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This paper tries to answer the question whether the promising Content and Language Integrated Learning (CLIL) teaching method also has positive effects on the pragmatic competences of CLIL students compared to their peers in mainstream English as a Foreign Language (EFL) classrooms. To avoid deviances caused by other factors external to the teaching method, only students who have a similar language background were selected for the study by means of a questionnaire. Data on the articulations of requests, thanks, complaints, apologies, invitations, refusals and advice was collected during videotaped English role plays and role enactments. After the role plays/role enactments, students were interviewed about their performance and were given German Discourse Completion Tests (DCTs) to allow a comparison between respective articulations in their L1 and L2. Furthermore, teachers were questioned about the speech acts they used in CLIL and EFL classes and their judgements about the students’ possible activities.
We consider groups defined by non-empty balanced presentations with the property that each relator is of the form, where x and y are distinct generators and is determined by some fixed cyclically reduced word that involves both a and b. To every such presentation we associate a directed graph whose vertices correspond to the generators and whose arcs correspond to the relators. Under the hypothesis that the girth of the underlying undirected graph is at least 4, we show that the resulting groups are non-trivial and cannot be finite of rank 3 or higher. Without the hypothesis on the girth it is well known that both the trivial group and finite groups of rank 3 can arise.
In the last three decades many research studies focused on the topic of multiple representations and their role for learning mathematics. As a result, there is a broad consensus in the scientific community that dealing with multiple representations in the mathematics classroom is a highly relevant matter. However, research addressing the role of the teachers in this context is still scarce. Consequently, this dissertation study raises the question of how much teachers know about and acknowledge this key role of multiple representations for the mathematics classroom. To this end, not only different aspects of teachers' specific professional knowledge and their views were investigated, but also their noticing of changes of representations in instances of student-teacher interaction, which can be seen as a theme-specific noticing. Using a multi-layer model of professional knowledge, this study addresses in particular questions of how such specific aspects of professional knowledge are interrelated and what components of knowledge and views play a role for the teachers' theme-specific noticing.
These research interests were addressed in the scope of three substudies, each of them including two different subsamples (English pre-service teachers/German pre-service teachers, pre-service teachers/in-service teachers, respectively in-service teachers at academic track secondary schools/in-service teachers at secondary schools for lower attaining students), in order to explore the possible roles of cultural background, teaching experience, and school types.
The different aspects of specific professional knowledge and views were assessed by means of a questionnaire instrument. For eliciting the teachers' theme-specific noticing, vignette-based questions were implemented. The data was analyzed mainly by quantitative methods, was however complemented by a qualitative in-depth analysis focusing on how the teachers' theme-specific noticing was informed by different components of their professional knowledge.
The results of this study suggest that the participants did not fully understand the key role of multiple representations for learning mathematics in the sense of their discipline-specific signicance and thus indicate specific needs for teacher education and professional development. Differences between the subsamples of teachers became apparent especially regarding the teachers' more situated professional knowledge and their noticing with respect to dealing with multiple representations. Furthermore, the findings of this study underpin the assumption that within the spectrum between teachers' situated and global professional knowledge and views regarding dealing with multiple representations, different components may be distinguished and suggest that in particular all of these components may play a role for teachers' theme-specific noticing.
This volume is largely about nontraditional data; this paper is about a nontraditional visualization: classification trees. Using trees with data will be new to many students, so rather than beginning with a computer algorithm that produces optimal trees, we suggest that students first construct their own trees, one node at a time, to explore how they work, and how well. This build-it-yourself process is more transparent than using algorithms such as CART; we believe it will help students not only understand the fundamentals of trees, but also better understand tree-building algorithms when they do encounter them. And because classification is an important task in machine learning, a good foundation in trees can prepare students to better understand that emerging and important field. We also describe a free online tool—Arbor—that students can use to do this, and note some implications for instruction.
