[kdejute]

Thank you. That does help.

–Kyle DeJute and some APH colleagues

[kdejute]

Thank you. That helps.

–Kyle DeJute and some APH colleagues

[kdejute]

It is great news that tactile graphic arrows are a possibility for this transcription.

The committee believes strongly that brailled arrows are confusing in this situation. Tactile graphic arrows would much better fulfil the role of the arrows here, which is to connect a label to a specific piece of the math expression.

The attached image shows one possible way of placing/arranging the arrows, the expression's pieces, and the labels.

That possible transcription includes a transcriber's note that says, "The equation is shown twice in braille: once without labels and again with labels."

Then the equation (2×_ = _) is brailled on its own line. Next comes a blank line. Then the labels ("cups each day", "days in 2 weeks", and "total cups") are brailled on one line, with two blank cells between the labels. The labels are followed by two lines where the arrows are drawn, all pointing straight downward to the line where the equation is brailled again spaced out horizontally so that the arrows can point from each label to the relevant part of the equation.

Please let us know if you have follow-up questions or notes!

–Kyle and NBA's UEB Technical Material Committee

Attachments:

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[kdejute]

Thank you for sharing your question, including pictures of the print and your proposed braille! The committee is now discussing it.

For now, please let me ask: Are tactile arrows a possibility in this transcription?

–Kyle

[kdejute]

We have been discussing this as a committee, and we have come to some consensus.

First, Let's be careful to focus on transcription and not instruction/teaching.
If we look at this as a transcription issue, then the conventional wisdom is "follow print."
To answer the specific questions:

1) BANA does not necessarily recommend transcribing the equation without the "shown work" before transcribing the fully worked-out problem. With that being said, we as a committee do not see a problem including the equation first in this situation. We should certainly use a transcriber's note if we present the problem twice; perhaps, "The example problem is shown twice: first without any calculation text and a second time with the calculation text included."
The suggested transcription that is attached here does give the example problem twice with a tn explaining that the problem is shown twice. The suggested transcription uses one continuous numeric passage for all of the example problem and also the rest of the exercise set. The alignment of the suggested transcription attempts to follow the mathematical logic of the problem's layout without rearranging or breaking down the print layout.

2 & 3) These questions seem to be focused on teaching a braille reader how to show their work, and that is not really the role of a transcriber. We must trust the teacher (or aid or paraprofessional or someone else directly in the instructional environment) to tailor instruction on how to show work to the specific braille user.

Are there aspects of your question that we did not address? How else can we help?

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[kdejute]

We really are still working on this.

[kdejute]

Susan,

Thank you for your question! I appreciate your citing a section of Rules of UEB 💖🧠💖

I see that the directions in the example you shared say, "Write the decimal point in each product so that the equation is correct."

Thus, I am comfortable saying the spaces in the situation you shared are, as part of RUEB §6.6 says, "a separator in a single number."

And so it would make great sense to use the numeric space.

Consequently, item b from your example might look as follows:

braille: #j4ec"8#e "7 #b"f"e

print: b. 0.53×5 = 2 6 5

Braille on!
–Kyle

• This reply was modified 4 weeks, 1 day ago by kdejute. Reason: added quotation of directions from example shared
• This reply was modified 4 weeks, 1 day ago by kdejute.

[kdejute]

(cont.)

Even though Braille Formats 2016 §10.8.4 says, "Format exercise examples in the same manner as the following questions/answers. ..." we think that transcribing the spatial example problem more than once would be more confusing than helpful. Again, we are convinced that even though the example problem includes all of its carrying and borrowing and so will look different than the exercise problems that follow it, the example problem should be transcribed one time.

We are working on a suggested transcription for the print you shared.

–Kyle

[kdejute]

Thank you for the questions! I'll start answering these now; though, it will likely take some time and discussion to address them all.

You asked first, "Does BANA ever recommend including the math text without annotations before introducing the annotated text?"

The example you shared implies that what you mean by "annotations" is things like carried numbers, omissions, etc.

I cannot point to any place where BANA or ICEB addresses the possibility of brailling a math expression twice (once without certain aspects and then a second time with all printed aspects included). So, we do not have official guidance right now.

Personally, I would NOT recommend transcribing the math without its full work/calculation. If you wanted to clarify for the reader what is the core expression, you might include a short transcriber's note to say so. (e.g., The worked example shown below is 42×36.)

–Kyle

P.S. I am still working on your other questions.

[kdejute]

What follows is a brief summary of conversation outside of this forum.

I have found these non-Arabic numeration systems described in the document Addendum 1 to the Nemeth Code for Mathematics and Science Notation, 1972 Revision: Ancient Numeration Systems. What if we used the keys described in that [e.g., "e", "p", and "r" for the "eye," "pebble," and "rod" that make up the Mayan numeration system, with a subscript indicator used to show the placement of the rod(s) and "e", "p", and "r" for the "eye," "pebble," and "rod" that make up the Mayan numeration system,]?

