Reflections on information, knowledge, understanding, intelligence, wit, acuity, aptitude, instruction, etc.
I recently watched Salman Khan’s 2011 TED talk. The video itself is interesting, but to summarize it briefly Khan makes educational videos which can be assigned as homework, leaving classroom time for exercises; his team also makes metrics and tools to assist teachers knowing who needs help on what. Those of his videos on programming that I watched were decent, though not outstanding. Those who want to get their hands wet with Python but find textual tutorials unpleasant might want to give them a go. Rather than discuss the details of his work, which I mostly support, I want to discuss a few other thoughts that were stimulated by his presentation. As is often the case with me, these were things that I found notable by their absence.
education Khan points out that for the imparting of information, lecturing is a remarkably bad technique. It is often asserted that only 5–15% of lectured material is retained by students 5–15 days after the lecture. In other words, in a 50-minute class about 5 minutes of material are retained. Note that my experience in college is quite different. Since I do not hesitate to take control of my classroom by derailing the instructor with many questions, difficult classes often became a conversation between the teacher and myself, with an audience of mostly-silent students. My observation of college courses is that lecture is usually a time waster and real learning happens through the lab experience with one-on-one TA guidance. That long-standing reversed-classroom design is augmented by readings and group work to create some form of learning. The technique Khan describes sounds like a better design, merging the benefits of textbooks and lectures and adding additional tutor-time.
But the question I want to ask is more fundamental: what is the goal of education?
I think the dominant view of education puts it’s goals as the imparting of information, skills, and understanding. By imparting I mean constructing in the student’s mind a structure similar too that held in the teacher’s mind. Information, or facts, are isolated concepts: the meaning of π, the elements of the Marshall Plan, what an addition means. Skills are often integrated with information: students are taught to add as an implicit definition of addition. Understanding is the ability to use information and skills in ways not directly modeled by the teacher; I display understanding of addition and the Marshall Plan when I think to add up the costs of various elements of that plan to arrive at an overall cost.
Teaching understanding is hard, and I have informally heard it upheld as the pinnacle for which educators are striving. But I pose that it is actually fairly low in the list of desirable teaching objectives. I think most of the others I will identify have traditionally been considered innate attributes, but my experience does not support that assumption.
What about trying to teach intelligence or critical thinking, the ability to see the unspoken context and limitations of each datum? Teach students to ask good questions that have not been asked before. Teach them to seek out new data from which to construct revised understandings. I am confident this can be done; I’ve been taught it myself, An isolated example that springs to mind was a bit of intelligence transfered to me by Sean Warnick which I described as part of an essay several years ago. though I confess I was not paying attention to how the message was conveyed.
We might also be able to teach wit or acuity, the ability to rapidly process and react to circumstances, filtering out the boilerplate and focusing on the informative kernel. I feel like this should be decomposable as a collection of data and skills. It might also have the benefit of reducing the clutter in communication.
I might go on… it is not clear to me that any of the intellectual traits that we admire in some are not transferable, given an appropriate teaching environment.
It may be that my brain is a more powerful stochastic processor that others. It may be that my spirit is a better mind-driver than some. But I think people call me bright mostly because I have been blessed by excellent teachers and because I have spent the bulk of my time learning things I enjoy learning. That, I think, is genius.
People express shock that I cannot play any musical instrument with a frequency I frankly do not understand. This has caused me to ponder why it is I do not. The answer is quite simple: I want to learn to play just a bit less than I want to do spend my time learning other things. I’ve never doubted this, so I’ve never wasted more than an hour or two learning about musical instruments. If I had spent thousands of hours on an instrument I still would not have risen to greatness because my attention would not be fully invested. I’d rather think about the Gödel incompleteness theorem or practice guessing what people will say next.
I offer, then, this definition of genius (which I do not fully endorse):
A genius is a person who has spent a lot of time learning things they found interesting.
This may also partially explain savant syndrome: those who lack awareness of social pressure to engaging in boring activities may spend much more time on learning that does interest them.
I do not believe in structured education. By that I mean, I am confident that dictating what people learn when causes the average student to spend the bulk of their time on tasks they don’t care about. That, in turn, means they are wasting the bulk of their time, developing negative feelings of education as unpleasant and uninteresting, and (unless taught how to avoid this false generalization) deciding that pointless activities are better fun than is learning. I was fortunate enough to be allowed to ask the “why”s every toddler loves without very little being told to stop asking or to think about something else instead; and this delightful habit continues through the present time.
This brings me to both the most exciting and most disappointing element of Khan’s talk: the knowledge dependency graph. But that is a topic large enough to deserve its own post.
Education appears, to me, to remain largely a craft rather than an art or technology. That is, most educational approaches seem to grow out of shared practice and not out of individual passionate expression or out of reasoned decomposition of purpose and means. Even the most basic task of defining the goals of education appears to be based on what others have achieved in the past rather than on a more teleological consideration of the intended aim. I hope that the present discontent at our failing system will lead not only to improvements in the craft, such as those Khan proposes, but also to a larger structure that aims toward a worthy end.