On the Road to Developing
Nemeth Braille Code
Competencies
for Beginning TVIs:
Findings of a Two-Part Study
L. Penny Rosenblum, Ph.D.
University of Arizona
Derrick Smith, Ed.D.
University of Alabama at Huntsville
Development of Literary Braille
Competencies
AER Personnel Preparation Division formed a group
to investigate the development of standards for
literary braille.
 Sandy Lewis, Frances Mary D’Andrea and L. Penny
Rosenblum conducted a Delphi Study (JVIB, 2012).
 Next logical step was to conduct a Delphi Study to
investigate the development of standards for
Nemeth code.

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Paul Ajuwon
Sheila Amato
Donna Brostek Lee
Tina Herzberg
Sunggye Hong
Cheryl Kamei-Hannan

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Beth Harris
Patricia Myers
L. Penny Rosenblum
Derrick Smith
Sandy Smith
Adam Wilton
Kim Zebehazy
Nemeth Delphi Committee
Members
Committee Procedure
Questionnaire developed to collect
demographic data
 A list of Nemeth code skills was developed
 A list of skills in other codes (foreign language,
music, computer), abacus, and tactile graphics
was developed

Purpose of the Demographic Study
To gather information on how university
programs prepare future teachers of
students with visual impairments in the
areas of the Nemeth braille, foreign
language braille, computer braille, music
braille codes, the abacus, and tactile graphics.
Study Procedure
39-item questionnaire using online survey
software
 Open to university programs in the United
States and Canada for six weeks in fall 2011
 22 individuals representing 26 universities
participated

Delivery of Course Content
Face-to
Face
On-Line
Hybrid
Literary Braille
7
7
11
Nemeth Braille
7
9
9
Foreign Language
Braille
8
8
6
Music Braille
6
7
6
Computer Braille
8
6
7
Abacus
7
9
8
Tactile Graphics
7
5
13
Content
How Content is Delivered
Content
Primary
Embedded Correspond
N/A
Literary Braille
25
1
0
0
Nemeth Braille
24
1
1
0
Foreign Language
Braille
3
18
0
5
Music Braille
2
16
1
7
Computer
Braille
Abacus
3
18
0
5
10
13
3
0
Tactile Graphics
4
21
0
1
Tools Used to Produce Braille
Perkins
S&S
Literary Braille
26
26
22
16
14
Nemeth Braille
26
1
18
4
4
Foreign Language
Braille
14
0
8
1
1
Music Braille
9
0
9
0
0
Computer Braille
10
0
11
4
4
Abacus
--
--
--
--
--
Tactile Graphics
--
--
--
--
--
Content
Brl Em. Brl.Tran. Elec.
All University Programs Required
Students to Demonstrate Mastery
Numerals
 Numeral indicator
 Punctuation
indicator
 English letter
indicator
 Fraction indicator

Fractions
 Operations
 Comparison
 Decimals
 Problems in Linear
Format

Most University Programs Required
Students to Demonstrate Skills
Mastery
Basic
Knowledge
None
Problems in
Spatial Format
25
1
--
Level Indicator
25
1
--
Groupings
25
1
--
Radical Indicator
21
5
--
Multipurpose
Indicator
21
5
--
Radicals
10
5
1
Skill
Algebra and Geometry
Had More Variability
Mastery
Basic
Knowledge
None
Absolute Value
17
7
2
Shapes
17
9
--
Arrows
15
11
--
Angles
15
11
--
Lines
12
13
1
Arcs
9
10
7
Skill
Advanced Math
Had Even More Variability
Mastery
Basic
Knowledge
None
Functions
8
12
6
Logarithms
4
9
13
Advanced Math
6
13
7
Matrices
2
10
14
Skill
Nemeth Resources
Resource
Required
Rec.
Shown
No
Unsure
An Introduction to
Braille Mathematics
14
3
3
5
2
The Nemeth Braille
Code for Mathematics
and Science Notation
9
12
3
1
1
Mathematics Made
Easy for Children with
Visual Impairment
2
2
1
20
3
Braille Codes and
Calculations
5
2
6
11
3
Nemeth Resources
Required
Recom.
Shown
No
Unsure
Learning Nemeth Braille
Code
13
4
3
6
0
Strategies for
Developing
Mathematics Skills in
Students Who Use
Braille
7
4
8
6
1
Chapter on Nemeth
code in New
Programmed Instruction
in Braille
11
3
1
10
2
Braille Code of Chemical
Notation
1
0
8
16
1
Resource
Resources Shared with Students
TSBVI web site (n=10)
 APH web site and/or reference sheet
(n=9)
 National Braille Press web site or books
(n=5)
 BANA web site or books (n=5)
 Project Math Access web site or materials
(n=4)

