I usually avoid current events, but recent skirmishes in the math world prompted me to chime in. To recap, there've been heated discussions about math education and the role of online resources like Khan Academy.
@YatharthROCK: “Can’t we all get along?” So why are you falsely accusing others of “undermining” and “not getting” the meaning of Kalid’s excellent post? Please don’t be so intemperate, but share in the learning!
Hey K–
As I’m sure you know, David Foster Wallace wrote a book on infinity called “Everything and More.” I just started it so I can’t comment yet on its overall quality, but in the preface he says something that reminded me on you. He says that he disliked and did poorly in every math class he ever took, save one, which was taught by “one of those rare specialists who can make the abstract alive and urgent.”
Amen, brother.
Hi Alex, thanks for the note! I agree, communication is key: can we convey the heart of the idea? (And not all the technical gibberish that surrounds it, just get to the idea itself?). Once we have the intuition, we can “firm it up” with all the rules.
I really don’t like the “math person” or “history person” distinction. We don’t say someone is a “reading person” or a “listening person”. Nope. These are skills which are within our grasp. Thanks for sharing your thoughts!
Hi there,
Technically, what you’ve provided under “The Big Misunderstanding” is a big misunderstanding in and of itself–that is not an equation, but an inequality. Just a bit of pedantry 
“Select Your Math Hero”, I choose… Justin Bieber. What’s wrong with getting Bieber to teach algebra 101? As long as someone else write the lesson plan, of course. Can’t we just work together?
You have made an excellent point here. It is not that I agree with the methods of Khan Academy, but honestly, their videos have helped a lot of students around the world, regardless of the soundness or unsoundness of their pedagogy.
@Shiv I agree. While KhanAcademy is good for complete novices and getting the gist of things, I’ve always found videos tedious and boring. “What, a one-hour video! I don’t have that much time…” I find myself saying. I often find myself scanning through YouTube’s ‘interactive transcriptions’.
With text (and picture!) articles, I can go at my own pace. Stop, go for a walk to really digest the stuff and then come back and pick off where I left. I can also scan ahead and skip to a section and decide if it’s worth reading at all (problem with YouTube).
Lastly, I think we should highlight the forums a bit more. I find them to be an excellent resource and allows for interaction and specific questions to be answered…
Each of us learn differently. My endless search online has landed me in betterexplained.com. I find intuitive methods taught by Kalid more appealing but I can’t keep my attention with Khan’s videos. Should I conclude that the Khan’s videos are not effective and his pedagogy is wrong? No! My friend’s kid loves Khan’s videos; millions of people love them.
Instead of judging the teaching methods and content of others the critics should spend the time creating and sharing learning materials. Let us lead people away from endless entertainment to life long learning and teaching! How about federated online content, curated, and mapped to age groups?
One idea: Make a curated, collaborative, easy-to-explore teaching resource.
As someone who follows KA daily, this is actually a goal of KA. Khan said in an interview that the ultimate goal is to have multiple teachers for a certain topic with games, simulations, and projects to customize curricula.
Khan Academy also accepts requests to donate videos by emailing sample videos.
@Michael: Awesome, thanks for the info! I follow KA casually and wonder how many other teachers know about this? I think the word needs to get out.
It’d be great to have a collection of 2-3 different video styles for each topic [conceptual vs. tutorial vs. story-based].
The problem with a lot of the ‘Anti-Khan’ movement, as I see it, is that these people are all physicists or mathematicians who teach at that level. Having worked in these fields for decades, they possess an extremely well-grounded high-level understanding of their material: They read and derive proofs, they work at building new physical models, etc. In Devlin’s words: “…all the other KA critics in the educational world are interested in facilitating something quite different: real learning among their students.”
This is all well and good, but…there are steps to real learning. One’s intellect does not simply pop into the arena of true theoretical understanding. It is an endeavor that takes years and years of work and practice! A huge part of this practice is, like it or not, solving repetitive and formulaic math and science problems.
Take, for example, conservative fields from vector calculus. In order to fully understand conservative fields, there are a lot of ‘qualifications’ that must be kept in mind–smooth curves in regions that are both connected and simply connected. Most courses teach these qualifications right away. (Mine did). Mathematicians would encourage this practice, always striving to be perfectly correct, but I absolutely abhor it. It’s far more valuable to get students working on calculations as soon as possible–the component test, finding potential functions, etc. Later, when a numerical understanding of the concept starts to arise, it’s much more effective to introduce the limitations inherent in the techniques that have been taught.
