Beginnjahr 2014 Abschlussjahr 2016


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Schlagwörter EnglischTheory of Inquiry Learning Arrangements, inquiry learning, AuRELIA concept, special self-efficacy, mathematics didactics

This article explores the application of a self-determined Inquiry Learning arrangement according to the AuRELIA-concept in the field of mathematics didactics and shows its effectiveness with regard to the special self-efficacy of student teachers concerning the realisation of inquiry-based learning arrangements. Moreover, it aims to show to what extent student teachers consciously experience the criteria of Inquiry Learning when carrying out an AuRELIA-project.

This article deals with the application of the AuRELIA-concept of self-determined Inquiry Learning in the context of teacher education. AuRELIA is an acronym for “Authentic Reflective Exploratory Learning and Interaction Arrangement”. The project referred to in this article explores possible ways in which the new concept might be implemented in academic teacher education by testing and evaluating the learning arrangement, which was developed in the context of secondary education,in the field of mathematics didactics. Moreover, using the example of mathematics didactics, it will be discussed if AuRELIA, which claims to be open to all subject areas, especially to the natural sciences (Reitinger, 2012a, p. 75), can live up to these expectations.

This article provided a brief introduction of the concept AuRELIA, a learning arrangement which facilitates self-determined Inquiry Learning, and described how student teachers became acquainted with and experienced the concept in a seminar about mathematics didactics. Subsequent studies to prove Hypotheses 1 and 2 showed that experiencing the learning setting brought about an increase in the self-efficacy of the student teachers concerning their own realization of the concept in a school class (H1).

Likewise, it could be shown that the criteria of Inquiry Learning according to Reitinger evolved to a large extent in the phase of learning according to the AuRELIA-concept (H2). It is hoped that student teachers will be able to draw on their individual learning experiences and knowledge gained concerning ways in which the concept can be organized in their attempts to conduct lessons according to the AuRELIA-concept themselves.

Lit: Reitinger, J. (2012a). „... hinter den Dingen...“. Exemplarische Beiträge zur Naturwissenschaftsdidaktik. Aachen, Germany: Shaker.


Hypothesis 1: The implementation of the AuRELIA-concept increases the special self-efficacy concerning self-determined arrangements for Inquiry Learning.

Hypothesis 2: Students who were taught according to the AuRELIA-concept rate the extent to which they experienced Inquiry Learning higher than students who were taught in a traditional seminar setting.

The design of the study includes three measuring points (O1-O3) for each of its parts. At O1, a questionnaire including items to measure self-efficacy was used. In the following treatment phase, groups MB 2 and MB 4 experienced self-determined Inquiry Learning according to the concept AuRELIA. The control groups MA 2 and MA 4 dealt with similar topic areas in a traditional seminar setting in which the tutor introduced the contents frontally, followed by a phase of solving pre-defined tasks. At the end of the treatment phase for groups MB 2 and MB 4, the questionnaire covering self-efficacy was used again in groups MB 2, MB 4, MA 2,and MA 4.

Following this phase, MB 2 and MB 4 switched roles with MA 2 and MA 4, as described above. MA 2 and MA 4 experienced learning according to the concepts AuRELIA and MB 2 and MB 4 served as control groups which differed from MA 2 and MA 4 insofar as those student teachers had experienced AuRELIA in the treatment phase before and had, therefore, already gained insight in Inquiry Learning. At the end of this second treatment phase for groups MA 2 and MA 4, the questionnaires were used for a third time (O3) in all groups.

In addition, groups MB 2 and MB 4 were asked to fill in another questionnaire after trying out and going through self-determined Inquiry Learning in a seminar in Mathematics education (Treatment phase) which aimed to measure the extent to which they self-assessed their learning to be characterized by the criteria of Inquiry Learning in order to collect data for hypothesis 2. Moreover, groups MA 2 and MA 4 were asked to complete the questionnaire about Inquiry Learning after trying out and going through self-determined Inquiry Learning in a seminar in Mathematics education (Treatment phase) which aimed to collect data that could be analysed in order to prove Hypothesis 2.

