[BlindMath] Trouble With UEB

[Neil Soiffer]

Two big caveats to what I write:
1. I'm sighted and don't read braille, but I have implemented both UEB and
Nemeth braille for MathCAT and so I am familiar with many of the rules.
2. MathCAT currently only does linear braille because it is targeted to
refreshable braille displays. When grid displays get to be more common,
then there will be a strong reason to implement 2D math in MathCAT.

With those out of the way, the main reason to do 2D braille math is that it
should make understanding some problems much easier. For example, in
elementary math such as addition and multiplication, using 2D math allows
the ones column, tens column, etc., to be aligned so you can move your
finger down the page to understand what needs to be added, etc.

Apologies if you already know this... Printed 2D addition, etc. is layed
out with one number above the other, aligned on a decimal point. If no
decimal point is present, numbers are right-aligned. Typically there are
two numbers above each other and below them is a line, with the operation
symbol (+, -, times) to the left of the second number. That's where there
are horizontal indicators in Nemeth and UEB. In UEB, the first two
characters you mentioned start the underline and then the later character
continues it. Underneath the line the answer is written. It should be
decimal-aligned with the numbers above it. Long division is similar, but
much messier.

When you move to algebra 2 or beyond, you get into systems of equations and
matrices. Aligning the variables between the equations makes them much
easier to understand and manipulate. Similarly, for matrices, a 2D layout
corresponds to how operations work on them (some go down a column, others
across a row, and others still pick out the same position in two different
matrices).

As for the number/numerical indicators. You are already familiar with the
single dot-3-4-5-6 character numerical indicator. In UEB, there are rules
that say how long the "numeric mode" continues. You are probably also aware
of the grade 1 indicator (dot-5-6). There are rules about the extent for
that. There are also grade 1 word indicators (two dot-5-6) and grade 1
passage indicators (three dot-5-6). In a similar manner, two numerical
indicators say that what follows is in numeric mode until you see the
numeric passage terminator (dot-3-4-5-6, dot-3).

I hope that is of some help.

Good luck in your studies,

    Neil

On Tue, Aug 8, 2023 at 1:56 PM dana mohsen via BlindMath <
blindmath at nfbnet.org> wrote:

> Hello Blind Mathers,
> Quick question: I'm currently learning math UEB and am using the APH
> tutorial:
> https://uebmath.aphtech.org/
> However, I got stuck on the lesson discussing spatial arrangements (lesson
> 3.2). I'm confused by the use of the double-numerics, and, most of all, the
> vertical and horizontal line indicators (dots5+dots 2 5 and dots 4 5 6,
> respectively.)
> How is spatial arrangement even helpful?
> I hope I'm making some sense. :)
> Best,
> Dana
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