n-Neighbourhood
n-Neighbourhood
Knowledge Space Theory
The original aim of knowledge space theory was to develop a framework for a non-quanitative assessment, i.e. an assessment that delivers not only some score but more concrete items about what exactly a learner knows and what not. In knowledge space theory, a domain of knowledge is described by a set Q of test problems or items. A learner is desribed by his/her knowledge state, i.e. the subset K ⊆ Q of items s/he is able to solve. A set of knowledge states is called a knowledge structure if it contains the empty set and the full set of items. The set of possible knowledge states can be delimited by prerequisite relationships between the items. Such a knowledge structure is called a knowledge space.n-Neighbourhood
For the learning process, the neighbourhood of the learner's current knowledge state K is very interesting, i.e. the set of knowledge states K' which differ from K by upto n items. Those are the states whence the learner may have come from or which s/he is ready to get to.Further Reading
- Falmagne, J.-C., Koppen, M., Villano, M., Doignon, J.-P., & Johannesen, L. (1990). Introduction to knowledge spaces: How to build, test and search them. Psychological Review, 97, 201-224
- Heller, J., Hockemeyer, C., & Stefanutti, L. (2017). Knowledge Space Theory. Moodle course.
Example Spaces
As example data, knowledge spaces provided by the R package pks (Heller & Wickelmaier, 2013; Wickelmaier et al., 2016) are used. Concretely, the following spaces are used:- Chess
- Held, Schrepp and Fries (1995) derive several knowledge structures for the representation of 92 responses to 16 chess problems. See Schrepp, Held and Albert (1999) for a detailed description of these problems. This app uses the projection of their DST1-structure reduced to the fiurst five items.
- Density
- Taagepera et al. (1997) applied knowledge space theory to specific science problems. The density test was administered to 2060 students, a subtest of five items each is included here.
- Matter
- Taagepera et al. (1997) applied knowledge space theory to specific science problems. The conservation of matter test was administered to 1620 students, a subtest of five items each is included here.
- Doignon & Falmagne
- Fictitious data set from Doignon and Falmagne (1999, chap. 7).
References
Doignon, J.-P., & Falmagne, J.-C. (1999). Knowledge spaces. Berlin: Springer. Held, T., Schrepp, M., & Fries, S. (1995). Methoden zur Bestimmung von Wissensstrukturen — Eine Vergleichsstudie [Methods for determining knowledge structures — a comparing study]. Zeitschrift für Experimentelle Psychologie, XLII (2) ,205–236. Heller, J. & Wickelmaier, F. (2013). Minimum discrepancy estimation in probabilistic knowledge structures. Electronic Notes in Discrete Mathematics, 42, 49-56. Schrepp, M., Held, T., & Albert, D. (1999). Component-based construction of surmise relations for chess problems. In D. Albert & J. Lukas (Eds.), Knowledge spaces: Theories, empirical research, and applications (pp. 41--66). Mahwah, NJ: Erlbaum. Taagepera, M., Potter, F., Miller, G.E., & Lakshminarayan, K. (1997). Mapping students' thinking patterns by the use of knowledge space theory. International Journal of Science Education, 19, 283--302. Wickelmaier, F., Heller, J., & Anselmi, P. (2016). pks: Probabilistic Knowledge Structures. R package version 0.4-0. https://CRAN.R-project.org/package=kstUsing this App
This App illustrates the n-neighbourhood of knowledge states. It consists of five tabs: a very short introduction into used concepts of knowledge space theory, information about the example spaces used in this app, this usage information, the interactive core of the app, and some author and context information. If you do not know knowledge space theory, you should best start with the short introduction.The "Your Turn" Tab
On the left side, you see two dropdown selections where you can select a knowledge space, a knowledge state within this space, and a distance/the size of the n-neighbourhood. On the right side, you see a Hasse diagram of the knowledge space where the selected state and its n-neighbourhood are marked.
The above Hasse diagram shows the knowledge space
with the selected state marked in green and its
1-Neighbourhood marked in yellow
About this App
This App was created within the QHELP project.QHELP was co-funded by the Erasmus+ Programme of the European Commission.
© 2022 Cord Hockemeyer, University of Graz, Austria