Ausbildung algebraischen Struktursinns im Klassenunterricht : Lernbezogene Neudeutung eines mathematikdidaktischen Begriffs

When confronted with algebraic expressions, many see little more than a random combination of letters, numbers, and other signs. However, others easily approach the algebraic structures formed by the symbols; they manipulate expressions, evaluate them, get solutions. They have algebraic structure sense. This work investigates the processes of the development of algebraic structure sense in classroom instruction, drawing on data from two teaching units (one on linear equations, one on linear funtions) that were planned in cooperation with the mathematics teacher of the class. Two networked theoretical views - the GCSt model by Bikner-Ahsbahs and the Theory of Objectification by Radford - allow for the identification and interpretative description of situations in which students see structures and under the right circumstances develop algebraic structure sense. Using the documentary method, the long-term observations of classroom action are first understood in their complexity and then analyzed for their meaning with regard to the research questions. As a result, the development of algebraic structure sense can be described as a process of becoming familiar with the activity connected to the respective algebraic structure. With regard to linear equations a detailed pathway for this process is laid out. It is shown how the new view on the algebraic structure manifests itself in verbal descriptions and inscriptions. Furthermore, the role of prior knowledge is discussed. However, the development of algebraic structure sense is not a purely mental achievement: Situational interest and established roles influence the learning process. A social form of interaction is described that integrates all these aspects: Students tune their views on the algebraic structure with that of the teacher. In the closing discussion the empirical results are bound to the theories that were used. Furthermore, connections are made to the wider research landscape and it is shown how the results from this work are of relevance beyond its concrete topic

The filter‐house of the larvacean Oikopleura dioica. A complex extracellular architecture: From fiber production to rudimentary state to inflated house

While cellulose is the most abundant macromolecule in the biosphere, most animals are unable to produce cellulose with the exception of tunicates. Some tunicates have evolved the ability to secrete a complex house containing cellulosic fibers, yet little is known about the early stages of the house building process. Here, we investigate the rudimentary house of Oikopleura dioica for the first time using complementary light and electron microscopic techniques. In addition, we digitally modeled the arrangement of chambers, nets, and filters of the functional, expanded house in three dimensions based on life-video-imaging. Combining 3D-reconstructions based on serial histological semithin-sections, confocal laser scanning microscopy, transmission electron microscopy, scanning electron microscopy (SEM), and focused ion beam (FIB)-SEM, we were able to elucidate the arrangement of structural components, including cellulosic fibers, of the rudimentary house with a focus on the food concentration filter. We developed a model for the arrangement of folded structures in the house rudiment and show it is a precisely preformed structure with identifiable components intricately correlated with specific cells. Moreover, we demonstrate that structural details of the apical surfaces of Nasse cells provide the exact locations and shapes to produce the fibers of the house and interact among each other, with Giant Fol cells, and with the fibers to arrange them in the precise positions necessary for expansion of the house rudiment into the functional state. The presented data and hypotheses advance our knowledge about the interrelation of structure and function on different biological levels and prompt investigations into this astonishing biological object.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Peer Reviewe

Siegener Beiträge zur Geschichte und Philosophie der Mathematik 2015

Die "Siegener Beiträge zur Geschichte und Philosophie der Mathematik - SieB" bieten ein Forum für den interdisziplinären Diskurs im Bereich Philosophie und Geschichte der Mathematik, der eine Pluralität an Themen, Perspektiven und Methoden mit dem Bemühen um ein besseres Verständnis ’der’ Mathematik vereint. Im Sinne der Leitfrage nach dem "Wesen" der Mathematik enthält der vorliegende Band Beiträge zur Mathematik- und Logikgeschichte und zugleiche Beiträge zur Philosophie der Mathematik

Phytodiversité, traits fonctionnels et conditions du sol des savanes herbeuses sur cuirasse latéritique (bowé) au sud-est du Burkina Faso

