Teachers In Our Lives

                            "Reach out and touch someone..." 

                                              -- old AT&T ad slogan

I attended (long enough ago that a 50-year reunion is coming up!) a private secondary school where the phrase “in loco parentis” was oft-discussed. In case any don’t know, it translates to ‘in place of the parent’ which carried one meaning, or at least set of applications, for our school administrators, and rather different interpretations favored by we students. At a private boarding school teachers/administrators, as the primary adults that students see each-and-every day, really must take on the partial role of substitute parent. But even in the public school system almost all students will experience at least a few teachers who partly play that role.

I won’t claim that I had very many teachers who had a strong or major impact on my life or career, but there were probably a couple. Moreover, there were teachers who even without impacting my career I simply enjoyed learning from; who made education what it should be: something to relish and look forward to.

Two years ago in an idle moment I looked up my favorite teacher from 7th grade on the internet only to discover he had just passed away a few months prior.  I think at the time I had him for class he knew how much I enjoyed him… but in the 50+ years since I had no contact with him.

I look back now with some regret of how few of these educators I ever re-touched base with after taking their class; and the few I did, how infrequently; realizing only later in life how much it probably meant to them to hear positively from former students; even just a small note of appreciation, a Christmas card, a phone call, an acknowledgement that they were fondly remembered or had an impact…

I bring this all up now because of a poignant, personal entry Patrick Honner posted about a recent experience he had relating to the challenge of teaching and the "constant struggle to find... the balance between expectations and patience; between being tough and being understanding; between pushing a young person and letting them be":

http://mrhonner.com/archives/18340

...And one of the reasons I savor (and suspect we all do!) Fawn Nguyen’s writings about teaching, is because of the love for her students that shines through her musings (even when she's employing 4-letter words!), and that delicate dance teachers do between being teacher/parent/friend/disciplinarian, pulling students in close while still maintaining a distance… and never knowing if, once they leave your school, you will ever hear from them again.

Almost exactly 4 years ago I had occasion to ask Fawn (via email) what her favorite post on her blog was and she cited one. I don’t know for sure if 4 years later it’s still her top pick, and until the very end it doesn’t even have that much to do with the teacher/student relationship, but it’s still one I’ll offer up here (and if you can reach the end without a tear in your eye, well….):

http://fawnnguyen.com/you-are-a-girl-female/

Finally, I’m reminded too of a favorite timeless volume occasionally touted here for any who have missed it:  Steve Strogatz’s “The Calculus of Friendship,” about his lifetime relationship with a high school math teacher; on one level based upon a shared love of calculus, but of course at a different level much more (…and by the way there’s real math in it as well).

Anyway, readers here probably all know of Patrick, Fawn, and Steve… I don’t need to draw any more attention their way. What I do hope to do though is maybe make you think, amidst this season of graduations, about the teachers in your own lives who were somehow special or inspiring or supportive, who perhaps parented you along the way a bit even if you only realized it much later.  Get in touch, let them know, drop an email; it’s only too late if they pass from this Earth never knowing.

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Addendum:  In a bit of coincidence, Patrick Honner informs me that (unbeknownst to me) this week is national “Teacher Appreciation Week” ….sometimes the world operates in mysterious ways ;)

Keith Devlin Explains MY Past (maybe)

The debate over what content to teach in math and how to teach it seems to go on forever (as did the first draft of this post!)….

First off, I'll mention that Richard Feynman famously had his own outspoken views on science school textbooks, which he covered in a chapter of one of his books, reprinted here:

http://www.textbookleague.org/103feyn.htm

It's a long (but entertaining) read so I'd wait and come back to it at the end, but I do think it's a must-read if you've not heard him address the subject before.

Recently, Keith Devlin, among others, posted a number of tweets about math education. I'll offer just two of those from Dr. Devlin that seem to capture the essence of what he is arguing (and has publicly said for quite awhile):

"I would not say math is a skill. It requires skills to do it. But it's really a way of knowing/thinking/acting."

"Mastery of arithmetic was REALLY important until around 1955. No longer so. Math thinking is important now."

