kdejute
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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
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!
–KyleThank 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:
- Use only UEB symbols
- Follow any applicable formats from Braille Formats 2016
- Explain formatting in a TN wherever necessary
Braille on!
–Kyle
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
Yes, that method is still valid. 👍
It is not the only right way. But it can be a practical solution.
Braille on!
–KyleThank 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
Rae,
Thank you for your sharp questions.
- I agree that a letter next to an enlarged grouping symbol is not standing alone.
- 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
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
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
Thank you for your question!
First, any format we choose should accomplish two goals:
- be something we can do consistently for all similar instances
- allow the braille user to easily navigate the steps, choosing to read or skip the explanations as they choose
How can we do this? We might use nested indentation, based on principles from Braille Formats 2016. So, each step of a math problem could be formatted in 1-5, and each commentary could be formatted in 3-5. This differentiates the calculation content from the commentary about it (including runovers of both calculation and commentary).
Alternatively, we might go rogue and take inspiration from §26.4.5 of The Nemeth Braille Code for Mathematics and Science Notation, 2022 and follow the format described there: "Comments within math problems are placed on the line following the expression, blocked four cells to the right of the runover position of the expression."
However, our guidelines for formatting a UEB Math/Science transcription are Rules of UEB and Braille Formats 2016, so we should use tools from those sources and use a nested list format.
Please let us know if you have any follow-up questions or examples!
–Kyle
Thank you. Yes, I agree wholeheartedly that those directional arrows make tactile graphics the right choice.
–Kyle
Fred,
Is there any chance you can share an image of the print you’re working with? I’m not certain I know what you mean by “mapping diagrams (input/output tables).”
–Kyle
Connie,
Thank you for your question!
For a "nothingness" like that which follows the equals in "2+2 = ", UEB does not tell us to use a visible space indicator (or anything else). So, I strongly advocate for following print and simply not putting anything.
#b"6#b "7
I would do this whether the expression were embedded within text or displayed or part of a series of expressions.
Again, thank you for the question. Please let me know if you need more information or have follow-up questions!
–Kyle
