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I am never comfortable with my understanding of a topic until I can teach it (or at least pass it on). There's just always an annoying, niggling feeling that if

I am never comfortable with my understanding of a topic until I can teach it (or at least pass it on). There's just always an annoying, niggling feeling that if I were to be faced with a student who kept asking "why", I'd be a bumbling mess. I was the same as you for linear algebra. Everyone was always so happy to learn the rules, answer the questions like its a script and pass the exam. This frustrated me immensely. Sat down last year and started from the beginning, and I'm glad I did. Sometimes the key is to wipe the slate of existing knowledge clean and start again!

k__ 11y ago
hehe... Funny thing is, if people who learn about software engineering ask me "why" I often know the answers. But I wouldn't know how to start teaching someone this topic... Linear algebra was one of those parts of math that I understood rather fast.
derekp7 11y ago
For me, the "why" came from the word (or story) problems -- the exact problems that most people really hated. There is one problem from calculus that really stuck with me, and made me really understand limits: "You are on an island, which is 10 miles from the shoreline. You can row a boat 4 miles an hour, and you can run 7 miles an hour. You have a friend in need that lives on the shore, 6 miles down from the part of the (straight) shoreline that is closest to the island. Where on the shore do you need to land the boat to minimize your travel time?" So obviously, aiming the boat directly to your destination minimizes your distance, but you are only going to be traveling at 4 mph. And if you aim straight to the shore you minimize your time in the slow boat, but your distance is longer. The visual solution is to plot the total time based on various landing points on the shore, then find which one is minimal. The exact solution is to make a formula that represents both legs of the trip with the landing point being your variable, take a derivative of the formula and solve for 0 (if I remember correctly).
RankingMember 11y ago
I agree, and would say that teaching others something forces you to look for weak points in your own understanding and firm them up. Teaching, for me, makes me think about the "why" more, which is something I always struggle with. Going through the motions is the easy part.
martylookalike 11y ago
I definitely had similar issues with learning math when I was in school. You mention that you sat down last year and started from the beginning... would you mind sharing a little more about where you started, that is what your beginning was, and what sorts of resources you used? I'm thinking of doing something similar and am looking for avenues to take.
- dandermotj 10y ago
  Well funnily enough I started back at what a matrix really is. What does it mean to multiply them, add them, invert them and so on. The first good resource I used was Better Explained! I also took out some Linear Algebra text books from the library. First was Linear Algebra for Dummies (don't knock it!) and then an undergraduate text book. I've still a ways to go but it was a good start.

k__ 11y ago

hehe... Funny thing is, if people who learn about software engineering ask me "why" I often know the answers. But I wouldn't know how to start teaching someone this topic... Linear algebra was one of those parts of math that I understood rather fast.

derekp7 11y ago

For me, the "why" came from the word (or story) problems -- the exact problems that most people really hated. There is one problem from calculus that really stuck with me, and made me really understand limits: "You are on an island, which is 10 miles from the shoreline. You can row a boat 4 miles an hour, and you can run 7 miles an hour. You have a friend in need that lives on the shore, 6 miles down from the part of the (straight) shoreline that is closest to the island. Where on the shore do you need to land the boat to minimize your travel time?" So obviously, aiming the boat directly to your destination minimizes your distance, but you are only going to be traveling at 4 mph. And if you aim straight to the shore you minimize your time in the slow boat, but your distance is longer. The visual solution is to plot the total time based on various landing points on the shore, then find which one is minimal. The exact solution is to make a formula that represents both legs of the trip with the landing point being your variable, take a derivative of the formula and solve for 0 (if I remember correctly).

RankingMember 11y ago

I agree, and would say that teaching others something forces you to look for weak points in your own understanding and firm them up. Teaching, for me, makes me think about the "why" more, which is something I always struggle with. Going through the motions is the easy part.

martylookalike 11y ago

I definitely had similar issues with learning math when I was in school. You mention that you sat down last year and started from the beginning... would you mind sharing a little more about where you started, that is what your beginning was, and what sorts of resources you used? I'm thinking of doing something similar and am looking for avenues to take.

dandermotj 10y ago
Well funnily enough I started back at what a matrix really is. What does it mean to multiply them, add them, invert them and so on. The first good resource I used was Better Explained! I also took out some Linear Algebra text books from the library. First was Linear Algebra for Dummies (don't knock it!) and then an undergraduate text book. I've still a ways to go but it was a good start.