[UEB Maths] Some more on formatting and computability

[Janet Reynolds]

I just went back to check the dot configuration that Joe had put forward
as a possibility, and you will all have noticed that it was dots 146,
not dots 346 as I accidentally memorised when I went home for the long
weekend. So ignore what I said about the Nemeth plus sign, the comments
about it being a "heavy" sign still hold. I have edited my message below
so feel free to delete my first one to avoid confusion!=20
Janet

-----Original Message-----
From: uebmaths-admin@nbp.org [mailto:uebmaths-admin@nbp.org] On Behalf
Of Janet Reynolds
Sent: Tuesday, 7 June 2005 12:59 p.m.
To: uebmaths@nbp.org
Subject: RE: [UEB Maths] Some more on formatting and computability


This is a long reply, but I have some specific questions for folk at the
end!

Thinking about the two issues of the use of grade 1 indicators and the
option of function indicators has made me focus on the different roles
that the Maths Rules have to fulfil. Firstly there are those school
students who are unlikely ever to study Maths or Science beyond aged 15
but need basic numeracy and the option to gain a qualification in Maths
that may include trigonometry and baby algebra. UEB has the potential to
give them and their support folk Maths that is somewhat bulky but easy
to learn to read, to produce, and to teach. Secondly there are the
braille readers who decide to study Maths or Science at senior school or
tertiary level. They will be using trigonometric and other functions
within calculus and other aspects of higher maths. Thirdly there are the
readers of literary texts that include small amounts of technical
material that in the past they have not been able to easily access in
braille.=20

Because the UEB design is based on unambiguous symbol definition, all
those three areas have the potential to make use of computer power more
than in the past. It's a help to the student and the teacher at all
levels if braille maths can be easily turned into print and print maths
into braille. And for the literary reader, it's great if the translation
software can just include the technical bits, which can be easily
interpreted with the use of a special symbols page.

I know that we are all familiar with these goals, and I think the
problems the five of us are having in dealing with the indicator issues
is that we need to include advice in the rules that works in all three
areas, helping the mathematically challenged, the mathematically gifted
and the general reader.

My worries when I look at the grade 1 indicators are to do with the
mathematically challenged learner (or teacher!). I'm not so worried in
this context about the extra "clutter" of  numeric indicators and grade
1 indicators used to distinguish letters from numbers. For the
struggling learner I think those will be a help rather than a hindrance.
What worries me is the intrusiveness of the indicators when you have
square roots, algebra and general fractions. If you omit them then it
won't back translate properly, if you put them within the expression
then the rules for when they are needed are complicated. So in my
rewrite of 1.4 I was leaning towards encouraging the liberal use of
passage indicators if there was any doubt. However educators I have
talked to want those indicators out of the way so the child can put
their fingers at the beginning of the line in question and focus on the
maths.  Which was why I suggested having them on a line of their own,
preferably without the clunky "use" indicator.

Then Joe suggested the 146 symbol as a possible alternative for the
three dots 56.  And Stephen said he liked it because it was short and
rather like the BAUK  opening computer indicator. But my initial
reaction was horror which is why I've been doing a lot of thinking!=20

I guess I don't like the 146 because it is a "heavy" symbol that the
student or teacher would worry about. At least the three dots 56 are
obviously grade 1 thingies and are irritating rather than a distraction
from the Maths.=20

But then if I start thinking about the student studying at a higher
level, they might quite like the 146 because it is quick to key in.

So is there a case for having both forms of the starting grade 1 passage
indicators available? Or does that just make the advice we would have to
put into 1.4 even more confusing?

I agree with Joe that missing them out altogether and using indentation
instead is a bit of a worry because of the computability issues.

So now onto the function indicators. And again I am split depending on
which of the three areas the reader falls into. If they and their
teacher are struggling with right angled triangles then best if sin and
cos are spelt out with a space before the variable. (Incidentally, when
I talk about struggling teachers here, I am not thinking about someone
supporting a braille reading student in a special school, or even
mainstreamed in an urban centre, I am talking about someone in a rural
area who maybe has a braille reading student on their books for the
first time in 5 years and is brushing up their own braille skills, this
is often the reality for us here in NZ and I am sure we are not alone).

However, if a student is specialising in Maths or Science, then all the
things Bruce and Stephen are concerned about come into play. Functions
are a concept that runs throughout higher maths. They are typeset in a
certain way and tags can be made available for them in markup languages.
As Stephen says, they are word fragments and ideally should be
distinguished so as to avoid ambiguity. If we are going to distinguish
them in braille, then I liked the idea of the dots 16 to open and the
dot 3 to close (though I would welcome Joe's thoughts on the viability
of the dot 3). Stephen's examples quite tempted me, they really are
quite elegant. And I also agree with Stephen's more recent comments that
we need to think carefully about the types of intervention needed when
translation software interprets Maths.

On the other hand when I taught higher Maths back in the 80's and marked
my students hand written examples I never had any problems with
ambiguity, even though in formulae like absinC the letters all just ran
together.. And as a Nemeth transcriber, I always just accepted that
functions are best spelt out as they are in print with a space after the
function name. So in raising the whole issue of function indicators I am
speaking on behalf of Bruce and Bill Jolley in Australia, who found the
trig indicators so powerful when they were braille reading students at
that level.  And I'm quite prepared to be personally convinced that they
are essential in UEB if the arguments are strong enough and the code can
cope with it.  Could they be made available as an alternative, only to
introduced at a certain level in the school curriculum?

So my next question I guess for Bruce and Stephen is whether the
function indicators could be extended to cover inverse trig functions
etc. (I'm not currently familiar enough with how that is currently done
in BAUK or ABA).=20

And for Joe, how viable is that dot 3 is as a single cell function
terminator.

And I'd be interested to know from Helen what Canadian thinking about
the passage indicators is, has anyone had any feedback from Canadian
educators, and how you think they might react to the dots 146
suggestion.

And for everyone, at what stage in all this would you like a
teleconference?

Janet

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