1. THE NEMETH CODE TUTORIAL FOR THE BRAILLENOTE THE FINAL REPORT

2. THE NEMETH CODE TUTORIAL: A FINAL REPORT Gaylen Kapperman Gaylen Kapperman Jodi Sticken Jodi Sticken Visual Disabilities Program Visual Disabilities Program Department of Teaching and Learning Department of Teaching and Learning Northern Illinois University Northern Illinois University DeKalb, IL 60115 DeKalb, IL 60115

3. The Nemeth Code Tutorial for the BrailleNote Interactive software for the BrailleNote, an electronic notetaking device manufactured by Humanware Group Interactive software for the BrailleNote, an electronic notetaking device manufactured by Humanware Group Designed to assist blind students in learning to read and write the code of braille mathematics Designed to assist blind students in learning to read and write the code of braille mathematics Software was field tested by blind students and their teachers over a 2-year period Software was field tested by blind students and their teachers over a 2-year period

4. Available through Humanware: www.humanware.com www.humanware.com Teacher’s Reference (print version of software with additional quick reference charts and teaching tips) available for free download: Products, Braille & Speech, BrailleNotes, Nemeth Code Tutorial for KeySoft, More Information About Nemeth Tutorial, Features, link for free download of Teacher’s Reference

5. 18 Chapters 18 Chapters Each Chapter divided into several lessons; most lessons contain the following four components: Each Chapter divided into several lessons; most lessons contain the following four components: Explanation Explanation Writing exercises Writing exercises Reading exercises Reading exercises Proofreading exercises Proofreading exercises Program will indicate errors and permit revisions in interactive exercises Program will indicate errors and permit revisions in interactive exercises

6. designed for use with a wide range of academically-oriented BrailleNote users from the fifth grade through college level designed for use with a wide range of academically-oriented BrailleNote users from the fifth grade through college level younger students require teacher’s guidance; older students may use independently as a self-study course of instruction younger students require teacher’s guidance; older students may use independently as a self-study course of instruction students who cannot read braille cannot benefit from this tutorial students who cannot read braille cannot benefit from this tutorial

7. Contents of Program 1: Braille Numbers and Basic Indicators 1.1The numeric indicator 1.2 The mathematical comma 1.3 The comma in lists or series 1.4 Mathematical comma as a mark of punctuation 1.5 The punctuation indicator, dots four five six 2: Plus, Minus, and Equals Sign 2.1Signs of operation and signs of comparison 2.2Directed (signed) numerals 2.3The equals sign 2.4Punctuation used with equals sign

8. 3: Decimal Point and Related Symbols 3.1The decimal point 3.2The multipurpose indicator 3.3Monetary signs: dollar, pound sterling, cent 3.4Percent sign 3.5Symbols used to indicate degree 3.6Symbols used to indicate minutes, seconds, feet, inches, prime, and double prime 3.7Signs showing omitted symbols 3.8Infinity and null 4: Multiplication Signs

9. 4: Multiplication Signs 4.1Multiplication cross 4.2Multiplication dot 4.3Mathematical parentheses, signs of grouping 5: Division and Fraction Signs 5.1Division and fraction sign overview and the divided-by sign 5.2Curved and straight division signs 5.3Fractions 5.4Mixed number indicators 5.5Other uses of the slash

10. 6: Spatial Arrangements 6.1Spatial arrangements for addition and subtraction 6.2Addition and subtraction with fractions 6.3Addition problems with regrouping (carrying) 6.4Subtraction problems with regrouping (borrowing) 6.5Multiplication 6.6Long division 6.7Long division with additional elements

11. 7: Roman Numerals and Odds and Ends 7.1Roman numerals 7.2Roman numerals in a mathematical context 7.3Abbreviations 7.4Function names 7.5Plural, possessive, and ordinal endings, and contractions adjacent to mathematical symbols 7.6Contractions and short ‑ form words 7.7Special symbols

12. 8: More Signs of Operation 8.1Signs of operation: plus or minus, minus or plus, and horizontally joined plus and minus 8.2Radical (also known as root) 8.3Factorial, union, intersection, and hollow dot 8.4 Asterisk 9: Use of Letters, Symbols, and Numbers 9.1The use of letters, symbols and numbers 9.2Letters not used in mathematical expressions 9.3Specialized alphabets

13. 10: Signs of Grouping 10.1 Signs of grouping 10.2 Signs of grouping: spacing, plural endings, and parts of words 10.3 Signs of grouping: brackets 10.4 Signs of grouping: enlarged brackets 10.5 Signs of grouping: braces 10.6 Signs of grouping: vertical bars 11: More Signs of Comparison 11.1 Signs of comparison: not equal, approximately equal, identity, similar to, and congruent to 11.2 Signs of comparison: ratios, inequalities, set notation, and vertical bars