How Students Demonstrate
Competence
Homework or weekly tests (n=23)
 Final exam (n=18)
 Midterm exam (n=5)
 Less frequently mentioned:

◦ Lesson plans
◦ Postings on discussion boards
◦ Adapting materials
Procedures
13 programs allowed students to
resubmit homework.
 7 programs did not allow students to
resubmit homework.
 1 program required students to write out
what rules were not followed.
 Few programs allowed students to
remediate final or midterm exams.

Foreign Language Braille Code
Foreign language braille was at the
exposure level.
 Few programs required a homework
assignment.
 BANA web site was shared as a resource.

Foreign Language, Computer
and Tactile Graphics Resources
Content
Interim Manual for
Foreign Language
The Computer
Braille Code Made
Easy
Computer Braille
Code
Tactile Graphics
Required
Recom.
Shown
No
Unsure
1
4
5
14
1
1
1
8
12
1
6
6
6
7
1
0
4
10
11
1
Computer Braille Code
Almost all programs gave a brief
introduction to computer braille code.
 2 programs indicated that computer
braille code was integrated into an
assistive technology course.

Music Braille Code
Dancing Dots and Library of Congress
were web sites shared with students.
 Few programs required students to
complete a braille music homework.

Music Resources
Content
Who is Afraid of
Braille Music
How to Read Braille
Music
Music Braille Code
Required
Recom.
Shown
No
Unsure
1
1
5
16
3
0
2
10
11
3
3
7
8
9
2
Abacus
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Five programs required students to complete an
abacus course from Hadley School for the
Blind.
Thirteen programs had students on an exam
compute using an abacus.
Three programs had students do homework
assignments with an abacus.
Three programs had students teach a child to
compute with an abacus.
Eight programs allowed students to redo abacus
assignments and ten did not.
Abacus Resources
Resource
Use of the Cranmer
Abacus
The Abacus Made
Easy
Abacus Basic
Competency: A
Counting Method
Required
Recom.
Shown
No
Unsure
10
2
8
4
3
5
3
10
7
3
3
2
11
8
3
Tactile Graphics
Five programs shared BANA guidelines.
 Ten programs shared APH guidelines and
materials (e.g., Draftsman, models).
 Nineteen programs had specific
assignments and activities.
 Twenty-three programs required students
to prepare tactile graphics.
 Three programs had exam questions
about tactile graphics.

Rosenblum, L. P. & Smith, D. (2012).
Instruction in Specialized Braille Codes, Abacus,
and Tactile Graphics at Universities in the
United States and Canada. Journal of Visual
Impairment & Blindness, 106(6), 339-350.
NEMETH DELPHI
Development of the Delphi
Instrument
13-member focus group developed 29
statements that could be competencies.
 Panelists rated each statement for reading
and writing.
 For each statement panelists rated the
level of importance and the type of
references to be used (none, code
reference, book).
 Agreement level was set at 85%.

