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The "Mathlash" To Silicon Valley's Move Into Education

While Khan Academy’s videos flourish, a growing chorus of math teachers are calling out the site for emphasizing an unhelpful and rote version of mathematics. The only antidote: real, live human teachers.

"Khan Academy may be one of the most dangerous phenomena in education today," declared a recent blog posting by Karim Ani, the founder of Mathalicious, a site that offers richly integrated math videos and curricula.

Ani’s comments triggered an outpouring of reactions from mathematics teachers around the U.S. A couple of days later, Dan Meyer, a former math teacher now working on his Ph.D. at Stanford, weighed in with his own attack—this less about Khan Academy per se and more about Silicon Valley entrepreneurs’ approach to capturing math in a computer program.

"The medium defines, changes, and distorts the message," he wrote. "When you attempt to distribute mathematics through any of these media [such as YouTube videos, digital photos, MP3s, PDFs, blog posts, spoken words, and printed text] it changes the definition of mathematics.

"Silicon Valley’s entrepreneurs, venture capitalists, and big thinkers assume a shared definition of 'mathematics.' They innovate around the delivery of that mathematics. CK-12 has PDFs. Khan Academy has YouTube videos. Apple has iPad apps. ALEKS and Junyo have computer adaptive tests. Very few of them understand that each of those delivery media changes the definition of mathematics.

"Even worse, at this moment in history, computers are not a natural working medium for mathematics (PDF)."

Some 150 or so comments later—along with another hundred or so comments on HackerNews—the tensions between the teacher-centric and the entrepreneur-centric viewpoint continue to emerge.

Some teachers have been stung by the notion that Khan—a guy in his pajamas who doesn’t seem to give a wit about decades of pedagogical research—is teaching online. Others are distressed that when he gives away his lessons for free, no one else will be able to make a living selling their more carefully constructed curricula. (Mathalicious’s Ani has a foot in this camp.)

Still others (including both Ani and Meyer) grind their teeth at Khan’s here’s-how-you-solve-it approach to math. "This paint-by-numbers method of instruction emphasizes procedures—how to do math—but ignores the conceptual understanding that’s central to authentic learning: what math means. At its core, this is a function of ineffective instruction, which to a large degree is related to ineffective content," writes Ani.

Meyer takes the argument a step further, contending that most edtech tools take a "just solve it" approach to math that is fundamentally incompatible with a more experiential approach. He writes: "The argument that these innovations are all supplements to one another, and all of them to a teacher, and that none are meant as a complete solution is a common one in [Silicon Valley]. But I think it is a mistake to assume that the different definitions of mathematics promoted by each of these different innovations will all harmonize with one another."

Part of the confusion stems from uncertainty about the purpose of education. Most people would agree we don’t simply want children to succeed at taking tests. (Even on this point, however, some contend that test scores— such as 8th grade math scores—are a good predictor of later success, notes Harvard’s Roland Fryer).

Most of us also want students to be creative, curious, and ready to learn new skills no matter what direction their lives take them. That doesn’t happen in every classroom: "The reality is we only need Khan style edu to outrun the 50% of teachers who are just horrible (so we can increase class size), scare 40% of them to work harder using Khan in the new bigger classes, and reward the last 10% with sizable pay raises," contends Morgan Warstler on Meyer’s blog.

At the very least, educators (and parents) hope students will understand how to reapply their newly acquired knowledge to broader mathematical situations. That is a tricky skill to teach, however. On Meyer’s blog, teacher David Wees wrote:

"What I find frustrating is that the over-emphasis on the value of the data [Khan has] collected. I used the Khan Academy with my students (mixed in with a problem solving and project based approach) at the beginning of this year, and within 6 weeks I abandoned it (after two assessments I’d given to students external to the program) because I found no relationship between what my weakest students had 'mastered’ according to the types of questions the Khan Academy provides, and the students ability to use their calculations in any other context. They could do 30 problems in a row flawless related to the rules of exponents, for example, but not solve any problem directly related to the rules of exponents that they hadn’t seen on the Khan Academy videos or exercises. The transferability of what my weakest had learned was extremely low. By contrast, the approach absolutely worked fine for my stronger mathematics students, who were able not only to transfer what they had learned, but to work at a pace I could not hope to match."

Finally at the core of the debate is a deep tension that all Internet denizens should recognize: Who’s in charge? Should educators, deeply versed in pedagogical research and countless years of feet-in-the-classroom, be calling the shots? Who gave the newcomers, typically entrepreneurs, many whom last set foot in class when they were students, the right to frame education?

