**Executive Summary** The UEB (Unified English Braille) is a unified braille code that is proposed as a replacement for the literary braille code, the mathematics
portion of the Nemeth braille code, and the chemistry code currently used in Canada.

One reason teachers favor a unified code is because they hope it will be more consistent, and thus easier for students, than separate codes.

However, the UEB has separate modes which sometimes require the same information to be represented in different ways.UEB mathematics is entirely different from Nemeth and is untried in the classroom. It is hoped that the information in this article will allow experienced braille teachers to anticipate some of the problems that might be encountered were the UEB to be adopted as the basis for teaching mathematics. Feedback from teachers of early braille learners is most crucial since many experts have already agreed that the UEB may be inferior to the Nemeth code for advanced users.

Areas of special concern for early braille learners

- mode-switching may be required for worksheets
- alignment in spatial arithmetic requires more planning ahead
- expanded basic symbols are not "alphabetic", i.e. not one-for-one with print
- numeric mode (use of letters as numbers) less print-like than separate cells for letters and numbers

General issues

- more for user to keep track of
- symbols less mnemonic, less print-like
- effect of mode indicators can extend to symbol, word, or passage
- mode affects writing as well as reading
- most expressions are longer
- some subcripted and superscripted expressions require insertion of braille-specific grouping indicators
- no unique indicators for higher-order subscripts and superscripts
- no complexity indicators for complex fractions and nested radicals

- harder for sighted readers to dictate, no associated MathSpeak, reader has to anticipate more
- upper numbers are inconsistent with current approaches to the teaching and use of electronic calculators
- upper numbers are inconsistent with direct entry: direct entry of braille from a standard keyboard (ASCII Braille) or direct entry of print from a braille keyboard (computer braille) cannot be based on upper numbers (same characters used for digits and letters)
- mode-switching in word problems
- contracted email and Web addresses cannot be cut and pasted; some will be ambiguous

The UEB (Unified English Braille) is a unified braille code that is proposed as a replacement for the literary braille code, the mathematics portion of the Nemeth braille code, and the chemistry code currently used in Canada.

The UEB also includes representations for most of the symbols defined in the Computer Braille Code. However, since the UEB uses the same cells for letters as for digits, it is not possible to design an ASCII Braille or computer braille table like the ones built into notetakers that would be consistent with the UEB. (Appendix E An ASCII-Braille Machine Code or Font Based upon UEB of the latest UEB Project Report suggests the use of dot-6 numbers to address this issue.)

One reason teachers favor a unified code is because they believe it will be more consistent, and thus easier for students, than two separate codes with two different ways of representing the same information.

An item that users may find surprising is that although the UEB is a single code, it has different modes. In fact, there are many cases where the UEB has different ways of representing the same information depending on the mode. These cases arise when technical material is embedded in ordinary text and also in other situations.

A common example of embedded technical material occurs when chemical formulas such as H_{2}O, which is the well-known formula for water, are embedded in an ordinary contracted braille sentence. This formula is typeset in print with the two as a subscript. Since the UEB subscript indicator, (dots 26), is the same cell as the contraction for (en), the UEB requires a Grade 1 symbol indicator (dots 56) to be placed just before the subscript indicator when a subscripted item occurs in an Grade 2 sentence. However, the Grade 1 symbol indicator is not used for chemical formulas and other subscripted items that appear in displayed expressions where the Grade 1 passage indicator is already in force.

There are also a number of cases where UEB has different ways of representing information that has the same print represention.

Simple fractions where the numerator and denominator are both numbers don't use fraction indicators and use a special numeric fraction line, (dots 34). However, simple fractions involving letters or symbols do use fraction indicators and use the general fraction line, (dots 456 34).

Subscripted and superscripted items that don't qualify as single items require the insertion of braille grouping indicators.

The UEB even has cases where it uses two different braille symbols for the same print character. The UEB specifies that two braille symbols, (dots 236) and (dots 356), be used to represent the one (neutral) double quotation mark character on a standard keyboard. The UEB has new symbols, (dots 6, 236) and (dots 6, 356), for the so-called smart double quotation marks. (A similar situation applies for the various single quotation marks as well.)

