quality and techniques used when brailling math worksheets tina herzberg, ph.d. university of south...
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Quality and Techniques Used When Brailling Math Worksheets
Tina Herzberg, Ph.D.University of South Carolina Upstate
L. Penny Rosenblum, Ph.D.University of Arizona
G
As We Walked the Beach at GITWL 2009 We Wondered…
Who prepares math materials for learners who use braille and what are their qualifications?
How are math materials prepared for learners who use braille?
What is the quality of the math materials being prepared for learners who use braille?
Participants had to prepare math materials for students in grades K-12 using Nemeth code.
Participants had to prepare math materials within the last 3 years.
To Participate in the Study…
Completed an on-line demographic surveyCompleted, in hard copy braille, at least
one of five math worksheets1st grade3rd grade5th gradeAlgebraGeometry
Completed an on-line transcription survey
Our Participants…
Demographic Data are Reported in Rosenblum & Herzberg, 2011
Gender (n=166)160 Female6 Male
Years Preparing Math Braille Materials (n=166)37 1-3 years39 4-6 years31 7-10 years 21 11-15 years 38 16+ years
Job Role (n=166)80 TVIs23 Transcribers &
Paraprofessionals46 Transcribers17 Paraprofessionals
Quality of materials (n=162)30 Excellent109 Good21 Fair2 Poor
1st Grade Worksheet (n = 32)
Worksheet contains 27 single digit addition problems set up as a “game.”
The first square on the game board says "START" and the last says "HOME FREE.”
There is a "hint" box that says "Thinking Helps."
Three pictures are on the gameboard that don't tie to the game.
3rd Grade Worksheet (n=22)
A simple word problem Two digit addition spatially
aligned problems A problem where the student
has to mark a temperature on a thermometer
A problem where the student shows time on a clock
A problem where a square needs to be identified
5th Grade Worksheet (n = 21)
This worksheet is titled “Triangles and Quadrilaterals” and contains 12 problems.
The first 9 problems have shapes, and students must classify the shapes and/or find the missing angle.
The final problem shows a flag and asks students to classify colored parts of it.
Algebra Worksheet (n = 18)
The title of this worksheet is “Skills Practice: Writing Equations in Slope-Intercept Form.”
3 problems contain graphs that show lines on a coordinate plane.
For the other 8 problems students must write equations with the given information.
Geometry Worksheet (n = 15)
The title of the worksheet is “Geometry Practice.”
Worksheet contains a title, directions, and six unnumbered problems.
The first two problems require an understanding of rotation.
The other four problems require the calculation of area and/or perimeter for trapezoids and triangles.
Literary Nemeth Literary and Nemeth Formatting Tactile graphics, including labels and
keys Transcriber’s Note Other
Addition of material not on the worksheet Comments from the researcher(s) Miscellaneous
Coding Categories
Data Coding: 3rd Grade Worksheet,
Thermometer Included text of problem If problem reworded, how? How was 43⁰F brailled? Placement of first line of
problem Placement of runover Number of literary &
Nemeth errors Description of errors
2. Shade the thermometer to show 43°F.
Example of Data Collection for Literary and Nemeth
Data Coding: 3rd Grade Worksheet,
Thermometer Included thermometer Position of thermometer on
page Outline of thermometer
clear tactually Included labels Description of labels used Other degree markers
included Accuracy of other degree
markers Number of Nemeth errors Description of Nemeth
errors
Example of Data Collection for Tactile Graphics2. Shade the thermometer to show 43°F.
