Multilingual Mathematics in WebALT


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WebALT Workshop at Online Educa, 29 November 2006, Berlin.

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Multilingual Mathematics in WebALT

  1. 1. Multilingual Mathematics in WebALT Olga Caprotti Jordi Saludes, Gloria Casanellas Work funded by EDC-22253-WEBALT
  2. 2. WebALT Team of Linguists <ul><li>University of Helsinki: </li></ul><ul><ul><li>Lauri Carlson, Wanjiku Ng'ang'a, Anni Laine, several assistants </li></ul></ul><ul><li>Polytechnic University of Barcelona: </li></ul><ul><ul><li>Jordi Saludes, Sebastian Xambó </li></ul></ul><ul><li>Maths for More: </li></ul><ul><ul><li>Glòria Casanellas, Daniel Marquès </li></ul></ul>those to be thanked for the good work
  3. 3. Multilingual mathematics <ul><li>Multilingual mathematics is mathematics expressed in a variety of languages </li></ul><ul><li>Mathematics is abstract yet it can be verbalized using specialized jargon in natural language </li></ul><ul><li>Verbal mathematics is syntactically and symbolically different in the different languages </li></ul><ul><ul><li>93, “ninenty three”, “quatre vingt treize”, “drei und neunzig” </li></ul></ul><ul><ul><li>GGT, GCD, MCD </li></ul></ul>
  4. 4. Why multilingual math education <ul><li>Students need to learn how to express themselves, also mathematically </li></ul><ul><li>Linguistic differences must be preserved for cultural heritage </li></ul><ul><li>Linguistic minorities must not be discriminated </li></ul><ul><li>Multilingual mathematics can offer </li></ul><ul><li>a step forward in the Bologna process </li></ul><ul><li>while keeping cultural diversity </li></ul>
  5. 5. Mathematics: a universal language <ul><li>Due to its abstract and exact nature, </li></ul><ul><li>one can expect to be able to obtain verbalizations of math in natural language, without loss of information, </li></ul><ul><li>provided one generates them from an exact mathematical content </li></ul>EN FR ES IT DE FI SE CAT math
  6. 6. Language Generation in WebALT <ul><li>Short problems (numerical, drill) </li></ul><ul><ul><li>“ compute the determinant of M” </li></ul></ul><ul><ul><li>“ find n such that P(n)” </li></ul></ul><ul><ul><li>“ let x be positive, show that A(x)” </li></ul></ul><ul><li>Long problems, feedbacks and hints </li></ul>Generate multilingual verbalizations for mathematical problems Study of the state of the art in multilingual and multicultural creation of digital mathematical content. L. Carlson, J. Saludes, A. Strotmann. WebALT Project Deliverable D1.2., April 2005.
  7. 7. Multilingual problem rendering MathDox Multilingual Exercise in Moodle
  8. 8. Multilingual problem rendering Automatic Multilingual Exercise
  9. 9. Representation of problems <ul><li>Conceptually layered: </li></ul><ul><li>Mathematics, OpenMath </li></ul><ul><li>Sentence, WebALT extended OpenMath </li></ul><ul><ul><li>MULTILINGUAL </li></ul></ul><ul><li>Problem + algorithmic flow, Math-QTI </li></ul>for interactivity and multilinguality Problem Sentence Sentence Mathematics
  10. 10. OpenMath, MathML, Math-QTI <ul><li>OpenMath is a standard language for the representation of mathematical content geared to digital processing. It focuses on the meaning of the mathematical objects. </li></ul><ul><li>MathML is the W3C recommendation for an XML representation of mathematics. It is mainly adopted for typesetting math on the web. </li></ul>Math-QTI is the extension of QTI , IMS Questions and Testing Interoperability, where mathematics is done using OpenMath. Developed by Serving Mathematics Project.
  11. 11. Multilingual Short Problems <ul><li>Math is represented in OpenMath </li></ul><ul><ul><li>extensible: e.g. by our own NLG primitives </li></ul></ul><ul><ul><li>language independent </li></ul></ul><ul><ul><li>embeds in Math-QTI and renders with MathML-P </li></ul></ul><ul><li>Multilingual Generation is done on </li></ul><ul><ul><li>well-formed </li></ul></ul><ul><ul><li>language-independent rich encoding </li></ul></ul>EN FR ES IT DE FI SE CAT OpenMath
  12. 12. Attrib([nlg:mood nlg:imperative nlg:tense nlg:present, nlg:directive nlg:determine],plangeo1:are_on_line(A,B,C)) Determine if A, B and C are collinear. Määritä ovatko A, B ja C suoralla. Determina si A, B y C son colineales. Déterminer si A, B et C sont sur une droite. Determina se A, B e C sono su una linea. Bestäm om A, B och C är på en linje. Note the linguistic differences: Imperative vs. Infinitive Adjectives vs. Adverbial phrases
  13. 13. Grammatical Framework <ul><li>Grammar formalism, based on type theory, and supporting: </li></ul><ul><ul><li>Multilinguality by abstract grammar + concrete grammars for parallel languages </li></ul></ul><ul><ul><li>Semantics, like well formedness of expressions </li></ul></ul><ul><ul><li>Modular grammar engineering: abstract grammar reflects mathematics </li></ul></ul><ul><ul><li>Reusable grammars as software components </li></ul></ul><ul><li>Resource Grammar Library: Danish, English , Finnish , French , German, Italian , Norwegian, Russian, Spanish , Swedish . (Catalan, Swahili) </li></ul>Aarne Ranta, Chalmers
  14. 14. Mathematical Problem Grammars <ul><li>Operations: sentences </li></ul><ul><li>OpenMath: math </li></ul><ul><li>Ground: variables, literals, integers </li></ul>Abstract Grammars 175 OpenMath symbols 36 categories 12,000 lines of code 158 source files (Not including the catalan resource grammar. This part itself contains a bit less than 10,000 lines). Concrete Grammars
  15. 15. Multilingual Sentence Editing
  16. 16. WebALT NLG Service <ul><li>Natural language renderings for well-formed sentences can be obtained from the web service running at </li></ul><ul><li>parameters: </li></ul><ul><ul><li>input1: The OpenMath object represented in XML encoding (a string). </li></ul></ul><ul><ul><li>Input2: The language codified as ISO-639 two-letter code (a string). </li></ul></ul><ul><ul><li>protocol: SOAP, see </li></ul></ul>
  17. 17. Hands-On Session <ul><li>Multilingual Tools, </li></ul><ul><ul><li>Abel Pau , WebALT Multilinguality in MapleTA </li></ul></ul><ul><ul><li>Gloria Casanellas , Test the TextMathEditor </li></ul></ul><ul><ul><li>Jordi Saludes , All about GF </li></ul></ul><ul><li>Labs, Phil Yasskin and Douglas Meade </li></ul><ul><ul><li>Play with the Maplets for Calculus </li></ul></ul>
  18. 18. The future <ul><li>Extend grammar coverage for short problems </li></ul><ul><li>Extend types of sentences to cover more feedback </li></ul><ul><li>Swahili, in progress </li></ul><ul><li>Find applications of the technology </li></ul>