The impact of learners' spatial capacity and world views on their spatial conceptualisation: a case study

This multi-sited case study aims to explore spatial capacity through pen-and-paper and hands-on activity tests, and explore world view perceptions of space in an attempt to show that spatial conceptualisation is a rich and complex blend of spatial capacity and world view. This study is oriented in a interpretive-naturalistic paradigm and characterised by multi-dimensional quantitative and qualitative methods. The research, set in five secondary schools in the Eastern Cape, was carried out with 32 Grade 11 learners and was designed around seven stages. This study attempts to understand spatial conceptualisation by recognising that all learners have epistemological macrostructures (world views) that shape their perceptions of the world in general and of space in particular. The main contention of this study is that spatial conceptualisation cannot be understood in isolation, through studying achievements on traditional pen-and-paper tests only. A comprehensive understanding of an individual's spatial conceptualisation involves the recognition of hands-on skills and world views as well. Spatial capacity, defined here in terms of spatial visualisation and orientation constructs, was explored through a pen-and-paper and a hands-on activity test. The results show only a weak to moderate correlation between the two tests, suggesting that performance in a traditional pen-and-paper test was not necessarily a good predictor for performance in a hands-on activity-based test. The investigation of world views was underpinned by a logico-structuralist process centred in conversations around nine bi-polar themes. Through a process of content- and meta- analyses involving the participation of a validation team, world-view profiles were established.In terms of the applied pen-and-paper test which explored spatial capacity, this study confirms males' dominance in all spatial tasks, particularly in three-dimensional problems. This was also found to be true for learners from the participating rural school and for those from disadvantaged socio-economic backgrounds. In the hands-on activity test, however, the study revealed no observable gender difference in favour of the males, except for items that were characterised by the spatial orientation construct. Both the participating rural and township schools performed poorly in items characterized by the spatial visualisation and orientation construct compared to the other participating schools. Although participants from the rural and township schools found it difficult to articulate their world views in depth, the world-view perspectives of space of this sample reveal rich and complex profiles that are similar across all the schools. Despite leaning towards a Newtonian division of absolute and relative space and containing strong religious elements, this sample generally views space as mysterious, infinite and somewhat obscure. It often refers to space in Kantian ideas and related space in terms of subjective feelings. Females in particular, refer to their own `space bubble', for example. Out of the world-view profile analysis, a meta-analysis was conducted which explored thinking skills in terms of capacity to abstract, to be insightful, deal with complex issues, engage critically, and be imaginative.This reveals that for this case, females were rated on a higher level than their male counterparts for their capacity to abstract and be complex (the capacity to identify related parts and to deal with composites), whereas males rated higher for showing insight, being imaginative, and being critical. Although there appear to be high correlations between the various tests, meta-levels and school performance for some of the participants, the same cannot be said for the sample as a whole. The world-view aspect of this study reveals a rich, often complex, understanding of space, strengthening the notion that world views are integral to a learner's cognition process

Teachers' use of verbal language to evoke visualizations in multilingual mathematics classes

Research into the importance of teachers’ use of verbal language in multilingual classes where teaching and learning is done in a language other than the learners’ first, is crucial. Such research aimed at improving multilingual learners’ access to conceptual understanding of mathematical concepts is becoming increasingly urgent. In this paper, we specifically report on a study that inter alia focused on how three purposively selected South African (Eastern Cape) Grade 11 multilingual mathematics teachers used learners’ first language, through code switching, to evoke visualizations for promoting conceptual understanding during the teaching of geometry and trigonometry. The study found that conceptual understanding was enhanced when teachers spoke in their learners’ first language using mostly everyday familiar words to evoke visualizations of some geometry and trigonometry concepts. Teachers also used isiXhosa terminology, the dominant language of the Eastern Cape Province in South Africa, to describe some mathematical constructs. A number of instances were noted in which teachers used pictorial illustrations from the learners’ environment when words or phrases were not immediately available to them, to promote conceptual teaching of mathematics. However, none of the strategies used were planned for; they were used spontaneously and on an ad hoc basis. We concluded that in multilingual mathematics classes, teachers should choose their verbal language carefully and purposefully to precisely demonstrate and make visible the intended mathematical ideas. Such use of verbal language is particularly important in situations where teachers cannot bring the actual or physical artefact of the mathematical idea to class. The underpinning theory that framed this paper was situated-sociocultural theory

Taming Instabilities in Power Grid Networks by Decentralized Control

Renewables will soon dominate energy production in our electric power system. And yet, how to integrate renewable energy into the grid and the market is still a subject of major debate. Decentral Smart Grid Control (DSGC) was recently proposed as a robust and decentralized approach to balance supply and demand and to guarantee a grid operation that is both economically and dynamically feasible. Here, we analyze the impact of network topology by assessing the stability of essential network motifs using both linear stability analysis and basin volume for delay systems. Our results indicate that if frequency measurements are averaged over sufficiently large time intervals, DSGC enhances the stability of extended power grid systems. We further investigate whether DSGC supports centralized and/or decentralized power production and find it to be applicable to both. However, our results on cycle-like systems suggest that DSGC favors systems with decentralized production. Here, lower line capacities and lower averaging times are required compared to those with centralized production.Comment: 21 pages, 6 figures This is a pre-print of a manuscript submitted to The European Physical Journal. The final publication is available at Springer via http://dx.doi.org/10.1140/epjst/e2015-50136-