Demographics of Worksheet Participants (n=59)
Professional Role TVIs (n=18) Transcriber &
Paraprofessionals (n = 9)
Transcribers (n=22) Paraprofessional
(n=10)
NLS Certification Not certified (n=35) Certified literary only
(n=17) Certified literary &
Nemeth (n=5) Certified literary, Nemeth
& textbooks (n=1) Certified literary &
textbooks (n=1)
107
worksheets
transcribed
Demographics of Worksheet Participants (n=59)
Years Preparing Math Materials 1-3 years (n=10) 4-6 years (n=14) 7-10 years (n=12) 11-15 years (n=6) 16+ years (n=17)
Hours Preparing Math Materials Per Week 1-5 hours (n=15) 6-10 hours (n=11) 11-15 hours (n=7) 16-20 hours (n=7) 21-25 hours (n=4) 26+ hours (n=5)
Demographics of Worksheet Participants (n=59)
Level of preparedness to produce math & science materials for tactile learners Got all of what needed to know through training
(n=3) Some gaps in training that had to be filled in
once work began (n=5) Many gaps in training that had to be filled in
once work began (n=14) Learned most of what needed to know on the job
(n=32)
Participants’ Ratings of Their Skills
Tactile Graphics Production
Beginner (n=12) Intermediate
(n=36) Advanced (n=10)
Technology
Beginner (n=7) Intermediate
(n=38) Advanced (n=14)
Tools Used
Tool 1st Grade (n=32)
3rd Grade (n=22)
5th Grade (n=21)
Algebra (n=18)
Geometry (n=15)
Perkins Brailler
10 3 2 3 1
Braille Trans-lation Software
22 19 19 14 12
Other 0 0 0 1 0
65% of the time braille translation software was used to prepare worksheets.
Planning Time
Time 1st Grade (n=32)
3rd Grade (n=22)
5th Grade (n=21)
Algebra (n=18)
Geometry (n=14)
> 15 minutes
29 20 13 13 10
16-30 minutes
2 1 4 4 1
31-45 minutes
1 1 3 1 3
46-60 minutes
0 0 1 0 0
80% of the time less than 15 minutes was spent in planning
Production Time
Minutes
1st Grade (n=32)
3rd Grade (n=22)
5th Grade (n=21)
Algebra (n=18)
Geometry (n=14)
> 15 17 4 7 3 1
16-30 9 7 3 4 3
31-45 3 7 4 5 4
46-60 3 1 3 1 2
61+ 0 3 4 5 4
54% of the time less than 30 minutes was spent in production
Braille Authority of North America (2011). Braille formats - Principles of print-to-braille transcription. Retrieved from http://www.brailleauthority.org/formats/2011manual-web/index.html Braille Authority of North America (2010). Guidelines and standards for tactile graphics. Retrieved from http://www.brailleauthority.org/tg/web-manual/index.html Nemeth, A. (1972). The Nemeth braille code for mathematics and science notation. Louisville, KY: American Printing House for the Blind.
Sources for the Rules on theFollowing Slides
1st Grade Worksheet (n=32)
6 out of 32 participants set up as a game board
1 participant omitted one problem
1 participant omitted three problems
No participants included the 3 pictures
6 out of 32 participants put all problems in linear format
THINKING HELPS:• “1 more” or “1
less” than 10• Share
Boxed Material
TVIs (n=9)
Trans. (n=17)
Trans. & Paras. (n=6)
Paras. (n=8)
Before problems56%
(n=5)43%
(n=3)17% (n=1)
50 (n=4)
Following problems (location in print copy)
11% (n=1)
57% (n=4)
68%(n=4)
37% (n=3)
Omit completely33%
(n=3)- -
13%(n=1)
3rd Grade Worksheet (n=22)
Variability in what part of the title was included
21 participants showed the ice cream cones in groups of 4.
20 participants placed the ice cream symbol before the 12 ice cream cones were shown.
TVIs (n=18)
Trans. (n=22)
Trans. & Paras. (n=9)
Paras. (n=10)
Omitted NI when labeling thermometer
0%(n=6)
10%(n=10
)
0% (n=2)
25%(n=4
)
Omitted NI when labeling clock
66.7% (n=6)
60% (n=10
)
50% (n=2)
75%(n=3
)
Numbers on the Thermometer and Clock
NI should
be
omitted!
Shade the thermometer to show 43°F.
How do you braille…
TVIs (n=6)
Trans. (n=10)
Trans. & Paras. (n=1)
Paras. (n=4)
(ELI)(cap)(F)(.)16.7
%(n=1)
30% (n=3)
-25%
(n=1)
(cap)(F)(.)16.7
% (n=1)
30% (n=3)
-50%
(n=2)
(cap)(F)(PI)(.)50%
(n=3)40%
(n=4)-
25% (n=1)
Other - -100% (n=1)
-
The ELI is
used
before a
one-letter
abbreviati
on
followed
by a
period
that ends
the
sentence.
