Enhanced Personalised Learning Support of Computer Algebra Systems Christian Gütl Institute of Information Systems and Computer Media (IICM), Graz University of Technology, Austria School of Information Systems, Curtin Univerity of Technology, Perth, WA Alexander Nussbaumer (Presenter) Department of Psychology, University of Graz, Austria Knowledge Management Institute, Graz University of Technology, Austria CADGME 2009 Hangenberg, Austria 12 July 2009
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Enhanced Personalised Learning Support of Computer Algebra Systems
Enhanced Personalised Learning Support of Computer Algebra Systems. Christian Gütl Institute of Information Systems and Computer Media (IICM), Graz University of Technology, Austria School of Information Systems, Curtin Univerity of Technology, Perth, WA Alexander Nussbaumer (Presenter) - PowerPoint PPT Presentation
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Enhanced Personalised Learning Support of Computer Algebra Systems
Christian GütlInstitute of Information Systems and Computer Media (IICM), Graz University of Technology, Austria
School of Information Systems, Curtin Univerity of Technology, Perth, WA
Alexander Nussbaumer (Presenter)Department of Psychology, University of Graz, Austria
Knowledge Management Institute, Graz University of Technology, Austria
CADGME 2009Hangenberg, Austria
12 July 2009
12 July 2009 CADGME 2009 2
Agenda
• Introduction
• Isabelle for Calculations in Applied Mathematics (ISCA)
• Competence-based Knowledge Space Theory (CbKST)
• Combining both Approaches
• Implemenation
• Conclusion and Outlook
12 July 2009 CADGME 2009 3
Introduction
Isabell for Calculations in Applied Mathematics Project
ISAC System
Single stepping CAS
Focus on micro level (single problems)
+ help on solving problems
- no adaptation, learning path, profile
Competence-based Knowledge Space Theory
CbKST Tools
Psychological theory and application
Focus on macro level (combination of problems)
+ user knowledge, learning paths
- assessment items are "black boxes"
Combining both approaches
=> assessment and guidance on micro and macro level
=> improvement of ISAC through CbKST
=> improvement of CbKST through ISAC
12 July 2009 CADGME 2009 4
Isabell for Calculations in Applied Mathematics (ISAC)
ISAC can automatically solve algebraic tasks … and …..
ISAC is useful for educational purposes, because:
• solution can also be done step by step (single stepping system) by rewriting terms
• interaction with learner
• learner gets feedback from ISAC after each step
• rules applied in each step are revealed to the learner
• learner is supported in each step
• ISAC "knows" the rules needed to solve a term
• ISAC "knows" if the learner can solve a problem AND "knows" which rules the leaner can apply or not apply
Usually mathematical learning systems only "know" if a learner can solve a problem or not
12 July 2009 CADGME 2009 5
Isabell for Calculations in Applied Mathematics (ISAC)
12 July 2009 CADGME 2009 6
Isabell for Calculations in Applied Mathematics (ISAC)
12 July 2009 CADGME 2009 7
Isabell for Calculations in Applied Mathematics (ISAC)
12 July 2009 CADGME 2009 8
Competence-based Knowledge Space Theory (CbKST)
Knowledge Space Theory (KST) - behaviouristic theory
• knowledge domain (Q) := set of problems
• prerequisite relations between problems due to psychological reasons
• knowledge state := problems a person can solve (subset of Q)
• learning goal := problems a person should be able to solve
Example: Q = {a, b, c, d, e}
a) 378 x 605 = ?b) 58.7 x 0.94 = ?c) 1/2 x 5/6 = ?d) 30% of 34?e) Gwendolyn is 3/4 as old
as Rebecca. Rebecca is 2/5 as old as Edwin. Edwin is 20 years old. How old is Gwendolyn?
c
e
b
d
a
12 July 2009 CADGME 2009 9
Competence-based Knowledge Space Theory (CbKST)
Knowledge Space Theory (KST) - behaviouristic theory
• knowledge structure := set of possible knowledge states with respect to prerequisite relations between problems