[BlindMath] Trouble With UEB

[Shannon Pruitt]

Neil, thank you for that great explanation to bridge the braille to the spatial math. The only thing I would add that may help is this…

The double numeric indicator sets numeric mode so you don’t have to continue to use the numeric indicator since adding the numeric indicator in some instances will increase the area taken up and also it could make it more difficult to vertically align some corresponding place values which is the entire point of spatial math. 

In spatial print math, anytime there is a horizontal line that indicates an “equals” in the calculation. 

As for the vertical horizontal line in long division, although in print we typically view the long division symbol as one symbol, it is made up of two symbols which are a vertical bar followed by a vinculum OR a right parentheses followed by a vinculum. A vinculum is a horizontal line/bar above values. 

So in the case of Example 3 in the tutorial,  the problem is 12 divided by 4. Written out spatially in print it is written divisor vertical bar dividend (with vinculum) or 4 vertical bar 12 (with vinculum).  The answer or quotient then ends up on top of the vinculum so place values line up. The math to determine the answer gets worked below. 

So in that same example you would have 4 vertical bar 12 (with vinculum) and the answer 3 is on top of 12 where the 3 lines up in the ones position. 


Hope that helps and doesn’t make it any more confusing. 

Shannon

On Aug 8, 2023, at 8:53 PM, Neil Soiffer via BlindMath <blindmath at nfbnet.org> wrote:
> 
> 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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