Criteria to Join the Nemeth Delphi
Panel
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In the last three years taught at least one
course on how to read and write Nemeth code
Taught the Nemeth code for at least three
semesters / quarters
Taught the Nemeth code for at least three or
more years
Taught in the United States or Canada
Taught skills for students to read and write
Nemeth code
Read/Write in Context Linear
Problems

Reading
◦ Importance: Extremely Important
(100%, n = 20)
◦ References: No References (94%, n = 17)

Writing
◦ Importance: Extremely Important
(95%, n = 19)
◦ References: No References (94%, n = 17)
Read/Write
Punctuation Signs, Symbols used in
Nemeth

Reading
◦ Importance: Extremely Important
(100%, n = 20)
◦ References: No References (94%, n = 17)

Writing
◦ Importance: Extremely Important
(100%, n = 20)
◦ References: No Agreement
Read/Write Simple Fractions/Mixed
Numbers

Reading
◦ Importance: Extremely Important
(100%, n = 20)
◦ References: No References (94%, n = 19)

Writing
◦ Importance: Extremely Important
(100%, n = 20)
◦ References: No Agreement
Read/Write Computation in Spatial Format

Reading
◦ Importance: Extremely Important
(100%, n = 20)
◦ References: No References (94%, n = 17)

Writing
◦ Importance: Extremely Important
(100%, n = 20)
◦ References: No References (94%, n = 17)
Read/Write
Expressions w/Grouping Symbols,
Including Parentheses

Reading
◦ Importance: Extremely Important
(100%, n = 20)
◦ References: No References (94%, n = 17)

Writing
◦ Importance: Extremely Important
(95%, n = 19)
◦ References: No Agreement
Read/Write
Expressions w/Decimals,
Percentages, Negative Numbers

Reading
◦ Importance: Extremely Important
(85%, n = 17)
◦ References: No References (94%, n = 16)

Writing
◦ Importance: Extremely Important
(100%, n = 20)
◦ References: No Agreement
Read/Write
Expressions w/More Advanced
Signs of Comparison

Reading
◦ Importance: Extremely Important
(94%, n = 17)
◦ References: Code Reference (89%, n = 16)

Writing
◦ Importance: No Agreement
◦ References: Code Reference (94%, n = 17)
Read/Write Expressions with Superscripts

Reading
◦ Importance: Extremely Important
(94%, n = 16)
◦ References: Code Reference (89%, n = 16)

Writing
◦ Importance: Extremely Important
(85%, n = 17)
◦ References: No Agreement
Read/Write Expressions with Subscripts

Reading
◦ Importance: Extremely Important
(89%, n = 16)
◦ References: No Agreement

Writing
◦ Importance: No Agreement
◦ References: No Agreement
Read/Write Expressions with Radicals

Reading
◦ Importance: Extremely Important
(94%, n = 17)
◦ References: Code Reference (89%, n = 16)

Writing
◦ Importance: No Agreement
◦ References: No Agreement
Read/Write
Expressions with Complex Numbers

Reading
◦ Importance: No Agreement
◦ References: No Agreement

Writing
◦ Importance: No Agreement
◦ References: Reference Book (89%, n = 16)
Read/Write
Letters Representing Measurement Units

Reading
◦ Importance: Extremely Important
(94%, n = 17)
◦ References: No References (89%, n = 16)

Writing
◦ Importance: Extremely Important
(94%, n = 16)
◦ References: Code Reference (89%, n = 16)
Read/Write
Nemeth Code Signs of Comparison

Reading
◦ Importance: Extremely Important
(89%, n = 16)
◦ References: Code Reference (89%, n = 16)

Writing
◦ Importance: No Agreement
◦ References: Code Reference (89%, n = 16)
Read/Write
Nemeth Code Signs for Rates
and Derived Measurements

Reading
◦ Importance: Extremely Important
(89%, n = 16)
◦ References: No Agreement

Writing
◦ Importance: No Agreement
◦ References: No Agreement
Read/Write
Formulae for Area/Volume of Geometric Figures

Reading
◦ Importance: No Agreement
◦ References: No Agreement

Writing
◦ Importance: No Agreement
◦ References: Reference Book (90%, n = 18)
Read/Write
Letters Used to Symbolize Variables

Reading
◦ Importance: Extremely Important
(94%, n = 17)
◦ References: No References (94%, n = 17)

Writing
◦ Importance: Extremely Important
(94%, n = 17)
◦ References: No Agreement
Read/Write
Algebraic Equations w/Polynomials,
Rational Numbers

Reading
◦ Importance: Extremely Important
(89%, n = 16)
◦ References: Code Reference (89%, n = 16)

