kdejute
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Ah. Interesting.
Thank you for sharing your question!
First, let's make sure to say that this is not an NBA course, and I am not an expert in nor a mentor for the course you mention.
I do have a hypothesis though. It has to do with Guidelines for Technical Material (GTM) §7.7, which says:
If more than one superscript or subscript apply, work from bottom to top, or left to right. If the print indicates by the placing of the subscript that it is being applied after the superscript then the order can be reversed.
So, if we have "m superscript y and then subscript x" in print, the symbols-sequence ;;m9y5x pretty well captures that.
However, if we have "m subscript x and then superscript y" how do we capture the non-simultaneous nature of the x and y? The symbols-sequence ;;m5x9y is what we would use for "m with subscript x and at the same time (or in the same up-and-down print space) superscript y."
This is where, I suspect, the use of the braille grouping indicators comes in. If "m subscript x" is grouped together and then a superscript y is brailled, it captures that something is different from what ;;m5x9y means.
So, ;;<m5x>9y tries to capture that the subscript and superscript are staggered, not sharing the same up-and-down print space.
Sense make? What do you and your colleagues think?
–Kyle
Thank you for your questions!
First, line mode is a UEB concept, and Guidelines and Standards for Tactile Graphics, 2022 (GSTG) is built upon the rules of UEB (and the rules of The Nemeth Braille Code for Mathematics and Science Notation 2022). In other words, Rules of UEB is foundational, and GSTG is guidelines upon that foundation.
You asked: Should a vertical line segment transcribed using line mode (i.e., braille symbols) lead down to a letter in the midst of its word label (as is shown in GTM §4.4.1), or should it lead down to the first letter of its word label (as is implied by the placement of labels below scale marks in number line examples in GSTG [e.g., Example 6-4 UEB])?
We do not know of a definite answer to that question. The most important thing is that the tactile arrangement or diagram accurately conveys the information that is in print.
One way to think about this for something like what is shown in GTM §4.4.1 could be: Will the whole arrangement or diagram fit without runovers with vertical line segments aligned with the first letter of each word label? If yes, then do so, and you'll be following the formatting exemplified in the [North-America-focused] GSTG. If you put vertical line segments aligned with the first letter of each word label and the whole arrangement or diagram will NOT fit without ruovers, then center each word label on its related vertical line segment and see if that lets the whole arrangement fit without runovers. [If you want to keep going down this decision tree: Next, if you allow one runover and put vertical line segments aligned with the first letter of each word label, will the whole arrangement or diagram fit? What if you allow one runover and center each word label on its related vertical line segment? Then try two runovers, first with vertical line segments aligned with the first letter of each word label and then with each word label centered on its related vertical line segment. At that point, you should really stop and reassess.]
You also asked: Should UEB line mode symbols be listed on the Special Symbols page? We say yes, because line mode symbols may be unfamiliar to the reader.
Then—you asked—should UEB line mode symbols be made a separate category within the Special Symbols page (as we are told to do with number line symbols in The Nemeth Code 2022 §4.4.7)? We say yes, because this groups the line mode meanings of these symbols, which have other meanings outside of line mode.
Last, but not least, you asked: Should we or should we not use a numeric indicator before a number that occurs below a number line? No, according to GSTG §6.5.1.1, you should not use a numeric indicator before a number that occurs below a number line. GSTG §6.5.1.1 says,
"A numeric indicator is not used before a number if it occurs below the number line, whether the number is whole, fractional, decimal, or negative. A numeric indicator is used before a number above the number line. Follow these guidelines for the numeric indicator regardless of whether the number line is transcribed in UEB or Nemeth Code. ..."
You also asked if there is a distinction between "tactile graphics" and "diagrams using braille symbols representation" where inclusion of the numeric indicator is concerned. There is not.
You may ask, "But isn't following GSTG §6.5.1.1 breaking the rule implied in the examples of GTM §4?" No. In part, the answer is "no" because we could use a numeric passage to transcribe a number line just like those examples in GTM §4 but without numeric indicators on the numbers that occur below the number line. Another reason the answer is "no" is covered in the text at the beginning of GSTG Unit 6:
"Do not include the numeric passage indicator or numeric passage terminator when transcribing tactile graphics. A note must be included on the Transcriber’s Note page alerting the reader of the omission. The "Use and Omission of Numeric Indicator" chart on page 3 explains when numeric indicators should be used."
Thank you again for your questions! We welcome any more that you have.
–Kyle and NBA's UEB Technical Material Committee
Thank you for your question! I am spending some time with these questions and passing them along to the committee. We should be able to get back with you by the end of the week at the latest. –Kyle
I suspect you have already thought of it, but I have to ask if you are including in braille the fact that one of the numbers in the expression is printed in blue while the rest of it is in black?
