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Based on a talk given by Dietrich Albert at
the 28th Annual Meeting of the Society for Mathematical Psychology,
a project was started to further investigate this topic as
a
contribution to nonnumerical test theory.
Abstract
Non-numerical test theory denotes a research program of current
interest in behavioural and social sciences for which some
components already exist. One example is the Knowledge Space
Theory originally developed by Doignon and Falmagne. One advantage
of the non-numerical test theory approach is the low requirement
of scale level combined with the possibility of empirical
validation. This corresponds closely to the status of theories
and research methods in many fields of psychology. A second
advantage is the interpretability of the relationships between
test items by surmise and prerequisite relations which are
non-bijective. For applications in different fields like cognitive,
developmental, educational, and personality psychology, a
generalization of this approach is needed where the tests
and not only the items are the basic elements. Then the prerequisite
relationships between different cognitive functions, developmental
stages, educational stages, and personality traits, respectively,
can be investigated on the basis of non-numerical tests. Thus,
we describe a project during which a theoretical model for
relations between non-numerical tests will be developed. Based
on this modeling and theoretical analysis, we will implement
a software system for generating and evaluating hypotheses
on non-bijective relations between non-numerical tests, for
partitioning and combining tests, and analyzing data. Besides
simulation studies a first application of model and software
to empirical data will be performed.
This project is financed by the Austrian
Science Fund (FWF)
| Project No.:
| P12726-SOZ
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| Applicants:
| O.Univ.-Prof. Dr. Dietrich Albert
Univ.-Prof. Dr. Wilhelm Schappacher
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| Duration:
| March 1998 - Sept 2000
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| Funding:
| ATS 1,373,300.- (EUR 100.000.-)
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Project Team
- Silke Brandt (Postgraduate mathematician
and teacher)
- Cord Hockemeyer (Postgraduate computer scientist)
- Susanne Pötzi (Postdoc mathematician
and teacher, programmer)
- Ali Ünlü (Postgraduate mathematician,
programmer)
- Gudrun Wesiak (Postgraduate psychologist)
Publications & Presentations
Albert, D., & Hockemeyer, C. (1999). Developing Curricula for Tutoring Systems Based on Prerequisite Relationships. In G. Cumming, T. Okamoto & L. Gomez (Eds.), Advanced Research in Computers and Communications in Education: New Human Abilities for the Networked Society (Vol. 2, pp. 325–328). Amsterdam: IOS Press. [PDF]
Albert, D., Wesiak, G., & Ünlü, A. (2007). How to Generate and Validate Hypotheses on Surmise Relations among Tests. Exemplified for Inductive Reasoning Tests. Unpublished manuscript.
Brandt, S., Albert, D., & Hockemeyer, C. (1998, September 28–30). Surmise Relations Between Tests. Talk at the International Conference on Ordinal and Symbolic Data Analysis (OSDA), University of Massachusetts, Amherst.
Brandt, S., Albert, D., & Hockemeyer, C. (1999). Surmise Relations between Tests - Preliminary Results of the Mathematical Modelling. Electronic Notes in Discrete Mathematics, 2 (electronical publication, 15 pages). [PDF]
Brandt, S., Albert, D., & Hockemeyer, C. (2003). Surmise Relations between Tests - Mathematical Considerations. Discrete Applied Mathematics, 127(2), 221–239. [PDF]
Hockemeyer, C. (2001). KST Tools User Manual (Unpublished Technical Report). Institut für Psychologie Karl–Franzens–Universität Graz, Austria. [PDF]
Hockemeyer, C., Albert, D., & Brandt, S. (1998). Prerequisite Relations between Courses. Journal of Mathematical Psychology, 42, 508. [DOC]
Hockemeyer, C., Albert, D., & Brandt, S. (1998, August 31 – September 2). Prerequisite Relationships between Courses. Talk at the 29th European Mathematical Psychology Group (EMPG) Meeting, University of Keele, UK.
Hockemeyer, C., & Pötzi, S. (2001). Documentation of the libsrbi Library (Unpublished Technical Report). Institut für Psychologie Karl–Franzens–Universität Graz, Austria.
Pötzi, S., & Wesiak, G. (2004). SRbT Tools User Manual (Technical Report). Institut für Psychologie, Karl–Franzens–Universität Graz, Austria. [URL]
Ünlü, A., Brandt, S., & Albert, D. (2004). Test surmise relations, test knowledge structures, and their characterizations. Discrete Applied Mathematics, submitted for publication, 76 pages. [PDF]
Wesiak, G. (2003). Ordering Inductive Reasoning Tests for Adaptive Knowledge Assessments: An Application of Surmise Relations between Tests. Unpublished doctoral dissertation, Karl–Franzens–Universität Graz, Graz, Austria. [URL]
Wesiak, G., & Albert, D. (1999, September). Component based Construction of Surmise Relations between Inductive Reasoning Tests. Talk at the 5th Alps–Adria Psychology Conference `Psychology at the turn of the millenium´, Pecs Hungary. [URL]
Wesiak, G., & Albert, D. (1999, December). Vermutungsrelationen zwischen Tests im Bereich des Induktiven Denkens. Vortrag auf der 4. Wissenschaftlichen Tagung der Österreichischen Gesellschaft für Psychologie, Graz, Österreich. [URL]
Wesiak, G., & Albert, D. (2001). Knowledge Spaces for Inductive Reasoning Tests. In K. W. Kallus, N. Posthumus & P. Jimenez (Eds.), Current psychological research in Austria. Proceedings of the 4th scientific conference of the Austrian Psychological Society (ÖGP) (pp. 157–160). Graz: Akademische Druck- u. Verlagsanstalt. [PDF]
Wesiak, G., & Albert, D. (2002, March). Strukturierung Induktiver Denktests auf Basis der Wissensraumtheorie [Structuring inductive reasoning tests based on knowledge space theory]. Vortrag auf der 5. Wissenschaftlichen Tagung der Österreichischen Gesellschaft für Psychologie, Wien, Österreich. [URL]
Wesiak, G., & Albert, D. (2002, September). Strukturierung Induktiver Denktests als Basis für adaptive Diagnoseverfahren [Structuring inductive reasoning tests for adaptive assessment procedures]. Vortrag am 43. Kongress der Deutschen Gesellschaft für Psychologie, Berlin, Deutschland. [URL]
Wesiak, G., & Albert, D. (2003). Adaptive assessment of inductive reasoning based on prerequisite relationships. Poster presented at the 11th Biennial Meeting of the International Society for the Study of Individual Differences, Graz, Austria. [URL]
Software Development
- Software for Working with Surmise Relations
between Items
- Software for Working with Surmise Relations
between Tests
- Software for Generation of Hypotheses
- Generation via the Surmise Relation
- Generation via the Knowledge Space
- Software for Validation of Hypotheses
- Validation via the Surmise Relation
- Validation via the Knowledge Space
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