Proposal view
| Proposal Type: | Individual Paper |
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| Domain: | Teaching and Teacher Education |
| SIG: | Teaching and Teacher Education |
| Type | Submitted Paper |
| Equipment |
PC and projector |
| Paper Details |
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| Title | General instructional beliefs and situational beliefs of mathematics teachers |
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| Abstract | Mathematics instruction is required to support the acquisition of routines not only in a teacher-centred and small-stepped manner that emphasises the associationist aspect of learning, but also to stimulate the fostering of a deeper understanding of learning contents in the sense of a constructivist understanding of teaching and learning. The video-based study presented here compares 20 German and 18 Swiss mathematics teachers regarding their belief-system and related instructional actions, and examines links between general pedagogical content beliefs and situational beliefs (based on concrete instructional action). The general pedagogical beliefs focus on the constructivist and the associationist understanding of teaching and learning of the teachers, the situational beliefs on the concrete teaching actions in an instructional unit on the introduction to Pythagorean theorem, also measured by video. In the current study, the German teachers examined rate themselves on the one hand as more constructivist than the Swiss teachers, but by contrast, it was observed that Swiss teachers stimulate the linking of mathematical principles significantly more frequently in their instruction. Based on this finding, the current investigation looks for links between general and situational beliefs. The results indicate that for both the German and Swiss teachers, their general beliefs concerning a constructivist understanding of teaching and learning is hardly reflected in the situational beliefs. Possible explanations for this low correspondence include burdensome general conditions and a low self-efficacy of the teachers. Therefore, in a further step, the links between general instructional beliefs and situational beliefs were examined controlling for these two factors. In line with expectation, several systematic links between constructivist beliefs and situational beliefs were apparent, albeit primarily only in the Swiss teachers. |
| Summary | Mathematics instruction is required to not only support the acquisition of routines in a teacher-centred and small-stepped fashion, but also to stimulate the fostering of a deeper understanding of the learning contents (De Corte, 2004). These demands mark a transition from a more behaviourist inspired learning concept that emphasises the associationist aspect of learning, to a constructivist concept of teaching and learning that focuses on the active, constructive and cumulative character of the learning activity. While there is a broad consensus on this matter in the context of teaching and learning research, the question arises of the extent to which the constructivist teaching and learning concept are adopted by teachers and are reflected in their belief-system. According to the literature, e. g. (Calderhead, 1996), the belief-system consist of, inter alia, general beliefs on the one hand and situational beliefs related to concrete subjects, contents and instructional situations and actions on the other. This study compares 20 German and 18 Swiss mathematics teachers regarding their general pedagogical content beliefs and situational beliefs in terms of a constructivist understanding of teaching and learning processes as well as associated instructional actions, and examines links between general and situational beliefs. It is part of a German-Swiss study on teaching and mathematical understanding (Klieme & Reusser, 2003). Video recordings of the instruction are combined with complex surveys of teachers, pupils and pupils’ parents throughout the course of a whole school year and enable a microanalysis of the instruction with the greatest possible comparability. The general beliefs were measured through a questionnaire, the situational beliefs through a semi-structured interview. The interview took place after the observation of the three introductory lessons to Pythagorean theorem and referred to selected occurrences in the lessons. The interview was coded by means of content analysis, this allows the teacher statements to be categorized and quantified. The coding of the videotaped lessons was carried out using developed codings following the manual used in the TIMSS. Earlier investigations showed that German teachers assess themselves as more constructivist than Swiss teachers (Lipowsky, et al., 2003), but describe their instruction as more questioning-developing (Pauli & Reusser, 2003). In the current study too, the German teachers examined rate themselves as more constructivist