Sounds simple, but this is very very deep stuff in my opinion, not easily comprehended by most… and certainly debated by many (as tweets from others often indicate).
For a fuller take on Dr. Devlin's viewpoint see this older post of his that got a lot of buzz:

http://www.maa.org/external_archive/devlin/devlin_06_10.html

...and here's one 5th grade math teacher's favorable response to Keith's thoughts:
http://petalschools.com/Page/3390

I've gradually moved toward Dr. Devlin's view partly in sheer deference to his long-time work and knowledge in this arena… but also for another reason as well: It may finally account for my own math experience:

For 40 years I couldn't understand my failure to succeed as a math major in college, having loved math from a young age, and early on professing a desire to be a mathematician (or astrophysicist). I did excellently from primary school through high school (scoring 800 on the math SAT!), yet hit a brick wall in college. There were some practical reasons involved which I won't cover, but essentially, for decades, I've pondered, with no resolution, why my youthful number talents didn't carry me through.
After 40 years of puzzlement, Dr. Devlin's perspective finally offers some clue. Keith has long contended that primary/secondary mathematics is a completely different animal from college-level mathematics, so it isn't that unusual for someone to breeze through the former (which simply require a certain skill set), but get stuck on the latter, which requires a deeper, more abstract understanding.

Sidenote: Coincidentally, @mathmaniac tweeted one of my very favorite old (deceptively simple) geometry problems last week:

https://twitter.com/mathemaniac/status/451483080432185344/photo/1

As a teenager I remember working on this problem assiduously until someone showed me the "10-second" face-palm solution. I wonder now if problems like these are Rorschach tests separating those who truly think more mathematically from those who, like me, thought more computationally or mechanically??? Or perhaps it relates back to what Edward de Bono famously termed "lateral thinking" (sort of 'outside-the-box') versus the more common "vertical thinking." I'm not sure…
Anyway, this distinction between mathematical skills and more abstract mathematical thinking, intrigues me. So I sent Dr. Devlin a few questions to flesh out a little more of his thinking, and he responded [I've added some bold]:

*******************************

1)  You've written that "mastery of arithmetic was REALLY important until around 1955" but now "math thinking" is what's important. Do you recall when and what brought you to that distinction? And was it an epiphany of sorts for you, or more a gradual change of view over time with evolving technology?

Keith:  The reality is that what I now deliberately refer to as “mathematical thinking” is what I (and all creative mathematicians) have always understood by “mathematics”. I learned over many years of writing for, and interacting with, non-mathematicians (including my daughters’ mathematics teachers) that many non-mathematicians understood the word to mean something very different. It was probably reading Jo Boaler’s work, which I wrote about in my MAA blog in 2010 (http://www.maa.org/external_archive/devlin/devlin_06_10.html), that finally persuaded me to start using the term “mathematical thinking”. The real meaning of “mathematics” had been lost in the public mind. As Boaler’s research showed, popular impression was that mathematics is a collection of mindLESS techniques, and has nothing to do with reality.

My views on just how much mathematics had fallen victim to a “Reality Distortion Field” were driven home for me when I tried to secure NSF funding for a radically different video game concept I had developed (with good video game designers!) that embedded deep and challenging mathematics. We were turned down after one reviewer (that’s all it takes) said there was "not enough mathematical meat” in the game. The first game built on those ideas, Wuzzit Trouble, which the reviewer experienced in prototype form, is now out, built with private investment, and I suspect that reviewer is finding it mathematically challenging. I know of no other game (and I have played many) that requires greater deep mathematical thinking (i.e., “mathematics” problem solving). It just does not fill the screen with symbolic equations. (See http://www.americanscientist.org/issues/pub/the-music-of-math-games for a discussion of the design principles.) And guess what, people love it.

After that experience, I finally had to admit that the only possible answer to the provision of good education in this country is by private enterprise. The state system is a century out of date and broken beyond repair.

(BTW, that phrase “Reality Distortion Field” I just used? Apple employees used to use it to describe Steve Jobs' visions — you know, the ones that became the Macintosh, Pixar, iTunes, the iPhone, the iPad. What Jobs showed was that you see distortion from both sides. You just have to figure out which side is reality — and then make it so!)

