Der Mathematikunterricht der PISA-Schülerinnen und -Schüler

Der Beitrag besch?ftigt sich mit dem Mathematikunterricht der PISA-Schülerinnen und -Schüler in Deutschland und berichtet über Ergebnisse aus einer Zusatzstudie zu PISA 2003. Aufbauend auf der mathematik-didaktischen Rahmenkonzeption von PISA, die Unterricht als Gelegenheitsstruktur für verst?ndnisvolle Lernprozesse versteht, wurden Schülerinnen und Schüler und ihre Mathematiklehrkr?fte zu Merkmalen der Unterrichtsqualit?t befragt. Es zeigen sich schulformspezifische Unterrichtskulturen: Ein kognitiv aktivierender Umgang mit mathematischen Inhalten ist eher in Gymnasien zu beobachten, w?hrend vor allem in Hauptschulen die Unterrichtsform mit geringem kognitiven Gehalt und ausgepr?gter Unterstützung überwiegt. Dennoch wird die Angebotsstruktur des Mathematikunterrichts von Jugendlichen an Hauptschulen positiv beurteilt, w?hrend Gymnasiasten ihren Unterricht eher kritisch bewerten. Diese Differenzen sind vor allem durch Unterschiede in der individuellen Lernunterstützung durch die Lehrkr?fte zu erkl?ren, welche von Schülerinnen und Schülern an Hauptschulen als besonders ausgepr?gt, an Gymnasien eher als gering beschrieben wird.     

The Contribution of Reasoning to the Utilization of Feedback from Software When Solving Mathematical Problems

This study investigates how students’ reasoning contributes to their utilization of computer-generated feedback. Sixteen 16-year-old students solved a linear function task designed to present a challenge to them using dynamic software, GeoGebra, for assistance. The data were analysed with respect both to character of reasoning and to the use of feedback generated through activities in GeoGebra. The results showed that students who successfully solved the task were engaged in creative reasoning and used feedback extensively.     

Tangible User Interfaces and Contrasting Cases as a Preparation for Future Learning

In this paper, we describe an experiment that compared the use of a Tangible User Interface (physical objects augmented with digital information) and a set of Contrasting Cases as a preparation for future learning. We carried out an experiment (N?=?40) with a 2?×?2 design: the first factor compared traditional instruction (“Tell & Practice”) with a constructivist activity designed using the Preparation for Future Learning framework (PFL). The second factor contrasted state-of-the-art PFL learning activity (i.e., students studying Contrasting Cases) with an interactive tabletop featuring digitally enhanced manipulatives. In agreement with prior work, we found that dyads of students who followed the PFL activity achieved significantly higher learning gains compared to their peers who followed a traditional “Tell & Practice” instruction (large effect size). A similar effect was found in favor of the interactive tabletop compared to the Contrasting Cases (small-to-moderate effect size). We discuss implications for designing socio-constructivist activities using new computer interfaces.     

Primary Teachers’ Reflections on Inquiry- and Context-Based Science Education

Inquiry- and context-based teaching strategies have been proven to stimulate and motivate students’ interests in learning science. In this study, 12 teachers reflected on these strategies after using them in primary schools. The teachers participated in a continuous professional development (CPD) programme. During the programme, they were also introduced to a teaching model from a European project, where inquiry- and context-based education (IC-BaSE) strategies were fused. The research question related to teachers’ reflections on these teaching strategies, and whether they found the model to be useful in primary schools after testing it with their students. Data collection was performed during the CPD programme and consisted of audio-recorded group discussions, individual portfolios and field notes collected by researchers. Results showed that compared with using only one instructional strategy, teachers found the new teaching model to be a useful complement. However, their discussions also showed that they did not reflect on choices of strategies or purposes and aims relating to students’ understanding, or the content to be taught. Before the CPD programme, teachers discussed the use of inquiry mainly from the aspect that students enjoy practical work. After the programme, they identified additional reasons for using inquiry and discussed the importance of knowing why inquiry is performed. However, to develop teachers’ knowledge of instructional strategies as well as purposes for using certain strategies, there is need for further investigations among primary school teachers.     