14. 12: Level Indicators 12.1 Level indicators 12.2 Level indicators: multiple levels, fractions, grouping symbols, negative exponents, left positioned, and punctuation 12.3 Level indicators: subscripts 12.4 Level indicators: non ‑ decimal bases and combined superscript and subscript indicators 12.5 Level indicators: Spatial arrangements 12.6 Level indicators in matrices and determinants 13: More Radicals and Groups 13.1 Index ‑ of ‑ radical 13.2 Nested radicals 13.3 Radicals: Division, fractions, superscripts and subscripts

15. 14: The Shape Indicator 14.1 Signs of shape: shape indicator, two ‑ celled shape symbols, spacing and punctuation 14.2 Signs of shape: level indicators, English letter indicator, as signs of omission, and identified shape symbols 14.3 Signs of shape: shaded and filled ‑ in, positioning, star as a reference 14.4 Signs of shape: arrows 14.5 Signs of shape: structural modification, interior modification

16. 15: Different Type Forms 15.1 Type ‑ form indicators with numbers 15.2 Type ‑ form indicators with letters 15.3 Type ‑ form indicators with labeled mathematical statements, words, and phrases 16: Formats for Geometric Proofs 16.1 Formats for geometric proofs 17: Fractions: Complex and Hypercomplex 17.1 Complex fractions 17.2 Hypercomplex fractions 17.3 Spatial arrangement of fractions for cancellation

17. 18: Integrals, Sigma Notation, and Limits 18.1 Sigma notation 18.2 Limits 18.3 Integrals and partial derivatives

18. Assessment of each student’s ability to read and write Nemeth code was conducted at the beginning of the school year (pre-test) Assessment of each student’s ability to read and write Nemeth code was conducted at the beginning of the school year (pre-test) Students in the treatment group received instruction in the use of the tutorial; instruction was delivered by their special education teachers Students in the treatment group received instruction in the use of the tutorial; instruction was delivered by their special education teachers Students in the control group were not exposed to the software Students in the control group were not exposed to the software Assessment of each student’s ability to read and write Nemeth code was conducted at the conclusion of the school year (post-test) Assessment of each student’s ability to read and write Nemeth code was conducted at the conclusion of the school year (post-test) Field Test, Year One

19. Year Two Assessment of each student’s ability to read and write Nemeth code was conducted at the beginning of the school year (pre-test) Assessment of each student’s ability to read and write Nemeth code was conducted at the beginning of the school year (pre-test) Students in the control group received instruction in the use of the tutorial; instruction was delivered by their special education teachers Students in the control group received instruction in the use of the tutorial; instruction was delivered by their special education teachers Students in the treatment group were allowed to continue their work with the tutorial if they chose to do so Students in the treatment group were allowed to continue their work with the tutorial if they chose to do so Assessment of each student’s ability to read and write Nemeth code was conducted at the conclusion of the school year (post-test). Assessment of each student’s ability to read and write Nemeth code was conducted at the conclusion of the school year (post-test).

20. The data analysis shown in the following slides represents the outcome of the first year’s activities The data analysis shown in the following slides represents the outcome of the first year’s activities The results of the data analysis indicate that the tutorial is a very effective tool in helping blind students learn to read and write the code of braille mathematics The results of the data analysis indicate that the tutorial is a very effective tool in helping blind students learn to read and write the code of braille mathematics

21. Sample Treatment and control group students were matched based on: Treatment and control group students were matched based on: Grade level Grade level Math grade level Math grade level Reading grade level Reading grade level Discrepancy between actual grade level and math grade level Discrepancy between actual grade level and math grade level One student from control group was excluded from analyses to facilitate matching One student from control group was excluded from analyses to facilitate matching

22. Instrumentation Math Reading Test Math Reading Test 75 items 75 items Three raters scored each item Three raters scored each item Mean consistency of raters across items: 96% (pre- test), 92% (post-test) Mean consistency of raters across items: 96% (pre- test), 92% (post-test) Total score = number of correct items Total score = number of correct items Math Writing Test Math Writing Test 75 items 75 items Three raters scored each item Three raters scored each item Mean consistency of raters across items: 95% (pre- test), 92% (post-test) Mean consistency of raters across items: 95% (pre- test), 92% (post-test) Total score = number of correct items Total score = number of correct items

