the founder of highly popular education site
betterexplained.com, Kalid Azad who has agreed to do
this exclusive interview. The full unedited version is
Hi Kalid, firstly I wish to thank you for shelling out some time from your busy schedule to do this interview.
Definitely! Thanks for asking :).
Tell your fans something fascinating about yourself not previously made known to the world.
Hrm, I wish I had an amazing superpower I could reveal -- not so, unfortunately. I really enjoy martial arts -- I've practiced Uechi-Ryu karate since high school, and dabble with Brazilian Jiu Jitsu when I'm able. For whatever reason, there seems to be a large overlap between math/computer enthusiasts and martial arts.
What exactly inspired you to start betterexplained.com?
I had an awful math class during my freshman year of college. You know the type: the professor comes in, starts (but probably does not finish) a proof, then shuffles off. I did really poorly on the midterm, which bothered me because I had always enjoyed math!
While cramming for the final exams, after hours and hours, I stumbled upon an intuitive way of looking at the material (it was vector calculus, which can be visual, dealing with flows and rotations). With a few analogies, the material seemed to click -- and I didn't need to memorize the equations (any more than you "memorize" that a circle is round -- if you intuitively understand a circle, you can just "see" that it must be round).
I was really happy to have these explanations, but immensely frustrated that nobody had shared them. Why? Why did everyone suffer silently, class to class?
I began writing the insights on my university website, in the language that I would have wanted to read if I were just starting the class. This site evolved into betterexplained.com
betterexplained.com has garnered a solid reputation within the online Mathematics community over the years-how has running this website shaped/changed your perspectives on learning in general?
Thanks for the kind words. I think my biggest change is realizing there's no timeline to learning. We think "Oh, you learn math in school and use it in the real world". Not true, in my experience -- you are constantly learning and re-learning subjects.
It's like reading poetry -- you read Shakespeare as a 14-year old... but shouldn't you read it again, as an adult? Aren't there new things you'd pick up?
Similarly, I'm going back and re-learning the math I thought I knew (e, ln, imaginary numbers...) and seeing huge gaps that I need to fill. So, I'm realizing learning is a constant process of going back and filling in the cracks. We all have them.
Is there anything about the site you would have done differently if we could wind the clock backwards?
I wish I started earlier! I had a hiatus (didn't work on the site for my first 3 years after college, on my first job) and it would have been good to just keep it going. I don't have any huge regrets otherwise -- a blog is a blog, and there's few mistakes that can't be undone :).
Do you feel too many math/science students are interested in only the "how" but not the "why" these days, perhaps due to education systems placing an excessive premium on scoring good grades?
There is a chicken and egg problem with "We need to measure your learning, here's the test" and "They're going to measure my learning, I'll study what's going to be on the test (and forget)". I think it's an individual bias though -- some students recognize that if you understand the "why" then the "how" comes much more easily. You don't need to choose!
At present, what in your professional opinion is painfully lacking (or blatantly wrong) in the American schools? What remedies would you recommend?
It's really hard to make suggestions for schools because, from my understanding, it's a complex web of politics, unions, educational pedagogies, and so forth. That said, my approach is to honestly focus on what learning would have helped me most when starting out. What types of lessons develop a genuine understanding and enjoyment of the material? It's a bit like defining art, though -- if you start making rigid tests, you warp what is being studied.
Here's some ideas: What are the 1, 2, 5 and 10-year memories from education? If you're going to test something, see if someone has ever read another math book (for fun) after completing a math education. If they never have, there's a good chance the "education" just drilled a hatred of exploration and learning. (Would you consider a "Reading" education where someone never reads again a success? Isn't that a better test than what their vocabulary is?).
I think you have to look at more meta-measures to avoid the potential for gaming scores.
In this vein, I'd much, much prefer students to graduate high school knowing and loving elementary algebra than struggling through and hating trig and calculus. Why? Because the kids who loved algebra will probably learn the rest on their own. The kids who were pushed through rote procedures will forever hate math. What, exactly, was taught?
Sure, some kids would jump ahead and learn Calculus, etc. in high school. Great. But don't force march people through a curriculum and kill their love of learning.
And the sneaky little secret: without the pressure to jam everything into high school, the kids might learn new things on their own. They might pick up calculus in high school anyway.
I've realized I'm more concerned with mathematical "fluency" (how well can you think in terms of math?) than mathematical "vocabulary" (how many arcane formula do you know?).
Similar to the language analogy, I see mental calculuation as spelling. You need to know enough to avoid obvious mistakes and communicate clearly. For serious work, you have tools to help you.
Competitions to compute math mentally are like spelling bees: they are cute, but have little to do with real understanding. How many spelling bee champions went on to write great novels, or poetry, or scholarly articles? And was their great spelling the real differentiator?
You have another online venture Instacalc which is a virtual platform providing wholesome and efficient calculation tools. What is your take on the ability to mental calculate basic stuff ?
Conrad Wolfram has a good TED talk on the use of computers in the classroom. Setting up the equations from real-world situations is the hard part; the actual computation can be handled by machines. That said, it'd be useful if everyone knew the times tables (12x12) and were able to do order-of-magnitude estimates (100x100 = ten thousand, 1000x1000 = million). What's the common set of words everyone should be able to spell? :)
If it isn't a "I can tell you, but I'd have to kill you" industrial secret, would you be willing to offer a little sneak preview of future plans/intentions for your site?
I wish I had something that secret! My plans involve making it easier to share the key analogies that helped us learn.
Currently, my articles are a like a "house" built up of many insights. But, it might turn out that a specific piece was the most useful. I'd like to make it easy to extract these from the article and say "In this article, the following 5 analogies were the most helpful". Those can be refined and used by teachers individually (if fitting). I think it'd be awesome to say "If you're learning about e, here's the 3 most helpful ways to think about it". Sure, the house is there, but maybe a teacher wants to assemble a new explanation of their own. Great!
Along those lines, I'm planning on sharing more "mini-articles" which are just a simple analogy that seemed to help. That smaller insight can be refined, and over time, several great insights re-assembled into a full "house" article (by me, or others).
In a sentence: Let's make it easier to extract and share the specific aha! moments that helped us learn.
Any final words of advice for our readers?
I've noticed there's a huge "Emperor's Clothes" problem in education. We trot out horrible explanations that don't work, but nobody wants to stand up and say "Hey, I think I'm a reasonably smart guy, but this just is not working for me. Why? Is this the best explanation we have?"
No teacher ever acknowledged (to me) how weird imaginary numbers were and how to resolve the dilemma, which is puzzling -- they're called "imaginary" because they were so controversial!
The real reason is the teacher does not have a resolution, an intuition for the material, but won't admit that. So the teacher pretends to teach, and the student pretends to learn. By the way, it's perfectly ok to not have an intuition -- that's how you start finding one!
So, my advice would be to listen carefully to your heart, and don't "pretend to learn". If something isn't clicking, recognize it, and look for a better way to see it!
Once again, a big sincere thank you for agreeing to this e-mail interview.
Thanks, it was fun!