A theory-based assessment of the learning process in primary school mathematics

Zur Erfassung individueller Lernentwicklungen in leistungsheterogenen Schulklassen werden aussagekräftige Verfahren zur Lernverlaufsdiagnostik benötigt, die adaptiv an die unterschiedlichen Lernausgangslagen der Kinder angepasst werden können. Die Entwicklung adaptiver Einzeltests kann nicht über parallele Messungen realisiert werden, sondern setzt eine alternative Herangehensweise an die Testkonstruktion voraus. Am Beispiel der Konstruktion einer Lernverlaufsdiagnostik für den mathematischen Anfangsunterricht wird im vorliegenden Beitrag die Vorgehensweise einer auf einem Entwicklungsmodell basierenden theoriegeleiteten Testentwicklung vorgestellt. Auf Basis des Entwicklungsmodells arithmetischer Konzepte (Fritz, Ehlert, & Balzer, 2013) wurden N = 68 Aufgaben konzipiert, welche die unterschiedlichen Entwicklungsniveaus des Modells operationalisieren. Diese Aufgaben wurden in einer längsschnittlichen Untersuchung mit N = 279 Erstklässler/innen einer empirischen Prüfung unterzogen und in Bezug auf ihre Änderungssensibilität untersucht. Ziel ist es, unter Verwendung der probabilistischen Testtheorie einen Aufgabenpool aufzubauen, der zukünftig auch für adaptives Testen eingesetzt werden kann. Die Aufgaben erwiesen sich als reliabel, valide und geschlechterfair und eignen sich zur Abbildung erster Lernentwicklungen. Es zeigte sich allerdings, dass die Aufgaben noch nicht alle Leistungsbereiche abdecken. Es bedarf weiterer schwierigerer Aufgaben, die die arithmetischen Konzepte der höheren Entwicklungsniveaus erfassen. (DIPF/Orig.)In order to assess individual learning progress in heterogeneous classrooms, sound progress monitoring measures are needed, which can be adjusted to the various levels of knowledge within a given class. The development of adaptive tests cannot be realized via parallel measurements and thus requires an alternative method of test construction. This article introduces the concept of a theory-driven test construction based on a developmental model, using the construction of a progress monitoring measure for early numeracy in primary school as an example. Based on the developmental model of arithmetic concepts (Fritz et al., 2013), N = 68 tasks were designed that operationalize the different developmental levels of the model. These tasks were empirically examined in a longitudinal study with N = 279 first grade students, focusing in particular on their responsiveness to learning progress. The purpose of this study is to generate an item pool using the item-response-theory, which can later be applied in adaptive tests. The tasks proved to be reliable, valid and gender fair, and are suitable for showing initial learning progress among students. However, it was found that the items do not cover all performance ranges. More difficult items are needed to measure the higher levels of the developmental model. (DIPF/Orig.

Structural development of HDPE in injection molding

This study investigated some relevant structure/properties relationships in shear-controlled orientation in injection molding (SCORIM) of high-density polyethylene (HDPE). SCORIM was used to deliberately induce a strong anisotropic character in the HDPE microstructure. Three grades with different molecular weight characteristics were molded into tensile test bars, which were subsequently characterized in terms of the mechanical behavior by tensile tests and microhardness measurements. The structure developed upon processing was also characterized by polarized light microscopy (PLM), scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and wide-angle X-ray diffraction (WAXD). SCORIM allows the production of very stiff molded parts, exhibiting a very well-defined laminated morphology. This morphology is associated with both an M-shaped microhardness profile and a pronounced mechanical anisotropy. These characteristics are supported by an analogous variation in the crystallinity and a high level of molecular orientation, as indicated, respectively, by calorimetric measurements and X-ray diffraction resultsSubprograma Ciência e Tecnologia do 2° Quadro Comunitário de Apoio, Ministério da Ciência e Tecnologia (Portugal)

AdS boundary conditions and the Topologically Massive Gravity/CFT correspondence

The AdS/CFT correspondence provides a new perspective on recurrent questions in General Relativity such as the allowed boundary conditions at infinity and the definition of gravitational conserved charges. Here we review the main insights obtained in this direction over the last decade and apply the new techniques to Topologically Massive Gravity. We show that this theory is dual to a non-unitary CFT for any value of its parameter mu and becomes a Logarithmic CFT at mu = 1.Comment: 10 pages, proceedings for XXV Max Born Symposium, talks given at Johns Hopkins workshop and Holographic Cosmology workshop at Perimeter Institute; v2: added reference

The S-matrix bootstrap. Part I : QFT in AdS.

We propose a strategy to study massive Quantum Field Theory (QFT) using conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study correlation functions of its boundary operators. We show that these are solutions of the crossing equations in one lower dimension. By sending the curvature radius of the background hyperbolic space to infinity we expect to recover flat-space physics. We explain that this regime corresponds to large scaling dimensions of the boundary operators, and discuss how to obtain the flat-space scattering amplitudes from the corresponding limit of the boundary correlators. We implement this strategy to obtain universal bounds on the strength of cubic couplings in 2D flat-space QFTs using 1D conformal bootstrap techniques. Our numerical results match precisely the analytic bounds obtained in our companion paper using S-matrix bootstrap techniques

Schr\"odinger Deformations of AdS_3 x S^3

We study Schr\"odinger invariant deformations of the AdS_3 x S^3 x T^4 (or K3) solution of IIB supergravity and find a large class of solutions with integer and half-integer dynamical exponents. We analyze the supersymmetries preserved by our solutions and find an infinite number of solutions with four supersymmetries. We study the solutions holographically and find that the dual D1-D5 (or F1-NS5) CFT is deformed by irrelevant operators of spin one and two.Comment: 23 page

Real-time gauge/gravity duality: Prescription, Renormalization and Examples

We present a comprehensive analysis of the prescription we recently put forward for the computation of real-time correlation functions using gauge/gravity duality. The prescription is valid for any holographic supergravity background and it naturally maps initial and final data in the bulk to initial and final states or density matrices in the field theory. We show in detail how the technique of holographic renormalization can be applied in this setting and we provide numerous illustrative examples, including the computation of time-ordered, Wightman and retarded 2-point functions in Poincare and global coordinates, thermal correlators and higher-point functions.Comment: 85 pages, 13 figures; v2: added comments and reference

Small Group Math Instruction in the Middle School Classroom

This study includes the impact of small group instruction in the middle school classroom. This study takes place at Dakota Meadows Middle School in Mankato, MN. The participants included 24 seventh grade students who are only partially proficient in math according to their standardized state assessments. Data was collected using a pretest, formative assessments, posttest and a student survey (See Appendices A, B, C, D). There was growth from the pretest scores to the posttest scores as well as growth in formative assessment scores. The student survey indicated most students felt the small group instruction benefitted them positively. Small group instruction will continue to take place in the middle school classroom to individualize instruction and improve assessment scores until proficiency is met