Melissa,
Thank you for your question! You have it correct!
We believe the vertical juxtaposition indicator (GTM 14.3.3) should be used in transcribing "question mark over equals sign."
So, what we recommend for ≟ is ;;8]"7
Explanation:
The vertical juxtaposition indicator (instead of the directly above indicator) more accurately communicates the intent of the symbol ≟, because it lets the question mark and the equals sign have separate meanings instead of making the equals sign's meaning be "modified" by the question mark.
APH's UEB Math Tutorial describes this method for transcribing a "question mark appears directly above the equal sign in print" in its Lesson 6.7.
–Kyle
A little discussion with a teacher brings up how *very* difficult it is to align a slate and stylus or a braille writer with specific blank space, even on a consumable worksheet.
So, we would likely use a visible space for all blanks to be filled in and write a tn explaining the situation, probably including a suggestion to write answers on a separate piece of paper.One possible solution is to use small drawn squares on page 69 and large drawn squares (with the same line texture) on page 63.
A rough rule of thumb for how big to make the squares that an answer is to be written in might be two cells wider than the correct answer will be and one cell taller than a braille cell (i.e., draw the top box line half a braille cell above where the answer will be written, and draw the bottom box line half a braille cell below where the answer will be written).
Let me see if I can get some input from a "boots on the ground" teacher about this, too.
–Kyle
Tiffanie,
Thank you for your question!
You are quite right that a good place to start is "Guideline 10: Expendable (Consumable) Material" of the BANA Guidelines for the Transcription of Early Educational Materials from Print to Braille.
As you know, 10.1.1.h of those guidelines says,
Omit lines, dashes, circles, boxes, etc., indicating a required answer, before or after questions. (Braille Formats 2016, Section 10.5.1)
Notably, 10.1.1.f says,
Leave enough blank space, or lines, for the insertion of the answer with braille writer or slate and stylus. It takes skill to line up a braille writer to insert an answer. Extra blank space is needed.
I suspect that in the examples you shared, the student will not be expected to write in any answers on page 69 but *will* be expected to write in answers on page 63 (which includes larger text and boxes indicating missing material and also says, "Find the number that makes each equation true.").
Hmmm.
One more place to look for guidance is the Math Examples at the end of the BANA Guidelines for the Transcription of Early Educational Materials from Print to Braille. On print page 52 of those guidelines, the commentary to the UEB Math/Science Math Example 3 says,
The visible space symbol (+) representing a space to be filled in is used in textbooks. (UEB Guidelines for Technical Material, 2014, 3.6) However, for worksheets or homework sheets intended for a specific student it may be beneficial to draw squares to identify the missing number as shown on the following page.
Thank you for posting this question!
Most of us on the committee would go with your Example 2 (brailling each line continuously using a runover position when necessary.)
None of use would go with your Example 1, because it requires some pretty complex navigation on the part of the reader.
(One additional suggestion was to consider tweaking Example 2 by forcing a line break after each comma so that every expression from "column 2" starts its own braille line. This may help the reader to navigate the material, especially when trying to revisit parts of it.)
–Kyle
Third and last, even when dealing with chemical notation that requires grade one indication past the 3rd cell in an expression, a transcriber should use a grade one word indicator instead of a grade one symbol indicator.
That's what it says in #5 in BANA's "Provisional Guidance for Transcribing Mathematics in UEB."
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).
[Will the final (i.e., not provisional) version of BANA guidance say the same thing? I believe it will say something different. But, for now, we should follow what is published.]
Second, I very much sympathize with your question about, "How should we format formal proofs (and other labeled statements) in UEB Math/Science transcriptions?"
In short, Braille Formats is our formatting guide for anything not covered in RUEB, GTM, or BANA's "Provisional Guidance for Transcribing Mathematics in UEB."
One covered issue that is related to formal proofs comes from the "Provisional Guidance for Transcribing Mathematics in UEB." The first paragraph in #3 of that document says the following.
For technical materials, use margins 3-1; do not use blocked paragraphs. If the entire textbook is in blocked paragraphs, note the change to indented paragraphs in a TN.
So, in a UEB Math/Science transcription, we would probably format the print of "Example 26-73: Theorem with Auxiliary Captions" of The Nemeth Code as follows.
