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.

Untersuchungen von Salatrauke (Eruca sativa) mit den drei Bildschaffenden Methoden Kupferchloridkristallisation, Steigbildmethode und Rundfilterchromatographie

Ten encoded rocket samples from 2009 were taken from a field trial on the comparison of nitrogen supply and different organic and conventional production systems at Hennef, Germany. The samples were examined with the image forming methods biocrystallization according to Pfeiffer, capillary dynamolysis according to Wala and circular chromatography according to Pfeiffer. The images of the encoded samples were a) characterised and b) assigned to experimental factors. The factors investigated were i) nitrogen supply, ii) fertilizer type, and iii) horn silica application. The ten samples were assigned 100% correctly to low and high N supply, to mineral fertilization and manure fertilization and to with or without horn silica application

Differenzierung und Identifizierung von Weizen aus ökologischen und konventionellen Anbausystemen durch die kombinierte Anwendung von drei Bildschaffenden Methoden

By combined application of the three picture forming methods biocrystallization ac-cording to Pfeiffer, capillary dynamolisis according to Wala and circular chromatogra-phy according to Pfeiffer encoded food samples from different production systems have been repeatedly differentiated and identified by Dr. Ursula Graf. In the present study we tested whether by using the combined three picture forming methods en-coded food samples from different production systems could also be differentiated and identified in a different laboratory by another trained person. Ten encoded wheat samples each from 2000 and 2005 harvests were taken from the long-term DOK- trial in Oberwil/Switzerland and examined with the pictomorphological methods. The wheat samples derived from the production systems ‘bio-dynamic’, ‘bio-organic’, ‘unfertil-ized’, ‘mineral fertilization’ and ‘conventional’ (mineral fertilization combined with ma-nure application) could be differentiated and identified, with partial differentiation and identification of the two production systems ‘bio-dynamic’ and ‘bio-organic’

Untersuchungen von Weizen (Triticum aestivum L.) mit den drei Bildschaffenden Methoden Kupferchloridkristallisation, Steigbildmethode und Rundfilterchromatographie

Ten encoded wheat samples from 2008 were taken from a field trial on the comparison of different organic and conventional production systems at Hennef, Germany. The samples were examined with the image forming methods biocrystallization, capillary dynamolysis and circular chromatography. The images of the encoded samples were a) characterised and b) assigned to experimental factors. The factors investigated were i) nitrogen supply, ii) fertilizer type, and iii) horn silica application. The ten samples were assigned 100% correctly to low and high N supply. Within the production methods, samples were assigned correctly to mineral fertilization and manure fertilization

Insights Into First Grade Students' Development of Conceptual Numerical Understanding as Drawn From Progression-Based Assessments

Early numeracy has been found to be one of the strongest predictors for later success in learning. Equipping children with a sound conceptual numerical understanding should therefore be a focus of early primary school mathematics. Assessments that are aligned to empirically validated learning progressions can support teachers to understand their students learning better and target instruction accordingly. This study examines numeracy learning of 101 first grade students over the course of one school year using progression-based assessments. Findings show that the students' performance increased significantly over time and that the initial conceptual numerical understanding had a positive effect on the students' learning progress as well as their end of school year performance. Analyzing the performance data based on the levels of the underlying developmental model uncovered an increasing elaboration of conceptual numerical understanding over time, but also individual differences within this process that need to be addressed through targeted intervention

Untersuchungen von Traubensaft aus den Jahren 2007-2010 von unterschiedlichen Produktionssystemen mit drei Bildschaffenden Methoden

33 encoded grape samples from 2007-2010 were taken from a long-term field trial on the comparison of different organic and conventional production systems at Geisenheim, Germany. The samples were examined with the image forming methods biocrystallization, capillary dynamolysis and circular chromatography. The pictures of the encoded samples were i. differentiated and ii. characterised. The origin of 31 out of 33 encoded samples derived from ‘conventional’, ‘bio-organic’, ‘bio-dynamic‘ production was determined with highest accuracy

Untersuchungen von Wein aus Integriertem, Organischem und Biologisch-Dynamischem Anbau mit Bildschaffenden Methoden

Nine encoded wine samples from a German long-term field trial on the comparison of different cultivation systems were examined with the image forming methods biocrystallization, capillary dynamolysis and circular chromatography. The images of the encoded samples were i. differentiated into three groups of images with similar form expression, ii. characterised as ‘fresh – aged’ based on a catalogue of reference images, iii. ranked (according to the quality characterization) and iv. assigned to the different cultivation systems (classified). Images gained with samples from integrated farming showed more structures indicating enhanced degradation compared with the samples from organic and especially from biodynamic origin. Based on these observations, a correct assignment of all encoded samples to cultivation systems was possible. These results are interpreted as indicating higher product quality of biodynamic and organic wine compared to wine from integrated farming