Others had the same idea, though they could not find their copy of that Addendum.

I agree that utilizing the information about ancient numeration systems in the Addendum 1 to the Nemeth Braille Code is inspired.
🧠✨
The only thing I might do differently is use the "directly under" UEB indicator instead of the subscript indicator, but I think the meaning becomes clear to the braille user either way.
–Kyle

P.S. One more note: This is not the only way to tackle this situation. And, of course, any solution would require a thorough transcriber's note.

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[kdejute]

Thank you for sharing  your question!

Yes, I can certainly understand why you would request input on how to represent non-Arabic numeration systems in a braille document. [My favorite is the Mayan system, with its base-twenty and a shell that means zero.]

GTM 11.5.7 is a good reference to highlight. As you noted, it uses transcriber-defined symbols for Babylonian numerals, and that example only has to tackle two symbols.

You have many more than two symbols that do not have any UEB definition, distributed into four systems (Chinese, Egyptian, Babylonian, and Mayan).

My first answer is: If it were my child who was encountering this material, I would want them to have 3-D representations of the various symbols, with a distinct category of material for each system (e.g., Wikki Stix in various shapes for Egyptian numeration, puff painted shapes for Babylonian numeration, sticks and stones and shells for Mayan numeration, etc.).

I know that is not practical for us to produce for a braille book. So, failing that, I think there is a strong argument for using tactile graphics to represent all of the non-Arabic numeration systems.

If we must use braille symbols, then could we define the whole set of UEB's seven transcriber-defined symbols anew for each numeration system? And use a tn to note which set is used in print each time?

I am very wary of using Nemeth Code symbols in UEB, because the two codes have different foundations for symbol creation.

Alternatively, I strongly suspect that transcriber-defined shapes are our best bet here. Those would let us define a full set of shapes for each numeration system. The transcriber-defined shapes will be time-consuming to read, but a print user will very likely also take a lot of time to read the non-Arabic shapes. For this solution, I fervently hope that print includes a well-organized key of the numeration systems' printed components so you can follow that in creating your four sets of transcriber-defined shapes.

Hopefully that gives you more to work with.

If you need more, please let us know.

–Kyle

[kdejute]

What follows is a brief summary of our conversation outside of this forum.

In spatial material we use the cancelation rule in GTM 4.1.6. The issue that we run into when
dealing with this is that the definition for an item in GTM 12.1 is interpreted several ways and
can tend to cause confusion.

...

What if I have a spatial calculation with something like "1,99" and then a space for alignment, and only that second 9 is cancelled? How should I limit the effect of the "line through previous item" indicator?

I had to revisit the examples in the 2020 NBA workshop "Spatial Problems: Rules and Advice" [a recording of which is on NBA's website] and the decisions that Jason Armour, other members of the NBA UEB Tech Committee, and I made before I could respond confidently. Now that I've done that, I can say that the solution proposed in Mr. Sullivan's message is in line with the best information we have at this point, and – most importantly – gives rise to accurate braille. In short, I think it best to use braille grouping indicators (rather than spaces) to limit the effect of the "line through previous item" indicator.

Braille on!
–Kyle

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[kdejute]

Thank you for your question, Daniel.

In short, yes; when a format is not covered in Rules of UEB, the BANA "Provisional Guidance for Transcribing Mathematics in UEB," or Braille Formats: Principles of Print-to-Braille Transcription, 2016, then we may design a practical solution.

I see you say in the attachment, "For UEB Technical there is no information to fall back on [for formatting formal proofs,] so the only available resource is the 2022 NEMETH Code book." I would not say "only." However, I agree so far as to say that our North American primary source books for UEB Technical (aka UEB Math/Science) transcriptions do not cover formal proofs explicitly. AND, in such a circumstance, we are free to come up with a clear and sustainable format. And we may take inspiration from The Nemeth Code to do that.

So, again, yes, you may follow the principles described in §26.7 of The Nemeth Braille Code for Mathematics and Science Notation 2022. As you do so, please remember to:

1. Use only UEB symbols
2. Follow any applicable formats from Braille Formats 2016
3. Explain formatting in a TN wherever necessary

Braille on!

–Kyle

[kdejute]

Daniel, I'm afraid I do not see an attachment. Perhaps it was too big? If that is the case, maybe you could "zip" it into a folder and try again? Or you could possibly email it to kdejute@nationalbraille.org.

–Kyle

[kdejute]

Yes, that method is still valid. 👍

It is not the only right way. But it can be a practical solution.

Braille on!
–Kyle

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