 [WOW!, interesting, and discouraging :-( to hear Keith say that public education is "broken beyond repair" and to surmise that only "private enterprise" can provide good education -- I hear his frustration, but hope he's ultimately wrong about that.]

2)  When you first started making this distinction, and new emphasis on "mathematical thinking," did you feel at all like a lone wolf crying in the wilderness? And who would you now point to as other writers/educators worth reading who share/espouse your emphasis?

Keith:  To some extent maybe I was a lone wolf at the start. But not for long. At the schools level, Dan Meyer came along and shook up the math ed world with one 15 minutes TED talk, and at university level Ed Frenkel has come storming in. None of us is unique in these views, but we have bigger media pulpits than most others who say the same thing.

3)  To what degree (if any) is the distinction you're drawing between "skills" and "thinking" applicable to other scientific fields beyond mathematics… physics, biology, chemistry, computer science…?

Keith:  It applies to all of those fields. The US is not alone, but definitely leads the way, in having an education system that takes learning — something evolution hard-wired into us as an instinctive activity that gives us pleasure (the dopamine fix) — and turns it into a test-driven drudgery.

In the 19th Century, when our K-12 education system was being developed, being a well-trained, rule-following drone was the key to lifetime security by way of a job-for-life.

But today’s world is very, very different -- as millions of out-of-work well-educated people will attest. But our education system is still a century behind. Our political leaders, who maintain this status quo, are either ignorant or else have a vested interest in keeping as many people on the bottom rung of society's ladder as possible. (Both may apply.)

*******************************

Dr. Devlin has an ongoing MOOC course covering all this. I'm sure out of the 1000s who sign up for his course each go-around many MISconceive what the course will be about and drop out disenchanted, so different is "mathematical thinking" from most peoples' idea of math (and Dr. Devlin does explain ahead-of-time what the course will and won't entail) -- p.s. high percentages drop out of most MOOCs.

The so-called "New Math" of the 1960s (which I experienced, much to my dismay) was a short-lived failed experiment in math education that most here know about. Sometimes parts of Common Core, or the sort of learning Dr. Devlin encourages, get referred to scornfully as the "new New Math." The original New Math was of course perfectly valid mathematics, but was often critiqued as being inappropriately targeted at youngsters not cognitively ready for it. Of course, cognitive styles, even of young children, may be highly variable -- indeed, I believe they're more variable than perhaps recognized. And once again that seems to be a central issue in the current debates... what are different age groups really prepared for in the way of content? Is it even possible to generalize? Another recent article (via The Atlantic) on the success of Maria Droujkova's "Natural Math" for youngsters, indicates what children are capable of.  Perhaps the real problem with most math reforms has less to do with children's abilities, than with a failure to adequately train their teachers in the new approaches. I don't pretend to know...?

There's so much more out there on this topic, but I don't wish to drag this post out, so will just leave you with some additional links which offer varying perspectives (...if you've read this far you're likely already aware of most of this!), but again I'd start with Richard Feynman, because, well, anytime you can begin with Feynman, that ain't a bad way to start!
 
A few others:

The perspective of an expatriate math tutor:
http://expattutor.wordpress.com/2013/09/05/the-new-math-part-i-why-we-have-it/

http://expattutor.wordpress.com/2013/09/05/the-new-math-part-ii-why-its-not-working-so-many-schools/

2012 piece on Jo Boaler's experience:
http://www.metafilter.com/121036/Boaler-and-the-math-wars

David Wees recently trying to sum up what "effective mathematics teaching" entails:
http://davidwees.com/content/what-does-effective-mathematics-teaching-look

And in addition to Dr. Devlin's piece that I started with, he has MANY other Web-accessible discussions of math education, thinking, etc.. Here are three:

wonderful hour-long podcast:  http://tinyurl.com/k54fvfu
blogpost:  http://profkeithdevlin.org/2013/06/19/faulty-logic-in-the-new-math-wars-skirmish/
hour-long video:  https://www.youtube.com/watch?v=bSByo3kOGjs

And if you're on Twitter, and interested in these sorts of issues, the #mathed and #mathchat hashtags are sources of ideas/debates from many thoughtful folks.

