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Doing Mathematics

Doing Mathematics. Klaus Miesenberger University of Linz, Institut Integriert Studieren Altenbergerstrasse 69, A-4040 Linz E-mail: bernhard.stoeger|klaus.miesenberger@jku.at WWW:http://www.integriert-studieren.jku.at Tel: +43-732-2468-9232 Fax: ...-9322. Four Challenges.

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Doing Mathematics

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  1. Doing Mathematics Klaus Miesenberger University of Linz, Institut Integriert Studieren Altenbergerstrasse 69, A-4040 LinzE-mail: bernhard.stoeger|klaus.miesenberger@jku.at WWW:http://www.integriert-studieren.jku.at Tel: +43-732-2468-9232 Fax: ...-9322 Paris 08, Klaus Miesenberger

  2. Four Challenges • 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) Paris 08, Klaus Miesenberger

  3. 1. Access: eDocuments More dimensional: • DotsPlus • ViewPlus • Triangle • Math Project Linear: • Aster • HRTeX/LaBraDoor • Lambda • MathProject • MahtTalk • MathGenie • TechRead • IGUMA • BraMaNet • Math2Braille • Infty • MMBT/Vicky Paris 08, Klaus Miesenberger

  4. 2. Navigation: problems • You will not easily 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 • … Paris 08, Klaus Miesenberger

  5. Collapse/ Expand Paris 08, Klaus Miesenberger

  6. 3. Presentation/Communication • From MathML, LaTeX, OpenMath to Braille/Audio • Form Braille to MathML, LaTeX, OpenMath • From context sensitive to context free • Logic Programming • Synchronization visual / audio / Braille Paris 08, Klaus Miesenberger

  7. Synchronize Paris 08, Klaus Miesenberger

  8. 4. Doing (not only authoring)                7a2 + 16a2 + 13a2 = 36a2  9b2 + 4b2 + 17b2 = 30b2  12ab + 5ab + 2ab + 23ab = 42ab  13 + 68 + 44 + 17 - 298 = - 156  36a2 + 30b2 + 42ab = 156 Paris 08, Klaus Miesenberger

  9. Simplify Paris 08, Klaus Miesenberger

  10. Multiply Paris 08, Klaus Miesenberger

  11. MAWEN Paris 08, Klaus Miesenberger

  12. Trends in math education Paris 08, Klaus Miesenberger

  13. Doing: old example Paris 08, Klaus Miesenberger

  14. PEN INPUTInkML: XML for ink data: Net Meeting, Moodle, class room, …, nothing new in doing: Paris 08, Klaus Miesenberger

  15. “Hello World” in InkML <ink> <trace> 10 0, 9 14, 8 28, 7 42, 6 56, 6 70, 8 84, 8 98, 8 112, 9 126, 10 140, 13 154, 14 168, 17 182, 18 188, 23 174, 30 160, 38 147, 49 135, 58 124, 72 121, 77 135, 80 149, 82 163, 84 177, 87 191, 93 205 </trace> <trace> 130 155, 144 159, 158 160, 170 154, 179 143, 179 129, 166 125, 152 128, 140 136, 131 149, 126 163, 124 177, 128 190, 137 200, 150 208, 163 210, 178 208, 192 201, 205 192, 214 180 </trace> <trace> 227 50, 226 64, 225 78, 227 92, 228 106, 228 120, 229 134, 230 148, 234 162, 235 176, 238 190, 241 204</trace> <trace> 282 45, 281 59, 284 73, 285 87, 287 101, 288 115, 290 129, 291 143, 294 157, 294 171, 294 185, 296 199, 300 213</trace> <trace> 366 130, 359 143, 354 157, 349 171, 352 185, 359 197, 371 204, 385 205, 398 202, 408 191, 413 177, 413 163, 405 150, 392 143, 378 141, 365 150</trace> </ink> Paris 08, Klaus Miesenberger

  16. @Science Project at • presentation • demonstration • hands on workshops with tools Paris 08, Klaus Miesenberger

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