TY - THES A1 - Le, Tuan Anh T1 - Applying realistic mathematics education in Vietnam : teaching middle school geometry T1 - Der Einsatz von ‘Realistic Mathematics Education’ in Vietnam : Geometrieunterricht an Mittelschulen N2 - Since 1971, the Freudenthal Institute has developed an approach to mathematics education named Realistic Mathematics Education (RME). The philosophy of RME is based on Hans Freudenthal’s concept of ‘mathematics as a human activity’. Prof. Hans Freudenthal (1905-1990), a mathematician and educator, believes that ‘ready-made mathematics’ should not be taught in school. By contrast, he urges that students should be offered ‘realistic situations’ so that they can rediscover from informal to formal mathematics. Although mathematics education in Vietnam has some achievements, it still encounters several challenges. Recently, the reform of teaching methods has become an urgent task in Vietnam. It appears that Vietnamese mathematics education lacks necessary theoretical frameworks. At first sight, the philosophy of RME is suitable for the orientation of the teaching method reform in Vietnam. However, the potential of RME for mathematics education as well as the ability of applying RME to teaching mathematics is still questionable in Vietnam. The primary aim of this dissertation is to research into abilities of applying RME to teaching and learning mathematics in Vietnam and to answer the question “how could RME enrich Vietnamese mathematics education?”. This research will emphasize teaching geometry in Vietnamese middle school. More specifically, the dissertation will implement the following research tasks: • Analyzing the characteristics of Vietnamese mathematics education in the ‘reformed’ period (from the early 1980s to the early 2000s) and at present; • Implementing a survey of 152 middle school teachers’ ideas from several Vietnamese provinces and cities about Vietnamese mathematics education; • Analyzing RME, including Freudenthal’s viewpoints for RME and the characteristics of RME; • Discussing how to design RME-based lessons and how to apply these lessons to teaching and learning in Vietnam; • Experimenting RME-based lessons in a Vietnamese middle school; • Analyzing the feedback from the students’ worksheets and the teachers’ reports, including the potentials of RME-based lessons for Vietnamese middle school and the difficulties the teachers and their students encountered with RME-based lessons; • Discussing proposals for applying RME-based lessons to teaching and learning mathematics in Vietnam, including making suggestions for teachers who will apply these lessons to their teaching and designing courses for in-service teachers and teachers-in training. This research reveals that although teachers and students may encounter some obstacles while teaching and learning with RME-based lesson, RME could become a potential approach for mathematics education and could be effectively applied to teaching and learning mathematics in Vietnamese school. N2 - Seit 1971 wurde an dem renommierten Freudenthal Institut in Utrecht ein als Realistic Mathematics Education (RME) bezeichneter mathematikdidaktischer Ansatz entwickelt. Die Philosophie von RME beruht auf Hans Freudenthals Auffassung von Mathematik als menschlicher Aktivität. Der Mathematiker und Didaktiker Prof. Hans Freudenthal (1905 – 1990) plädierte dafür, dass Mathematik an den Schulen nicht als Fertigprodukt unterrichtet werden sollte. Im Gegensatz dazu forderte er, den Schülern an ‚realistischen’ Situationen nicht-formale und formale Mathematik wieder entdecken zu lassen. Obwohl die mathematische Schulbildung in Vietnam in den letzten Jahrzehnten schon einige Fortschritte gemacht hat, steht sie noch vor großen Herausforderungen. Derzeit ist die Reform der Unterrichtsmethoden eine dringliche Aufgabe in Vietnam. Augenscheinlich ermangelt es der Mathematikdidaktik in Vietnam an dem dazu notwendigen theoretischen Rahmen. Die Philosophie von RME eignet sich grundsätzlich als Orientierung für die Reform der Unterrichtsmethoden in Vietnam. Allerdings ist die Potenz von RME für die mathematische Schulbildung in Vietnam und die Möglichkeiten, RME im Mathematikunterricht anzuwenden, noch zu klären. Das Hauptziel dieser Arbeit war zu erforschen, wie RME beim Mathematik-Lernen und -Lehren in Vietnam eingesetzt werden kann und die