree however that the Fortune 500 shouldn't dictate what gets taught in schools.
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.
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/orientation/
[2] 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
Review by Roger Howe of Knowing and Teaching Elementary Mathematics by Liping Ma
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
[4] "Racial Equity Requires Teaching Elementary School Teachers More Mathematics" by Patricia Clark Kenschaft
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.
An article link I was just posting in an edit in my comment in this thread[1] relates just how hard it is now to find elementary school teachers in the United States who can even give a general description of how to find the area of a rectangle knowing the lengths of the rectangle's sides. That's bad.
Anecdote: My friend is a high school math teacher. We both have kids of similar ages, going through the same schools. When the kids were toddlers, he voiced the same opinion about letting the professionals do their job. Today, with his kids in middle school, he is no longer of that opinion.
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.