Sir Charles Scott Sherrington (1857–1952)

Twentieth century bore witness to remarkable scientists who have advanced our understanding of the brain. Among them, Sir Charles Scott Sherrington’s ideas about the way in which the central nervous system operates has continuing relevance even today. He received honorary doctorates from twentytwo universities and was honoured with the Nobel Prize in Physiology or Medicine in the year 1932 along with Lord Edgar Adrian for their work on the functions of neurons. He developed our modern notion of the reflex as a model for how the periphery and spinal cord connect sensation and action.     

Petrochemical wastewater treatment with a pilot-scale bioaugmented biological treatment system

In solving the deterioration of biological treatment system treating petrochemical wastewater under low temperatures, bioaugmentation technology was adopted by delivering engineering bacteria into a pilot-scale two-stage anoxic-oxic (A/O) process based on previous lab-scale study. Experimental results showed that when the concentrations of COD and NH4 -N of the influent were 370~910 mg/L and 10~70 mg/L, the corresponding average concentrations of those of effluent were about 80 mg/L and 8 mg/L respectively, which was better than the Level I criteria of the Integrated Wastewater Discharge Standard (GB8978-1996). According to GC-MS analysis of the effluents from both the wastewater treatment plant (WWTP) and the pilot system, there were 68 kinds of persistent organic pollutants in the WWTP effluent, while there were only 32 in that of the pilot system. In addition, the amount of the organics in the effluent of the pilot system reduced by almost 50% compared to that of the WWTP. As a whole, after bioaugmentation, the organic removal efficiency of the wastewater treatment system obviously in- creased.     

Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity

We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential re- quirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc1-norm of the velocity gradient is locally integrable in time.     

Characterization of the mean velocity of a circular jet in a bounded basin

A circular jet has broad and important applications in practical engineering. Most research in this area has focused on a free jet, a wall jet or a vertical jet in a bounded domain. In this study, the mean velocities of circular offset jets were studied for four jet exit Froude numbers (Fr), three offset heights (S) (S/d=1, 2, 3) and three submergence ratios (ht/S) (surface jet, mixed jet, and submerged jet) in a bounded basin. Based on the results, we propose a velocity decay formula for a circular jet. The lateral velocity spread was more consistent with Gaussian and Cauchy–Lorentz distributions than the vertical velocity. Moreover, Fr had little effect on the decay of the mean velocity for a circular jet when Re>1×10⁴. The lateral and vertical spreads showed a quadratic relationship with the streamwise distance for different values of Fr at X/d<10. The positions of maximum mean velocity decay were independent of Fr and S/d when X/d<10. The spread rate was more uniform in the lateral direction than that in the vertical direction in a certain region for different S/d and ht/S. Therefore, the decay, spread, and maximum velocity position of the mean velocity for a circular offset jet can remain stable under different values of Fr, offset height, and submergence ratio.     

Factors affecting the adoption of e-learning systems in Qatar and USA: Extending the Unified Theory of Acceptance and Use of Technology 2 (UTAUT2)

This study examines the major factors that may hinder or enable the adoption of e-learning systems by university students in developing (Qatar) as well as developed (USA) countries. To this end, we used extended Unified Theory of Acceptance and Use of Technology 2 (UTAUT2) with Trust as an external variable. By means of an online survey, data were collected from 833 university students from a university in Qatar and another from USA. Structural equation modelling was employed as the main method of analysis in this study. The results show that performance expectancy, hedonic motivation, habit and trust are significant predictors of behavioural intention (BI) in both samples. However, contrary to our expectation, the relationship between price value and BI is insignificant. Our results also show that effort expectancy and social influence lead to an increase in students’ adoption of e-learning systems in developing countries but not in developed countries. Moreover, facilitating conditions increase e-learning adoption in developed countries which is not the case in developing countries. Overall, the proposed model achieves an acceptable fit and explains its variance for 68% of the Qatari sample and 63% of the USA sample. These results and their implications to both theory and practice are described.