1 / 11

Enhancing Aplusix with New Representations of Algebraic Expressions

This presentation discusses the ReMath project, aimed at enriching the Aplusix interface for learning algebra through innovative representations of mathematical objects. It explores the natural representation of algebraic expressions using tree structures, emphasizing the epistemological and didactical motivations behind these models. The research involves empirical studies conducted in real educational settings, focusing on how these new representations can improve student autonomy and understanding of algebraic concepts. Key insights, experiments, and graphical representations used in Aplusix are also highlighted.

rumer
Télécharger la présentation

Enhancing Aplusix with New Representations of Algebraic Expressions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Adding new Representations of Mathematical Objects to Aplusix Denis Bouhineau, Hamid Chaachoua, Jean-Francois Nicaud & Christophe Viudez 1 ICTMT’2007

  2. What’s next ? • The ReMath project • Natural representation of algebraic expressions in Aplusix • Tree & Natural representation of algebraic expressions in Aplusix • Motivations • Questions raised • Answers • Experiments • Graphical representation of algebraic expressions in Aplusix • Conclusion 2 ICTMT’2007

  3. The ReMath project • The ReMath project (IST4-26751 European project, Dec 2005) • Representing Mathematics with Digital Media • ITD-CNR (Genova), NKUA – ETL, Talent S.A (Athens), UNISI (Sienna), METAH (Grenoble), Didirem (Paris), LKL-UOL (London) • Objectives • Enrich state-of-the-art dynamic digital artefacts for doing mathematics with new representations of mathematical objects • Work on scenarios for the use of these artefacts • Carry out empirical research involving cross-experiments in realistic educational contexts 3 ICTMT’2007

  4. Natural representation of algebraic expressions in Aplusix • Aplusix • A microworld and an exerciser for doing algebra • Students freely write algebraic expressions • Algebraic expression • Natural representation of algebraic expressions • Natural editing of algebraic expressions • Representation of the reasoning processes with a tree 4 ICTMT’2007

  5. Natural representation of algebraic expressions in Aplusix • Two fundamental feedbacks • Semantic equivalence between successive steps • Syntax of the final expression • Users (students) • Gain autonomy • Learn algebra • Feel happy • Available • free for research, http://aplusix.imag.fr/Dir-Vers-Rech • or see publishers : Chartwell&Yorke (uk), Les éditions Archimède (fr), MediaDirect (it) 5 ICTMT’2007

  6. Tree & Natural representation of algebraic expressions in Aplusix • Motivations (ideal) • epistemological : trees are natural representations of algebraic expressions • didactical : • introduction of trees = change of register • mapping between natural & tree object  understand the syntactical structure of algebraic expression • computer science : trees are fundamental objects • Motivations (pragmatic) • ReMath • Didactician’s ask 6 ICTMT’2007

  7. Tree & Natural representation of algebraic expressions in Aplusix • Questions about the kind of trees: • internal trees used by Aplusix ? • special algebraic trees ? • abstract trees ? • Questions about the link between tree representations and natural representations : • just a way to display object / edit ? • ill-formed ? • Mathematical questions : • ‘-’ operator ? • ‘(‘ and ‘)’ ? 7 ICTMT’2007

  8. Tree & Natural representation of algebraic expressions in Aplusix • Answers • authentic objects of our microworld • abstract trees • 4 modes ( 4 representations) • natural • mixed • free mode • controlled mode • Other answers • -, (): depends on mode • Demos of the current prototype 8 ICTMT’2007

  9. Tree & Natural representation of algebraic expressions in Aplusix • New sorts of exercise • build the tree representation of an expression given in the natural representation • build the natural representation of an expression given in the tree representation • Prototypes • First in Dec 2006 (for demo) • Current (June 2007) for colleagues and tests • Experiments • planed in France and Italy in late 2007 9 ICTMT’2007

  10. Graphical representations of algebraic expressions in Aplusix • Objective : only display • Motivations • asked by teachers • present in curriculum • combining symbolic and graphical representations • Questions raised • How to represent the solution of equations ? • How to represent identical objects ? 10 ICTMT’2007

  11. Conclusion • Adding new Representations of Mathematical Objects • Decide whether the representation will be an object or just a new way of displaying object • Think about experiments and use cases (à la UML) • Work with colleagues from other laboratories and different cultures • (plan time enough for debugging !) 11 ICTMT’2007

More Related