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 survey  Completed, in hard copy braille, at least one of five math worksheets  1 st grade  3 rd grade  5 th grade  Algebra  Geometry  Completed an on-line transcription survey Our Participants…

Demographic Data are Reported in Rosenblum & Herzberg, 2011  Gender (n=166)  160 Female  6 Male  Years Preparing Math Braille Materials (n=166)  years  years  years  years  years  Job Role (n=166)  80 TVIs  23 Transcribers & Paraprofessionals  46 Transcribers  17 Paraprofessionals  Quality of materials (n=162)  30 Excellent  109 Good  21 Fair  2 Poor

1 st 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 game board that don't tie to the game.

3 rd 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

5 th 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: 3 rd 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: 3 rd 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 Graphics 2. 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)  years (n=6)  16+ years (n=17)  Hours Preparing Math Materials Per Week  1-5 hours (n=15)  6-10 hours (n=11)  hours (n=7)  hours (n=7)  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 Tool1 st Grade (n=32) 3 rd Grade (n=22) 5 th Grade (n=21) Algebra (n=18) Geometry (n=15) Perkins Brailler Braille Trans- lation Software Other % of the time braille translation software was used to prepare worksheets.

Planning Time Time1 st Grade (n=32) 3 rd Grade (n=22) 5 th Grade (n=21) Algebra (n=18) Geometry (n=14) > 15 minutes minutes minutes minutes % of the time less than 15 minutes was spent in planning

Production Time Minutes1 st Grade (n=32) 3 rd Grade (n=22) 5 th Grade (n=21) Algebra (n=18) Geometry (n=14) > % 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 web/index.html web/index.html Braille Authority of North America (2010). Guidelines and standards for tactile graphics. Retrieved from 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 the Following Slides

1 st 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 problems 56% (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 completely 33% (n=3) -- 13% (n=1)

3 rd 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 abbreviation followed by a period that ends the sentence.

5 th 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 1 st grade worksheet, rarely were graphics left off of the worksheet.  5% left off on the 3 rd grade worksheet  1.5% left off on the 5 th 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

Dr. L. Penny Rosenblum Dr. Tina Herzberg We would love to hear from You!