kdejute
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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
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
[In a perfect world, I think these long web addresses would be digital so that the user could simply click them without having to wade through their coding/navigation components. ... If we were feeling like going way above and beyond to create accommodations, we could conceivably use bit.ly or another service to create a shortcut for these web addresses and share that shortcut in a transcriber's note.]
Belated greetings, Shawn:
I do not know of any specific guideline or rule that applies to breaking a long "nonsense" string of letters that is unspaced.
I suspect you already know that 14.7 of the Instruction Manual for Braille Transcribing – UEB Edition, 2015 says, " Make the division at a logical break and at a point that is not between two letters or between two digits." I acknowledge that isn't helpful in the case you describe.
First, I would double-check for any punctuation or words and endeavor to break between words or after any punctuation.
After checking that, if you still have to force a braille line break in a string of letters that is unspaced, I would endeavor to make the line break where it does not interrupt any contractions.
The braille user is lucky to have someone who is working hard to make even the messy web addresses be as reader-friendly as they can be.
Braille on!
–KyleGreat question. Thank you, Lucas.
Personally, I would put a grade 1 symbol indicator between the minus symbol and the letter. But I have cross-posted this question in NBA's tactile graphics forum so we can get further input. In that forum, the question is titled Number Line Question, negative lowercase letter below number line.
–Kyle
Thank you for your question, Susan!
We think it is alright to use the visible space symbol without any grade 1 indicators as long as it does not follow a letter.
If we use the one-cell visible space symbol instead of the box that print shows to indicate an omission, we should explain that change in a transcriber's note. For example, "The visible space symbol .=+ is used in braille where print has a box."
A possible transcription of item 1 from the print you shared is attached (as a picture and as a BRF).
What do you think? Does this help?
–Kyle
