The Myth of Exponential Time?

George Haines has constructed an interesting argument refuting the idea that because we live in exponential times that we need to change how our schools operate.

George says:

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."

My response was:

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.





  • After three readings I still wasn’t able to decipher the thrust of his argument. He seems to suggest curriculum designers know what they’re doing, and that teachers should … submit(?) to this expertise. However, he appears to think teachers resist this submissiveness because of a ‘misguided drive for autonomy’. Further, he seems to say there has ‘always’ been too much information to teach, so today is no different from yesterday.

    If this is the central axis of his argument, I think he’s missing the boat. It may be the case that curriculum theorists understand their field, but this doesn’t translate into understanding individual students or classroom events. Generalizing from the macro to the micro is very problematic, and probably irresponsible.

    Re. ‘autonomy’, teachers aren’t autonomous, don’t have access to autonomy, and have no basis from which to exercise autonomy. This is a completely vacuous ground for critique.

    Finally, re. ‘too much information to teach’, he’s problematized this poorly. It may be the case that there has ‘always’ been too much to teach, but that is not the same as saying that the sum total of human understanding is accelerating. He seems to be saying classrooms should be somehow isolated from the world outside, and doesn’t seem to acknowledge the ‘shelf-life’ of understandings. It’s not just a matter of too much to teach, but that different understandings replace or supercede each other. Therefore, if curriculum theorists value or privilege understandings which are obsolete, they’re not facilitating education but indoctrination.

    Teachers must navigate these waters. Curriculum theorists can help, but they can’t presume themselves to be defenders of the faith.

  • David Wees wrote:

    This I think is the crux of my argument.

    "It’s not just a matter of too much to teach, but that different understandings replace or supercede each other."

    It will become increasingly difficult to determine exactly what content should replace current content, and what content is no longer relevant. How will we know what should be cut, and what should be kept? Can we determine this using a small group of people we call curriculum designers? Should a much larger group of people have input into the "what should be known" part of developing curriculum? Would this even help?

    I’m struggling to think of a way to select a subset of total human knowledge which is both compelling, feels useful, and can keep up with an accelerating knowledge base.

    In a world with services like Wolfram Alpha, for example, I wonder if we have already missed the boat in this curriculum discussion.

  • Hi, Tobey!

    Thanks for engaging on this subject. I apologize if my post left you guessing about my meaning. Let me try to put a finer point on my post.

    1. We have always had an insanely large store of human knowledge. Educators have known this since the dawn of time. Some educators read a quote like Schmidt’s and without actually processing the mundane quality of the statement, pass it along implying that it is a revelation specific to out time period. We know this isn’t true, we know there has always been way more information than we could hope to teach students.

    2. Based on this fact(what I would call common sense) educators began to make decisions about what core elements of this vast store of knowledge would help learners establish a schema. Because higher order thinking skills are so vital to human progress, and because higher order thinking skills only emerge from a broad, vast schema, it should be fairly obvious why it is so important to establish this broad, vast schema.

    Without a broad, vast schema people can not learn many new things. If people have not learned something, they can not critically think about it. They can not solve problems related to things they have no knowledge of in the first place.

    So over the course of the last few thousand years, educators began to notice that students couldn’t learn “B” if they didn’t already know “A”.

    Example 1: It is virtually impossible to teach English Literature to students who don’t speak English.
    Example 2: 1st grade students would fail high-school level reading comprehension tests because they don’t have the vocabulary to understand what they are reading yet.

    There are certain sequences of learning within a school year and certain scaffolded sequences across a scholastic career that make a huge difference. These sequences of learning were cultivated over thousands of years by hundreds of thousands of educators field testing student’s ability to learn and apply new skills and knowledge.

    I think educators who wish they had more autonomy in designing their own curriculum have an instant gratification, short-term view of how this process works.

    Like I stated in my post, it is important to remember that as information changes and grows, the sequence and scaffolding process has to evolve as well. The one thing that won’t change is the fact that people can only learn what attaches to their established schema. The smaller our schema, the more difficult it is to learn new things.

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