On 10 December 2012 02:10, William Tanksley, Jr <wtanksle...@gmail.com> wrote: > 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"
I am perfectly aware that every notation has problems, and I have never denied this fact, so please don't – again – put words in my mouth. What I (and all whom I know) don't observe at all, however, is those problems causing any difficulties to students when they learn algebra at school. In fact, most of those notational problems do not even manifest themselves in school mathematics. > 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.) That's my point: no need to replace conventional notation. But, if using J to teach math in school is proposed, as was the case, this *is* a replacement of a kind, or at least there would be a huge overlapping, thus presenting an apparent source of confusion to the kids. I also maintain that parsing and mentally computing J expressions is, in general, much more difficult than doing that with conventional notation. >> 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". You said: > it is not my experience that traditional algebraic notation is easy for kids > or college students to learn. which I understand as a statement that the notation presents a problem by being difficult. Then you said: > ... I also had a hard time, as did all the people I knew growing up. > And all the people I've ever talked to about it, including several > accomplished > mathematicians. which I understand as 'massive' (at least by universally manifesting itself). And this is what I disagree with. > 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. I don't see how this can be avoided. Even using the language as a calculator (and, incidentally, this is all what I myself am using it for), it seems to me that some form of programming is inevitable. Constructing expressions is already programming: isn't that a major characteristic of APL and J? But then the problems related to precedence, parsing, binding scopes, etc. immediately show up. That parsing is dynamic (i.e. depends on the values involved) in J is a problem serious enough in the context we are discussing. > You're critiquing J ..... To be precise, I am not criticizing J itself – I am very sceptic about the feasibility of using it in teaching mathematics to children. It seems to me that those who suggest such usage severely underestimate the difficulties involved. And it is hardly accidental that nobody *really* makes such use – as contrasted with making claims about how great that would be. > ..... for a > problem that "traditional notation" can't have because it can't DO > that stuff. In a sense, yes, but that is not unfair. As the expected benefits from introducing J to school mathematics are inseparable from problems intrinsic to software-based computing and to J in particular, they too must be taken into account. The concept of executable notation that we owe to Iverson is so attractive that it is easy to not notice its drawbacks, but that does not make them disappear. > As a side comment -- you use the expression "very good for what it has > been designed." Traditional notation wasn't designed. Not in one day, by a single person and as a whole piece, of course, but nevertheless marked by deliberateness. >>> 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 said that 'traditional algebraic notation is very good for what it has been designed, and much easier to learn for kids than parsing J …' which I don't think is 'almost exactly' 'J notation is inadequate'. There is no 'inadequate' in my words, which would be stronger than I intended. And it's important to not drop the context of school and children, because doing so results in very different meaning. The difference is very clear to me despite my rather poor proficiency in English; it should be even more obvious to you as a native speaker of the language. > 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. It is not at all complementary. I pointed out some of the difficulties that introducing J would entail, because such introducing was proposed – that was precisely the purpose of my post. I didn't need to discuss traditional notation other than mentioning that it's much easier for children to cope with. You, on the other hand, stated that you have been discussing J, which was plainly not true. >> 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. Then what you were discussing is irrelevant to the topic being debated upon, namely, the difficulties of traditional notation and J, as compared in the context of their use in school education in mathematics. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
