@phdthesis{Boehne2019,
  author    = {B{\"o}hne, Sebastian},
  title     = {Different degrees of formality},
  doi       = {10.25932/publishup-42379},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-423795},
  school      = {Universit{\"a}t Potsdam},
  pages     = {VI, 167},
  year      = {2019},
  abstract  = {In this thesis we introduce the concept of the degree of formality. It is directed against a dualistic point of view, which only distinguishes between formal and informal proofs. This dualistic attitude does not respect the differences between the argumentations classified as informal and it is unproductive because the individual potential of the respective argumentation styles cannot be appreciated and remains untapped. This thesis has two parts. In the first of them we analyse the concept of the degree of formality (including a discussion about the respective benefits for each degree) while in the second we demonstrate its usefulness in three case studies. In the first case study we will repair Haskell B. Curry's view of mathematics, which incidentally is of great importance in the first part of this thesis, in light of the different degrees of formality. In the second case study we delineate how awareness of the different degrees of formality can be used to help students to learn how to prove. Third, we will show how the advantages of proofs of different degrees of formality can be combined by the development of so called tactics having a medium degree of formality. Together the three case studies show that the degrees of formality provide a convincing solution to the problem of untapped potential.},
  language  = {en}
}
@phdthesis{Kollosche2014,
  author    = {Kollosche, David},
  title     = {Gesellschaft, Mathematik und Unterricht : ein Beitrag zum soziologisch-kritischen Verst{\"a}ndnis der gesellschaftlichen Funktionen des Mathematikunterrichts},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70726},
  school      = {Universit{\"a}t Potsdam},
  year      = {2014},
  abstract  = {Die vorliegende Studie untersucht die gesellschaftliche Rolle des gegenw{\"a}rtigen Mathematikunterrichts an deutschen allgemeinbildenden Schulen aus einer soziologisch-kritischen Perspektive. In Zentrum des Interesses steht die durch den Mathematikunterricht erfahrene Sozialisation. Die Studie umfasst unter anderem eine Literaturdiskussion, die Ausarbeitung eines soziologischen Rahmens auf der Grundlage des Werks von Michel Foucault und zwei Teilstudien zur Soziologie der Logik und des Rechnens. Abschließend werden Dispositive des Mathematischen beschrieben, die darlegen, in welcher Art und mit welcher pers{\"o}nlichen und gesellschaftlichen Folgen der gegenw{\"a}rtige Mathematikunterricht eine spezielle Geisteshaltung etabliert.},
  language  = {de}
}
@phdthesis{Vu2014,
  author    = {Vu, Dinh Phuong},
  title     = {Using video study to investigate eighth-grade mathematics classrooms in Vietnam},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72464},
  school      = {Universit{\"a}t Potsdam},
  pages     = {273},
  year      = {2014},
  abstract  = {The International Project for the Evaluation of Educational Achievement (IEA) was formed in the 1950s (Postlethwaite, 1967). Since that time, the IEA has conducted many studies in the area of mathematics, such as the First International Mathematics Study (FIMS) in 1964, the Second International Mathematics Study (SIMS) in 1980-1982, and a series of studies beginning with the Third International Mathematics and Science Study (TIMSS) which has been conducted every 4 years since 1995. According to Stigler et al. (1999), in the FIMS and the SIMS, U.S. students achieved low scores in comparison with students in other countries (p. 1). The TIMSS 1995 "Videotape Classroom Study" was therefore a complement to the earlier studies conducted to learn "more about the instructional and cultural processes that are associated with achievement" (Stigler et al., 1999, p. 1). The TIMSS Videotape Classroom Study is known today as the TIMSS Video Study. From the findings of the TIMSS 1995 Video Study, Stigler and Hiebert (1999) likened teaching to "mountain ranges poking above the surface of the water," whereby they implied that we might see the mountaintops, but we do not see the hidden parts underneath these mountain ranges (pp. 73-78). By watching the videotaped lessons from Germany, Japan, and the United States again and again, they discovered that "the systems of teaching within each country look similar from lesson to lesson. At least, there are certain recurring features [or patterns] that typify many of the lessons within a country and distinguish the lessons among countries" (pp. 77-78). They also discovered that "teaching is a cultural activity," so the systems of teaching "must be understood in relation to the cultural beliefs and assumptions that surround them" (pp. 85, 88). From this viewpoint, one of the purposes of this dissertation was to study some cultural aspects of mathematics teaching and relate the results to mathematics teaching and learning in Vietnam. Another research purpose was to carry out a video study in Vietnam to find out the characteristics of Vietnamese mathematics teaching and compare these characteristics with those of other countries. In particular, this dissertation carried out the following research tasks: - Studying the characteristics of teaching and learning in different cultures and relating the results to mathematics teaching and learning in Vietnam - Introducing the TIMSS, the TIMSS Video Study and the advantages of using video study in investigating mathematics teaching and learning - Carrying out the video study in Vietnam to identify the image, scripts and patterns, and the lesson signature of eighth-grade mathematics teaching in Vietnam - Comparing some aspects of mathematics teaching in Vietnam and other countries and identifying the similarities and differences across countries - Studying the demands and challenges of innovating mathematics teaching methods in Vietnam - lessons from the video studies Hopefully, this dissertation will be a useful reference material for pre-service teachers at education universities to understand the nature of teaching and develop their teaching career.},
  language  = {en}
}
@phdthesis{Krey2011,
  author    = {Krey, Olaf},
  title     = {Zur Rolle der Mathematik in der Physik : Wissenschaftstheoretische Aspekte und Vorstellungen Physiklernender},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59412},
  school      = {Universit{\"a}t Potsdam},
  year      = {2011},
  abstract  = {Mathematik spielt im Physikunterricht eine nicht unerhebliche Rolle - wenn auch eine zwiesp{\"a}ltige. Oft wird sie sogar zum Hindernis beim Lernen von Physik und kann ihr emanzipatorisches Potenzial nicht entfalten. Die vorliegende Arbeit stellt zwei Bausteine f{\"u}r eine begr{\"u}ndete Konzeption zum Umgang mit Mathematik beim Lernen von Physik zur Verf{\"u}gung. Im Theorieteil der Arbeit werden zum Einen wissenschaftstheoretische Aspekte der Rolle der Mathematik in der Physik aufgearbeitet und der physikdidaktischen Forschungsgemeinschaft im Zusammenhang zug{\"a}nglich gemacht. Zum anderen werden Forschungsergebnisse zu Vorstellungen Lernender {\"u}ber Physik und Mathematik sowie im Bereich der Epistemologie zusammengestellt. Im empirischen Teil der Arbeit werden Vorstellungen zur Rolle der Mathematik in der Physik von Sch{\"u}lerinnen und Sch{\"u}lern der Klassenstufen 10 und 12 sowie Physik-Lehramtstudierenden im Grundstudium mit Hilfe eines Fragebogens erhoben und unter Verwendung inhaltsanalytischer bzw. statistischer Methoden ausgewertet. Die Ergebnisse zeigen unter Anderem, dass Mathematik im Physikunterricht entgegen g{\"a}ngiger Meinungen bei den Lernenden nicht negativ, aber zumindest bei j{\"u}ngeren Lernenden formal und algorithmisch konnotiert ist.},
  language  = {de}
}