Fragestellungen zur Konzeptualisierung und Messung professionsbezogener Kompetenzen von Lehrkräften stellen ein hochaktuelles Thema in der mathematikdidaktischen Forschung dar (z.B. Kunter et al., 2013; Kaiser et al., 2015). Trotz unterschiedlicher Ansätze in diesem Bereich besteht weitgehend Konsens darüber, dass Kompetenzen die persönlichen Voraussetzungen zur erfolgreichen Bewältigung berufsspezifischer situationaler Anforderungen beschreiben (Baumert & Kunter, 2013) und prinzipiell erlernbar und vermittelbar sind (Weinert, 2001b). Es gibt jedoch keine „Kompetenz“ per se, da die Beschreibung einer solchen stets einen relevanten berufsspezifischen Kontext voraussetzt (Hartig, 2008). Der Ausgangspunkt zur Beschreibung und Definition einer professionsbezogenen Kompetenz für Lehrkräfte sind folglich die beruflichen Anforderungen, die Lehrkräfte erfüllen müssen, um in Interaktion mit den Schülerinnen und Schülern die Lerngelegenheiten bereitzustellen, die verständnisvolle Lernprozesse ermöglichen (Lindmeier, 2011; Koeppen et al., 2008; Baumert & Kunter, 2013). Für Mathematiklehrkräfte wurde der Umgang mit vielfältigen Darstellungen als eine solche zentrale Anforderung beschrieben (Hill, Schilling & Ball, 2004; Ball, Thames & Phelps, 2008). Zahlreiche Studien weisen darauf hin, dass hierbei die Wechsel zwischen unterschiedlichen Darstellungsformen komplexe kognitive Prozesse erfordern und oftmals für viele Schülerinnen und Schüler zu einer Lernhürde werden (z.B. Ainsworth, Bibby & Wood, 1998; Duval, 2006; Ainsworth, 2006). Lehrkräfte benötigen daher spezifisches Wissen in diesem Bereich, um die Lernenden bei Darstellungswechseln unterstützen zu können (Duval, 2006; Mitchell, Charalambous & Hill, 2014; Dreher & Kuntze, 2015a, b). Lehrkräfte müssen jedoch auch in der Lage sein, Unterrichtssituationen zum Umgang mit Darstellungen zu analysieren, also Beobachtungen in Unterrichtsituationen mit diesem Wissen zu verknüpfen, um potentiell schwierige Darstellungswechsel erkennen zu können (Friesen, Dreher & Kuntze, 2015; Friesen & Kuntze, 2016). Es besteht weitgehend Konsens darüber, dass diese Analyse von Unterrichtssituationen eine wesentliche Voraussetzung dafür darstellt, dass Lehrkräfte überhaupt passende Lernangebote und Hilfestellungen zur Verfügung stellen können (z.B. Sherin, Jacobs & Philipps, 2011; Schoenfeld, 2011; Santagata & Yeh, 2016). Dennoch bleibt in aktuellen Konzeptualisierungen professionsbezogener Kompetenzen von Lehrkräften das Analysieren von Unterrichtssituationen im Hinblick auf potentiell hinderliche Darstellungswechsel weitgehend unberücksichtigt (z.B. Baumert & Kunter, 2013; Kaiser et al., 2015). Im Rahmen dieser Studie wird daher ein solches fachdidaktisches Analysieren von Unterrichtssituationen als wichtige professionsbezogene Kompetenz von Mathematiklehrkräften beschrieben. Da es bislang kaum empirische Studien gibt, in denen eine solche Kompetenz untersucht wurde, soll somit auch ein Beitrag zur Messung fachdidaktischer Analysekompetenz geleistet werden.
Um Kompetenzen von Lehrkräften unterrichtsnah zu erfassen, gelten vignettenbasierte Erhebungen als besonders geeignet (Kaiser et al., 2015; Blömeke, Gustafs-son & Shavelson, 2015). Entsprechend wurde im Rahmen dieser Studie ein vignettenbasiertes Testinstrument mit sechs Unterrichtssituationen aus dem Bereich Bruchrechnung (Klasse 6) entwickelt, in welchen der Umgang mit Darstellungswechseln eine zentrale Rolle spielt. Bislang gibt es wenige Untersuchungen dazu, welche Rolle unterschiedliche Vignettenformate für die Auseinandersetzung mit Unterrichtsvignetten (z.B. für die wahrgenommene Authentizität) und die Analyse zum Umgang mit vielfältigen Darstellungen spielt, dasselbe gilt für unterschiedliche Frageformate. Da die spezifischen Eigenschaften unterschiedlicher Vignet-tenformate und Frageformate bei der Kompetenzmessung jedoch durchaus eine Auswirkung auf die Schwierigkeit der Items haben können (Hartig, 2008), sind Untersuchungen hierzu im Rahmen dieser Studie von besonderem Interesse. Um dem beschriebenen Forschungsinteresse nachzugehen, wurde jede der sechs Un-terrichtssituationen im Testinstrument in drei Formaten (Text, Comic, Video) umgesetzt und offene sowie geschlossene Frageformate zur Analyse des Umgangs mit Darstellungen in den Unterrichtssituationen vorgelegt. Das beschriebene Testinstrument bearbeiteten N = 298 Lehramtsstudierende, Lehramtsanwärterinnen und Lehramtsanwärter sowie praktizierende Lehrkräfte. Die erhaltenen Daten wurden mit Raschmodellen analysiert, um die Qualität der vorgenommenen Kompetenzmessung zu prüfen (Bond & Fox, 2015).
