Jürgen Heller

On the Link between Cognitive Diagnostic Models and Knowledge Space Theory

The present work explores the connections between cognitive diagnostic models (CDM) and knowledge space theory (KST) and shows that these two quite distinct approaches overlap. It is proved that in fact the Multiple Strategy DINA (Deterministic Input Noisy AND-gate) model and the CBLIM, a competence-based extension of the basic local independence model (BLIM), are equivalent. To demonstrate the benefits that arise from integrating the two theoretical perspectives, it is shown that a fairly complete picture on the identifiability of these models emerges by combining results from both camps. The impact of the results is illustrated by an empirical example, and topics for further research are pointed out.

Assessing the local identifiability of probabilistic knowledge structures

Given a collection Q of problems, in knowledge space theory Doignon & Falmagne, (International Journal of Man–Machine Studies 23:175–196, 1985) the knowledge state of a student is the collection K ⊆ Q of all problems that this student is capable of solving. A knowledge structure is a pair (Q, ), where is a collection of knowledge states that contains at least the empty set and Q. A probabilistic knowledge structure (PKS) is a knowledge structure (Q, , π), where π is a probability distribution on the knowledge states. The PKS that has received the most attention is the basic local independence model BLIM; Falmagne & Doignon, (British Journal of Mathematical and Statistical Psychology 41:1–23, 1988a, Journal of Mathematical Psychology 32:232–258, 1988b). To the best of our knowledge, systematic investigations in the literature concerning the identifiability of the BLIM are totally missing. Based on the theoretical work of Bamber and van Santen (Journal of Mathematical Psychology 29:443–473, 1985), the present article is aimed to present a method and a corresponding computerized procedure for assessing the local identifiability of the BLIM, which is applicable to any finite knowledge structure of moderate size.

Minimum Discrepancy Estimation in Probabilistic Knowledge Structures

Practical applications of the theory of knowledge structures often rely on a probabilistic version, known as the basic local independence model. The paper outlines various procedures for estimating its parameters, including maximum likelihood (ML) via the expectation-maximization (EM) algorithm, the computationally efficient minimum discrepancy (MD) estimation as well as MDML, a hybrid method combining the two approaches.

Behavioral and Neurocognitive Evaluation of a Web-Platform for Game-Based Learning of Orthography and Numeracy

Recent years have seen a considerable increase in informal educational environments complementing formal educational settings such as schools. In this chapter, we will report results on the efficacy of a web-platform for game-based learning of orthography and numeracy. Besides the behavioral assessment of the platform, we focused specifically on neurocognitive changes due to training on the platform. These neurocognitive data are particularly informative to understand how game-based learning leads to performance improvements, and also might help us to develop new instructional designs. Our web-based platform hosts several learning games, aiming at fostering orthography and numeracy skills. Learning games enable individual learning independent from formal learning environments—anytime and anywhere. Behavioral results revealed promising learning effects, particularly for orthography. In the next step, neurocognitive changes during arithmetic learning were assessed. Results indicated that arithmetic learning in our informal environment led to strategy changes, previously reported for the development of arithmetic competencies in formal learning settings for both adults and children. Altogether, the findings suggest that improvements in orthography and numeracy can be achieved in joyful and less stressful informational environments such as our web-platform for game-based learning. We suggest that the additional implementation of adaptivity in such learning games to better meet individual needs should further increase obtained training effects in the future. Instructional implications of these findings and the relevance of neurocognitive data for learning are discussed.

Recent Developments in Competence-based Knowledge Space Theory

A saying attributed to Kurt Lewin (1951) states ‘There is nothing so practical as a good theory.’ Accordingly, the theory and models outlined in Chapter 11 of this volume have many practical consequences and can be applied for instance in personalized competence assessment, individualized eTeaching and eLearning, and expert query. Furthermore, for practical reasons recent developments in Competence-based Knowledge Space Theory (CbKST) have to be taken into account.

Applying competence structures for peer tutor recommendations in CSCL environments

Competence structures of the content and competence modelling of the learners provide well-suitable means for finding appropriate peer tutors in CSCL based on asynchronous messaging and annotations. Various criteria for the appropriateness of potential peer tutors can be discussed. An internet-based system used as a large scale Web experiment can then also deliver data for evaluating such criteria.

Mittenbildung bei achromatischen Farben

Zusammenfassung. Experimentelle Befunde zur Wahrnehmung achromatischer Farben basieren nahezu ausschlieslich auf ordinaler Information aus Farbabgleichen. Zur Untersuchung von Invarianzeigenschafte...

Prosodiya - A Mobile Game for German Dyslexic Children.

Approximately 4–10% of the German population suffers from developmental dyslexia. The learning disorder afffects educational, personal, and social development of children in a negative way. Mobile serious games have the potential to support dyslexic primary-school children in addition to school support and learning therapy. We propose such a mobile serious game called “Prosodiya”, with the help of which dyslexic children can improve their reading and writing performance. Prosodiya includes innovative and evidence-based interventions that focus on improving the awareness of linguistic features related to syllable stress. We report the results of a pilot study of a preliminary version of the game. Results indicate that the children enjoyed playing the game, that their motivation was maintained, and that they wanted more levels.

The locus of perceived equidistance in binocular vision

Empirical studies of the locus of perceived equidistance in binocular vision have revealed a characteristic change of its form, depending on absolute distance. This result is commonly taken to indicate influence of vergence-related binocular information, a conclusion that is by no means exclusively dictated by the data. Heller (1997) has suggested an alternative theoretical account that is based on the idea of independently combining the outcome of monocular input transformations without any form of binocular interaction. This article provides an experimental test of the structural assumption lying at the core of the axiomatic foundation of Heller’s theory. I test the so-called Reidemeister condition under reduced cue conditions in two settings for each of 7 subjects. The results provide strong evidence for the validity of the Reidemeister condition and thus challenge the view that the locus of perceived equidistance depends on vergence-related binocular information. The discussion of the factors contributing to the monocular input transformations emphasizes the role of the optical properties of the eyes.

An Invitation to Knowledge Space Theory

It has been mentioned on many occasions that Formal Concept Analysis and KST, the theory of Knowledge Spaces, introduced by J.-P. Doignon and J.-C. Falmagne, are closely related in theory, but rather different in practice. It was suggested that the FCA community should learn from and contribute to KST. In a recent workshop held at Graz University of Technology, researchers from both areas started to combine their views and tried to find a common language. This article is a partial result of their effort. It invites FCA researchers to understand some ideas of KST by presenting them in the language of formal contexts and formal concepts.