In this phase, the control groups dealt with the topic areas of ”modelling“ and “considerate estimation”, as these areas seemed to perfectly match the ones which were chosen by student teachers for their AuRELIA-projects.


Discussion of the Results: Hypothesis 1

In general, the means of the self-assessment concerning the special self-efficacy were relatively high in all test groups at the beginning of the project. In groups MB 2 and MA 2, no significant differences could be determined at the three measuring points, however, the means showed an increase in both groups MB 2 and MA 2 in the phase after the treatment, which hints at a positive effect of the treatment. The t-tests for independent groups in group MB 4 and MA 4, which showed a highly-significant result with a large-sized effect at O2, confirm the effectiveness of the treatment with regard to self-efficacy. This significant difference cannot be detected anymore at O3. This supports the conclusion that the treatment was also effective concerning the hypothesis in group MB 4 and MA 4.

The pairwise comparisons show a significant result with a large-sized effect between O2 and O3 (Treatment-phase) in group MA 2. This increase can be attributed to the effectiveness of the treatment. For the same reason a significant increase with a large-sized effect could be determined in group MB 4 between O1 and O2 (Treatment-phase). In group MA 4 a significant difference with a large-sized effect was shown between O2 and O3 (Treatment- phase), which could be ascribed to the treatment. However, because of the small sample size, generalization can only be made with reservations.

Discussion of the Result: Hypothesis 2

The application of the AuRELIA-concept led to a highly significant result in all test groups with large-sized, resp. very large-sized effects concerning experiencing the criteria of Inquiry Learning. Thus, it could be shown by means of the scale CILI-ß that student teachers who tried out AuRELIA in mathematics didactics met the criteria of Inquiry Learning according to Reitinger (2015b) to a large extent, and Hypothesis 2 was confirmed by the results of the study. However, the small sample size relativizes this difference. For the same reason, the results obtained by application of interference statistics should not be overgeneralized.

Lit.: Reitinger, J. (2015b). Self-Determination, Unpredictability, and Transparenca: About the Nature and Empirical Accessibility of Inquiry Learning. In: Schulpädagogik heute. Transparenz – im Unterricht und in der Schule. Heft 12, 6. Jahrgang. Kassel, Germany: Prolog-

Erhebungstechniken und Auswahlverfahren

In this project, first and second year student teachers of mathematics were encouraged to experience the seven phases of the AuRELIA-concept. They were asked to develop and solve tasks with regard to Inquiry Learning related to “modelling”, one of the areas of competence in mathematics, choosing freely within the topic areas “numbers, data, facts” in the context of a teacher training college and its teacher trainees.

The study focuses on teacher education. It aims to find out to what extent student teachers consider themselves enabled to apply the concept in a classroom after experiencing and testing the situation of the inquiry learner themselves (see Hypothesis 1). Moreover, the study explores if and to what extent teacher trainees implemented the criteria of Inquiry Learning when carrying out the learning arrangement (see Hypothesis 2). A quantitative analysis was carried out in order to examine the following hypotheses.

In order to examine the two hypotheses, four seminar groups were taught according to the AuRELIA-concept. These groups included in the project and the survey equalled the ones which had already been formed for various other classes in the two different years of teacher training, namely MB 2, MA 2, MB 4, and MA 4. The seminar was taught by the same person in all groups.

Publikationen (+ link zum OBV)
  • Hauer, B. (2016). AuRELIA meets Mathematic Didactics: Inquiry Learning in Student Teacher Training. In J. Reitinger, C. Haberfellner, E. Brewster & M. Kramer. (Eds.). Theory of Inquiry Learning Arrangements: Research, Reflection, and Implementation, S 121 – 136
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Lehren und Lernen (Prozesse und Methoden)
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