⠀⠀⠘⠂⠠⠮⠕⠗⠑⠍⠀⠘⠂⠼⠙⠲⠀⠠⠊⠋⠀⠞⠺⠕⠀⠇⠔⠑⠎⠀⠜⠑⠀⠉⠥⠞⠀⠃⠽
⠁⠀⠞⠗⠁⠝⠎⠧⠻⠎⠁⠇⠀⠯⠀⠁⠀⠏⠁⠊⠗⠀⠷⠀⠁⠇⠞⠻⠝⠁⠞⠑⠀⠔⠞⠻⠊⠕⠗
⠁⠝⠛⠇⠑⠎⠀⠜⠑⠀⠑⠟⠥⠁⠇⠂⠀⠮⠀⠞⠺⠕⠀⠇⠔⠑⠎⠀⠜⠑⠀⠏⠜⠁⠇⠇⠑⠇⠲
⠀⠀⠨⠂⠠⠛⠊⠧⠢⠒⠀⠠⠇⠔⠑⠎⠀⠰⠠⠠⠁⠃⠀⠯⠀⠰⠠⠠⠉⠙⠀⠉⠥⠞⠀⠃⠽
⠞⠗⠁⠝⠎⠧⠻⠎⠁⠇⠀⠠⠠⠗⠎⠀⠁⠞⠀⠏⠕⠔⠞⠎⠀⠰⠠⠑⠀⠯⠀⠰⠠⠋
⠗⠑⠎⠏⠑⠉⠞⠊⠧⠑⠇⠽⠆⠀⠸⠪⠭⠀⠐⠶⠀⠸⠪⠽⠲
⠀⠀⠨⠂⠠⠞⠕⠀⠨⠂⠠⠏⠗⠕⠧⠑⠒⠀⠰⠰⠰⠠⠠⠁⠃⠀⠼⠇⠀⠠⠠⠉⠙⠲⠰⠄
First, let's tackle the Dot Locator for "Use" (RUEB2024 §3.14)
I agree, the fourth paragraph in GTM 4.1 Spatial calculations (quoted below) gives us guidance regarding blank lines in relation to the numeric passage indicator or terminator that we simply do not have regarding blank lines in relation to grade 1 indicators, capitalized passage indicators, or their respective terminators.
The line above and below spatial calculations should either be blank, or should only contain the numeric passage indicator or terminator.
I would advocate for your #2 example, where you have replaced the blank lines around displayed material with a line that contains only the grade 1 passage indicator and a line that contains only the grade 1 terminator. For our convenience, I have attempted to recreate that example below.
⠼⠊⠲⠀⠠⠔⠙⠊⠉⠁⠞⠑⠀⠞⠗⠥⠑⠀⠕⠗⠀⠋⠁⠇⠎⠑⠒
⠐⠐⠿⠰⠰⠰
⠀⠀⠀⠀⠀⠀⠠⠎⠐⠖⠠⠕⠢⠼⠃⠀⠳⠕⠀⠠⠎⠠⠕⠢⠼⠃⠀⠳⠬
⠀⠀⠀⠀⠀⠀⠠⠓⠠⠉⠇⠀⠳⠕⠻⠘⠳⠪⠀⠠⠓⠔⠐⠖⠐⠖⠠⠉⠇⠔⠐⠤
⠀⠀⠀⠀⠀⠀⠠⠅⠠⠊⠐⠖⠠⠊⠢⠼⠃⠀⠳⠬⠳⠩⠀⠠⠅⠠⠊⠢⠼⠉
⠐⠐⠿⠰⠄
⠀⠀⠠⠁⠲⠀⠠⠞⠗⠥⠑
⠀⠀⠰⠠⠃⠲⠀⠠⠋⠁⠇⠎⠑
Thank you for your question, Fred.
Though I do not doubt our braille-using friends, students, and neighbors would make sense of contracted comments within a numeric passage, I cannot recommend it.
A numeric passage indicator sets grade 1 mode until the numeric terminator ends that grade 1 mode (RUEB2024 §6.9.1). If we use contracted braille within a numeric passage, then we use symbols that have a grade 1 meaning in an environment that says their grade 1 meaning is what's important.
In responses to your questions:
Q: Yes, everything within a numeric passage is in grade 1.
1) A math comment like 300×32, would be brailled without the numeric indicators within a numeric passage.
2) No. For the sake of clarity, translatability, and consistency, we should not braille text comments contracted within a numeric passage.
Regarding your key for comments: I really like your placements of the key letters (i.e., each following the quotient piece to which it applies). However, remember what RUEB2024 § says: "... any lowercase letter a-j is preceded by a grade 1 indicator." Since you'll have to use a grade 1 symbol indicator for each of those letters, I think you should get rid of the periods. Also, in your key listing, please check the formation (and grade 1 indicating) of your letters (especially the b). One more note: you do not need a blank line before the braille line that contains only a numeric terminator (GTM §4.1, last paragraph before 4.1.1).
In other words, regarding your #3, it is a good choice to use a key for the comments, and it seems practical to use a TN to explain the printed down arrows showing numbers in the dividend moving.
Last, but not least, I agree, spatial division with operation signs is challenging; I think you've done a very good job of aligning by place value and placing the symbols of operation where they apply.
Braille on!
–Kyle