Frage zu beantworten: Wie kann RME den Mathematikunterricht in Vietnam bereichern? Dazu wurde insbesondere der Geometrieunterricht in der Sekundarstufe I betrachtet. Im Einzelnen beinhaltet die Untersuchung: • eine Analyse der vietnamesischen Mathematikdidaktik in der ‘Reformperiode’ (etwa von 1980 bis 2000) • die Konzeption, Durchführung und Auswertung einer Befragung von 152 Mittelschullehrern aus verschiedenen vietnamesischen Provinzen und Städten zum Mathematikunterricht in Vietnam • eine Analyse von RME einschließlich der Freudenthalschen Sicht von RME und der Charakteristika von RME • die Diskussion, wie man RME-basierten Unterrichtseinheiten gestalten und diese in den Mathematikunterricht in Vietnam integrieren kann • Test solcher Einheiten in vietnamesischen Mittelschulen • Analyse der Rückmeldungen anhand der Schülerarbeitsblätter und der Lehrerberichte • Diskussion der Chancen und Probleme von RME-basierten Unterrichtseinheiten im Geometrieunterricht vietnamesischer Mittelschulen • Diskussion von Vorschläge zur Entwicklung und zum Einsatz RME- basierter Unterrichtseinheiten in Vietnam, einschließlich von Hinweisen für Lehrende und der Konzeption von Ausbildungs- und Fortbildungskursen zu RME Die Untersuchung zeigt, dass – obwohl Lehrer wie Schüler zunächst einige Hindernisse beim Lehren und Lernen mit RME- basierten Unterrichtseinheiten zu bewältigen haben werden – RME ein mächtiger mathematikdidaktischer Ansatz ist, der wirkungsvoll im Lehren und Lernen von Mathematik in vietnamesischen Schulen angewandt werden kann. KW - Didaktik der Mathematik KW - Vietnam KW - Geometrieunterricht KW - Sekundarstufe I KW - Realistic Mathematics Education KW - Vietnam KW - middle school KW - geometry Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13480 ER - TY - THES A1 - Zhang, Quanchao T1 - Shape-memory properties of polymeric micro-scale objects prepared by electrospinning and electrospraying N2 - The ongoing trend of miniaturizing multifunctional devices, especially for minimally-invasive medical or sensor applications demands new strategies for designing the required functional polymeric micro-components or micro-devices. Here, polymers, which are capable of active movement, when an external stimulus is applied (e.g. shape-memory polymers), are intensively discussed as promising material candidates for realization of multifunctional micro-components. In this context further research activities are needed to gain a better knowledge about the underlying working principles for functionalization of polymeric micro-scale objects with a shape-memory effect. First reports about electrospun solid microfiber scaffolds, demonstrated a much more pronounced shape-memory effect than their bulk counterparts, indicating the high potential of electrospun micro-objects. Based on these initial findings this thesis was aimed at exploring whether the alteration of the geometry of micro-scale electrospun polymeric objects can serve as suitable parameter to tailor their shape-memory properties. The central hypothesis was that different geometries should result in different degrees of macromolecular chain orientation in the polymeric micro-scale objects, which will influence their mechanical properties as well as thermally-induced shape-memory function. As electrospun micro-scale objects, microfiber scaffolds composed of hollow microfibers with different wall thickness and electrosprayed microparticles as well as their magneto-sensitive nanocomposites all prepared from the same polymer exhibiting pronounced bulk shape-memory properties were investigated. For this work a thermoplastic multiblock copolymer, named PDC, with excellent bulk shape-memory properties, associated with crystallizable oligo(ε-caprolactone) (OCL) switching domains, was chosen for the preparation of electrospun micro-scale objects, while crystallizable oligo(p-dioxanone) (OPDO) segments serve as hard domains in PDC. In the first part of the thesis microfiber scaffolds with different microfiber geometries (solid or hollow with different wall thickness) were discussed. Hollow microfiber based PDC scaffolds were prepared by coaxial electrospinning from a 1, 1, 1, 3, 3, 3 hexafluoro-2-propanol (HFP) solution with a polymer concentration of 13% w·v-1. Here as a first step core-shell fiber scaffolds consisting of microfibers with a PDC shell and