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Der „epistemologische Nebel“. Irritationen als Chance
Abstract
Die Qualität von Unterricht kann langfristig nur über Lehrpersonen verbessert werden. Innovative Designs können diese Lehrpersonen aber irritieren und erhöhte Unsicherheit erzeugen. Ob diese Unsicherheit als Ausgangspunkt von Veränderung genutzt wird, hängt sehr davon ab, wie das Design fachlich und fachdidaktisch gedeutet wird, welche Erfahrungen damit gemacht werden und wie diese reflektiert werden. Dies wiederum wird gefiltert durch die epistemologischen Beliefs sowie durch die Trias beliefs – assumptions – knowledge zum Lehren und Lernen des Faches, kurz BAKs genannt. Vorgestellt wird eine duale Fallstudie zu zwei Mathematiklehrpersonen, die auf das gleiche innovative Design unterschiedlich reagieren. Irritationen mit dem Design und seine Implementation können als Chance und Anschub genutzt werden, den eigenen Unterricht und sein professionelles Umfeld zu verändern, etwa durch den Aufbau kollegialer Kooperation, die unterschiedliche primäre Bedürfnisse erfüllen können. Ist diese Irritation gering oder bleibt sie gar aus, dann gibt es auch keinen Anlass für explizit innovative Veränderungsschritte. Dennoch kann sich Unterricht weiter entwickeln, etwa durch langsames Einflechten passender Ideen in die eigene Unterrichtskonzeption und deren Umsetzung, wie in der vorliegenden Fallstudie berichtet wird.
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This paper is about the development of a task sequence to help overcome the fragmented understanding of the ‘function’ concept that students often bring with them into the initial stage of upper secondary school level. Our aim is to make the students’ use of functions more flexible in certain respects, for example when functions are required to be used as tools for modelling. The core idea of our task design is to interpret formulas as functional relations. The tasks are developed along the lines of a Design-Based Research approach in which several theoretical approaches are employed in a complementary way. The paper will show how this complementarity frames and informs the design as well as the analysis of data about how a student solves the tasks. Mediated by the task sequence, students’ development in terms of how their use of functions becomes more flexible is reconstructed. In the analysis, a key constraint for developing a flexible use of functions is identified: their poor understanding of the coordinate system and its scaling and utilization as a reference space for graphical representations of functions.
In this chapter, we describe a methodology for conducting educational design research to support system-wide instructional improvement in mathematics and draw on one of the few design studies that does this as an illustrative case. Design studies conducted at the level of an educational system are interventionist in nature, and can address both the complexity of educational settings and the problems that educational system leaders, school leaders, and teachers encounter as they work to improve the quality of classroom instruction, school instructional leadership, and ultimately, students’ mathematics learning. This chapter describes the theoretical background for this approach, in which the issue of what it takes to support instructional improvement on a large scale is framed as an explicit focus of empirical investigation.
Issues of developing lesson study practices as a model of professional learning across
boundaries are explored in this paper from a Cultural and Historical Activity theoretic
perspective. We consider the work of professional learning communities as teachers
seek to expand the object of their classroom activity and in doing so identify systemic
contradictions and personal conflicts that arise, leading to the potential for expansive
learning. Further to this, we identify potential use for theory-in-action and directions
for future research and development.
The Regional Educational Laboratory - Southwest (REL Southwest) conducted a systematic and comprehensive review of the research-based evidence on the effects of professional development (PD) on growth in student achievement in three core academic subjects (reading/ELA, mathematics, and science). The primary goal of this study was to address the question, What is the impact of teacher participation in professional development on student achievement? Nine studies emerged as meeting What Works Clearinghouse (WWC) evidence standards, from more than 1,300 manuscripts identified as potentially relevant. Although the number of studies that met evidence standards was small, the average overall effect size of 0.54 was observed when examined within the three content areas included in the review. The consistency of this effect size indicates that across all forms and content of PD, providing training to elementary school teachers does have a moderate effect on their students' achievement. However, because the average number of contact hours averaged almost 49 hours across the nine studies, the total contact hours must be substantial to get such an effect size. Because of the limited number of studies and the variability in the PD that was represented among the nine studies we examined, we were unable to make any conclusions about the effectiveness of specific PD programs or about the effectiveness of PD by form, content, or intensity. The following are appended: (1) Methodology; (2) Protocol for the review of research-based evidence on the effects of professional development on student achievement; (3) Key terms and definitions related to professional development; (4) List of keywords used in electronic searches; and (5) Relevant studies, listed by coding results. (Contains 3 boxes, 2 figures, 9 tables, and 3 notes.) [This report was produced for the National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences (IES) by Regional EducationalLaboratory Southwest administered by Edvance Research.]