Of Education and Game-playing

 I often try to steer clear of these education debates, but did enjoy Cathy O'Neil's recent quick take on Diane Ravitch and Common Core standards:

http://mathbabe.org/2014/01/29/diane-ravitch-speaks-in-westchester/

A stupendous amount has been written (pro and con) about Common Core in the last year-or-two, so don't mean to single out Cathy's piece above other views, except I like the approach she's taken.

I grew up at a time when several of my peers were graduating high school without basic reading, writing, and math skills… how these particular students were even being passed along from grade-to-grade, let alone graduating high school, was hard to comprehend. It was, frankly, an embarrassing, deplorable (even fraudulent) situation. Universities found, to their surprise, that entering freshman sometimes lacked the necessary skills for college work… significant remedial programs had to be instituted.

So when, understandably, standardized proficiency-testing programs began implementation state-by-state, I eagerly supported it. Since then, I've often participated in the 'grading' of these standardized tests, and what became apparent within a few years was that teachers were 'teaching to the test.' It had all become, almost inevitably, a sort of game for teachers, whose own evaluation was often based in part on how well their own students did on such tests. So they gamed the system, likely skirting some teaching responsibilities, creativity, and effectiveness in the process.

I've written earlier that I believe the use of 'flipped classrooms,' MOOCs, and digital resources in general is one of the most fascinating, even 'paradigm-shifting' changes in education coming along, yet grappling with "standardized testing" remains a hugely difficult nut to solve. Not only must there be some sort of standardized requirements (especially for mathematics) that all students should meet before graduating high school (…and really, LONG before graduating high school), but I believe they should indeed be national, and not variable state-by-state standards. BUT these should be truly bare, minimalist levels of literacy and numeracy for our adult population (or each grade level), not "high-bar" or accomplished standards.
In some ways Common Core seems like one of those near-comical results portrayed when 'designing things by committee': http://tinyurl.com/mcay7uq

I once attended a college that required a "swim test" (long since dropped) for graduation. The idea was not that everyone should be a good or fast or very capable swimmer, but simply that everyone ought have some ability to float and dog paddle and move through the water, in the event of an emergency -- that this was simply a life skill (even if not an academic skill) one ought have as a college graduate.
The whole nature of "literacy" is rapidly changing… in the future, basic societal "literacy" won't so heavily entail reading-and-writing skills, but rather computer, coding, and office-suite sorts of skills -- THESE will be basic needs to successfully 'swim' in society (having read and discussed "Hamlet" in high school, or knowing how to diagram a sentence, will be of virtually no use!) So I still believe some form of standardized proficiency testing is necessary, but I too have reservations about rigid Common Core standards, as configured -- almost inevitably, they will set in motion another round of diversion and educational game-playing, stifling creativity... while raking in big bucks for the private enterprises developing/administering them.

Perhaps we have become such a society of manipulators, shirkers, and system-gamers that
there is simply no good solution to such a double-edged problem (both no-uniform-testing and mandatory standardized testing are problematic), but only least-bad solutions…. but as Cathy concludes, the first, necessary steps really involve, not reforming our educational system, but alleviating poverty and related underlying conditions that undermine learning. And on THAT score, our nation seems to be moving entirely in the wrong direction. (...Long, one of the most lunatic things to me, has been the way our public schools are funded largely through local property taxes -- a system insuring wide disparity in quality between schools... but that's a topic for a whole different discussion.)

Of course, a LOT more thoughts/news on math Common Core available through Google:
http://tinyurl.com/l547xsb

Flipped Classrooms, MOOCs, and Having a Blast

Timing is everything....

Well, this was great… I was planning to write a post musing a bit more about math education in regards to both "flipped classrooms" and MOOCs… but then discovered Keith Devlin has just put up a new (longish) post on his MOOC blog saying most of what I wanted to say, and with more authority than I could say it. So please read it:

http://mooctalk.org/2013/06/03/the-mooc-will-soon-die-long-live-the-moor/

Do note that I think his title may be a bit misleading so follow carefully all he has to say. I was afraid his long lapse in blogposts might mean that the 2nd rendition of his 'mathematical thinking' MOOC hadn't proceeded well (though his insanely busy schedule could also account for it), and luckily it doesn't sound like that was the case… though he does still write with caution about MOOCs, and will have more to say in the future about this last go-around.