sacrificial poly(ethylene glycol) (PEG) core are generated. The hollow PDC microfibers were achieved after dissolving the PEG core with water. The utilization of a fixed electrospinning setup and the same polymer concentration of the PDC spinning solution could ensure the fabrication of microfibers with almost identical outer diameters of 1.4 ± 0.3 µm as determined by scanning electron microscopy (SEM). Different hollow microfiber wall thicknesses of 0.5 ± 0.2 and 0.3 ± 0.2 µm (analyzed by SEM) have been realized by variation of the mass flow rate, while solid microfibers were obtained by coaxial electrospinning without supplying any core solution. Differential scanning calorimetry experiments and tensile tests at ambient temperature revealed an increase in degree of OCL crystallinity form χc,OCL = 34 ± 1% to 43 ± 1% and a decrease in elongation of break from 800 ± 40% to 200 ± 50% associated with an increase in Young´s modulus and failture stress for PDC hollow microfiber scaffolds when compared with soild fibers. The observed effects were enhanced with decreasing wall thickness of the single hollow fibers. The shape-memory properties of the electrospun PDC scaffolds were quantified by cyclic, thermomechanical tensile tests. Here, scaffolds comprising hollow microfibers exhibited lower shape fixity ratios around Rf = 82 ± 1% and higher shape recovery ratios of Rr = 67 ± 1% associated to more pronounced relaxation at constant strain during the first test cycle and a lower switching temperature of Tsw = 33 ± 1 °C than the fibrous meshes consisting of solid microfibers. These findings strongly support the central hypothesis that different fiber geometries (solid or hollow with different wall thickness) in electrospun scaffolds result in different degrees of macromolecular chain orientation in the polymeric micro-scale objects, which can be applied as design parameter for tailoring their mechanical and shape-memory properties. The second part of the thesis deals with electrosprayed particulate PDC micro-scale objects. Almost spherical PDC microparticles with diameters of 3.9 ± 0.9 μm (as determined by SEM) were achieved by electrospraying of HFP solution with a polymer concentration of 2% w·v-1. In contrast, smaller particles with sizes of 400 ± 100 nm or 1.2 ± 0.3 μm were obtained for the magneto-sensitive composite PDC microparticles containing 23 ± 0.5 wt% superparamagnetic magnetite nanoparticles (mNPs). All prepared PDC microparticles exhibited a similar overall crystallinity like the PDC bulk material as analyzed by DSC. AFM nanoindentation results revealed no influence of the nanofiller incorporation on the local mechanical properties represented by the reduced modulus determined for pure PDC microparticles and magneto-sensitive composite PDC microparticles with similar diameters around 1.3 µm. It was found that the reduced modulus of the nanocomposite microparticles increased substantially with decreasing particles size from 2.4 ± 0.9 GPa (1.2 µm) to 11.9 ± 3.1 GPa (0.4 µm), which can be related to a higher orientation of the macromolecules at the surface of smaller sized microparticles. The magneto-sensitivity of such nanocomposite microparticles could be demonstrated in two aspects. One was by attracting/collecting the composite micro-objects with an external permanent magnet. The other one was by a inductive heating to 44 ± 1 °C, which is well above the melting transition of the OCL switching domains, when compacted to a 10 x 10 mm2 film with a thickness of 10 µm and exposed to an alternating magnet field with an magnetic field strength of 30 kA·m-1. Both functions are of great relevance for designing next generation drug delivery systems combining targeting and on demand release. By a compression approach shape-memory functionalization of individual microparticles could be realized. Here different programming pressures and compression temperatures were applied. The shape-recovery capability of the programmed PDC microparticles was quantified by online and off-line heating experiments analyzed via microscopy measurement. The obtained shape-memory properties were found to be strongly depending on the applied programming pressure and temperature. The best shape-memory performance with a high shape recovery rate of about Rr = 80±1% was obtained when a low pressure of 0.2 MPa was applied at 55 °C. Finally, it was demonstrated that PDC microparticles can be utilized as micro building parts for preparation of a macroscopic film with temporary stability by compression of a densely packed array of PDC microparticles at 60 °C followed by subsequent cooling to ambient temperature. This film disintegrates into individual microparticles upon heating to 60 °C. Based on this technology the design of stable macroscopic release systems can be envisioned, which can be easily fixed at the site of treatment (i.e. by suturing) and disintegrate on demand to microparticles facilitating the drug release. In summary, the results of this thesis could confirm the central hypothesis that the variation of the geometry of polymeric micro-objects is a suitable parameter to adjust their shape-memory performance by changing the degree of macromolecular chain orientation in the specimens or by enabling new functions like on demand disintegration. These fundamental findings might be relevant for designing novel miniaturized multifunctional polymer-based devices. KW - shape-memory effect KW - microparticles KW - hollow microfibers KW - geometry Y1 - 2018 ER - TY - THES A1 - Hain, Tobias Martin T1 - Structure formation and identification in geometrically driven soft matter systems T1 - Strukturbildung und Identifikation in geometrisch getriebenen weiche Materie-Systemen N2 - Subdividing space through interfaces leads to many space partitions that are relevant to soft matter self-assembly. Prominent examples include cellular media, e.g. soap froths, which are bubbles of air separated by interfaces of soap and water, but also more complex partitions such as bicontinuous minimal surfaces. Using computer simulations, this thesis analyses soft matter systems in terms of the relationship between the physical forces between the system's constituents and the structure of the resulting interfaces or partitions. The focus is on two systems, copolymeric self-assembly and the so-called Quantizer problem, where the driving force of structure formation, the minimisation of the free-energy, is an interplay of surface area minimisation and stretching contributions, favouring cells of uniform thickness. In the first part of the thesis we address copolymeric phase formation with sharp interfaces. We analyse a columnar copolymer system "forced" to assemble on a spherical surface, where the perfect solution, the hexagonal tiling, is topologically prohibited. For a system of three-armed copolymers, the resulting structure is described by solutions of the so-called Thomson problem, the search of minimal energy configurations of repelling charges on a sphere. We find three intertwined Thomson problem solutions on a single sphere, occurring at a probability depending on the radius of the substrate. We then investigate the formation of amorphous and crystalline structures in the Quantizer system, a particulate model with an energy functional without surface tension that favours spherical cells of equal size. We find that quasi-static equilibrium cooling allows the Quantizer system to crystallise into a BCC ground state, whereas quenching and non-equilibrium cooling, i.e. cooling at slower rates then quenching, leads to an approximately hyperuniform, amorphous state. The assumed universality of the latter, i.e. independence of energy minimisation method or initial configuration, is strengthened by our results. We expand the Quantizer system by introducing interface tension, creating a model that we find to mimic polymeric micelle systems: An order-disorder phase transition is observed with a stable Frank-Caspar phase. The second part considers bicontinuous partitions of space into two network-like domains, and introduces an open-source tool for the identification of structures in electron microscopy images. We expand a method of matching experimentally accessible projections with computed projections of potential structures, introduced by Deng and Mieczkowski (1998). The computed structures are modelled using nodal representations of constant-mean-curvature surfaces. A case study conducted on etioplast cell membranes in chloroplast precursors establishes the double Diamond surface structure to be dominant in these plant cells. We automate the matching process employing deep-learning methods, which manage to identify structures with excellent