[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 9 months ago by kdejute. Reason: added quotation of directions from example shared
• This reply was modified 9 months 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

[kdejute]

Thank you for sharing this question and these examples, Fred.

I can certainly understand why you are interpreting some of the fractions in your examples to be spatial and "for teaching purposes." Being able to read a series of denominators across a single line, for instance, makes excellent instructional sense.

It looks like you have placed symbols of operation and comparison on the same braille line as a spatial fraction's horizontal line. I tend to agree with that placement, with the note that I am not 100% sure about having the minus symbol (and by extension any other operation symbol) UNspaced from the horizontal line of a spatial fraction.

Let me gather thoughts from the other members of this UEB Tech committee and get back with you.

–Kyle

[kdejute]

Rae,

Thank you for your sharp questions.

1. I agree that a letter next to an enlarged grouping symbol is not standing alone.
2. I believe you are quite right that in the example under GTM 15.3, there is a braille error; namely, in two instances, _| (456, 1256) should be ,_| (6, 456, 1256).

If we can get you more thorough explanation, we will share it here.

–Kyle

[kdejute]

Braille ninja skills! 😍

I do not think lead lines are necessary for any of the examples you shared.

Your attempt at displayed fractions, with a label for the numerators and also a label for the denominators is effective, I think.

Yes, it is ok to use a few different solutions within the same book? Often we need different solutions for different sorts of content, even within one book. (What we should strive for is consistency in transcription of any one sort of content throughout a book.)

–Kyle

[kdejute]

Thank you for sharing your question! I love the question, "Which fractions should be transcribed as spatial material?"

One good place to start is considering the benefits of spatial layout. (Spoiler: after listing a couple of benefits, we will weigh the benefits against the drawbacks.)

Spatial layout has the benefit of making a direct connection between a label and the specific component that is being labeled.

In addition, spatial layout can pretty closely reproduce the print layout. This can make it easier for a sighted teacher or classmate to discuss content with the braille user.

Now let's talk drawbacks.

Reading a spatial layout can be a challenging proposition, forcing the braille user to recognize and remember connections both horizontally and vertically simultaneously while also traversing some utterly blank space. Another challenge is that if a label applies to multiple components, a spatial layout can make it seem like it applies only to one.

With that, and a few other things in mind, I might use something like the following criteria to identify which fractions should be transcribed as spatial material:

• Each label in print applies to one component ... ... or the components to which any label applies can clearly be indicated with two (or maybe three) tactile graphic lead lines
• The text explicitly discusses the spatial nature of the content.

Lastly, remember you can present a fraction twice – once linearly without labels and then again spatially. (This is like what we do with a poem with scansion marks. Braille Formats 2016 §13.9.3)

Please let us know if you need anything more or different!

–Kyle

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