23. Treatment group (received Nemeth code training): n = 28 Treatment group (received Nemeth code training): n = 28 Mean age = 13.3 Mean age = 13.3 Mean grade level = 6.9 Mean grade level = 6.9 Mean math grade level = 6.7 Mean math grade level = 6.7 Mean reading grade level = 6.4 Mean reading grade level = 6.4 54% male, 46% female 54% male, 46% female 71% Caucasian, 11% African-American, 14% Hispanic, 4% Other ethnicity 71% Caucasian, 11% African-American, 14% Hispanic, 4% Other ethnicity Control group (did not receive Nemeth code training): n = 28 Control group (did not receive Nemeth code training): n = 28 Mean age = 12.7 Mean age = 12.7 Mean grade level = 6.4 Mean grade level = 6.4 Mean math grade level = 6.1 Mean math grade level = 6.1 Mean reading grade level = 6.2 Mean reading grade level = 6.2 50% male, 50% female 50% male, 50% female 79% Caucasian, 7% African-American, 11% Hispanic, 1% Other ethnicity 79% Caucasian, 7% African-American, 11% Hispanic, 1% Other ethnicity

24. Mean Age Mean Grade Level Mean Math Grade Level Mean Reading Grade Level Treatment (n = 28)13.36.96.76.4 Control (n = 28)12.76.46.16.2 Mean Grade Levels for Treatment and Control Groups

25. Treatment Group Frequency (percent) Control Group Frequency (percent) Gender Male15 (54%)14 (50%) Female13 (46%)14 (50%) Ethnicity Caucasian20 (71%)22 (79%) African-American3 (11%)2 (7%) Asian4 (14%)3 (11%) Other1 (4%) Demographic Characteristics of Treatment and Control Groups

26. Instrumentation (ctd.) Split-half reliability Split-half reliability

27. Descriptive Statistics

28. Descriptive Statistics (ctd.)

29. Distribution of Growth Scores (Treatment Group)

30. Distribution of Growth Scores (Control Group)

31. Math Reading Test Scores

32. Math Writing Test Scores

33. Math Reading Growth Difference in growth between treatment and control groups was statistically significant (t(27) = 2.58, p =.016), with a moderate effect size (d = 0.49) Difference in growth between treatment and control groups was statistically significant (t(27) = 2.58, p =.016), with a moderate effect size (d = 0.49)

34. Math Writing Growth Difference in growth between treatment and control groups was statistically significant (t(27) = 5.37, p <.001), with a large effect size (d = 1.01) Difference in growth between treatment and control groups was statistically significant (t(27) = 5.37, p <.001), with a large effect size (d = 1.01)

35. Non-parametric Tests Because distribution of growth scores showed some skewness, we additionally carried out non-parametric tests for differences in growth Because distribution of growth scores showed some skewness, we additionally carried out non-parametric tests for differences in growth Results again showed significant differences in growth for Math Reading (p =.014) and Math Writing (p <.001) Results again showed significant differences in growth for Math Reading (p =.014) and Math Writing (p <.001)

36. Variability Treatment group showed more variability in growth scores than control group Treatment group showed more variability in growth scores than control group

37. Possible Reasons for Variability in Growth Gender Gender Ethnicity Ethnicity Age Age Time spent on tutorial Time spent on tutorial

38. Gender Differences in Growth Difference between males and females was non- significant for both Math Reading Growth (t(26) = 0.06, p =.95) and Math Writing Growth (t(26) = 0.58, p =.57).

39. Ethnic Differences in Growth Difference between minority students and non- minority students was non-significant for both Math Reading Growth (t(26) = 0.22, p =.83) and Math Writing Growth (t(26) = 0.82, p =.42).

40. Relationship of Student Age to Math Reading Score Correlation was statistically non- significant (r =.19, p =.33)

41. Relationship of Student Age to Math Writing Score Correlation was statistically non- significant (r =.09, p =.67)

42. Relationship of Total Time Spent on Tutorial to Math Reading Score Correlation was statistically significant (r =.52, p <.01)

43. Relationship of Total Time Spent on Tutorial to Math Writing Score Correlation was statistically significant (r =.46, p =.01)

44. Credits The following individuals contributed significantly to this project, and we appreciate their efforts: Professor Thomas Smith: data analysis Professor Thomas Smith: data analysis Julie Hart, project assistant: organization of the countless minutiae, and maintaining lines of communication between field testers and researchers Julie Hart, project assistant: organization of the countless minutiae, and maintaining lines of communication between field testers and researchers Professors Kim Zebehazy and Stacy Kelly: evaluation of pre- and post-tests Professors Kim Zebehazy and Stacy Kelly: evaluation of pre- and post-tests Field test students and teachers: their participation was the heart and soul of this project Field test students and teachers: their participation was the heart and soul of this project

45. The Nemeth Code Tutorial Project was supported by funding from the U.S. Department of Education Office of Special Education and Rehabilitative Services Grant No. H327A050093