THE NEMETH CODE TUTORIAL FOR THE BRAILLENOTE

1. THE NEMETH CODE TUTORIALFOR THE BRAILLENOTE  THE FINAL REPORT

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

3. The Nemeth Code Tutorial for the BrailleNote 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 Software was field tested by blind students and their teachers over a 2-year period

4. Available through Humanware: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 Each Chapter divided into several lessons; most lessons contain the following four components: Explanation Writing exercises Reading exercises Proofreading 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 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

7. Contents of Program 1: Braille Numbers and Basic Indicators 1.1 The 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 2.1 Signs of operation and signs of comparison 2.2 Directed (signed) numerals 2.3 The equals sign 2.4 Punctuation used with equals sign

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

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

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

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

12. 8: More Signs of Operation 8.1 Signs of operation: plus or minus, minus or plus, and horizontally joined plus and minus 8.2 Radical (also known as root) 8.3 Factorial, union, intersection, and hollow dot 8.4 Asterisk 9: Use of Letters, Symbols, and Numbers 9.1 The use of letters, symbols and numbers 9.2 Letters not used in mathematical expressions 9.3 Specialized 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) 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 Assessment of each student’s ability to read and write Nemeth code was conducted at the conclusion of the school year (post-test)

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) 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 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 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: Grade level Math grade level Reading grade level Discrepancy between actual grade level and math grade level One student from control group was excluded from analyses to facilitate matching

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

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

26. Instrumentation (ctd.) 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)

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)

35. Non-parametric Tests 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)

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

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

38. Gender Differences in Growth

39. Ethnic Differences in Growth

40. Relationship of Student Age to Math Reading Score

41. Relationship of Student Age to Math Writing Score

42. Relationship of Total Time Spent on Tutorial to Math Reading Score

43. Relationship of Total Time Spent on Tutorial to Math Writing Score 

44. Credits The following individuals contributed significantly to this project, and we appreciate their efforts: Professor Thomas Smith: data analysis 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 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 ServicesGrant No. H327A050093