Other industries have grappled with this tension, too, as the Internet became the dominant platform. In industries where "experience" mattered more than degrees or credentials, the newcomers have rewritten the rules. Travel agents, for instance, have seen their profession redefined by the likes of Travelocity and Kayak. Traditional journalistic organizations have similarly absorbed a body blow as the influence and credibility of bloggers has grown.

But professions where credentials are essential have changed more slowly: Lawyers still handle most legal affairs. Although online medical sites have flourished, few patients have severed their relationship with a flesh-and-blood doctor because they preferred the likes of

So what about teachers? Are they more like credentialed doctors who should have a commanding say over what tools are introduced into their practices or more like journalists, forced to prove their value every day? Or can teachers themselves learn to work with the entrepreneurial community to deliver curricula that have rich pedagogical roots? From the vantage of the millions who are Khan fans, that middle ground looks compelling:
"I have watched more than 700 videos on Khan Academy, over the past 11 months, and to me the single most significant impact of the videos is that it inspires me to learn more," wrote one commentator on Meyer’s blog.

"Can’t you work with Khan Academy, and the teachers trying to implement it in class rooms, to 'convey complementary definitions of mathematics’? Can’t you use the excitement generated by Khan Academy to raise the standard of teaching and learning in classrooms, and elsewhere?"

Add New Comment


  • inspiredworlds

    Online education and technological innovation such as mobile apps can be a great supplement to offline teaching. It can enhance and augment traditional teaching and as the comment in the article suggest, it can re-invigorate and inspire students to learn. What technology has done is lowered the barrier to getting information, the cost associated with it and enabled information to be dispersed  rapidly. Its made education more accessible.

    For example, Stanford university put some of their entrepreneurial and computing classes online, and it can now be accessed by people who didn't not have chance to attend the campus and enrol in the course. Innovation like Class Dojo (from the latest Imagine K12 batch), enables teachers to give virtual encouragement to students. 

    At Native Tongue, we've introduced a fun and engaging way to learn languages with arcade style gaming. With multi-sensory touch and immersion, we believe it is a great way for students to learn both inside and outside the classroom. It has also enabled people that want to be casual learners and lowered the barrier for them to start learning a language.

    I believe there is a way for entrepreneurs that are disrupting the educational industry with new ideas and insights to work with educators who have a pedagogical and curriculum based approach.Matthew Ho
    Native Tongue


  • Geoff Roulet


    The issue is not online versus face-to-face instruction,
    but in fact the pedagogical approach. The Khan Academy style of direct "paint-by-numbers"
    instruction can be, and unfortunately often is, employed in live classrooms.
    The results here are similar to those a number of comments attribute to the
    Khan Academy – students who can perform well on repeats of questions they have
    already seen, but who cannot transfer skills to other contexts. To claim that
    the Khan Academy is the only online approach makes as much sense as claiming
    that all classroom teaching involves direct instruction. We all know that there
    are teachers who engage their classes in rich mathematics investigations, and
    through these help students develop a deep understanding of mathematical processes.


    Silicon Valley entrepreneurs like the direct instruction Khan Academy approach
    since it can be programmed and then run without human intervention. Humans
    expect to be paid and this cuts into profits. But "online" does not
    have to mean "without human interaction". When I visit my cousin's
    Facebook page to see what he is up to, I am online and technology is supporting
    the link, but I am essentially interacting with him and not a computer. Online
    education can take the same form – interaction between students supported by
    multiple web-based tools.


    the Math-Towers (
    website, designed for students in Grades 6 to 10, the computer presents mathematics
    challenges to a class and provides tools for exploration, but the mathematics
    is generated through the conjectures and discussion posted by the students.
    Research in this space suggests that the statement "At this moment in
    history, computers are not a natural working medium for mathematics" is in
    fact false.  

  • David Wees

    I think something is really missing from this debate on the Khan Academy; NO educational method should go uncontested. People here seem to be saying "oh but there are good things about the Khan Academy" which is true; however, there are also problems and if you just ignore the problems, then YOU are part of the problem in math education. Transferability of skills is a key unsolved problem in education, and not one that the Khan Academy appears to make any effort to solve. Too often children learn skills which they cannot use later.

    I think the Khan Academy is a great step in improving the textbook, as for replacing teachers, it has significant work before to do before it is ready to do that.

