Wednesday, February 23, 2011

The myth of exponential knowledge

Last year Google CEO Eric Schmidt made a big splash by telling us that more information is created every two days than was created from the dawn of time until 2003. This is an alarming find, even if the numbers are fudged quite a bit. The quote wasn't aimed at educators, but many in the EdTech community took this quote and ran with it. The message Schmidt delivered fit very neatly into the narrative many radical educators subscribe to-- that teaching specific factual knowledge is "20th century" and we should be teaching "how to find knowledge" in real time or whatever.

It doesn't take an expert critical thinker to see the huge hole in this line of reasoning. The reason this is a somewhat meaningless factoid is that there has always been more knowledge in the world than we could possibly teach to students. I can remember sitting in the library on SUNY Stony Brook's campus and looking around at the over-stuffed shelves of books on just one bookshelf on one floor and thinking "I will never be able to read even a respectable fraction of the books in here."

This should be obvious prima facie to any objective person, yet that quote gets passed around, re-tweeted, quoted, time and again in EdTech circles. Why?

My theory is that many educators would rather teach their own curriculum or let students design their own curriculum than deliver content designed, sequenced and scaffolded by others. I can understand this sentiment and relate. Having autonomy is a wonderful feeling for teachers and students alike. Just because it feels great and makes you look forward to learning doesn't mean it is the best way to educate an individual, however.

I sat on a curriculum planning team and got to see firsthand that the sequence and scaffolding of the concepts were well thought-out. The age-appropriate lessons for 4th grade were extensions and expansions of the lessons for 3rd grade. The lessons for 3rd grade were extensions and expansions of the lessons for 2nd grade and so on up and down the line. I once had a discussion with Clay Shirky about Math curriculum and he unequivocally told me that the current progression is about as good as he can imagine.

Curriculum is about giving people a foundation to learn more. Cognitive science teaches us that people learn things that build on previous knowledge. This latticework of previous knowledge is called a schema. In other words, skipping steps or zig-zagging around a well-planned sequence of lessons makes learning more difficult.

A curriculum is not meant to be a complete information dump of an all-encompassing human knowledge base. It is meant to provide a broad enough schema for people to absorb and internalize new understandings as they encounter them. Information that does not connect to our existing schema is either ignored or quickly forgotten. Once we understand this fact about how we learn we can see how off the rails the conclusions we draw about exponential information can be.

So let's translate conclusions people draw from Schmidt's quote into the language of cognitive science:

"We need to spend less time building the schemata vital to acquiring new understandings and spend more time teaching people how to do keyword searches on Google for things they won't understand once they read them."

Okay, maybe that's a bit snarky, but it is also accurate.

Curriculum designers are knowledge cartographers- they have been down the road we want our students to travel and they share their experience. We don't need to re-invent the wheel ourselves because we have the benefit of the wisdom of experienced designers.

There is a counter-lesson in here though. Maps get updated because roads and rivers change course. I am a firm believer that curriculum needs to be examined and tweaked on a regular basis, but to discard acquired knowledge as "mere facts" is to deeply misunderstand curriculum design. Is there a kernel of truth in Schmidt's statement? Yes, I think there is more than a kernel in fact. What this means for us as educators is that curriculum design is more important now than ever because it is becoming more difficult to build a broad enough general schema.


  1. George
    I love your posts. They are always well thought out and expertly presented. This post fits that bill as well.I see nothing in your post that would prohibit the use of Tech as a tool for learning within the curriculum. We are talking about the method of teaching and not the content. We can focus on the delivery of specific topics and facts, but it does not have to be a directed learning lesson every time. We can get beyond Stand and deliver lectures. I have seen the results of alternate methods using tech by your students. It was a great presentation of Animal Farm by your students that highlighted your success and the achievement of your students.I agree with all you have presented here, but I would ask for a balance in the use of tech as a tool for learning. We will always have a use for directed learning lessons as well as lectures, but there are great opportunities for other methods using tech for accumulation, creation, communication, and collaboration of information. This would take us beyond the somewhat mindless procedures of a Google Search.
    Thanks for raising the thought level once again.

  2. Tom, thanks for the kind words. I really appreciate you taking the time to share your thoughts. It means a lot to me that an esteemed educator like yourself stops by and joins the conversation.

    Obviously, I am a Tech teacher so I agree that tech should be part of the design for learning.
    No argument there.