Here are a few of the most trenchant comments he makes (I've added some emphasis):

"the vast majority of people under twenty now interact far more using social media than in person.
We could, of course, spend (I would say “waste”) our time debating whether or not this transition from physical space to cyberspace is a good thing. Personally, however, I think it is more productive to take steps to make sure it is – or at least ends up – a good thing. That means we need to take good education online, and we need to do so for the same reason that it’s important to embed good learning into video games…
"The media of any age are the ones through which we must pass on our culture and our cumulative learning."

"Something else that digital technologies and the Web make possible is rapid iteration guided by huge amounts of user feedback data – data obtained with great ease in almost real time."

The one place where I think Keith sounds a little too negative is when he writes:

"Experimentation and rapid prototyping are fine in their place, but only when we all have more experience with them and have hard evidence of their efficacy (assuming they have such), should we start to think about giving them any critical significance in an educational system which (when executed properly) has served humankind well for several hundred years. Anyone who claims otherwise is probably trying to sell you something."

Actually, I think "experimentation and rapid prototyping" may now be an integral part of our quickly evolving world and education system… more than ever before change can happen with such speed that we may try 4 failed experiments and still succeed at #5 in an acceptable/practical amount of time (even before the "hard evidence of efficacy" is fully in or agreed upon. Just the speed with which the MOOC movement has grown is a testament to that, and as Keith implies, the time is ripe for us to "make sure" they [MOOCs] work in some form.

So much for MOOCs…
What actually got me thinking again about education was a recent Twitter tweet that led me to this blog I was previously unfamiliar with:

http://flippingwithkirch.blogspot.co.uk/

Despite the uk URL appendage it's from a California high school math teacher (Crystal Kirch) focused on the "flipped classroom" concept. Just scanning over it, it looks interesting and impressive to me, but as someone not in the loop of secondary education I don't want to assume too much. What definitely caught my attention though (and those of you in secondary education likely already knew this) was the sheer number of other blogs with a similar focus on flipped instruction (as well as a network of teachers with this interest) that Mrs. Kirch links to. The "flipped classroom" has been around long enough that LOTS of teachers are trying it, tweaking it, playing/experimenting with it, blogging about it, and just generally sharing their experiences (good and bad) with their peers. What a great collaborative endeavor!!… and not brought on by some agency-directed-commissioned group-on-high, but by the spontaneous interest of those who share similar goals. Again, before the internet this sort of rapid cross-communication effort wasn't possible.

The term "flipped classroom" came about, so far as I'm aware, from early uses of Khan Academy videos (and Khan Academy still has many vocal critics), but of course there are now MANY internet resources available to choose from, and Khan itself constantly evolves. (Some have noted that the 'idea' of the flipped classroom, though not the term itself, actually long precedes Khan Academy.)

It is fascinating to me how both "flipped classrooms" and MOOCs, which in some ways share little in common, and operate on different levels of education, have simultaneously sprouted up like mushrooms in the cyber landscape, both controversial and rapidly-evolving, yet giving tremendous promise.

As Keith writes so aptly at the end:

"Those of us in education are fortunate to be living in a time where there is so much potential for change. The last time anything happened on this scale in the world of education was the invention of the printing press in the Fifteenth Century. As you can probably tell, I am having a blast."

And some of us are just having a blast... watching those of you who are in the trenches having a blast.
To Keith, and Mrs. Kirch, and all others doing the nitty-gritty work that will shape the education of future generations... THANK YOU!

