Wow - this exchange is very heavy! My comments are on a very
simple level: I am very good in math, I use it a lot, but when I look at the
index of a first- or second- year algebra text I have no idea what the terms
mean in the chapter headings; I can do it all once I read the problem, but the
categorization is beyond me. If I were a kid learning this stuff I would be really
put off - there is too much totally unnecessary vocabulary.

Hi,
Irene, good that you are bringing the thread back to its original idea. I think
that everyone agrees that the vocabulary puts kids off. There are two big
problems, however: (a) nowadays almost everything else in mathematics courses,
not just the vocab, puts kids off. (b) Which vocab should one get rid of? After
all, certain vocab will be necessary for some of the kids who have contact
later on with mathematics, so we can't replace everything. Any suggestions?

Irene's concerns is one of the communication problem in
horizontal mathematics. This proves the claim of Realistic st that there should
be Horizontal and Vertical Mathematics. And also give the account of School
Mathematics that one of the nature of school mathematics is Communication; and
thus the talk about the relationship between Mathematics and language is
relevant. Whilst Vertical Mathematics is the business of Pure Mathematicians,
and advance or adult learner. For the outsiders or the younger learner of
mathematics concrete mathematics will be more realistic. Whilst what Marty's
did by his model of communication is a very highly and sophisticated approach
of using technology to offer the schema of a very specific communication with
the specific aims and specific results. This further a proof that communication
has its various dimensional contextually, culturally, psychologically and
philosophically. Therefore I do not see that Marty's Models are able to give
solution to Irene's problems. Again I wish to remain to whom it may concern
that we need to approach our younger generation with mathematics of their
world.

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