accuracy. N2 - Die Unterteilung eines Raums durch Grenzflächen führt zu Raumaufteilungen, die für die Selbstorganisation weicher Materie relevant sind. Bekannte Beispiele sind zelluläre Medien, wie z.B. Seifenschaum, der aus Luftblasen besteht, getrennt durch Wände aus Wasser und Seife, und komplexere Partitionen, wie sie z.B. durch bikontinuierliche Minimalflächen erzeugt werden. In dieser Arbeit werden mit Hilfe von Computersimulationen Systeme weicher Materie in Bezug auf den Zusammenhang zwischen dem im System vorherrschenden, physikalischen Kräften und der Struktur der resultierenden Grenzflächen oder Partitionen untersucht. Der Schwerpunkt liegt hierbei auf zwei Systemen, eine Copolymerschmelze und das sogenannte Quantizer Problem, bei denen der treibende Faktor der Strukturbildung, nämlich die Minimierung der freien Energie, aus einem Zusammenspiel der Minimierung der Oberfläche der Grenzflächen und der gleichzeitigen Minimierung der Elastizitätsenergie besteht. Unter diesen Gegebenheiten bevorzugen solche Systeme Zellen gleichmäßiger Größe. Im ersten Teil der Arbeit befassen wir uns mit der Bildung von scharfen Grenzflächen in Systemen von Copolymeren. Wir analysieren die zylindrische Phase eines Copolymersystems, das gezwungen wird, sich auf einer kugelförmigen Oberfläche zu organisieren. Die Topologie dieser Oberfläche erlaubt es der optimalen Konfiguration, dem Sechseckgitter, nicht, sich zu bilden. Für dreiarmige Copolymere wird die entstehende Struktur durch Lösungen des sogenannten Thomson Problems beschrieben. Letzteres sucht nach der Konfigurationen von abstoßenden Ladungen auf einer Kugeloberfläche mit minimaler Energie. Auf einem Substrat haben wir eine Kombination aus drei ineinandergreifende Lösungen des Thomson Problems gefunden, wobei der Typ der Lösungen statistisch von dem Radius des Substrates abhängt. Anschließend untersuchen wir die Bildung von amorphen und kristallinen Strukturen im Quantizersystem, einem teilchenbasierenden Modell, dessen Energiefunktional keine Oberflächenspannung enthält und möglichst kugelförmige Zellen gleicher Größe begünstigt. Wird das System quasistatisch im thermodynamischen Gleichgewicht abgekühlt, kristallisiert das Quantizersystem in den geordneten BCC Grundzustand. Wird das System allerdings zu schnell abgekühlt, sodass es sich nicht mehr im thermodynamischen Gleichgewicht befindet, bildet sich eine amorphe, annähernd hyperuniforme Struktur aus. Wir konnten zeigen, dass diese Struktur bemerkenswert unabhängig von den Ausganszuständen, sowie der Art der Energieminimierung zu sein scheint. Im Ausblick erweitern wir das Quantizersystem, indem wir Oberflächenspannung einführen. Unsere Ergebnisse deutet darauf hin, dass dieses so erweiterte Modell Mizellenphasen in Polymersystem modellieren kann. Wir beobachten einen Phasenübergang von einer ungeordneten, flüssigen Phase hin zu einer festen Frank-Caspar-Phase. Der zweite Teil der Arbeit behandelt bikontinuierliche Grenzflächen, die den Raum in zwei netzwerkartige Domänen aufteilen. Wir führen eine Open-Source Software ein, das die Identifizierung von Strukturen anhand derer Mikroskopaufnahmen ermöglicht. Hierzu erweitern und verbessern wir eine Methode, die durch den Abgleich experimentell zugänglicher Projektionen in Mikroskopaufnahmen mit berechneten Projektionen potenzieller Strukturen basiert. Dieses Verfahren wurde erstmal von Deng und Mieczkowski (1998) eingeführt. Die simulierten Strukturen basieren auf einer Nodalflächenmodellierung von dreifach-periodischen Flächen konstanter mittlerer Krümmung. Wir führen eine Fallstudie an Zellmembranen von Etioplasten, den Vorläufern von Chloroplasten, durch. Wir konnten die Struktur dieser Etioplasten als die Diamond-Struktur identifizieren. Als Ausblick automatisieren wir den Identifizierungsproyess mit Hilfe von Deep-Learning-Methoden. Erste Ergebnisse zeigen, dass mit diesem Ansatz die Identifizierung von Strukturen mit ausgezeichneter Genauigkeit gelingt. KW - soft matter KW - geometry KW - self-assembly KW - structure formation KW - quantizer KW - polymer KW - Geometrie KW - Polymere KW - Quantizer KW - Selbstassemblierung KW - weiche Materie KW - Strukturbildung Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-558808 N1 - Parts of this publication are reproduced with permission from the Royal Society of Chemistry and AIP Publishing. ER -