  • Kim Wilkens

    Wasn't it the students struggling with math that found Khan Academy in the first place and then the educators/adults came along.  This is a pattern that seems to repeat over and over with emerging technologies like social media, youtube, video gaming, etc.  The kids aren't waiting for us to get on board with these programs - they are all in.  I don't know why this needs to be an either or proposition, shouldn't it be and, and, and…

  • AlastairCompSci

    I think a group people are deeply threatened financially by khan than actual teaching concerns. If you actually used khan academy you should he focuses on intuition and trying to develop formula's from first principles, not how to.

  • Telemorph

    The Khan Academy approach is obviously flawed, and yet it represents an enormous step in the right direction.  Recorded video is a poor way to teach, but it does have the benefit of letting students review material, or study at their own pace 'off-line', with a medium that they are very comfortable with.   It represents an important step towards harnessing the power of technology to empower students to learn at their own pace, and in a way that works best for them.

    Ventures like the Khan Academy point to an exciting future in which powerful experiential (or experimental) learning of abstract concepts will dramatically improve the cost effectiveness of education.  For a hint of what that future might look like, check out this video 

  • Lizjames2

    My 8th grade son is in the gifted science and math program at his school and as such has always accelerated in these areas.  However he became more disillusioned over time with math because his teachers either could not teach or because of the diversity of skills in the class focused on a specific subset of students. In the end he was falling behind.  Because of Kahn and other youtube instructions he was able to get past these humps and essentially self teach.  Without this he would likely have eventually given up.  I simply don't buy into the premise that math at these levels are much more then rote learning it is just the grammar of mathematics not its elocution.  By the way I have a PhD in Biophysics from Johns Hopkins so I do have an idea of what math should and can be.

  • bun

    It is not just the grammar of mathematics. These first few years lay the foundations for being able to understand mathematics on a more complex and theoretic level.  No student will understand how the laws of associativity relate to more complex mathematics if they do not understand the fundamentals for why they work in concrete examples.  Understanding binary relationships (and using them) form the basis for later theoretic math that cannot happen without this primary exposure and explanation of why these things happen.

  • Cahowclan4

    bingo...same son has finally found the answer's to his boggled algebra questions...we are loving home school limits us sometimes...this has been an answer to prayer for us...and many of my home school frustrated moms as well...its a keeper in our home...just wish we knew about it back in the early days of home schooling when my older kids were schooling!

  • Eric

    Lizjames - I disagree with you on this point:
    "I simply don't buy into the premise that math at these levels are much more then rote learning it is just the grammar of mathematics not its elocution. "

    Math, as a tool, is used to describe and understand the world. While there is a lot to be gained in learning the "grammar" of math, the critical skill our kids need to learn is how to take the concepts and tools gained in their various classes and apply them effectively to a diversity of problems. That's not going to be learned by merely teaching the mechanics of solving for x - that's going to be learned by practicing the translation of real-world problems into meaningful expressions that describe the problems in clear, meaningful mathematical language, and by practicing translating those expressions back into meaningful conclusions about the problems being described. 

    I believe strongly that that skill is a major missing point in education. Don't get me wrong - rote application of formulae and processes will get you pretty far, but it won't make you truly competent. I know many people that made it through my electrical engineering program with me who came out he other end with straight A's and an abysmal understanding of the actual physics and principles behind their discipline. Give them a textbook problem or a well-bounded problem that worked with the formulaic toolsets they had spent years collecting, and they had no problem finding an adequate solution. But give them an ill-defined problem, a system they had never seen before, or a difficult optimization problem, and they'd be stopped in their tracks. The problem is the same - they had been taught the grammar but not the meaning. More fundamentally, I think, is that they had been *taught only to learn* the grammar rather than the meaning ... and I think that needs to be fundamental to math and science education down to the most basic lessons if we're going to produce more than formulaic thinkers. 

    There are two reasons, in my mind, why that's important: 
    1. Understanding is always better than memorization. If you can understand, truly, how something works and why it works that way, you will be better off. With math, it's a little chicken-and-egg - math is a language to describe the world, so you need the language before you can speak it, but knowing how to use that language as you learn it makes a big difference in both comprehension and assessing if the results make sense. People like to analogize math to learning a foreign language ("grammar vs elocution"), but we forget that we start with an understanding of what French is trying to accomplish when we set out to learn it. We don't start with that with math ... could you imagine trying to learn a series of symbols and their relationships with no basis for what they mean or how to apply them? 
    2. At some point, it's too late. If you've skipped the critical application lesson for too long, at some point, you can't cover that ground to make up for lost time. There isn't enough understanding of the basic applications, and trying to explain how to apply calculus without an understanding of how to apply algebra is as bad as (if not worse than) teaching the grammar of calculus before someone knows what a variable is. The result is people who can do math, but who can't apply math. Or people who give up on math because it just never became a natural language for them. 

