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Designing a Proof GUI for Non-Experts

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Martin Homik
Martin Homik

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

Économie & financeTechnologie
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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
Motivation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Motivation (2) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Expert GUI: Loui
Towards a User Centered GUI ,[object Object],[object Object],[object Object],[object Object]
Experiment Setting ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Design (120 min) Presentation (15 + 10 min) Discussion
Experiment Remarks ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
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.“
Group A: Text-based Textual presentation of a proof. The same way as taught at school. ,[object Object],[object Object],[object Object],√ 2 is irrational check proof complete proof automatically feedback no logical notation √ 2 is irrational Statement access
Group A: Operator Application ,[object Object],[object Object],[object Object],√ 2 is irrational ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Group B: Bridge Building ,[object Object],[object Object],[object Object],Assumptions Forward Reasoning Goals Backward Reasoning
Group B: Control Panel History System support
Group B: Method Iconisation (Definition-) Expansion Contradiction Insert island (Definition-) Collapse
Group B: Operator Application
Bridge Construction Example Upper bank Lower bank √ 2 is not rational Action: definition application (Hypotheses) (Theorem) ,[object Object],[object Object],[object Object],Action: indirect proof Action: term rewriting ,[object Object],[object Object],[object Object],m 2 =2*n 2 Contradiction
Placing Islands ,[object Object],[object Object],[object Object],m 2 =2*n 2 m is even n is even
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
Group C: Masking Operator Names √ 2 is irrational √ 2 is rational √ 2 is rational ,[object Object],[object Object],[object Object],[object Object], m  n: √ 2=m/n m, n are coprime
Group D: Notebooks ,[object Object],[object Object],[object Object],√ 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
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
Conclusion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Conclusion (2): System Support ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Future Work ,[object Object],[object Object],[object Object]

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Designing a Proof GUI for Non-Experts

  • 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
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  • 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.“
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  • 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
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  • 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
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  • 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
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  • 23.