Grassavannen auf Lateritkrusten sind charakteristische Landschaftselemente der sudanischen Savannen. Im zu Burkina Faso gehörenden Teil des W-Nationalparks und seiner Umgebung wurde die pflanzliche Diversität der Savannen auf und in der Umgebung von 19 Bowé-Flächen entlang von Transekten untersucht. Vegetationsstruktur und Artenzusammensetzung der Kraut- und Gehölzschicht, Bodentiefe, Körnung und die Gehalte an Na+, K+, Mg2+, Ca2+, H+, C und N wurden auf jeder Fläche und in deren Umgebung ermittelt. Unsere Ergebnisse zeigen, dass die Böden auf den Lateritkrusten im Vergleich zu denen der umgebenden gehölzreichen Savannen ziemlich flach und sauer sind. Die Nährstoffverfügbarkeit ist daher vergleichsweise niedrig. Die Flora umfasst 130 Arten, insbesondere aus den Familien Combretaceae, Cyperaceae, Leguminosae und Poaceae, wobei Therophyten dominieren. Bemerkenswert ist auch ein verhältnismäßig hoher Anteil an C4 Arten. Auf den Nationalpark umgebenden beweideten Flächen wurde eine höhere Artenzahl gefunden als innerhalb des Parkes, was auf die höhere Zahl von Pionieren, ruderalen und ungenießbaren Arten zurückzuführen ist. Aufgrund ihrer extremen edaphischen und hydrologischen Bedingungen besitzen die Savannen auf den Lateritkrusten eine deutlich von den angrenzenden Flächen unterschiedene spezifische Vegetation.Grass savannas on lateritic crusts are characteristic landscape elements of the Sudanian savannas. In the W National Park and its surroundings in SE-Burkina Faso, plant diversity of savannas on and adjacent to bowé was assessed by a survey of 19 bowal areas with relevés along transects in each of these. The vegetation structure and species composition of the herb and shrub strata, soil depth, particle size and the concentration of Na+, K+, Mg2+, Ca2+, H+, C and N were recorded on each bowal and its surroundings. Our results show that soils on lateritic crusts are rather shallow and acidic compared to the surrounding savanna woodlands. Nutrient availability is hence comparatively low. The observed flora comprises 130 species mainly belonging to the families Combretaceae, Cyperaceae, Leguminosae and Poaceae with a predominance of therophytes and a comparatively high share of C4 species. In the pastures surrounding the National Park a higher species richness was found than inside the Park due to the occurrence of pioneers, ruderal and unpalatable plants. Savannas on lateritic crusts exhibit due to their extreme edaphic and hydrological conditions a specific flora distinct from their surroundings.Les savanes herbeuses sur cuirasse lateritique sont des elements de paysage typiques de la savane soudanienne. Dans le Parc national de la W et ses environs au Sud-est du Burkina Faso, la phytodiversité des savanes sur bowé et à côté d'eux étais saisi sur 19 sites de bowal avec des relevés suivant des transects. La structure de la végétation et la composition spécifique des strates herbacée et ligneuse, la profondeur du sol, la taille du grain et la concentration de Na+, K+, Mg2+, Ca2+, H+, C et N étaient notés pour chaque bowal et ses environs. Nos résultants montrent que les sols sur cuirasse latéritique sont peu profonds et acidiques par rapport aux savanes voisines. La disponibilité de nutriments et relativement basse. Les 130 espèces observées pour la plupart font parti des familles Combretaceae, Cyperaceae, Leguminosae and Poaceae avec une prédominance des thérophytes et une proportion élevée des espèces C4. Dans les aires pâturées autour du parc national, une richesse spécifique plus élevée qu'à l'intérieur était trouvé par l'occurrence des espèces pionnières et des plantes rudéraux et non comestibles. Les savanes sur cuirasse latéritique montrent une flore distincte de ses environs à cause des extrêmes édaphiques et hydrologiques

Design and Investigation of a Touch Gesture for Dividing in a Virtual Manipulative Model for Equation-solving

publishedVersio

Effect of ABCG2, OCT1, and ABCB1(MDR1) Gene Expression on Treatment-Free Remission in a EURO-SKI Subtrial