    While I hated school as a kid, I am so grateful that my parents and teachers forced me to keep going and keep working because in the end, they knew better- they had more wisdom that I did about what was important to learn as a 9-year-old.

    The things I find most fascinating now at age 36 only spark my imagination because of the foundation I received from school. If it was up to me to design curriculum for myself all I would know at age 36 would be Dave Winfield's statistics and what The Incredible Hulk did to The Submariner in their #epic battle.

    Curriculum design is about the long view and sometimes I worry that the push for customized, student-centered, self-directed learning is about the short view.

  3. I agree with most of what you have said, but where I take issue is that I believe we ("curriculum designers") can't teach kids the same WAY we were taught and be successful.

    I am fortunate to teach at the same private school I attended 18 years ago, and now my 6 and 10 year are attending. Some of the teachers that I had are still here - and are still teaching the way they taught me. I just don't think that serves my children well and I am working hard to help our teachers keep the "wheel" they had before while "reinventing" the look, feel, and function of the wheel to meet the needs of today's learners.

    Successful student-centered learning, when designed and guided by the teacher properly, will force children to come to the same fundamental knowledge that we obtained from our "stand and deliver" educational model. The difference is that they learn to USE that information in a way that is relevant to them and develop collaborative and interpersonal skills for the modern era. Sure, making sure they obtain the knowledge is important, but you can't deny the fact that ANYONE with access to mainstream technology can find information at their fingertips in a flash. My 6 year old "Googles it" when he doesn't know - and hasn't been taught that by anyone other than his 10 year old brother. It IS critical that we discuss digital literacy with our children.

  4. L in Ok,
    Thanks so much for taking the time to write a thoughtful comment.
    I agree with everything you wrote and I try hard to make the model you describe manifest in my own classroom.

    Anyone can find anything on Google, but one issue to me is whether they can actually make sense of the answer.

    Another issue is that they have to know something exists before they can search for a deeper understanding. For example, in theory a child can teach themselves Mandarin on their own, but there is a mountain of information they need in their schema already to have a fighting chance.

  5. Hi, George. I agree whole-heartedly with your post. There are a LOT of things that I, as a music teacher, build upon from Kdg through 5th grade.

    My guess is that the majority of people in Ed Tech who are crying for less "facts" and more "know how" are not advocating that we turn it all over to search engines. You're exactly right that there are most definitely skill sets that build upon knowing specific facts. However, the problem that I see in MANY schools, including the one my daughter attends, is the over-emphasis on teaching facts and little to no emphasis on critical thinking skills.

    For example, in a high school Honors/AP History class, is it more important that my daughter memorize the dates of every battle in the Civil War- or more important to understand the themes of war, background of how each war began, and what resulted from the different wars? When I look at her exams, I'm saddened that the former is usually the case.

    To add to this, many teachers quiz or test kids over facts to ensure that the kids "did the reading." I can create a quality assessment that takes those kids into higher level questions and thinking without trying to catch the kids with the smallest factual detail to ensure they completed their reading assignments.

    Finally- regarding your point about student-centered, self-directed learning... and we're still talking about all ages here... if I'm guiding my students appropriately, they CAN discover some things on their own without me spoonfeeding it to them. If they stray off the path, I need to help steer them back, but that doesn't require me to stand and lecture at them the entire class period. AND... if a kid is passionate about something, as a teacher, I can find a way to use that passion to teach any variety of 'subject' areas. Will that be the only thing I learn with them? No. Is it a good strategy to employ some of the time. YES.

    Thanks for your thought-provoking post!

  6. Michelle,
    Thanks for stopping by and sharing your thoughts!

    I agree with you. You stated the case very well, the only thing I would add is this: facts and critical thinking are linked. Meaning, people can't critically think about the civil war if they don't know the order of events or the characters involved.

    I think we would both agree that there are ways to embed this factual knowledge in a larger, conceptual journey. I think we would also agree that regardless of the importance of facts, ignoring the critical thinking that is based on those facts is a terrible misuse of educational time.

  7. George, I do have one observation that I would like to make and we'll see if it pokes a hole in your argument or not.

    Things we agree upon:
    There has always been more knowledge available to know than what can possibly be taught to kids in schools.

    Someone needs to select a subset of the available knowledge to show to kids. Kids cannot possibly become completely self-directed. I would like to see much more self-direction than currently occurs, but I don't see kids as being able to learn how to read, or even adopt most critical thinking skills without a lot of interaction and support from adults.