The UEB unifies contracted braille and a mathematics code through the use of modes. At any given point in a UEB text, the outer mode is either Grade 1 mode or Grade 2 mode. (There are also numerous inner modes. For example, the numeric mode can occur within either Grade 1 mode or Grade 2 mode and the Grade 1 symbol mode can occur in the middle of the Grade 2 passage mode. )

The name Grade 1 is a bit misleading; Grade 1 mode is really a "higher math mode." The Grade 1 mode indicators are used to signal when cells that are normally used for contractions have special, mathematical meanings such as when dots 12356 is used as the fraction open indicator instead of as the contraction for "of".

UEB Grade 1 mode doesn't mean quite the same thing as uncontracted. Braille text is *permitted* to be uncontracted in either Grade 1 or Grade 2 mode but it is *required* to be uncontracted in Grade 1 mode. In other words, braille is only permitted to be contracted in Grade 2 mode.

The UEB design attempts to minimize the need for early braille learners to switch out of Grade 2 mode for beginning mathematics by the use of two related strategies.

First is the use of numeric mode, which is activated by the number sign in either Grade 2 or Grade 1 mode. In numeric mode, the letters a-j stand for the digits. Numeric mode also converts the meaning of (dots 256) from a period to a decimal point and the meaning of (dots 34) from the (st) contraction to a division slash so that simple numerical fractions, but not other fractions, can be handled in Grade 2 mode.

The second way that UEB avoids the need to switch out of Grade 2 mode for simple mathematics is by using expanded (two-cell) symbols for the key characters—plus, minus, times(dot), general fraction line, and the left and right parentheses—used in all levels of mathematics.

These two strategies—the use of the same cells for letters and numbers and the use of two-cell rather than one-cell symbols for the key special characters—are perhaps the most controversial aspects of the UEB.

This controversy is usually framed in terms of indicator clutter and longer expressions such as the quadratic formula's requiring 29 cells in the UEB rather than the 22 required in Nemeth mathematics. However, there are other issues, which have not been as well researched, that may turn out to be more serious.

- Expanded symbols may be more difficult for early readers who do better with alphabetic braille that uses one braille cell for one print symbol
- The use of letters as numbers may create conceptual problems for some learners
- The less print-like symbols may impede interactions with teachers, other students, and family members

UEB mathematics is completely different from Nemeth mathematics and there are many additional items which need to be carefully reviewed. This section includes short descriptions of some of these items.

Spatial mathematics requires the number sign to be used with all numbers, including those appearing in results. Additional samples are needed in order to understand how these changes will affect teaching. This is an area where the less print-like approach is expected to impede interactions with others.

The Nemeth code has a natural spoken form which sighted persons, with no familiarity with either math or braille, can usually learn in no more than 15 minutes. This spoken form allows sighted readers, parents, and teachers to dictate print math to Nemeth users who then directly enter the corresponding braille cells. According to the researchers currently developing a MathSpeak™, a fully-automated version of spoken Nemeth, "[The Nemeth] code ... allows a student superior access to mathematics by conveying the information unambiguously and concisely using a special grammar and lexicon unique to mathematics."

There is currently no spoken form specified for the UEB math. It is difficult to anticipate how this could be achieved given the need for the reader to anticipate the UEB mode indicators.

The use of electronic calculators and of computers—even just using internet-based search engines—often requires the braille user to directly enter ASCII characters, including the ASCII digits. Braille users can now enter ASCII characters directly from braille notetakers by using computer braille in "translate off" mode. Computer braille is quite similar to Nemeth. However, the use of upper numbers precludes the possibility of specifying a computer braille that is consistent with the UEB.

The UEB represents email and web addresses in contracted braille. This leads to ambiguity in some cases. Contracted braille addresses cannot be copied and pasted directly into other applications.

Adopting the UEB in Canada would be a long and expensive process. Teachers experienced in teaching Nemeth mathematics might find it useful to consider the following questions with respect to early braille learners in trying to decide whether the perceived advantages of UEB mathematics would outweigh the disadvantages pointed out in the present article. (These questions are modeled after those being researched in the ABC Study.)

- What differences are anticipated in comprehension, quantitative thinking, and mathematics achievement levels?
- What differences are anticipated in setting up spatial arithmetic?
- What differences are anticipated in attitudes towards mathematics?
- What differences are anticipated in the quantity and quality of mathematical literacy and interactive experiences in general education classrooms, the home environment, and in the community?

Posted 4/25/2005.

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