Number lines (4 questions)

[Taylor Goldhardt]

I have 4 distinct questions (which I have numbered for convenience).

<li style="font-weight: 400;">Does the number line begin in cell 1 or is it dependent on the context/exercise material? For Example, would the number line in the attached problem begin in cell 1 or cell 3 (for the runover)?
<li style="font-weight: 400;">Can a number line be placed in numeric passage mode to reduce the length/keep on the same braille line?
<li style="font-weight: 400;">Is there a required number of horizontal line indicators between an arrow or a crossing vertical line?
1. What do we do when a number line requires multiple braille lines? (Example, if we have a -40 to 40 number line where we need to be able to see every tick.) Sometimes we can get it to fit as a graphic, but I've seen a lot of number lines that are too big for a horizontal or a vertical graphic to work.

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[Chris Bischke]

I have the same questions 😉

[Taylor Goldhardt]

Huh. Apparently the formatting got messed up. Each line that talks about "formatting" is supposed to be a numbered list. The one that currently (to me) shows up as number 1 at the end is supposed to be number 4. Sorry about that; not sure what happened. It looked right when I was typing it up. And I can't edit it to make it look cleaner, either. Here is the list again, and hopefully the numbers will show up correctly this time.

1. Does the number line always begin in cell 1 or is it dependent on the context/exercise material? For Example, would the number line in the attached problem begin in cell 1 or cell 3 (for the runover)?
2. Can a number line be placed in numeric passage mode to reduce the length/keep on the same braille line?
3. Is there a required number of horizontal line indicators between an arrow or a crossing vertical line?
4. What do we do when a number line requires multiple braille lines? (Example, if we have a -40 to 40 number line where we need to be able to see every tick.) Sometimes we can get it to fit as a graphic, but I've seen a lot of number lines that are too big for a horizontal or a vertical graphic to work.

And an addition to question 1: If the number line is dependent on the runover, can we adjust the starting point to fit a slightly-too-long line on a single braille line? (So, a problem similar to the example might start in cell 1 or 2 instead of having the final item on a second line.)

[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.

[Taylor Goldhardt]

I guess I didn't specify clearly enough. All of these questions are in regards to number lines using UEB braille symbols - not tactile graphic number lines. That's why I put this in UEB Technical. I know that it's frequently better to use tactile graphics, but that's not always a valid option. The problem is that there's basically no information about number lines in Guidelines for Technical Materials. It does not tell us how to divide a number line between braille lines. Do we just cut it off? Do we use the line continuation indicator? Does the runover start two cells to the right (or is it based on the format of the surrounding material)? I know a number line can theoretically have a runover. But we still don't have any information on how to make the runover (among many other important things).

[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

[Taylor Goldhardt]

Thanks, that's helpful. And thanks (to you and the TG Committee) for the peek at the new TG guidelines!

[Taylor Goldhardt]

How do we handle mixed numbers, especially if we aren't using the numeric indicator? As you can see, it doesn't make sense (from a UEB perspective) to omit the numeric indicators.

#B#B/E
B#B/E
BB/E

So how do we handle mixed numbers?

[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]

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

 

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