Proof and application

This paper outlines an epistemological conception which attempts to relate the formal aspects of mathematical proof to its pragmatic dimensions. In addition to the key concept of application, the paper makes use of several concepts from the domain of analytical philosophy, to present a view of proof that might best be categorized as a dialectical one. A number of implications for teaching are discussed.     

On defining quality of education

In this paper quality of graduates is distinguished from quality of education, which is renamed efficiency of education. The first concept is defined in a quantitative manner, the second by way of a set of 66 statements concerning the efficiency of education derived from judgements about the effectiveness of particular teaching methods in the achievement of different types of teaching objectives.Paper presented at the conference on Efficiency of Teaching Methods in Higher Education, organized by the University Teaching Methods Unit of the University of London, 6–7 April, 1976.     

Soziale Ungleichheit in der Schulklasse und Schulerfolg

Zusammenfassung In dieser Arbeit verfolgen wir die Frage, ob sich auf den Schulerfolg nicht nur die sozio?konomische Lage der Herkunftsfamilie (SES) und der Erziehungsstil der Eltern auswirken, sondern auch die in jeder Schulklasse entstehende Ungleichheit der Kinder nach ihrem sozialen Rang. Zur Beantwortung stehen Daten aus einer Querschnittsuntersuchung an zwei Berliner Schulen zur Verfügung, an der 234 M?dchen und Jungen aus zehn Schulklassen der dritten und fünften Jahrgangsstufe untersucht wurden. Zun?chst zeigte sich, dass der Schulerfolg — hier gemessen an der Durchschnittsnote aus Mathematik, Deutsch und Sachkunde sowie am Urteil des Klassenlehrers über die Lernbef?higung — wie in der PISA-Studie von SES und Erziehungsstil der Eltern beeinflusst wird. Zus?tzlich h?ngen aber der soziometrisch gemessene Einfluss-und Beliebtheitsrang der Kinder und ihr Verhalten gegenüber anderen Kindern mit dem Schulerfolg zusammen, wobei dieser Zusammenhang mit dem Lehrerurteil über die Lernbef?higung noch ausgepr?gter ist als mit der Durchschnittsnote. Diese Zusammenh?nge bleiben erhalten, wenn für SES und Erziehungsstil kontrolliert wird. Dabei dürfte es sich um Wechselwirkungen handeln. Für künftige L?ngsschnittforschung richtungsweisend ist aber die generalisierende Interpretation und Feststellung: Die auf der Grundlage von Interaktionen und Kommunikationen unter Kindern entstehende Ungleichheit des sozialen Ranges der Kinder in der Schulklasse wirkt sich ebenso auf den Schulerfolg aus wie die soziale Ungleichheit des Familienhintergrundes. Auch Prozesse in der eigenst?ndigen Kinderwelt bef?rdern oder mindern Lern-und damit Lebenschancen.

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Summary Social inequality in schools and school success — An investigation in years 3 and 5 in Berlin primary schools This paper deals with the question of whether success in schools is not solely attributable to the socio-economic background of pupils’ families (SES) and the style of children’s upbringing, but also to the inequality of pupils in respect of their social rank in the classroom. This question will be investigated on the basis of data from two Berlin schools which includes 234 pupils from ten classes in the third and fifth years. The analysis shows how school success as measured by average marks in maths. German and general studies and by the judgment of children’s learning ability by their classroom teacher — as in the PISA-study — is influenced by SES and how parents bring up their children. Further, the socio-metric measurement of children’s popularity and influence and their behavior towards other children correlates with school marks and moreso still with teachers’ judgments of their learning ability. This correlation remains even when controlled for SES and style of upbringing. This is likely to be attributable to interdependencies. The following general interpretation will give the direction of future longitudinal studies: Inequalities of social rank between children, which emerge based on their interaction and communication with each other, influence success at school just as family background and style of upbringing do. Processes in children’s personal worlds, therefore, promote or hinder their chances for learning and subsequently for life.

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Das Projekt wurde von der DFG finanziert.     

Intra-active entanglements: What posthuman and new materialist frameworks can offer the learning sciences

This paper examines what new materialist and posthumanist frameworks can offer learning science research in diverse maker learning environments. We explore what is gained by grappling with the entanglements between humans, non-humans and more-than-humans. To do this, we draw on Karen Barad's ethico-onto-epistemology and agential realism where she redefines connections to the shared world by attuning to the entangled matter that is created within intra-actions. We use this framework across four international cases: digital media camps, a university-level classroom-based makerspace, a Saturday outdoor makerspace workshop and a classroom-based museum makerspace. Each case study attends to how intra-actions enact agential forces in maker education research—forces that posthuman and new materialist frameworks help us see. In so doing, these case studies challenge many of the assumptions prevalent in the learning sciences about mattering and its implications in research sites.     

The impact of physics teachers’ pedagogical content knowledge and motivation on students’ achievement and interest

This paper examines students’ achievement and interest and the extent to which they are predicted by teacher knowledge and motivation. Student achievement and interest are both considered desirable outcomes of school instruction. Teacher pedagogical content knowledge has been identified a major predictor of student achievement in previous research, whereas teacher motivation is considered a decisive factor influencing students’ interest. So far, however, most research either focused on knowledge or motivation (both on the students’ as well as the teachers’ side), rarely investigating them together or examining the instructional mechanisms through which the supposed effects of teacher knowledge and motivation are facilitated. In the present study, N = 77 physics teachers and their classes in Germany and Switzerland are investigated utilizing a multi‐method approach in combining data obtained from test‐instruments (teacher pedagogical content knowledge, student achievement) and questionnaires (teacher motivation, student interest, student perceived enthusiastic teaching) as well as videotaped instruction (cognitive activation rated by observers). Multi‐level structural equation modeling was used to support the assumptions that teacher pedagogical content knowledge positively predicted students’ achievement; the effect was mediated by cognitive activation. Teachers’ motivation predicted students’ interest which was mediated by enthusiastic teaching as perceived by students. Neither did teacher pedagogical content knowledge predict students’ interest, nor teacher motivation students’ achievement. This implies that in order to improve students’ cognitive as well as affective outcomes, both teachers’ knowledge but also their motivation need to be considered. © 2016 The Authors. Journal of Research in Science Teaching Published by Wiley Periodicals, Inc. J Res Sci Teach 54:586–614, 2017     

Email use in elementary school: an analysis of exchange patterns and content

Email was embedded in a project in design and technology education in elementary school. During four lessons children worked in groups on building a flying object. These groups communicated through email with groups of children from another school. The analyses of the emails, as viewed from distributed cognition theory, focus on the exchange patterns and content. Two characteristic exchange patterns are stacking and compounding. In stacking emails are sent out quickly enough to afford a "just-in-time" exchange of information. In compounding the emails transcend lessons. An "old" section of the email reacts to the partner's email about a previous lesson. A "new" section deals with the current lesson.
Question-answer exchanges accounted for only about 15% of the communications. Connected discourse with explicit or implicit references to the partner's email was likewise scarce. Groups mainly connected to each other through adoption, leading to shared scenarios of "We tell you our story—You tell us yours". The conclusion discusses the impact of the task on the children's communication. Among others, a precise definition and teaming of the task is deemed necessary to favour embedded email use. Because the genre of email use in elementary school is yet to be defined the authors caution against imposing many constraints on what children write to each other.