Boyko Bantchev <boyk...@gmail.com> wrote: > William Tanksley <wtanksle...@gmail.com> wrote: >> "Let me know -- where did you teach that gave you the idea that people >> find traditional notation easy?" > I did, and I am teaching to both university students and school students. > I'll add that they are not the crowd that would fail at algebra, in fact they > are above average level.
Thank you for responding clearly. I don't know why our experience is SO disjoint. Shrug. But clearly I must agree with you that "my experience contradicts yours." > in mathematics for years. Neither my experience nor that of all those > people, or that of our students shows problems with the notation. > A person may be good at mathematics or similar subjects, or not, but > this has nothing to do with notation. Every notation has problems. If you don't see them, it's not because they're not there. It's enormously ironic that you're denying ALL problems with "traditional notation" while imputing huge problems to J specifically. I'll discuss the latter below, since you deny imputing any problems at all to J. > This is supported by observing that, to my best knowledge, notation > is not among the issues raised in articles, at conferences, etc. > where the problems of education are observed. I admit that since I graduated I haven't followed such things; so I'll happily take your word for that. And frankly, it makes some sense to me. But in another sense, I have to suspect that you're ignoring people's actual work on some types of innovation in favor of focusing on the great need to teach students to be literate in the writing system they're meet in the real world. Learning an alternate system to help think doesn't replace learning "traditional notation". (I think you made this point very clearly a while ago, and I agree with you -- there's no way to replace traditional notation in education except at the cost of ADDING something else.) But, at the same time, every text more advanced than high school algebra introduces its own notation. Even calculus has a small set of alternate notations used for different purposes. Is that a problem? Well, no. But isn't that interesting that (taking your word) no teaching conferences or journal articles ever address something that every book past a very beginning point has to deal with? > Consequently, I not only disbelieve your claims that the usual > algebraic notation used in school is massively problematic – I find > them ridiculous to the point of absurd. I didn't say anything even vaguely like that. "Massively" problematic? Not at all. I don't even think the notation is "problematic". Sure, it takes time to learn, but that seems to me to be inevitable -- so would any (hypothetical) replacement. But YOU have clearly and unmistakably been making claims about massive problems in J as a notation. "Traditional algebraic notation is very good for what it has been designed, and much easier to learn for kids than parsing J, let alone understanding the underlying computational model." You later added "J, as a notation and a computational model, is much harder to cope with than traditional notation." You also explained some of the complexities of J's grammar, as though children would be asked to read Iverson's or Apter's professional work while learning how to add polynomials. Now, when I read those carefully, I agree with them; your facts are correct. If we DID teach children to parse or to understand J's underlying computational model, we would indeed have a much harder problem. So... don't do that. There's a huge gap between teaching children to program and teaching children to use a computer language as a calculator and a notion checker. You're critiquing J for a problem that "traditional notation" can't have because it can't DO that stuff. As a side comment -- you use the expression "very good for what it has been designed." Traditional notation wasn't designed. >> than continuing the armchair psychoanalysis that did fill too much >> space in my post. > Psychoanalysis? I have no idea what you are talking about. > I simply and clearly reminded you I didn't intend to sound like I was blaming you. The psychoanalysis was in my own post -- you just continued doing what I started. My fault, not yours. > that your, or whoever else's difficulties > with mathematics might have been of a completely different source > than the notation that you blame. Nope, not blaming the notation. I'm just pointing out that it's not easy. (And you claim it is, so we're at an impasse.) Anyhow, I clearly didn't need the reminder -- like I said, I started trying to guess what the other problem might be. >> We're discussing your claim that J notation is inadequate >> compared to "traditional notation". > Now you are putting words in my mouth. I didn't say that. You said almost exactly that. See the quotes above. >> I countered that by pointing out >> that J notation covers more of mathematics with a standard notation >> than "traditional notation" does. > Apart from the fact that the discussion is not about what J 'covers' > but about how easy it is to school students, I don't see where you did > that. Your previous post didn't say a word about J – it was devoted > entirely to complaining against traditional notation So what? I could just as easily point out that your post does the complementary thing, by not talking about "traditional notation" but instead complaining about J. > and silly attempts to insult me. Insult? No. Contradict? Certainly. I'm not ashamed of that. > I am very well aware of > the breadth of topics that can be expressed in J, but that is not > at all what we are discussing. Oh. Actually, it was what I was discussing. Interesting. -Wm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
