Salman Khan, of the Khan Academy, sounds off on the potential of pre-recorded video lectures to change education in the video below. He calls it “flipping” the classroom, but around here we call it the inverted classroom.
I like especially that Salman made the point that the main effect of inverting the classroom is to humanize it. Rather than delivering a one-size-fits-all lecture, the lecture is put where it will be of the most use to the greatest number of students — namely, online and outside of class — leaving the teacher free to focus on individual students during class. This was the point I made in this article — that the purpose of technology ought to be to enhance rather than replace human relationships.
I hope somewhere that he, or somebody, spends a bit more time discussing exactly how the teachers in the one school district he mentions in the talk actually implemented the inverted classroom, and what kinds of issues they ran up against. Ironically, the greatest resistance I get with the inverted classroom is from students themselves, namely a small but vocal group who believe that this sort of thing isn’t “real teaching”. I wonder if the K-12 teachers who use this model encounter that, or if it’s just a phenomenon among college-aged students.
A partial answer to the questions I brought up in the last post about what authentic mathematics consists of, and how we get students to learn it genuinely, might be found in this TED talk by Conrad Wolfram called “Teaching kids real math with computers”. It’s 17 minutes long, but take some time to watch the whole thing:
Profound stuff. Are we looking at the future of mathematics education in utero here?
Arthur Benjamin thinks that the current model of the mathematics curriculum — leading from arithmetic to algebra and ultimately to calculus — is flawed and needs to be changed. Watch this 3-minute TED talk for what he thinks ought to be the real summit of the mathematics curriculum:
I am in a great deal of agreement with Prof. Benjamin here. The secondary school math curriculum does indeed seem poised to point students towards calculus. While that is appropriate for some, it is not appropriate for all; while on the other hand, a better knowledge of discrete math, especially probability and statistics, would be appropriate for everybody.
Moreover, Prof. Benjamin did not stress one of the most important selling points for refocusing on discrete math: The mathematical background requirements are a lot lower than they are for calculus. Students currently have to take two years of algebra, at least a semester of trigonometry, and often an entire course in Precalculus on top of all that just to have a fighting change in calculus. And even then it doesn’t always work. Probability and statistics, on the other hand, gets to good ideas, deep ones at that, without nearly so much training.
On the other hand, what about those students who do end up going into science, math, engineering, economics, or other fields requiring calculus? If probability and statistics becomes the summit of the secondary curriculum, then at what point do those kids get the precalculus training they need in order to complete calculus (which I interpret to mean a year of calculus) by the end of their freshman year in college? Would they be having to double up on math courses — statistics on the one hand and precalculus on the other? Would they need to decide that they wanted a STEM-related career early on in high school, and if so, is that good for them?
All snarks about $24M mansions being funded by calculus textbook sales aside, there is an emerging relationship between calculus and architecture that is really fascinating. Since WordPress.com now allows direct embedding of TED talks, I thought I’d share this talk from architect Greg Lynn on this subject. I ran across this a couple of weeks ago and I’ve been wondering about it ever since. The point about using calculus to change architecture from a “discrete” notion into a “continuous” notion is particularly interesting.
The annual TED conference (TED = Technology, Entertainment, Design) bills itself as “bring[ing] together the world’s most fascinating thinkers and doers, who are challenged to give the talk of their lives (in 18 minutes).” You see presenters at TED along the lines of Al Gore, Jane Goodall, Freeman Dyson, Marvin Minsky, and on and on. Many of the best TED talks are available for free as video podcasts at the iTunes store or from TED’s website. I was quite surprised to find, among these “best of TED” talks, a 27-minute lecture from 1998 by Billy Graham. His talk was on “Technology, Faith, and Human Shortcomings”. Here it is, in its entirety. You should really watch the whole thing.
I think it takes a lot of guts for an evangelical Christian — to say nothing of a then-80-year old with Parkinson’s Disease — to walk into TED, into a crowd of people who by and large have precious little sympathy for your position, and talk with such ease and boldness. But Billy Graham has been around the block a few times and been into more hostile environments than that.
I happen to agree with Graham’s conclusions about Jesus Christ (although not every point of his Southern Baptist theology). But even if you don’t, listen to the questions he asks and the points he raises*. What about human evil, death, and suffering? Technology won’t solve these problems; what will?
(* …and don’t respond by reflexively hurling insults at Christians like depressingly many of the commenters at TED’s web site do. If you disagree with Christianity, fine, but step up to the plate and put forth a viable answer to the question rather than simply name-call like a 5-year old on the playground.)