Access to Mathematics Bernhard Stöger Klaus Miesenberger University of Linz, Institut Integriert Studieren Altenbergerstrasse 69, A-4040 Linz WWW: Tel: Fax:

“Math: The Mother of Science, but the Bane of the Blind.” (A. Karshmer)

What is the problem? Steps towards solutions Contribution of Mathematicians systems, toolsHCIATuser

Four Basic Problems Access to mathematical content Navigation in mathematical expressions Presentation/Communication/Co-operation of mathematical information Doing Mathematics (carrying out calculations and computations at all levels, doing formal manipulation, solving exercises)

Access Linear rendering: Braille, speech Converter: Standard Braille Formatting for Braille, eBook, speech -> „Deliver valid, well defined content“

Access Linear: Aster LaBraDoor MahtTalk MathGenie TechRead IGUMA BraMaNet Math2Braille Infty MMBT/Vicky Lambda More dimensional: DotsPlus ViewPlus Triangle Math Project (more dimensional Braille) -> Based on LaTex OpenMath MathML

Navigation: problems You will not understand a complex math expression by sequentially reading it You need to scan passages of a formula repeatedly You need to jump over irrelevant portions of a formula Not every Braille notation makes structure of an equation immediate

Navigation From linear access to browsing Reduce complexity by structure: elapse, expand, jump/link Braille (structuring characters) or speech (using prosody, earcons) -> support of semantics presentation – content mark up

Navigation MatGenie AudioMath ReMathEx MathPlayer InftyReader IGUMA Lambda MAWEN …

Presentation/Communication From MathML, LaTeX, OpenMath to Braille Form Braille to MathML, LaTeX, OpenMath From context sensitive to context free Logic Programming MAVIS UMCL -> import, presentation of well defined and structured notations; context interpretation, semantics; content mark-up

7a 2 =16a 2 +13a 2 + 9b 2 +4b 2 +17b 2 = 12ab+5ab+2ab +23ab= = 36a 2 30b 2 42ab a 2 +30b 2 +42ab=156 Doing

Doing: difficulties Doing is based on visual methodologies: arrange, move, delete, sequence … IN SPACE ON PAPER (in school we learn methodologies!) Formulae tend to complexity Jumps, from exercise to result, within exercise or result Your memory is challenged

Doing Support environment: alternative for visual, paper based methodologies MAWEN InftyEditor MathPlayer … -> Access to Computer Algebra Systems

The IGUMA Group IGUMA: International Group for Universal Mathematics Access Developed out of the UMA project Plans a universal Math converter library, converting between formats such as: MathML LaTeX Nemeth Code Marburg Code French Braille Maths Code …

The IGUMA Group University of South Florida, Lakeland University of San Francisco Dublin City University University of Texas at Dallas Université Piere et Marie Curie, Paris New Mexico State University University of Linz Kiushu University …