5th Grade Worksheet (n=21)
9 of 21 participants included the print page number in the top right corner.
8 participants used literary page numbers, and 1 used Nemeth.
All participants included angle labels.
All participants included the flag and positioned it properly with clear lines between 3 regions.
18 of 21 participants had 3 regions that were tactually different.
14 of 21 did not use a key. Of the 7 using a key 5 placed it above the flag, one
below the flag and one to the left of the flag. 5 individuals used a lead line from label (e.g. red) to
region.
Flag
Algebra Worksheet (n=18)
16 participants who included the 3 graphs included the x-axis and y-axis.
The 16 participants had x-axis and y-axis that were tactually clear.
For the 16 participants the points on the line (e.g., -1, 4) were tactually clear.
TVIs (n=6)
Trans. (n=9)
Trans. & Paras. (n=3)
Paras. (n=6)
Number 0 (zero)
50% (n=3)
33% (n=3)
67% (n=2)
100% (n=6)
Letter o 50%
(n=3)66%
(n=6)33% (n=1)
-
Brailling the Origin
It seems unclear if the origin is labeled a zero or letter O in
print.
According to Guidelines and Standards for Tactile Graphics, if the origin cannot be determined in print and there are no numbers on the axes, then label the origin
as the letter O.
Geometry Worksheet (n=15)
12 out of 15 participants included the grid lines on the graphs.
All participants included the dashed lines, and in 12 instances they could easily be felt tactually.
All 15 participants included the right angles.
Inclusion of braille page numbers All pages = 65% Some pages = 7% No pages = 28%
77% of the time when included, all pages had braille page numbers Most often first page did not have a page number
Location of braille page numbers 45% were placed at the top right 55% were placed at the bottom right
Braille Page Numbering
Blank line in a word problem (e.g., A rectangle is ____ a rhombus) 55% of the time used a long dash (4 cells) 37% of the time used a general omission symbol 8% of the time another symbol was used
Omission for a blank line where student is to write an answer 61% of the time no symbol shown 30% of the time used a long dash (4 cells) 9% of the time another symbol was used
Omission
85% of the time participants omitted bold, italics or underlining that did not have meaning.
59% of the time when double capitals were used in the print participants used them in the braille.
Formatting Observations
Example:Calculate the area and
perimeter of each triangle below.
88% of the time when graphics were included they looked the way they did in the print.
Not counting the 1st grade worksheet, rarely were graphics left off of the worksheet. 5% left off on the 3rd grade worksheet 1.5% left off on the 5th grade worksheet 11% left off on the Algebra worksheet 1% left off on the Geometry worksheet
Observations of Tactile Graphics
84% of the time the elements (e.g., dashed lines, x-axis) were included.
94% of the time labels were included (e.g., angles on a shape, points on a graph).
89% of the time one could tactually feel the elements of the graphic clearly (e.g., crisp lines on graphs).
Observations of Tactile Graphics
Some spatial problems transcribed as linear problems. Order of problems on game board – most followed order of
the problems on the game board, but some did not. They went row by row instead.
There was great variation in what was used as the title of the worksheets.
Some participants did not follow capitalization of the print. There was great variation in the lengths of lines and sizes
of shapes on graphics. Some took an entire page for a simple graphic, and others placed 2-9 simple graphics on a page.
Other Items Noticed During Data Entry
45 almost always proofread their work. 25 out of 59 never have someone proofread
their work, and 17 do so on rare occasions. 36 out of 59 sometimes feel they need
additional support or information. 10 felt they produced excellent quality
science and math materials; 41 felt they produced good quality materials; 7 felt they produced fair quality materials.
A Few More Things Our Participants Shared…
What Are Our Future Plans?
Completion of a second article for JVIB Study with youth to gain information
about their experiences Development of a workshop, on-line
course, or other vehicle for professionals
Continued exploration of what we need to be teaching pre-service TVIs and other individuals preparing math & science materials for braille users