Es wird das Design-Projekt “Der Funktionsbegriff im Übergang zur Sekundarstufe II” aus der Mathematikdidaktik beschrieben. In diesem Projekt sollen Erkenntnisse darüber gewonnen werden, wie der fragmentierte Umgang mit Funktionen, den Lernende oft aus der Sekundarstufe I mitbringen, überwunden werden kann. Insbesondere soll der Frage nachgegangen werden, welche Aspekte der Lernökologie diesen Prozess fördern oder behindern können. Dazu wird ein Design konzipiert, das in seiner Umsetzung funktional-flexibilisierende Deutungen bekannter geometrischer Formeln anregt. Hierbei kommen Theorien zum Einsatz, welche die institutionelle Lernebene mit den individuellen und kollektiven Lernprozessen verbinden.
In research literature, the often lamented lack of teacher cooperation at German schools Is explained by the so-called uncertainty of the teaching profession. The authors develop a systematization of the present results of school-related research on uncertainty on the basis of the transactional model of stress according to Lazarus (1991), thus providing a gateway to this topic, which has so far been underrepresented in German-language research. The usefulness of this model of uncertainty for the formulation of complex research hypotheses and for the interpretation of empirical data is Illustrated on the basis of a re-analysis of the record of PISA-2003 I Plus.
We propose a new model for framing teacher education projects that takes both the research and the institutional dimensions into account. The model, which we call Meta-didactical Transposition, is based on Chevallard’s anthropological theory and is complemented by relevant elements that focus on the specificity of both researchers’ and teachers’ roles, while enabling a description of the evolution of their praxeologies over time. The model is illustrated with examples from different Italian projects, and it is discussed in light of current major research studies in mathematics teacher education.
Whereas much is known about designing effective continuous professional development (CPD) for teachers, little is known about spillover effects of CPD by fostering collegial interactions. In this respect, the self-efficacy expectancy of multipliers to spread CPD issues within their own school is an important predictor for scaling. Self-efficacy can be fostered through various sources within CPD courses, including role-plays and practice phases to test issues. One essential endeavor lies in initiating collaboration in professional learning communities (PLCs). The study discussed here focuses on two courses explicitly supporting multipliers to actively engage in PLCs. In a pre/post-design, participants’ development of self-efficacy was measured in relation to collaboration, and compared with that of a control group. As instrument we applied an adapted version of the self-efficacy scale by Schwarzer and Jerusalem (Skalen zur Erfassung von Lehrer- und Schülermerkmalen, (1999), which yielded a high internal reliability (Cr alpha = 0.950). Our results point to different developments within the two specific CPD courses, with one course featuring a significant development of middle size effect (d = 0.31). In addition, developments were found to differ with respect to the duration of the CPD course.
The literature on teacher uncertainty suggests that it is a significant and perhaps inherent feature of teaching. Yet there is disagreement about the effects of these uncertainties on teachers as well as about the ways that teachers should regard them. Recognition of uncertainties can be viewed alternatively as a liability or an asset to effective teaching. Findings from the literature on uncertainties in teaching are summarized and analyzed, including explanations in the research about what accounts for and contributes to uncertainties. Recommendations for research and professional development are provided.
In this dissertation, the field of mathematics teacher professional development is explored both from a theoretical and an empirical perspective. First, an overview on the main theoretical areas is given that encompasses identifying the relevant variables and processes. Second, the focus of the empirical approach is to get insight into what makes professional development successful from a teacher's perspective. The initiative "Mathematics Done Differently" in Germany is presented, in whose context the data of the empirical study was gathered. Quantitative and qualitative data yielded several dimensions relevant for mathematics teacher professional development. The empirical findings led to postulating a model describing teachers' individual growth pathways and providing implications for constructing practices that are based on what teachers really need.
J.): Foundations. A monograph for professionals in science, mathematics, and technology education - Professional Development That Supports School Mathematics Reform
- R Borasi
- J Fonzi