    Things that we do not agree upon:
    It will always be possible for a small team of educators to choose the best possible subset of skills or content for our students to learn, using our current systems of determining curriculum goals.

    The process of curriculum construction is linear. A bunch of people get together, they look at what is available to be known, they might examine market trends, read some research about future predictions, and then they carefully select a subset of that total knowledge to share with kids. The rate of change of the subset of knowledge is directly dependent on how many people are examining the curriculum. Mathematically, it is a linear function. While much of this base knowledge remains constant, some of it must change.

    If you buy the argument that the total amount of knowledge is increasing exponentially, then you must see that there is a serious problem here. An exponential amount of knowledge cannot be effectively processed using a linear method!

    This has already resulted, in my opinion, of some of what we are teaching kids, particularly in math and science, to be largely irrelevant. Why do we spend so much time teaching algebra when even professional mathematicians hardly do any algebra at all? If our objective is to teach logical thinking skills, that could be just as effectively done using computer programming skills which are vastly more important in even today's economy and society than algebra is.

    Yes, some people use algebraic reasoning to solve problems, I'm not disputing that. However, because a tiny subset of society is still churning out algebra problems by hand is no reason to massacre an entire population with the subject!

  8. David,

    Thanks again for sharing your thoughts with me and whoever else stops by this space. I enjoy your thoughts in 140 character increments, but it is much nicer to see fuller thoughts woven together in long form.

    I would say that I do not disagree with you much here at all. Here are my counter arguments.

    1. Information may be increasing exponentially but this has no effect on our capacity to learn. We will always be limited by our brains, regardless of how much the rate of knowledge accumulation increases. The practical effect of this is that professionals who specialize will be more different than specialists in the past. It will also take longer for specialists to reach a certain level of competence.

    Let's take an example of the exponential information and make this concrete. Engine repair. In years gone by there were X number of different engines. Now their are X times X. People who used to be able to repair any engine (models A, B or C) can now only repair a certain subset (A1, A2, A3). That subset (as a percentage of total engines in existence) will continue to shrink.

    So people will not be "engine repair specialists" they will be "A1 specialists" and so on.

    This is one specific example meant to illustrate a larger point of increasing diversity of information.

    We basically have 3 strategies here.
    a) Ignore any innovations, keep teaching how to repair A, B and C engines. (obviously bad)
    b) Re-center the fundamentals of engine repair that provide a solid base. (my choice)
    c) Teach them no specific facts about engines, but teach them how to target Google searches that may lead to tutorials on engine repair. (this is in the lead in the EdTech hive mind)

    2. re: Algebra
    I don't know enough about specific sub-disciplines in math to speak intelligently about what has more universal appeal and what doesn't. What I would say is that when I ask math teachers why kids need calculus or algebra if they won't be mathematicians when they grow up, I usually get a similar answer.

    Math people usually tell me we don't learn math for the specific content, we learn math because it teaches us how to solve abstract problems. I once spoke with a person much smarter than me (pretty common occurrence) and they said that saying we don't "use" calculus is like saying we don't use flash as a platform. It isn't a conscious thing, it is an unconscious, behind the scenes element to things we consciously use.

    That is my 2 cents.

  9. It stands to reason that if more people are capable of creating content, then there will be more of it to access, vet, organize, manage, synthesize, etc...Technology levels the playing field by allowing me to become not only a consumer but a producer of content in which I can readily and potentially share with millions of other people, who in turn can go out and share with millions of other people. That has not always been true. I no longer need to wait for content to show up in the library, school or my mailbox; I can retrieve it instantaneously, when I need and want it. That's a monumental shift.

    As for being grateful for the education you received, I'm glad you feel that way because I don't; my education left huge gaping holes in my life because I turned off to learning at age 14. For every kid who learned in the traditional educational system, I guarantee there is another one out there whose love for learning was completely extinguished because of the one-size-fits-all mentality of teaching.

    Now, I don't necessarily believe we should do away with curriculum; there are certainly core understandings we want our students to understand. However, there needs to be a measure of flexibility built into each school day to allow students time to delve deeply into topics that stir their souls and free their imaginations; time to construct and co-construct knowledge with people from all over the world. Fact is, it's time for us to create learning experiences that help ALL chldren learn; not just the ones who do the whole sit and git thing well.