Introduction Tyrosine kinase inhibitors (TKIs) can safely be discontinued in chronic myeloid leukemia (CML) patients with sustained deep molecular response. ABCG2 (breast cancer resistance protein), OCT1 (organic cation transporter 1), and ABCB1 (multidrug resistance protein 1) gene products are known to play a crucial role in acquired pharmacogenetic TKI resistance. Their influence on treatment-free remission (TFR) has not yet been investigated. Materials and Methods RNA was isolated on the last day of TKI intake from peripheral blood leukocytes of 132 chronic phase CML patients who discontinued TKI treatment within the European Stop Tyrosine Kinase Inhibitor Study trial. Plasmid standards were designed including subgenic inserts of OCT1, ABCG2, and ABCB1 together with GUSB as reference gene. For expression analyses, quantitative real-time polymerase chain reaction was used. Multiple Cox regression analysis was performed. In addition, gene expression cutoffs for patient risk stratification were investigated. Results The TFR rate of 132 patients, 12 months after TKI discontinuation, was 54% (95% confidence interval [CI], 46%-62%). ABCG2 expression (‰) was retained as the only significant variable (P = .02; hazard ratio, 1.04; 95% CI, 1.01-1.07) in multiple Cox regression analysis. Only for the ABCG2 efflux transporter, a significant cutoff was found (P = .04). Patients with an ABCG2/GUSB transcript level >4.5‰ (n = 93) showed a 12-month TFR rate of 47% (95% CI, 37%-57%), whereas patients with low ABCG2 expression (≤4.5‰; n = 39) had a 12-month TFR rate of 72% (95% CI, 55%-82%). Conclusion In this study, we investigated the effect of pharmacogenetics in the context of a CML treatment discontinuation trial. The transcript levels of the efflux transporter ABCG2 predicted TFR after TKI discontinuation

Development of algebraic structure sense in classroom instruction

When confronted with algebraic expressions, many see little more than a random combination of letters, numbers, and other signs. However, others easily approach the algebraic structures formed by the symbols; they manipulate expressions, evaluate them, get solutions. They have algebraic structure sense. This work investigates the processes of the development of algebraic structure sense in classroom instruction, drawing on data from two teaching units (one on linear equations, one on linear funtions) that were planned in cooperation with the mathematics teacher of the class. Two networked theoretical views - the GCSt model by Bikner-Ahsbahs and the Theory of Objectification by Radford - allow for the identification and interpretative description of situations in which students see structures and under the right circumstances develop algebraic structure sense. Using the documentary method, the long-term observations of classroom action are first understood in their complexity and then analyzed for their meaning with regard to the research questions. As a result, the development of algebraic structure sense can be described as a process of becoming familiar with the activity connected to the respective algebraic structure. With regard to linear equations a detailed pathway for this process is laid out. It is shown how the new view on the algebraic structure manifests itself in verbal descriptions and inscriptions. Furthermore, the role of prior knowledge is discussed. However, the development of algebraic structure sense is not a purely mental achievement: Situational interest and established roles influence the learning process. A social form of interaction is described that integrates all these aspects: Students tune their views on the algebraic structure with that of the teacher. In the closing discussion the empirical results are bound to the theories that were used. Furthermore, connections are made to the wider research landscape and it is shown how the results from this work are of relevance beyond its concrete topic

Solving equations : Gestures, (un)allowable hints, and the unsayable matter

International audienceThe goal of this paper is to contribute to the research on the introduction of solving linear equations. Subsumed in the " Comparing and Contrasting " category introduced in Prediger, Bikner-Ahsbahs and Arzarello's (2008) networking strategies, we contrast two episodes informed by two distinct theories and offer an insight into the teacher's role in introducing new knowledge in the classroom and the meaning-making narratives of hands-on didactic approaches to algebra. We examine the teachers' gestures and hints and what appears to be unsayable in the teacher-students' interaction

Analysis and classification of ECG-waves and rhythms using circular statistics and vector strength

The most common way to analyse heart rhythm is to calculate the RR-interval and the heart rate variability. For further evaluation, descriptive statistics are often used. Here we introduce a new and more natural heart rhythm analysis tool that is based on circular statistics and vector strength. Vector strength is a tool to measure the periodicity or lack of periodicity of a signal. We divide the signal into non-overlapping window segments and project the detected R-waves around the unit circle using the complex exponential function and the median RR-interval. In addition, we calculate the vector strength and apply circular statistics as wells as an angular histogram on the R-wave vectors. This approach enables an intuitive visualization and analysis of rhythmicity. Our results show that ECG-waves and rhythms can be easily visualized, analysed and classified by circular statistics and vector strength