The Lambda system Enrico Bortolazzi Veia Progetti s.r.l. – Verona – Italy Flavio Fogarolo

1. The Lambda system Enrico Bortolazzi Veia Progetti s.r.l. – Verona – Italy Flavio Fogarolo CSA – Vicenza - Italy

2. The problem Notwithstanding information technologies, blind students are still disadvantaged in scientific studies.

3. Thanks to information technologies, blind students can cope much better with nearly any study field than in the past.Main advantages: Access to any e-document Higher functionality and speed with respect to traditional Braille devices Directly accessible texts even to those who do not have any knowledge about Braille

4. However, this is not valid for Maths so far Access to any e-document Higher functionality and speed with respect to traditional Braille devices Directly accessible texts even to those who do not have any knowledge about Braille

5. LAMBDA project It suggests an integrated system made up by: • An editor for writing maths expressions in a linear, powerful and efficient way • A linear maths code connected to the MathML, compact and accessible to the blind • A conversion system able to manage the most common maths writing formats, in and out.

6. LAMBDA allows the blind student to: • read the mathematical text and offers tools to facilitate the comprehension of complex structures; • write the mathematical text, with functions that facilitate the input of symbols not present on the keyboard; • manipulate the mathematical text, that is to modify it to calculate expressions, solve equations, demonstrate theorems…

7. The LAMBDA Editor

8. The LAMBDA Editor LAMBDA editor presents the math document to the user, written in LAMBDA code, in the most suitable way for him. The operation is similar to the one done by Latex or MathML browsers: <mroot> <mrow> <mi>x</mi> <mo>+</mo> <mi>y</mi> </mrow> <mn>3</mn> </mroot> Browser Latex - MathML

9. The LAMBDA Editor But for blind users the most suitablevisualisation is linear and compact. Furthermore the user has at his disposal not only a browser but also an editor to write and modify the text. ä3:x+yÊ <mroot> <mrow> <mi>x</mi> <mo>+</mo> <mi>y</mi> </mrow> <mn>3</mn> </mroot> Browser Editor ä3:x+yÊ LAMBDA

10. The LAMBDA Editor Main feature of linear notation is the block structure (open/close). It’s known that the comprehension and the management of linear structured documents gets very difficult with a high number of blocks, especially in lack of visual information.

11. The LAMBDA Editor To give an efficient management of the blocks of the mathematical writing is one of the main aims of LAMBDA system. The editor is not only a system to register a sequence of characters, as a normal text editor, but it’s a software that recognizes the blocks, that is it knows to which close tag each open is connected and viceversa.

12. The LAMBDA Editor This way it’s possible to offer the user efficacious tools of support and help: - Commands to select (and delete, copy, paste) a whole block, - Commands to pass from a tag to the correspondent one, - Command to delete with only one operation all the tags of a block ...

13. Compensative functions

14. Compensative functions Through the management software we try to reduce the disadvantages due to linear notation and manipulation through the keyboard. The active editor recognizes the maths elements and their interactions and helps in surfing.

15. Compensative functions Particularly important are the commands for alternative visualization , with which it’s possible to hide the content of the blocks, choosing a level of depth, to show up the structure of an expression and facilitate its comprehension.

16. Compensative functions äË(x+1)^2Æ(x+1)(x-1)ñ+Ëx^2Æx-1ñÊ For a sighted user is easy to identify blocks: square root, fractions, sum of fractions…

17. Compensative functions ä Ê Expanded expression – level 1

18. Compensative functions äË Æ ñ+Ë Æ ñÊ Expanded expression – level 2

19. Compensative functions äË( )^2Æ( )( )ñ+Ëx^2Æx-1ñÊ Expanded expression – level 3

20. Compensative functions äÊ Compressed expression – level 1

21. Compensative functions äËÆñ+ËÆñÊ Compressed expression – level 2

22. Compensative functions äË()^2Æ()()ñ+Ëx^2Æx-1ñÊ Compressed expression – level 3

23. Vocal synthesis

24. Vocal synthesis Lambda system is mainly designed for a combined use of Braille display and vocal synthesis. But it can be used, if necessary, also only with vocal synthesis or only with Braille display.

25. Vocal synthesis The synthesis offers different aids to keep the mathematical document under control, both in writing and in reading and manipulating.

26. Vocal synthesis The mathematical elements can be read: • Pronunciating their name • In short speech • In complete speech • In contracted form, making the most of pauses and speed of pronunciation to comunicate

27. Vocal synthesis The user can pass in any time from one mode of reading to another according with his needs of speed, the complexity of the text and the raising of doubts of interpretation

28. The code

29. The code For blind students, a contentlinear code is much more efficacious than a notation based on the description of the graphical aspectof a formula.

30. The code Aspect: Capital Sigma, underscript i=1, overscript n, in line a with index i Content: Summation i equals 1 to n of a index i

31. The code To decode a message written in presentation code the blind user must pass two phases: Mentally rebuild the graphical image of the formula message graphic formula To comprehend the meaning of the formula rebuilt content

32. The code The same message in content code is directly understood The comprehension of the message allows to immediately understand the meaning of the formula. message content

33. The code In consideration of this, LAMBDA system is mainly content – oriented, even if it doesn’t exclude, for compatibility with other systems or to respect the user’s preferences, the presentation notation.

34. The code It was not possible to define only one 8 dots code for all countries, because: • Each country uses different tables to represent characters as Braille symbols • The traditional 6-dots math systems are deeply different from country to country

35. The code • Each country builds itsown 8-dots Braille math code on a common structure. • This way Lambda documents can freely spread, only the way in which the final user reads them in his computer is different.

36. Code transparence

37. Code transparence Yet keeping its linear form, the maths text must be understood by sighted people too, even after a short training.

38. Code transparence äË(x+1)^2Æ(x+1)(x-1)ñ+Ëx^2Æx-1ñÊ

39. Code transparence With this mode of representation the teacher can understand the meaning of the text even if he doesn’t know braille, but he can also see how the student is working with the code. äË(x+1)^2Æ(x+1)(x-1)ñ+Ëx^2Æx-1ñÊ

40. Situation LAMBDA editor is available in various languages and used by several students, mostly in Italy and Spain. It’s used mainly in the secondary school for all the maths activities. Decision to adopt LAMBDA often arise directly from students and parents.

41. Plans for the future • The most requested feature is the possibility to connect LAMBDA with an OCR to import exercises and books (example Infty). • Students of the last years of secondary school often ask to connect with softwares like Derive, Maple or Mathematica (used by their sighted colleagues). • Graphics management/exploration

42. LAMBDA project Linear Access to Mathematics for Braille Device andAudio-sinthesis