[BlindMath] Trouble With UEB

[kperry at blinksoft.com]

Neil good description. Now what we need to do is add examples on the APH page so that this is clear.  For all your cases we should have examples for people to go through.  I will talk with the folks here at APH and see what they think.  It would be great to have a few matrix problems played out so people can see how special helps.  Same for something like long division with equations.  Thanks for the description.

-----Original Message-----
From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Neil Soiffer via BlindMath
Sent: Tuesday, August 8, 2023 8:52 PM
To: Blind Math list for those interested in mathematics <blindmath at nfbnet.org>
Cc: Neil Soiffer <soiffer at alum.mit.edu>
Subject: Re: [BlindMath] Trouble With UEB

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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