This is a companion discussion topic for the original entry at http://betterexplained.com/articles/adept-method/
I found this site when I was searching for a better explanation of imaginary numbers for myself and my students. WOW! this is how I like to teach. Sometimes I hit the mark, sometimes I don’t, but with your site, I think the bulls-eye just got a whole lot bigger. I am definitely going to hang out here a lot.
Dear Khaled- I liked the diagram which explains negative numbers with a circle along which a number can travel, from plus 1 through zero, via i, than on below the line, where I lost you a bit. But I was wondering, instead of a circle, what if we represented the journey of a number with a sphere? Obviously cannot be shown easily in two dimensions. In a circle, we divide up the possible points into degrees,minutes and seconds. In a sphere, how do we divide up the much greater number of possible points?
I had taken the Learning How to Learn course, Kalid, and was happy but not surprised to see you show up as the windup interview. I’m glad to see you offer it on this site, as well. ADEPT is a great tool!
Thanks Evan! I was really honored and humbled to be able to share my thoughts with the class. Glad the method’s clicking for you =).
Hi. I recently discovered your absolutely marvelous site. I am struggling on note taking technique right now. What tools did you use on drawing those diagrams? They looked great!
Hi Indra, thanks so much. I use PowerPoint to draw all the diagrams: there’s many nice default formatting styles that look very clean out of the box. Here’s an example:
http://betterexplained.com/examples/graphics/Exponential-growth.pptx
Maybe I’ll do a mini tutorial on PowerPoint graphics one day :).
Hello Khalid,
Thank you! Much appreciated! Richard Feynman is my Guru too! His ‘lectures on Electromagnetism’ were recommended as our text book for one of our courses. Reading the lectures was itself so enlightening! I would go back and read it all over again like a favorite novel. I wonder what it would feel like to have been his student.
Thanks again, wonderful post.
Abigail
You are “the man!” Please, keep on writing! You put many so called college “math professors” to shame! It’s clear you have a Passion for what you do, where most of the phony Profs are merely there for the paycheck, no wonder this country (US) lacks serious engineering talent; it’s our own fault for tolerating much too powerful teacher unions where tenure is a ticket to do whatever the hell one pleases, good for the profs, BAD for the students who PAY their salaries.
Brilliant stuff thanks! It confirms what I try to do on my best days, and then some! It’ll be a really useful format to consider when I’m figuring out how to introduce new topics, especially for A-level.
I really appreciate your skill and style Khaled. Thank you for another great lesson in process.
@Abigail: Thank you! I’ve been meaning to see more of Feynman’s lectures, especially since they’ve been opened up (http://research.microsoft.com/apps/tools/tuva/index.html#data=3|d71e62e2-0b19-4d82-978b-9c0ea0cbc45f||). I wish I could have been a student and dug into the intuitions he had as well.
@mj: Thanks for the encouragement =). Yes, unfortunately there’s a pressure on professors to publish or perish (not teach or perish). I think positions should deb split into research-only and teaching-only. It’s like forcing a chef to be a waiter, or a writer to be an actor too.
@Jonathan: Great question. As you suspected, we might want to move a number around in a 3d sphere, vs. a 2d circle. There are special numbers which have been invented to go to higher dimensions (called quaternions - which are actually 4d) and I hope to do some follow ups on them.
You can also skip labeling the individual dimensions, and start giving the angles you want (go forward 1.0, rotate 30-degrees in this direction, then rotate 45 degrees up, etc.). Part of math is figuring out the right system that helps describe what you want, or inventing a better one :).
@Anthony: Awesome, glad it’ll be helpful. It’s now my mental checklist that I have to fill out before I’m satisfied I really understood a topic.
@Mike: Thanks!
Hello Kalid,
How to explain that the sum of all positive integers is -1/12.
Will BE ADEPT help?
This way you put all your work in one single post! I really like this ADEPT approach which I think should be adopted by serious learners who want to grasp the thing and not just memorize a bunch of methods and formulae.
I am a big admirer of great physicist Richard Feynman and definitely your approach matches his style. Keep up the good work.
Harish Dobhal
@Nandeesh: Yep, in that case you might want to look at the existing proofs and work backwards. When explaining something to others, you start with the analogy and go forward, but with an existing result, you have to build up the plain-English, diagrams, etc. yourself.
@Harish: Thank you!
Great post! Is there some place on this website (now or in the future) where readers can contribute their own ADEPT explanations? I’m sure many of your readers have great explanations and are willing to share.
Hi Tony! Glad you found the site, that’s great to hear. I love sharing ideas & material with other teachers, feel free to poke around. Welcome aboard =).
Though I am usually not a phan of phorced acronyms ADEPT has actually been working for me as I try to explain just what and how it is that better explained explains. Keep up the awesome.
Thanks Mark =). I’d been struggling to describe the difference myself (I think I got lucky that I didn’t have to search for more letters).
your work is so great! gives so many aha moment , thanks a lot!