I think I’m missing the text of your argument on this, Art. All I see is “Can we finally get rid of the long division algorithm?”.

I guess I would not want to do that without really thinking about the consequences. Will anybody understand or know later how to deal with rational functions (quotients of polynomials)? Granted, most people use software to find antiderivatives, but someone has to understand how to do that. Where in mathematics courses would the necessary knowledge be taught that would convert, say, (x^3 + x^2 + 1)/(x+2) into x^2 – x + 2 – 3/(x+2)?

Jim, I apologize if I left out the link to the article, I was trying to grab it quickly. But to answer your questions, I would ask how many of us need to be able to deal with rational functions and wouldn’t those folks quickly learn how to do it if they needed to. About 1% of our college grads get a degree in math. It would seem to me that this group might want to learn to and have little trouble learning to deal with rational functions or any difficult algorithmic activity, but more likely would be turning to software to perform that task. In the perfect world where this stuff was trivial to learn quickly I might then ask “why not” but in our real world where so many fail to learn this stuff and need to learn so many other things like problem solving, spreadsheets, financial literacy, statistical literacy, programming, etc. is the division algorithm or for that matter any algorithm necessary to practice to mastery?

I hope you are having a great spring and i am enjoying our long distance conversation.

I think I’m missing the text of your argument on this, Art. All I see is “Can we finally get rid of the long division algorithm?”.

I guess I would not want to do that without really thinking about the consequences. Will anybody understand or know later how to deal with rational functions (quotients of polynomials)? Granted, most people use software to find antiderivatives, but someone has to understand how to do that. Where in mathematics courses would the necessary knowledge be taught that would convert, say, (x^3 + x^2 + 1)/(x+2) into x^2 – x + 2 – 3/(x+2)?

Jim, I apologize if I left out the link to the article, I was trying to grab it quickly. But to answer your questions, I would ask how many of us need to be able to deal with rational functions and wouldn’t those folks quickly learn how to do it if they needed to. About 1% of our college grads get a degree in math. It would seem to me that this group might want to learn to and have little trouble learning to deal with rational functions or any difficult algorithmic activity, but more likely would be turning to software to perform that task. In the perfect world where this stuff was trivial to learn quickly I might then ask “why not” but in our real world where so many fail to learn this stuff and need to learn so many other things like problem solving, spreadsheets, financial literacy, statistical literacy, programming, etc. is the division algorithm or for that matter any algorithm necessary to practice to mastery?

I hope you are having a great spring and i am enjoying our long distance conversation.

Art