In other words, there’s a tendency in mathematics today to put the horse before the cart, and teach students theoretical concepts before they’re fully equipped to understand them. KA has been so successful exactly because it procedurally and formulaically rejects this process. No wonder students love it and the Math Royalty don’t.
@Name: Yep, we need a common, curated area. Students and teachers shouldn’t have to do random google searches to find the best resources for well-known topics.
Er…in my very first sentence, I meant to write “these people are all physicists or mathematicians who teach at the UNIVERSITY level.” Whoops.
@Joe: Great point. I believe concepts need “progressive refinement”, i.e., you learn the high-level concept, try some examples, then deepen your understanding, try more examples, and so on.
One analogy I use is “explaining a cat”. First you show a cat, explain its basic features (furry, has a tail & claws) and observe it. Then you might explain that all cats (tigers, housecats, bobcats) descended from some common ancestor. Some cats are extinct today (sabre-toothed tigers).
Then, you explain that all cats share some common DNA [ACATACAT :)] which gives them their “catness”. This is the expert-level understanding [I’m vastly oversimplifying the biology here, but that’s the idea].
It’s very easy, especially in technical fields, to jump to the DNA-level description without first walking through the “here’s a picture of a cat” level.
We need a common ground to do everything. We need to know where to learn anything and where to teach anything. We need to know how to figure out how to do anything. We need a better way to search instead of typing keywords into search engines.
In 7th grade I hated math. Boring teacher who was very uninspiring. In 8th grade I loved math. The teacher made it fun. Ever since then I have loved pursuing math and science. Got to college and learned calculus and sort of learned network analysis and math behind electronics. Then picked up a book called “Calculus Made Easy” which helped me create a PID loop in a microcontroller. It helped me understand calculus better than I ever learned from a teacher. The teacher was good too.
How did I get here? I am trying to learn noise generation techniques for generating realistic terrains in a game engine. Somehow I ended up here. The point is that it was a good math teacher in 8th grade that helped me love the subject. I have had insights on my own (I need to write them down if I remember them) and completely agree on capturing what we can.
It will be a battle to unseat the elitism inherent in higher learning and science. As a science lover I have watched the painful politics in science. One good example was Pons and Fleischman. The top physicists did not even review the theory or findings when they denounced anything had been discovered. It was all politics and protecting research grants. That is what online learning resources are fighting. There is a “provider” for higher learning and they don’t want competition.
@Roberto Great links! Love all those resources (except CodeSchool which I haven’t tried but have heard of before)
@Reginalid: Yes, it may not be as easily discoverable, but there are some other contributors, like Vi Hart (http://www.khanacademy.org/math/vi-hart) and Brit Cruise (http://www.khanacademy.org/science/brit-cruise). However, there’s not alternative explanations for the basic topics. One difficulty might be getting enough videos from another contributor to help provide a consistent experience.
@Shiv: Yes, good teaching is maybe 30% content knowledge and 70% motivation, inspiration, empathy, etc. If you want pure content knowledge you can just read Wikipedia.
@Ralph: Cooking is such an awesome example of “real world” math, chemistry, physics, etc. I’m surprised it’s not used more. Practical examples help solidify ideas, theory gives you new ones, then you get practical examples of those new ideas, and so on. I see it as a spiral.
@Roberto: Awesome, thanks for the links. I read one of the “Head First” books on programming and enjoyed in. In general, I think we need a multitude of “teaching artists” to provide their expression. We don’t limit our appreciation of music to one band or composed, and similar to math. (The biggest hurdle is realizing math is something that can be appreciated like music or another art).
“But, really, the ultimate solution is Online learning + Good Teachers”
You meant the ultimate solution is “Good Teachers + Online Learning” right?
You have taken all of math education and reduced it to an argument about online learning and teachers. As if this is the heart of the problem.
I find it amusing how easily we continue to push this meme of “math-phobia” and thus need to reorient all of mathematics. It’s acceptable to say I hate math or it’s not my subject or I’m not very good at it socially but to say I can’t read or write very well would cause embarrassment.
Successive generations want life to be completely catered to them, everything has to come to them and society let this idea run amok.
So while you’re discussing a math-phobia society and online learning versus classroom, teacher learning, tell us have you looked at why other societies in the world don’t have these problems or are far more successful in terms of math education? Do you think these societies are creating math plays and movies and juggling acts to ‘sell’ math to their populations?
The private market wants to see public education destroyed. Here we give lip service to the idea that education is important. That died long ago and has been drowned out in a sea of consumerism.
The simple fact is that other nations place a higher focus on learning and spend more on education than we are willing to do in America.