Writing
◦ Importance: Extremely Important
(89%, n = 16)
◦ References: No Agreement
Read/Write
Algebraic Equations w/Logarithmic Numbers

Reading
◦ Importance: No Agreement
◦ References: Reference Book (94%, n = 17)

Writing
◦ Importance: No Agreement
◦ References: Reference Book (95%, n = 18)
Read/Write
Algebraic Equations using Periodic Functions

Reading
◦ Importance: No Agreement
◦ References: Reference Book (94%, n = 17)

Writing
◦ Importance: No Agreement
◦ References: Reference Book (85%, n = 17)
Read/Write
Algebraic Equations using Inequalities

Reading
◦ Importance: Extremely Important
(89%, n = 16)
◦ References: Code Reference (89%, n = 16)

Writing
◦ Importance: No Agreement
◦ References: No Agreement
Read/Write
Statements Using Shape Indicators

Reading
◦ Importance: Extremely Important
(94%, n = 17)
◦ References: No Agreement

Writing
◦ Importance: Extremely Important
(94%, n = 17)
◦ References: Reference Book (89%, n = 16)
Read/Write
Compass Directions Using Arrow Indicators

Reading
◦ Importance: No Agreement
◦ References: Reference Book (89%, n = 16)

Writing
◦ Importance: Somewhat Important
(89%, n = 16)
◦ References: Reference Book (85%, n = 17)
Read/Write
Symbols for Congruence,
Similar, Parallel, Perpendicular

Reading
◦ Importance: Important (89%, n = 16)
◦ References: No Agreement

Writing
◦ Importance: No Agreement
◦ References: Reference Book (89%, n = 16)
Read/Write Coordinate Indicators

Reading
◦ Importance: Extremely Important
(89%, n = 16)
◦ References: No References (94%, n = 17)

Writing
◦ Importance: No Agreement
◦ References: No Agreement
Read/Write
Indicators for Angles, Lengths, Arcs,
Perimeters, Areas,Volume

Reading
◦ Importance: No Agreement
◦ References: Reference Book (94%, n = 17)

Writing
◦ Importance: No Agreement
◦ References: Reference Book (85%, n = 17)
Read/Write
Trigonometric Indicators for Length
and Angle Measurements

Reading
◦ Importance: No Agreement
◦ References: Reference Book (95%, n = 18)

Writing
◦ Importance: No Agreement
◦ References: Reference Book (94%, n = 17)
Read/Write
Cartesian Coordinates, Navigational,
Polar, Spherical

Reading
◦ Importance: No Agreement
◦ References: Reference Book (89%, n = 17)

Writing
◦ Importance: No Agreement
◦ References: Reference Book (95%, n = 19)
Read/Write
Indicators for Plane,Vectors,
Function Notation, Matrices

Reading
◦ Importance: No Agreement
◦ References: Reference Book (95%, n = 18)

Writing
◦ Importance: No Agreement
◦ References: Reference Book (100%, n = 20)
Read/Write
Various Indicators/Equations
for Statistical Data

Reading
◦ Importance: No Agreement
◦ References: Reference Book (95%, n = 18)

Writing
◦ Importance: No Agreement
◦ References: Reference Book (100%, n = 19)
Final Thoughts



University programs place a greater
emphasis on literary & Nemeth braille codes
than other braille codes.
There is variability in the competencies
students must demonstrate in Nemeth code
when it comes to more advanced (middle
school and up) math.
Abacus computation is taught at most
universities though the level of proficiency
students must demonstrate varies.
Final Thoughts

The Delphi panel agreed on the following:
◦ The level of importance for 20 reading
statements
◦ The level of importance for 12 writing
statements
◦ The level of references for 22 reading
statements
◦ The level of importance for 17 writing
statements
What’s Next?
Publication of a second article in JVIB in
2013 (Smith & Rosenblum)
 Possible follow-up study to find out more
about what students at various age levels
are reading and writing in Nemeth code
 Discussion with the Personnel
Preparation Division about the adoption
of Nemeth code competencies by
university programs