and as less associationist than the Swiss teachers, but by contrast, it was observed that the Swiss teachers stimulate the linking of mathematical principles significantly more frequently in their instruction (Leuchter, et al., 2006). In order to look more deeply at the question of implementing the constructivist maxim in instruction, general beliefs and specific, situational beliefs were related to one another. Initially – without controlling for further conditions – no links were apparent between instructional quality aspects compatible with constructivist oriented teaching (as expressed in the interview) on the one hand and the constructivist beliefs of the teachers (as measured in the questionnaire) on the other. Thus it was confirmed that there is a great distance from knowledge to action. In this respect, our finding is in accordance with the incongruities between beliefs and actions of teachers repeatedly reported in the literature (for a summary, cf. Calderhead, 1996; Opdenakker & Van Damme, 2006). Pressure to act and burdensome general conditions might stand in the way of implementing pedagogical beliefs. In order to address this possibility, in our study, the influence of burdensome general conditions and self-efficacy on the association between general and situational beiliefs was also measured. If one controls for the perceived burden and the self-efficacy of the teachers, the comparison of the two country samples shows that in German teachers, the constructivist general beliefs hardly corresponds to analogous situational beliefs. A link in line with expectations is shown in the German teachers only with regard to the associationist orientation. By contrast, in Swiss teachers, several links are apparent between situational beliefs and both associationist and constructivist beliefs. The partial correlations therefore point in the expected direction: when controlling for burdensome general conditions and self-efficacy of the teachers, stronger links can be detected between the teaching and learning concept examined on a more general level and the situational beliefs. On the whole, the interviews relating to the instruction of the teachers show that the teachers have difficulties in relating theoretically based central ideas like those of a constructivist understanding of mathematical teaching and learning processes to concrete situations of their teaching and in reflecting the decisions made on the basis of this understanding. In order for a constructivist understanding of teaching and learning to be actually implemented on the action and interaction level in everyday teaching, however, corresponding competences and knowledge are necessary. These should put teachers in a position to, on the one hand, create suitable learning situations that are compatible with a constructivist understanding of teaching and learning, and, on the other hand, to analyse the instruction on the basis of a theoretically founded understanding of teaching and learning. Calderhead, J. (1996). Teachers: Beliefs and Knowledge. In D. C. Berliner & R. C. Calfee (Hrsg.), Handbook of Educational Psychology (S. 709-725). New York: Macmillan. De Corte, E. (2004). Mainstreams and Perspectives in Research on Learning (Mathematics) From Instruction. Applied Psychology, 53 (2), S. 279-310. Klieme, E. & Reusser, K. (2003). Unterrichtsqualität und mathematisches Verständnis im internationalen Vergleich - Ein Forschungsprojekt und erste Schritte zur Realisierung. Unterrichtswissenschaft, 31 (3), S. 194-205. Leuchter, M., Pauli, C., Reusser, K. & Lipowsky, F. (2006). Unterrichtsbezogene Überzeugungen und Kognitionen von Lehrpersonen. Zeitschrift für Erziehungswissenschaft, 9 (4), in press. Lipowsky, F., Thussbas, C., Klieme, E., Reusser, K. & Pauli, C. (2003). Professionelles Lehrerwissen, selbstbezogene Kognitionen und wahrgenommene Schulumwelt - Ergebnisse einer kulturvergleichenden Studie deutscher und Schweizer Mathematiklehrkräfte. Unterrichtswissenschaft, 31 (3), S. 206-238. Opdenakker, M.-C. & Van Damme, J. (2006). Teacher characteristics and teaching styles as effectiveness enhancing factors of classroom practice. Teaching and Teacher Education, 22, S. 1-21. Pauli, C. & Reusser, K. (2003). Unterrichtsskripts im schweizerischen und im deutschen Mathematikunterricht. Unterrichtswissenschaft, 31 (3), S. 238-272. |
| Keywords | Constructivism Mathematics education Teacher cognition |
| Appendices | |
| Authors | ||||||
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| Name | Surname | Institution | Country | EARLI Number | Presenting | |
| Miriam | Leuchter | Teacher Training University of Central Switzerland | Switzerland | miriam.leuchter@phz.ch | * | |
| Christine | Pauli | University of Zurich | Switzerland | cpauli@paed.unizh.ch | ||
| Kurt | Reusser | University of Zurich | Switzerland | reusser@paed.unizh.ch | ||
| Frank | Lipowsky | University of Kassel | Germany | Lipowsky@uni-kassel.de | ||