How MOOCs Are Organized… Devlin-style

Posting this here since I'm feeling a tad guilty about how often Math-Frolic posts reference back to Keith Devlin!!… but the man isn't simply prolific, he's incredibly insightful, curious, and hard-working... and, has an endearing British accent ;-).
Anyway, his latest post on the second edition of his (free) Stanford/Coursera MOOC course, "Introduction To Mathematical Thinking" (beginning in March, and still an experiment) ought not-be-missed if you've never taken a MOOC but wish to get a sense of how they proceed  (his optional book for the course, is available through Amazon) :

http://mooctalk.org/2013/02/24/how-are-moocs-organized/

The post is actually a bit dry reading but still chockfull of what to expect in the way of form and organization from this particular MOOC. And importantly I think, toward the end Keith writes, "This course is about learning to think a certain way – the focus is on the process not the product. You will need time to understand and assimilate new ideas. Particularly if you were a whiz at high-school math, you will need to slow down, and to learn to think and reflect (and ideally discuss with others) before jumping in and doing."

In the post Keith links to a 7-minute (low-resolution) YouTube sample of what a typical course lecture is like:



BTW, Keith writes this of the video lectures:

"The lecture videos are not carefully crafted, heavily edited productions. If you want a polished presentation of the course material, you can read the course textbook. My goal with the lectures is to provide as best I can the experience of sitting alongside me as we work through material together."

...Also in March, Keith's private company InnerTube Games releases its first math video learning games for younger folks (this is completely separate from MOOCs), so I know I'll be referring back to him yet again in the near future. (Go HERE to be notified when news of the games is released.)

And speaking of secondary/primary education, NPR's "TED Radio Hour" (based on TEDTalks) has a wonderful episode that includes Ken Robinson and Sal Khan talking about the nature of education (not specific to math, but more generally) -- even if you've seen their TEDTalks it's worth a listen (Sir Ken Robinson is one of the most popular speakers that has ever been on TED):

http://www.npr.org/2012/06/22/155224654/building-a-better-classroom

A LOT has now been written (and continues to be, pro-and-con) about the "flipped classroom" that Khan Academy spawned. Here is just one article from a couple months ago:

http://www.insidehighered.com/blogs/hack-higher-education/top-ed-tech-trends-2012-flipped-classroom

Or, if you want pieces more specific to flipping math classes you can check out this google search:

http://tinyurl.com/b2hsx7q

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The Times They Are a-Changin'

"Come writers and critics
Who prophesize with your pen
And keep your eyes wide
The chance won't come again
And don't speak too soon
For the wheel's still in spin
And there's no tellin' who
That it's namin'
For the loser now
Will be later to win
For the times they are a-changin'."
                   -- Bob Dylan


I don't usually write essays here, but will give it a try and see what happens… just an off-the-cuff piece on math education:

When Sol Lederman asked me, in a podcast, what I'd suggest to a parent of a youngster having difficulty with math, the best I could offer was to search the myriad digital-learning offerings of the Web (unavailable to previous generations) for something that the child would "click with." For one child it might be a Khan Academy type format, for another an animated cartoon setting, and for another an interactive game approach or other tutorial. ...But I'd like to broaden out that whole line of thought.

Anything I say here is merely shooting from the hip, since I'm not active in the loop of secondary education, but I do inevitably read the ongoing debates over secondary (and elementary) math education, and also Web-based tutorials. The usual constant refrain of course is that math education in this country (U.S.) is not very good; we're falling behind other countries; students are too often turned off to math; we must improve… and these concerns have been around for decades; today the internet simply amplifies the discussion.
A couple of my own youthful years involved the short-lived experiment that was the so-called "new math" which ended largely in disarray (not so much because the concepts behind it were poor, but because they just weren't age-appropriate for the young minds they were addressed to).  I too have always concurred that math education ought be improved. But the implication of all this sound-and-fury has long been that there was a magic bullet out there somewhere that would solve the problems if only we could find it, develop it, and spread it across the schools of the land.
I'm doubtful now of that one-size-fits-all scenario.

The longer the debate continues, the more likely I think it is that there is no magic bullet or "best way" to teach math (though certainly some techniques are better than others for most students). Instead, education may eventually move toward a highly "individualized" format… analogous to what is happening, slowly but surely, in medicine, wherein future treatments will be customized to the specific genomic profile of the individual.  Medicine of today, by comparison, will seem primitive, crude, even unempirical.