Die Ergebnisse belegen eine gute Auseinandersetzung der Teilnehmerinnen und Teilnehmer mit den Vignetten in allen drei Formaten (Text, Comic, Video), wodurch eine wichtige Voraussetzung für die Analyse der vorgelegten Unterrichtssituation gegeben war. Es zeigte sich, dass fachdidaktische Analysekompetenz zum Umgang mit Darstellungen unabhängig von den eingesetzten Vignetten-formaten (Text, Comic, Video) als eindimensionales Konstrukt modelliert werden kann. Während die drei unterschiedlichen Vignettenformate keinen systemati-schen Einfluss auf die Analyse der Teilnehmerinnen und Teilnehmer zum Umgang mit Darstellungen zeigten, wurde nachgewiesen, dass die Items aus den geschlossenen Formaten systematisch leichter zu beantworten waren. Die Analyseergebnisse der Teilnehmerinnen und Teilnehmer lassen auf eine eher niedrige Ausprägung fachdidaktischer Analysekompetenz zum Umgang mit vielfältigen Darstellungen schließen, da potentiell problematische Darstellungswechsel in den Unterrichts-vignetten häufig nicht erkannt wurden. Insgesamt konnte festgestellt werden, dass die drei Vignettenformate Text, Comic und Video vergleichbar zur Erhebung fachdidaktischer Analysekompetenz zum Umgang mit vielfältigen Darstellungen geeignet sind.
The saving of previously encoded information boosts both memory for subsequent information (saving-enhanced memory; SEM) as well as cognitive performance in general (saving-enhanced performance; SEP). These findings have been replicated in a setting that involves the assistance by an intelligent software that automatically structures and saves work content in an interactive sidebar. It is assumed that beneficial effects on cognitive performance due to (automatic) saving are caused by a reduction in current workload by means of cognitive offloading. We tested this assumption by measuring neural activity in the dorsolateral prefrontal cortex (DLPFC) via functional near infrared spectroscopy (fNIRS)—once after saving and once after deleting of previously collected information that had to be recalled later-on. On a behavioral level, there was a brief benefit of saving. However, cognitive offloading became most apparent on a neural level: after saving, participants showed significantly lower activation in the right DLPFC. Also, the more participants benefited from cognitive offloading, the more they were able to re-access previously collected, saved information. Thus, fNIRS results indicated reduced mental load after saving, confirming the assumption that saving triggers cognitive offloading.
The different facets of professional performance of teachers are being debated in the current educational
research discussion. Both qualitative and quantitative test constructions exist for vignette-based measurement of
competence. For economic reasons, a procedure with closed-ended items is often favored, a reference is required for
determining and comparing alternative responses. This paper sketches out the procedure for identifying adequate
reactions to responses that we call a technical education expert norm (PCK-T). This expert norm is generated from
a multi-step expert survey and, in addition, reveals possible validation steps that can be derived for developing
teaching situations. After a content validation (N1 = 8) a multi-step quantitative survey with specialised subject
experts at schools and universities, departmental heads at public colleges for education and teacher training, as well
as experienced teachers of technology was carried out (N2 = 79; N3 = 76). In order to assess teaching competencies
of pre-service teachers using a vignette-based test procedure, the generated technical education expert norm (PCKT) allows adequate responses to be differentiated from (rather) inadequate responses in the teaching situations
In this study, the relationship between religiosity and value priorities is differentiated, based on a multidimensional model of religiosity (Structure-of-Religiosity-Test). The structure of values is conceptualized using Shalom H. Schwartz’s two orthogonal dimensions of self-transcendence vs. self-enhancement and openness to change vs. conservation. The relationship between these two dimensions and the centrality of religiosity, seven religious orientations, seven emotions toward God, and three political orientations were tested with a correlational analysis in a sample of members of Abrahamic religions, the non-denominational, and organized secularists in Switzerland (n = 1093). The results show, that different values are preferred (self-direction, universalism, benevolence, tradition, security, and power values) depending on the content of the religious orientations and emotions toward God. The results indicate the importance of the content of religious orientations and emotions for predicting value-loaded behaviors.