Absicherung von Strompreisrisiken mit Futures: Theorie und Empirie

The regulatory changes in the german electric power market result in rising electricity price volatility. As a consequence electricity price risk management is essential for an electricity trader. The paper therefore analyzes the needed volume of futures hedging for an electricity trader, that ist tries to derive the optimal hedge ratio. In the first step the theoretical conditions for a preference-free optimal hedge ratio are discussed. In the second step these conditions are analyzed empirically with data for the german electricity exchange EEX and the scandinavian electricity exchange Nord Pool. --Electricity Price Risk,Electricity Futures,optimal Hedge Ratio

AN ANALYSIS OF LEARNERS’ SOLUTION STRATEGIES IN THE CONTEXT OF MODELLING TASKS

It remains a challenge for teachers to integrate modeling tasks in everyday mathematics classes. Many studies have been conducted that show the difficulties faced by teachers.  One of the challenging aspects in this regard is that of assessment. In the present study, a connection between structures of learners’ solution strategies and cognitive considerations is established to develop a practice-oriented instrument to determine and assess the complexity of solution strategies of modeling tasks. In this paper, the selected learners’ strategies’ structure was analyzed in-depth to identify the underlying cognitive structure. The results show that thought operations carried out in parallel complicated a solution strategy.  However, the results also support a purely sequential thought operation approach without weighting parallel thought operations, which corresponds to an intuitive assessment procedure by mathematics teachers. As assessment is a great challenge for many teachers in the context of modeling tasks, this study provides a promising frame of reference for further research in this important domain of assessment and modeling

Die Tibiavalgisationsosteotomie mittels Kallusdistraktion

Zusammenfassung: Operationsziel: Korrektur einer varischen Tibiaachse und Entlastung des medialen Kniekompartiments durch mediale Osteotomie im Tibiakopfbereich und Kallusdistraktion zur Valgisation. Indikationen: Symptomatisches Varusknie bei —medialem Postmeniskektomie-Syndrom, —medialer Gonarthrose, —Knorpelläsionen des medialen Kompartiments, —avaskulärer Osteonekrose des medialen Femurkondylus (Morbus Ahlbäck), —Osteochondrosis dissecans des medialen Femurkondylus, —posterolateraler und/oder anteromedialer Rotationsinstabilität des Kniegelenks. Kontraindikationen: Fortgeschrittene Pathologie der Kniegelenkflächen des lateralen Kompartiments. Fortgeschrittene Begleitarthrose des femoropatellaren Gelenks. Extensionsdefizit > 10°. Wenig aktive > 60-jährige Patienten. Operationstechnik: Anlegen eines Fixateur externe unter Bildwandlerkontrolle möglichst nahe zur Gelenklinie. Hautinzision medial der Tuberositas tibiae. Tibiaosteotomie zwischen den proximalen Schrauben des Fixateurs und der Tuberositas tibiae unter Schonung der lateralen Kortikalis. Intraoperative Kontrolle der Distraktion unter dem Bildwandler bis zur gewünschten Korrektur. Zuklappen der Distraktion. Weiterbehandlung: Distraktionsphase ab dem 5. postoperativen Tag mit 1 mm Distraktion pro Tag. Röntgenkontrollen am 5.-7. Tag, nach 6 Wochen und nach 8-10 Wochen nach Beginn der Distraktion, je nach Heilungsverlauf. Bei radiologisch erreichter Korrektur Beendigung der Distraktion und bei genügender Kallusformation Entfernung des Fixateurs unter Belassen der Schrauben. Bei unveränderter Korrektur nach Vollbelastung Entfernung der Schrauben. Ergebnisse: Zwischen 1998 und 2000 wurden bei 24 Patienten (sechs weiblich, 18 männlich, Alter 21-64 Jahre) 34 Kallusdistraktionen durchgeführt, bei zehn Patienten bilateral. 21 Patienten wurden nach 6-36 Monaten (Durchschnitt 23 Monate) nachuntersucht; eine Patientin wurde nach Implantation einer Totalendoprothese ausgeschlossen. Die femorotibiale Achse betrug präoperativ 179° (172-183°) und postoperativ 185° (179-191°). Die mediane Korrektur belief sich somit auf 6° (3-12°). 20 Patienten würden die Operation nochmals durchführen lassen. Der von den Autoren entwickelte Score verbesserte sich von präoperativ 15 auf postoperativ 10 Punkte, entsprechend einem guten Ergebnis. Komplikationen traten bei 15 Korrekturen (48%) auf, wovon acht (26%) eine operative Revision benötigte

Designing and making a difference: an exploration of technology education for rural school teachers

This qualitative study focused on a Technology Education programme for farm school teachers in the Eastern Cape province of South Africa. These teachers were faced with the challenge of incorporating Technology Education into their curriculum. The study was conducted within the context of an investigation into the conceptual nature of technology and an exploration of the theoretical underpinnings of Technology Education within both the international and South African context. Technology Education is being introduced into the South African curriculum against a background of educational transformation and the building of capacity to solve real life problems. This calls for a curriculum that will empower learners to be innovative, creative and skilled problem solvers. The introduction and incorporation of Technoiogy Education into the school curriculum poses a formidable challenge to farm schools in particular. Their unique history of neglect and legacy of underqualified teachers has made the introduction of any curriculum innovation process very difficult and challenging. This study analyses how an introductory Technology Education programme for farm school teachers in the Winterberg area of the Eastern Cape impacted~ on the teachers' professional and personal lives. It shows the importance of developing teclpological skills in conjunction with life skills in cO.ntributing to the empowerment, both in the work place and in the wider context, of rural school teachers. It highlights the need for supportive in-service education programmes and strengthens the argument for an integrative and mulitidisciplinary approach to the introduction of Technology Education in farm schools. Data was collected by means of questionnaires, interviews and photographs