Khan's analytics are the best. No doubt. Nobody comes close, at least as far as I know. When you have programming luminaries such as John Resig (creator of jQuery) on your team, the results are going to be outstanding. The Khan Academy team is small, lean, efficient, and full of energy. The analytic tools available at Khan Academy are the best, hands down, bar none.
Khan Academy is not the only game in town for massive online problem sets, however. Try the Temple COW. http://www.math.temple.edu/~cow/ for problems in calc 1, 2, 3, linear algebra, number theory, and even abstract algebra.
- Insight into the meaning of the mathematics. (not just rote problem-solving techniques)
- Clearly chosen examples and
- Well explained, nearly flawless delivery of any algebraic steps involved.
Here we go...
Math TV http://www.mathtv.com/videos_by_topic
Mr. McKeague is a lifelong educator who is one of my role models for pedagogy and professionalism. He has deep wisdom into teaching and life and he knows how to prepare and present sharply focused lessons that are approachable for students of all ages. His website focuses largely on middle and secondary school math (number sense, algebra, trig, calculus).
- Advice for new teachers (good advice for any professional, really)
- Following instructions (great for students!)
Midnight Tutors http://www.midnighttutor.com/
These guys were making online educational videos before Youtube was popular. Unfortunately, they seemed to have stopped, but virtually all topics in AP Calculus are covered. The main lecturer is professional educator and researcher in the sciences (rocket science, specifically) who has deep insight into the real life applicability of the math. He is passionate, chooses clear illustrative examples, and does more than walk a student through a "bag of tricks" -- he encourages a way of thinking about mathematics which is rarely seen elsewhere.
- Study tips -- applicable for all students
- "Was this integral designed to torture calc students, or does it have meaning?"
MIT OCW (math superstars)
As you know, MIT has been producing free online videos (and readings, and java applets, etc.) in a variety of topics since around 2002. Most of the video lectures are around 90 minutes in length, and not all of them are exactly the most engaging videos ever produced... but there are some gems out there! Here are just a few.
All of his videos have extremely well-chosen examples, encourages students to try the problem on their own before revealing the solution, and gives plenty of intuition and interpretation of the results to highlight subtle points about the theorem or technique being used. Pretty much any video with Joel Lewis is gold.
MIT filmed a calculus series back in the 70s with Dr. Herb Gross as the lecturer. The lectures he gives are tremendously insightful, rigorous, yet still accessible. Herb makes sure to give ample explanation of the intuition behind each step of his reasoning and makes sure to constantly keep the "big picture" in mind as he goes through each lesson. Also his accent reminds me of growing up in Bruk-Linn Noo Yawk. ;-p
- The Multivariable chain rule and higher order mixed partial derivatives (I've never seen anyone explain it so clearly!)
Arthur's writing (single variable calc, multivariable calc, diffeqs ) is just as good as his speaking. He uses clever metaphors to illustrate his examples and where such metaphors fail, he uses sterling clarity to choose examples to show where a theorem applies and where it may fail entirely. He has a deep mathematical understanding of complex topics and their relationships between one another, as well as a great sense of humor.
- Repeated Real Eigenvalues (Using the love between George Costanza and his wife Susan from Seinfeld to model & interpret a system of linear differential equations.)
PatrickJMT (not with MIT) His Playlists
Patrick's math videos are usually short, to the point, feature a single, very clearly worked example, and start with a short summary of the theorem or property being used in the video. His videos are great for illustrating example problems and a good strategy (for all videos, not just his) would be to pause and try to solve the problem before he does. His videos are plentiful and thoughtfully composed.