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Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
Designing a Proof GUI for Non-Experts
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Designing a Proof GUI for Non-Experts

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Results fron an experiment and brainstorm on how to design a GUI for teaching mathematical proofs.

Results fron an experiment and brainstorm on how to design a GUI for teaching mathematical proofs.

Published in: Economy & Finance, Technology
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    • 1. Designing a Proof GUI for Non-Experts Evaluation of an Experiment Martin Homik, Andreas Meier Presentation by Christoph Benzmüller UITP 2005, Edinburgh ActiveMath Group German Research Center for Artificial Intelligence DFKI GmbH, Saarbrücken
    • 2. Motivation
      • Typical proof GUI design:
      • Proof system centered
      • Too specific; For experts only
      • Non-Expert proof GUI design:
      • User centered
      • Deliver what the user needs!
    • 3. Motivation (2)
      • MIPPA Project goals :
      • Interactive learning tool for math. proof
      • Underlying proof engine:
      • Proof planner MULTI
      • Target group:
      • Undergraduate students
      • A-level pupils
    • 4. Expert GUI: Loui
    • 5. Towards a User Centered GUI
      • First step:
      • Paper&Pencil student experiment
      • Primary task:
        • Observe basic user wants and needs
    • 6. Experiment Setting
      • 4 Groups
      • 2 students in each
      • Background :
      • Computer Science, Math, Logic
      • No design restrictions:
      • creativity/underlying system
      • use/invent functionalities freely
      • Example Theorem:
      • Irrationality of √2
      • Use :
      • Definitions
      • Term rewriting
      • Island introduction
      • Contradiction
      Design (120 min) Presentation (15 + 10 min) Discussion
    • 7. Experiment Remarks
      • This is no HCI experiment:
      • We let users design.
      • Users were already familiar with PP/Loui.
      • Users were restricted to certain tasks.
      • Why?
      • First attempt: obtaining inspiration
    • 8. Textbook Example: √2 is irrational „ Assume that √2 is rational. Then, there are integers n,m that satisfy √2= n / m and that have no common divisors. From √2= n / m follows that 2* m 2 = n 2 (1), which results in the fact that n 2 is even. Then, n is even as well and there is an integer k such that n =2* k . The substitution of n in (1) by 2* k results in 2* m 2 =4* k 2 which can be simplified to m 2 =2* k 2 . Hence, m 2 and m are even as well. This is a contradiction to the fact that n,m are supposed to have no common divisor.“
    • 9. Group A: Text-based Textual presentation of a proof. The same way as taught at school.
      • There exist no two integers m and n:
        • m and n being coprime
        • √ 2 =m/n
      √ 2 is irrational check proof complete proof automatically feedback no logical notation √ 2 is irrational Statement access
    • 10. Group A: Operator Application
      • There exist no two integers m and n:
        • m and n being coprime
        • √ 2 =m/n
      √ 2 is irrational
      • select operator
      • (e.g. indirect proof)
      • There exist no two integers m and n:
        • m and n being coprime
        • √ 2 =m/n
      • mark statement with mouse
      • click „Pick“ button
    • 11. Group B: Bridge Building
      • Clear separation between:
        • Assumptions and Goals
        • Forward and Backward Reasoning
      Assumptions Forward Reasoning Goals Backward Reasoning
    • 12. Group B: Control Panel History System support
    • 13. Group B: Method Iconisation (Definition-) Expansion Contradiction Insert island (Definition-) Collapse
    • 14. Group B: Operator Application
    • 15. Bridge Construction Example Upper bank Lower bank √ 2 is not rational Action: definition application (Hypotheses) (Theorem)
      • There exist two integers m and n:
        • m and n being coprime
        • √ 2 =m/n
      Action: indirect proof Action: term rewriting
      • There exist no two integers m und n:
        • m and n being coprime
        • √ 2 =m/n
      m 2 =2*n 2 Contradiction
    • 16. Placing Islands
      • There exist two integers m and n:
        • m and n being coprime
        • √ 2 =m/n
      m 2 =2*n 2 m is even n is even
    • 17. Group C: Masking Operator Names Proof presented as trees of statements Edges = Story tellers „next do … to get … √ 2 is irrational √ 2 is rational  m  n: √ 2=m/n m, n are coprime
    • 18. Group C: Masking Operator Names √ 2 is irrational √ 2 is rational √ 2 is rational
      •  m  n: √2=m/n
      • m, n are coprime
      • √ 2 is irrational
      • contradtion
       m  n: √ 2=m/n m, n are coprime
    • 19. Group D: Notebooks
      • Linear proof style:
      • arrows denote relations
      • arrows labeled by operators
      √ 2 is irrational We assume: √ 2 is rational There exist two numbers n and m in Z, Being coprime, such that √2=n/m 2m=n 2 n 2 is even n is even
    • 20. Group D: Operator Application √ 2 is irrational We assume: √ 2 is rational There exist two numbers n and m in Z, Being coprime, such that √2=n/m 2m=n 2 n 2 is even n is even Search List all
    • 21. Conclusion
      • Used Argument: „As taught at school.“ (???)
        • A lot of „User Wants and User Needs“
        • Partly questionable
      • Discussion results:
      • Presentation
        • Simplified, nested statements
        • Bridge construction paradigm
        • Proof structuring (notebook, expansion, collapsing)
      • Standard interaction facilities
        • Copy&Paste, Drag&Drop, etc.
    • 22. Conclusion (2): System Support
      • Automation Support
        • Of simple steps
        • Verification of introduced islands
        • On demand completion of gaps
        • Copy&Paste for sub proofs
        • History
      • Feedback
        • Check proof/operator arguments
        • Help (e.g. explanations of operators)
      • Hints
        • General advice: „Derive a contradiction!“
        • Rank suggestions
        • Overcome failure (suggest suitable input arguments)
    • 23. Future Work
      • … towards a User Centered GUI ?
      • Prototype development
      • HCI evaluation

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