M1 M69 2009


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M1/M69 workshop for the ExPOUND project

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M1 M69 2009

  1. 1. A web-based tool for supporting student comprehension of proofs, derivations or other arguments Lara Alcock Charles Shields, Nicola Wilkinson, Lee Barnett, Arun Palipana © Loughborough University
  2. 2. <ul><li>Overview </li></ul><ul><ul><li>Proof comprehension </li></ul></ul><ul><ul><li>e-Proofs </li></ul></ul><ul><ul><li>ExPOUND </li></ul></ul><ul><ul><li>Discussion </li></ul></ul>© Loughborough University
  3. 3. <ul><li>Procedures  proofs </li></ul><ul><ul><li>Students may expect procedures </li></ul></ul><ul><ul><li>Students may equate ability to “do” with understanding </li></ul></ul><ul><ul><li>Students may ignore proofs </li></ul></ul><ul><ul><li>Disastrous to various degrees </li></ul></ul>© Loughborough University
  4. 4. <ul><li>Two problems: </li></ul><ul><ul><li>Attending to proofs </li></ul></ul><ul><ul><li>Proof comprehension </li></ul></ul><ul><li>What does proof comprehension involve? </li></ul>© Loughborough University
  5. 6. <ul><li>Basic knowledge </li></ul><ul><ul><li>New definitions/theorems appear daily </li></ul></ul><ul><ul><li>Interpreting logical statements </li></ul></ul><ul><ul><li>Attending to definitions </li></ul></ul>© Loughborough University
  6. 8. <ul><li>Inferring warrants </li></ul><ul><ul><li>Status not content of statements </li></ul></ul><ul><ul><li>Looking across proof </li></ul></ul><ul><ul><li>Interpreting conditional statements </li></ul></ul><ul><ul><li>Searching for warrants </li></ul></ul><ul><ul><li>Expectation of understanding </li></ul></ul>© Loughborough University
  7. 10. <ul><li>Identifying larger-scale structure </li></ul><ul><ul><li>Major steps / sections </li></ul></ul><ul><ul><li>Recognising standard proof types </li></ul></ul><ul><ul><li>Recognising where premises used and where conclusions appear </li></ul></ul>© Loughborough University
  8. 11. <ul><li>Lecturing </li></ul><ul><ul><li>All aspects of proof comprehension at once </li></ul></ul><ul><ul><li>Directing attention </li></ul></ul><ul><ul><li>Grasping logical relationships quickly </li></ul></ul><ul><ul><li>Different individual difficulties </li></ul></ul><ul><ul><li>Explanation not recorded </li></ul></ul>© Loughborough University
  9. 13. <ul><li>e-Proofs </li></ul><ul><ul><li>Give reminders of basic knowledge </li></ul></ul><ul><ul><li>Make warrants explicit </li></ul></ul><ul><ul><li>Point out structure </li></ul></ul><ul><ul><li>Point out where premises used and conclusion appears </li></ul></ul>© Loughborough University
  10. 14. <ul><li>Feedback from use in lectures / VLE </li></ul><ul><ul><li>“ I found hearing the lecturer explaining each line individually helpful in understanding particular parts and how they relate to the entire proof.” </li></ul></ul><ul><ul><li>“ Having proofs online does make it easier to go at my own pace whilst still having the lecturer explain each part.” </li></ul></ul>© Loughborough University
  11. 15. <ul><li>Feedback from use in lectures / VLE </li></ul><ul><ul><li>“ They were useful, but sometimes made the proofs seem more complicated than they actually were.” </li></ul></ul><ul><ul><li>“ e-Proofs did help understand better, however was still quite confused. Seems to be a lot to understand and remember.” </li></ul></ul>© Loughborough University
  12. 16. <ul><li>Usage issues </li></ul><ul><ul><li>In lectures? </li></ul></ul><ul><ul><li>To replace lectures? </li></ul></ul><ul><ul><li>Explanation decisions </li></ul></ul><ul><ul><li>Emphasis on detail or structure </li></ul></ul><ul><ul><li>Use by students? </li></ul></ul>© Loughborough University
  13. 17. <ul><li>On to ExPOUND… </li></ul>© Loughborough University
  14. 18. Aims and Objectives <ul><li>Build and release the open source ExPOUND authoring tool </li></ul><ul><li>Document and develop user guides and best practice </li></ul><ul><li>Build an ExPOUND user community </li></ul><ul><li>Support the development of a library of e-Proofs </li></ul><ul><li>Raise the profile of mathematical education research (specifically on the learning of proofs) </li></ul>
  15. 19. Functionality <ul><li>The ExPOUND authoring tool will offer the lecturer the following functionality to enable the construction of an e-Proof: </li></ul><ul><ul><li>Mathematical notation editor (LaTeX-based) for writing each line; </li></ul></ul><ul><ul><li>Facility to choose, for each “screen”, which parts are to be visible, invisible or “greyed out”; </li></ul></ul><ul><ul><li>Audio file import and facility to associate an individual file with an individual screen; </li></ul></ul><ul><ul><li>Facility to add arrows, boxes and other annotation to the screen, synchronising the appearance of these with the audio commentary; </li></ul></ul><ul><ul><li>‘ Playback’ control options; </li></ul></ul><ul><ul><li>Export to content package: *.zip file; the work required to export to appropriate standards (IMS CP / SCORM 1.2) will be scoped and inform the development roadmap. </li></ul></ul>
  16. 20. Work done to date <ul><li>Evaluated whats out there (Xerte) </li></ul><ul><li>Looked at LaTeX options </li></ul><ul><li>Interface design </li></ul><ul><li>Migration to building the ExPOUND tool in Adobe Flex </li></ul><ul><li>Functional Walk through Analysis </li></ul><ul><li>Initial screen architecture developed </li></ul>
  17. 21. Building to rule <ul><li>To make sure that the tool is consistent and the development is controlled we have rules to adhere to… </li></ul><ul><li>Any confirmation dialog will have ‘yes’ and ‘no’ buttons to suit the appropriate response. </li></ul><ul><li>Any layer component created always appears in the centre of the canvas and requires the move tool to displace it. </li></ul><ul><li>Every time a new layer is created it invokes a project save action. </li></ul><ul><li>The creation of an object on layer doesn’t invoke a project save action </li></ul><ul><li>Switching layers invokes a project save action </li></ul><ul><li>Clicking the browser back button does not invoke a project save action and data will be lost, as this is a browser function and not an ExPOUND function.. If at this point the browser forward button is clicked the user will be presented with ExPOUND login. </li></ul>
  18. 22. Interface structure ExPOUND Banner e-proof build area e-proof navigation bar Page and project timeline Menu palette Layers palette Tool Properties palette Tools palette
  19. 23. Interface Design
  20. 25. Into the Future <ul><li>Interface customisation/branding </li></ul><ul><li>Hosted services possibilities </li></ul><ul><li>Build a working prototype (pre beta) </li></ul><ul><li>Looking for prospective users </li></ul><ul><li>Open source release versions (beta, final) </li></ul><ul><li>Using the tool with students </li></ul><ul><li>Evaluations of the project and of how well the tool works </li></ul><ul><li>Developing tool sets based on ExPOUND </li></ul>
  21. 26. Questions
  22. 27. Contacts <ul><li>Website: http://expound.lboro.ac.uk </li></ul><ul><li>Email: [email_address] </li></ul><ul><li>Google code: http://code.google.com/p/expound-loughborough/ </li></ul>