    Personally, I think resources like Kahn Academy are valuable supplemental material. But they don't teach you how to learn or reason ... for that you need a quality teacher and an environment that supports deep learning. 

  • Larryalobo

    I think this article exposes lots of what's wrong in education.  The observation is at the heart of this controversy - "Should educators, deeply versed in pedagogical research and countless years of feet-in-the-classroom, be calling the shots? Who gave the newcomers, typically entrepreneurs, many whom last set foot in class when they were students, the right to frame education?"
     The present school or education structure serves some students ok - others flourish in this or many other structures because of home or other support and motivation - the present structure does not help many students (drop outs, students are behind grade level, students graduate from high school ill prepared for higher education, college or the workforce)  Those shaping the structure (teachers, principals, superintendents, professors who teach and train teachers, teacher unions - all from the Education department and teacher ranks - and the politicians who work with and protect them) give us what we have.  Mathilicous is for teachers to help them invigorate teaching math - a good objective and intention.  It does not address the lack of skill many teachers have in the first place even with years of classroom experiences - though some teachers are great. 
     To attack Khan Academy for not doing everything needed for students - transferring skills to different context - is lame.  I don't think that was the point of Khan or any other multi-media service from the likes of Silicon Valley.  Khan and others like it point to what can be done for students to help them learn on their own and fill in the gaps many students have since they did not learn some basics in lower grades or had teachers who did not teach well for their needs.  As long as teachers support the present education structure, even if they add some technology, rather than recognizing that with good support and good teaching (where ever it comes from) students can learn what they need to learn, it does not matter how they learn it.  We always need live humans (in class, online) to help make connections and put things in context.  Mathelicious is one company that demonstrates that many teachers themselves do not know how to make the connection of information they teach and make it contextual or interesting to a student's world.  We all need help, even parents. 
     A very different structure in education needs to be imagined.  Khan Academy or other such enterprises are just some of today's offerings.  Maybe Khan helps students catch up and become proficient and other sites or systems helps students put things in context.  Travel agents and journalistic organizations are being redefined by how people are using technology to improve our experiences and available information to do what we want to do.  ATMs redefined some of our banking experiences and did affect bank staff needs. 
     If what we want is for people to be well educated and get some stamp that shows they have achieved a level (diploma, certificate, degree, certification, license, credential), we can do this in many ways - MIT offers classes and lectures online and new developments are happening to provide us with instruction and information in many formats so more people can conveniently get what they need 24/7, 365.  What it will look like - don't know yet - but the structure of education is about to change - Apple, Self-publishing, Kuno, Tablets, computer programs, online classes, etc. are seeing to that.  The focus is on learning ideas, information, data and skills and how to put things in context and connect them to other things and what we know.  Information is more easily available today to find and get.  It’s the structure of how to present it and how to find it we can do on our own.  Others must help us make sense of it and have a greater understanding – but for today’s world, not only yesteryear’s images, views, metaphors, examples.  Many teachers are not prepared for this and many resist it to preserve what they know best – yesterday’s structures. 

  • Philip Mcintosh

    A very healthy discussion all around. The author mentions some things that seem to clearly frame the issue (at least in my mind). For some, Khan Academy and video-based learning is a great thing and works well. For others it has limited or no discernible effect. This is no different than what we see with ANY pedagogy.

    Bottom line? If it works for you, use it. If it doesn't, use what does work for you and quit trying to tell other people what works for them.

    The disruptions in education are just beginning. Get used to things not being the way YOU wish they were or the way YOU think they ought to be, because you are definitely wrong for some portion of the population of learners that are out there.

    I too would like to see some video learning materials that that do a better job of addressing conceptual and deeper, more intuitive understanding without immediately cutting to the algorithmic chase.

    The new MITx, MIT Relate, MIT OCW Scholar and other initiatives in the pipeline are headed in the right direction.

    Railing against new and disruptive methods are tantamount to tailors smashing the sewing machines upon their introduction. Better to learn to sew by machine, or better yet, make a better sewing machine.