[kdejute]

For the f: A → 𝒫(A), you might have already found the "function notation" question in this forum, which touches on the seven different mathematical uses for colons. I agree with your assessment that this is giving a name to a map, as defined by WolframMathWorld. As you said, in braille such a colon (for mapping) would be transcribed unspaced, and it would need a punctuation indicator.

For something like {x ∈ ℚ : x² < 2}, I agree with your assessment that the colon here means "such that." So, the expression {x ∈ ℚ : x² < 2} says, "x is an element of the set Q such that x-squared is less than 2." The "Colon and letters in sets of numbers" question in this forum talks about this "such that" role for a colon and recommends transcribing it unspaced (no blank braille cell before or after the colon meaning "such that").

Since we recommend transcribing both the mapping and "such that" colons completely unspaced, it may not be necessary for you to completely understand the difference between the two. For what it is worth, I agree with you that a "such that" colon is likely to be part of an expression within grouping symbols (most often curly braces). I would also suggest that a "such that" colon will have the same variable both before it and after it, like the x in our example expression above.

The print sign := (a colon followed by an equals sign) seems to mean "is defined as" (I first found this definition in a thread on StackExchange). How are you thinking about transcribing the := sign?

Regarding your concern about double-struck letters and the script P, what if you used the Nemeth Code script type form for the P's meaning "power set" and another Nemeth Code type form (italic, bold, or sanserif) for the letters that are double struck?

–Kyle

[kdejute]

Attached is an updated workable transcription. The ELI is not used when a letter precedes a symbol of comparison; technical material displayed to narrative text is formatted in 3-5; line breaks in an expression that spans multiple braille lines occur in places that allow for logical reading of the content and also reduce the number of lines required for the expression.

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[kdejute]

Thanks to our colleagues who are working on the updated TG Guidelines! They say that although transcription of mixed numbers below a number line is not explicitly covered in those guidelines, UEB Math/Science transcription of time labels (e.g., 1:30) is and a3#cj is the recommended transcription for the time 1:30 below a number line. So, it makes perfect sense that b#b/e would be the appropriate transcription for "two and two-fifths."

–Kyle

 

[kdejute]

There *might* be an argument for your second proposed transcription. 7.6.9 of the updated section 7.6 in the Rules of UEB says "When an opening double quotation mark ⠦ is immediately preceded by a grade 1 indicator, it will be read as a question mark."

However, that same transcription  ;(;8./#i) – with two grade 1 symbol indicators within the first three cells of the expression – goes against #5 in BANA's Provisional Guidance on Transcribing Mathematics in UEB, and it just interrupts the flow of the fraction in a way that is unhelpful to the reader.
We believe that ;;(8./#i) is the best transcription of the fraction "question mark over 9." The question mark in the numerator of a fraction is very unlikely to be misread as an opening quotation mark, not least of all because if we did have a quotation mark in that position, we would transcribe the fraction as follows: ;(,7./#i)

So, WE WOULD RECCOMMEND using the first transcription you proposed. ;;(8./#i) A transcriber's note to explain the situation might be in order (e.g., "A question mark is used in the following fraction.").

Thank you for this question!

–Kyle and the whole NBA UEB Tech Material Committee

[kdejute]

Lynette,

I couldn't see your .B2K file, but I think I know what you're proposing, and I think it's really good for clarity and instruction for the student An updated transcription of your item 13 is attached (in two file formats). I think this one is the winner.

–Kyle

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[kdejute]

Taylor,

I'm looking into it. I suspect your second proposed transcription (with no numeric indicator before the whole number but with a numeric indicator before the fractional part of the mixed number) will be the suggested solution.

–Kyle

[kdejute]

Taylor,

I feel the same. ;(;8./#I) is cringey. Also, it goes against #5 in BANA's Provisional Guidance on Transcribing Mathematics in UEB, which says in part:

Unless a math expression can be correctly represented with only a grade 1 symbol indicator in the first three cells or before a single letter standing alone anywhere in the expression, begin the expression with a grade 1 word indicator (or a passage indicator if the expression includes spaces).

I'm passing your question along to the members of NBA's UEB Technical Material Committee for their astute input so we can give you specific feedback.

–Kyle

[kdejute]

Melissa,

I think you're doing an excellent job of capturing the various components of these cards.

–Kyle

[kdejute]

A few further thoughts on number lines are below. Many thanks to members of the Tactile Graphics Committee for their input!