I suspect education is headed (slowly) in the same direction. We will find that different youngsters simply have different "learning styles" (perhaps even partially genetically-based) -- some very visually-oriented, some more auditorily so, some needing hand-eye coordination interaction or other movement, etc. etc. A very good math-teaching technique, rather than being effective with say 70-80% of students, may only be really effective with say 19% of students… while a different technique/format may work best for another 16%, and another technique for a different 14%, on down the line, but with no one method really predominant. (And, there will always be some subset of students for whom no technique is terribly successful, so weak is their aptitude for mathematical skills).

The greatest focus of controversy in recent times has been Khan Academy… with critics and proponents in abundance. But Khan Academy is not a finished product… it is a work-in-progress, bound to evolve over time, hopefully constantly improving (many criticize the quality of production, but that can easily change). It is likely effective or ineffective for different sets of individuals. I just don't see it as either good or bad overall.
Moreover, some vocal critics of Khan may, consciously or unconsciously, simply fear for their own careers (and thus lack full objectivity) if Khan-type resources too heavily infiltrate the educational system. More generally, some folks are claiming the video lecture style will never be an effective teaching device… I'm not convinced that isn't a premature judgment -- first, because I suspect some small percentage of young people actually DO learn effectively from video lectures (that they can view and pause on their own time, at their own pace), but moreover because it's still early in the technology. Those videos may eventually be in 3-D, which could make a large difference; or alternatively the videos may eventually be more interactive -- NOT interacting with the speaker who is still pre-recorded, but with a live (paid) individual who acts as tutor or assistant, or even an advanced Siri-like robot. Other future technological possibilities may be barely imaginable right now, but still come with a core component of video lecture, which, once embellished, is far more effective than today. It's just too early to tell.

Having said all this, Keith Devlin is coming out (any day now) with his own math learning video games, via his own private company (innertubegames.net once it goes live). I'll be hugely interested to see what his effort looks like... could it be the 'one-size-fits-all' I'm so doubtful of, effective with a great majority of students? (I'm skeptical, but also anxious to see it; a lot of time, study, and effort has gone into the project, and anything from Keith has to be taken very seriously).

At any rate I feel optimistic that the digital revolution in education, and specifically math education, will be an immense step forward in some form -- that in the future more young people will learn more math, earlier and faster, and with greater enjoyment than ever before, through a large array of disparate methods semi-customized to each individual. It won't come overnight or without intense arguments or even false paths and problems, but it's on the way, and best of all will be scalable worldwide. Sal Khan's ideal of a level playing field all across the globe, however it comes about, isn't just a noble goal, but a necessity for the future of human society.

The internet is chockfull of discussion of the controversy around the Khan Academy model. I'll just pass along one recent take on it here (but you can google to find so much more):

http://thejournal.com/articles/2013/02/07/the-math-of-khan.aspx


There is a related issue to all of this, which I almost view as the thorniest part though: I grew up in a day when some students graduated high school who could barely read or write let alone possess math literacy. I don't know how this routine "passing students along" from one level to the next ever came about, but it was certainly part of the motivation for the standardized "year-end" test requirements that were soon implemented to insure a level of achievement before moving on to a higher class level. And soon after standardized tests propagated so did "teaching to the test," the insidious tendency for teachers to forgo normal teaching material in order to concentrate on specific skills for passing tests.
I'm a believer in some form of "standardized testing" as the only way to really anchor or give meaning to widely-variable (and subjective) grading systems. But it's also true that any form of standardized testing can likely be gamed, and once a few teachers game it, everyone else is pressured to do so (math testing may be slightly more insulated from some of this since it is inherently more empirical than say, "verbal" testing, but it remains a concern). A recent Washington Post piece addressed the general issue via a letter from a retired high school teacher to a generic college professor, essentially apologizing for the academic quality of students being sent his way:

http://tinyurl.com/bg7mm2b

Wrapping up, I think the digital resources and methods for successfully teaching mathematics are probably already available or rapidly under development… THAT part of the education problem, will readily be resolved given time. But the issues surrounding fair and accurate achievement testing may be a harder conundrum-to-crack, especially to the extent that teachers themselves are reviewed/judged by their students' very test results.

But those of you who are in the trenches feel free to enlighten me; I'm just rambling off-the-cuff here….