How I Learned Linear Algebra Without Going to Class

The Khan Academy and letting students learn at their own pace

“Here I was, an analyst at a hedge fund. It was very strange for me to do something of social value.” -Sal Khan

A linear algebra problem

For the past month I have been skipping out on my math classes. We started a unit on linear algebra, which looks like the biggest jumble of letters and numbers ever, and I just could not pay attention. Going to lecture was a waste of time. Unfortunately, there isn’t much extra help for math above calculus so I was in a bind. I went to the professor’s office hours but they just weren’t enough to keep on schedule. Luckily, two weeks before the test, I found an open source education website called The Khan Academy that has videos on this subject. I ended up watching 10 x 15 minute videos which gave me the starting point to work on practice problems and with friends.

Intro to matricesmultiplying matrices 1multiplying matrices 2inverse matrices 1,inverse matrices 2inverse matrices 3matrices to solve a system of equations,eigenvalues of a 3×3eigenvectorslinear transformations

“So I see Sal Khan as a pioneer in an overall movement to use technology to let more and more people learn things, know where they stand … its the start of a revolution.” – Bill Gates

I am in my third year of college and I just don’t see why most of my classes are in lecture. I’d much rather have a grad student walk me through math and science concepts, English discussions or psychology issues. I am currently writing this in a lecture and the only students that are paying attention are in the first row. The other 70 students either figure this stuff out on their own or fail (I am guessing). This isn’t learning! I don’t understand why people are not enraged that they are paying hundreds of dollars a day to go to lecture when they learn the material themselves!

I learned calculus from grad students who worked in the math lab. I learned chemistry from my roomate who worked as a chemistry TA. I learned physics not from the professor but from the grad student who graded the homework. I didn’t learn anything in my psych classes (but I got A’s and B’s). I learned what it takes to be an entrepreneur from my previous job. I learned about trademark laws and how to form an L.L.C. from the Innovation Center and on-campus lawyer. The only classes that I have learned in are my education classes where we worked in small groups and the professor walked around and helped us.

“Eventually I want it to become the operating system for what goes on in the classroom where every student is allowed to work at the own pace and the teacher actually becomes more of a mentor or a coach.” – Sal Khan on his vision for The Khan Academy

One of my favorite classes at the University of Maine was ENG 245: American Short Story online. There were around 50 short stories, a forum and three multiple choice tests throughout the semester. At the beginning of the course, students signed a contract for the grade that they wanted. Students who wanted an A signed up to read the most stories, talk the most on the forums and had to get above an 80 average on the tests. I was able to read the stories that I wanted to read, discuss the stories that I wanted to discuss, and go at my own pace. I always knew that I was going to get an A in the class and all I had to do was devote 1 weekend out of a month to reading and discussing and testing.

So what would the downsides to letting students be in control of their education? It is impossible to stay on facebook forever, I don’t think that kids will just waste the whole day playing games and procrastinating. The only downside that I can see is that people might not learn subjects that they don’t like, however is it possible that they don’t like them because of the way it has been taught? According to Khan, referring to the students at Palo Alto Middle school in California who are using his videos instead of lecture,

“when you let every student work at their own pace, and we see it over and over and over again, you see students who took a little extra time on one concept or another but once they get through that concept they just race ahead. And so the same students who you thought were slow six weeks ago, you now would think are gifted.”

I have gained the perspectives of both being held back by teachers because of being too advanced and being left behind because of being too slow. I see these open source education platforms allowing everyone to be the best they can be – and I have spent countless hours working as a recruiter for a company and that is something that everyone wants. What do you guys think?

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8 Responses to How I Learned Linear Algebra Without Going to Class

  1. Gary Davis says:

    So you learned linear algebra? Tell me – what is an eigenvalue, and why calculate them?

  2. Sometimes when you perform an operation on a function you get the original function back times a scalar. If Ak = ck where A is an operation or square matrix, c is a constant and k is a vector, then c is the eigenvalue and k is an eigenvector of A. To find the eigenvalues and eigenvectors of a square matrix A, construct a matrix cI-A, solve cI-A = 0 for eigenvalues c, plug the eigenvalues into (cI-A)k = 0 and solve for k.

    • What are they used for? I am not exactly sure on that. I remember learning about them briefly in into to quantum mechanics, but Khan did not explain what they are used for in the videos that I watched and I did not need to know that for the test (I can’t believe I said that).

      On another note. Thank you for policing my work. The sentence “I ended up watching 10 x 15 minute videos, and learned linear algebra.” is completely ridiculous. It is impossible to learn a subject with that little work. I just added to that paragraph to better illustrate what happened.

  3. Pingback: What Happens to Learning When Grades Aren’t an Issue? | Stirring The Pot

  4. Pingback: The Science Learnification (almost) Weekly (May 8, 2011) « Science Learnification

  5. Frank says:

    I 100% agree. I am writing this comment from the back of a lecture right now…

  6. Gary Carrara says:

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    great deal and I view it that is professional, easy to understand.
    I congratulate you for this article that I am going to tell to the people around.

    I request you to recommend the page where each pupil or learner can find ratings
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