The revised TG Guidelines (not yet published) state that number lines are graphics and so should have a blank line before and after them. And number lines should start in cell 1 unless a single number line is the entirety of an identified item (e.g., each answer choice consists of only a number line). This is so a number line will (in most cases) fit on one line without division and be easy to find.

The revised TG Guidelines also tell us that a numeric passage is not necessary for the numbers below a number line to be transcribed without any numeric indicators. In other words, numbers below a number line don't have numeric indicators, and no numeric passage is necessary for this to be the case. Tactile Graphic Guidelines tells us that all number lines are considered to be tactile graphic representations, whether they are done with braille cells (grades 4 and up) or as line graphics (K through grade 3).

The collection of rules and guidelines that apply to a UEB Math/Science transcription is surprisingly diverse. UEB Guidelines for Technical Material (GTM) applies to most "dot level" issues. BANA's Provisional Guidance for Transcribing Mathematics in UEB applies, especially to formatting concerns not covered in GTM. Braille Formats 2016 applies to text format issues not covered in GTM or the Provisional Guidance mentioned before. Guidelines and Standards for Tactile Graphics (GSTG) applies to tactile graphic issues, including number lines. The updated version of GSTG will include the symbols appropriate for number lines in a UEB Math/Science transcription. These correspond quite closely to what is in the GTM. (The 2010 version of GSTG can tell us little or nothing about dot-level concerns in a UEB Math/Science transcription.)

Since GSTG applies to these number lines we're discussing, we can use its thorough information about how to transcribe number lines, including how to format runovers (GSTG 6.5.1.11). Namely, a continuation indicator is not shown at the end of a line; a break must occur so that a tick mark starts on the new line; and the runover is in cell 3 (with the very beginning of the number line in cell 1).

So, to revisit your original questions in brief:

1. A number line should almost always be formatted in 1-3 regardless of the context/exercise material.
2. According to GSTG, numbers below a number line do not get any numeric indicators, and no numeric passage is necessary for this to happen.
3. There is not a required number of horizontal line indicators between an arrow or a crossing vertical line. Spacing in a number line must be proportionally accurate based on the number line's content.
4. Runovers of number lines begin in cell 3, with a tick mark beginning the runover line; no continuation indicator should be used.

Phew! How is it going?

–Kyle

[kdejute]

It's coming together! I only have one question. Why does the braille show more layouts of the multiplication problems than print does? For example 5×2 is only shown in a linear layout in print but is shown first spatially and then linearly laid out in braille. (Maybe the other layouts are on a reverse side to the print cards that I can't see in the file?)

–Kyle

[kdejute]

Attached (as an image and in a .brf) is a possible transcription of the content from item 14 in your example. Do you think this will work for you?

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[kdejute]

Attached (as an image and in a .brf) is a possible transcription of the content from item 13 in your example. What do you think?

–Kyle

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[kdejute]

I think you'll get the best complete answers to your questions from NBA's Tactile Graphics Committee.

For what it's worth, if I were considering your questions for myself, I would take into consideration the following.

1. I know of no Tactile Graphic Guideline that says a graphic must be formatted according to Braille Formats 2016 or must be formatted beginning in cell 1. For all aspects of a transcription, I try to follow #3 of BANA's Provisional Guidance for Transcribing Mathematics in UEB, which includes the following:

  Follow Braille Formats: Principles of Print-to-Braille Transcription, 2016 for the format of displayed literary text except for paragraph format, which is never blocked. For displayed mathematical expressions, use blank lines preceding and following; and indent 2 cells from the runover position of the material to which they apply.
Use of the full braille line for a displayed technical expression (with runovers in cell 3), is appropriate for higher math where expressions are lengthy and more complicated. The spaces used to indent beyond the runover in effect can make the difference between dividing or keeping a mathematical unit together.

2. A numeric passage seems to make a lot of sense for a number line. My team and I often use a numeric passage for number lines.

3. I know of no rule that specifies a number of horizontal line indicators between ticks and/or arrows in a number line. Tactile Graphic Guidelines6.5.1 does tell us, "Number lines are used to teach relationships between numbers; therefore, it is essential that the proportional spacing between units be preserved."

4. Conceivably, a number line can have a runover.

[kdejute]

Chris,

You're right that our rule books for UEB Math/Science do not show any examples like the multiplication problems you shared (i.e., spatial multiplication problems whose factors include decimals). Following print alignment within the problem is likely your best approach. That is, right-align the factors, and do not align by place value in these multiplication problems.

One potential transcription of your example problems is attached (as an image and in a .brf).

–Kyle

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[kdejute]

I believe we should place the numeric indicators so that they are not in a column with any numbers.

–Kyle

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