Untersuchung von Traubensaft mit den drei Bildschaffenden Methoden Kupferchloridkristallisation, Steigbildmethode und Rundfilterchromatographie

Ten encoded grape samples from 2006 were taken from a long-term field trial on the comparison of different organic and conventional production systems at Geisenheim, Germany. The samples were examined with the picture forming methods biocrystallization according to Pfeiffer, capillary dynamolysis according to Wala and circular chromatography according to Pfeiffer. The pictures of the encoded samples were i. differentiated and ii characterised. Two encoded samples of each of the five production methods ‘conventional’, ‘bio-organic’, ‘bio-dynamic without horn silica’,‘bio-dynamic with three horn silica applications’ and ‘bio-dynamic with four horn silica applications’ were clearly differentiated with highest accuracy, i.e. 100%

Lake regionalization and diatom metacommunity structuring in tropical South America

Lakes and their topological distribution across Earth’s surface impose ecological and evolutionary constraints on aquatic metacommunities. In this study, we group similar lake ecosystems as metacommunity units influencing diatom community structure. We assembled a database of 195 lakes from the tropical Andes and adjacent lowlands (8°N–30°S and 58–79°W) with associated environmental predictors to examine diatom metacommunity patterns at two different levels: taxon and functional (deconstructed species matrix by ecological guilds). We also derived spatial variables that inherently assessed the relative role of dispersal. Using complementary multivariate statistical techniques (principal component analysis, cluster analysis, nonmetric multidimensional scaling, Procrustes, variance partitioning), we examined diatom–environment relationships among different lake habitats (sediment surface, periphyton, and plankton) and partitioned community variation to evaluate the influence of niche-and dispersal-based assembly processes in diatom metacommunity structure across lake clusters. The results showed a significant association between geographic clusters of lakes based on gradients of climate and landscape configuration and diatom assemblages. Six lake clusters distributed along a latitudinal gradient were identified as functional metacommunity units for diatom communities. Variance partitioning revealed that dispersal mechanisms were a major contributor to diatom metacommunity structure, but in a highly context-dependent fashion across lake clusters. In the Andean Altiplano and adjacent lowlands of Bolivia, diatom metacommunities are niche assembled but constrained by either dispersal limitation or mass effects, resulting from area, environmental heterogeneity, and ecological guild relationships. Topographic heterogeneity played an important role in structuring planktic diatom metacommunities. We emphasize the value of a guild-based metacommunity model linked to dispersal for elucidating mechanisms underlying latitudinal gradients in distribution. Our findings reveal the importance of shifts in ecological drivers across climatic and physiographically distinct lake clusters, providing a basis for comparison of broad-scale community gradients in lake-rich regions elsewhere. This may help guide future research to explore evolutionary constraints on the rich Neotropical benthic diatom species pool

Lake Regionalization and Diatom Metacommunity Structuring in Tropical South America

Lakes and their topological distribution across Earth\u27s surface impose ecological and evolutionary constraints on aquatic metacommunities. In this study, we group similar lake ecosystems as metacommunity units influencing diatom community structure. We assembled a database of 195 lakes from the tropical Andes and adjacent lowlands (8°N–30°S and 58–79°W) with associated environmental predictors to examine diatom metacommunity patterns at two different levels: taxon and functional (deconstructed species matrix by ecological guilds). We also derived spatial variables that inherently assessed the relative role of dispersal. Using complementary multivariate statistical techniques (principal component analysis, cluster analysis, nonmetric multidimensional scaling, Procrustes, variance partitioning), we examined diatom–environment relationships among different lake habitats (sediment surface, periphyton, and plankton) and partitioned community variation to evaluate the influence of niche‐ and dispersal‐based assembly processes in diatom metacommunity structure across lake clusters. The results showed a significant association between geographic clusters of lakes based on gradients of climate and landscape configuration and diatom assemblages. Six lake clusters distributed along a latitudinal gradient were identified as functional metacommunity units for diatom communities. Variance partitioning revealed that dispersal mechanisms were a major contributor to diatom metacommunity structure, but in a highly context‐dependent fashion across lake clusters. In the Andean Altiplano and adjacent lowlands of Bolivia, diatom metacommunities are niche assembled but constrained by either dispersal limitation or mass effects, resulting from area, environmental heterogeneity, and ecological guild relationships. Topographic heterogeneity played an important role in structuring planktic diatom metacommunities. We emphasize the value of a guild‐based metacommunity model linked to dispersal for elucidating mechanisms underlying latitudinal gradients in distribution. Our findings reveal the importance of shifts in ecological drivers across climatic and physiographically distinct lake clusters, providing a basis for comparison of broad‐scale community gradients in lake‐rich regions elsewhere. This may help guide future research to explore evolutionary constraints on the rich Neotropical benthic diatom species pool