Developing children's conceptual understanding of area measurement: A curriculum and teaching experiment

The present study examined the effectiveness of three instructional treatments which had different combinations of mathematical elements regarding 2-dimensional (2-D) geometry and area measurement for developing 4th-grade children's understanding of the formulas for area measurement and their ability to solve area measurement problems. Participants were 120 fourth graders. The results showed that the enriched curriculum, involving the geometry motions and area measurement connections effectively facilitated children's mathematical judgments and explanations demanding high-level conceptual understanding. The instructional curricula accentuating only 2-D geometry or numerical calculations for area measurement did not exhibit such effectiveness. Interview data revealed that the geometric operations of superimposition, decomposition, re-composition as well as the concept of congruence were deemed essential by children for the conceptualization of the formulas for area measurement.     

Private Funding for University Research in Europe — Some Models and Conceptions*

Social scientists have discovered only recently that there exists between the two major forces of modern (Western) societies (that is the market on the one hand and government on the other hand) a third sector. This sector is characterized by forces like voluntarism, idealism, generosity, autonomy of action in the public interest, brotherhood, charity and institutions like private giving, free associations and societies, philanthropic foundations and charitable trusts. The third sector is helpful in achieving voluntaty social justice outside the enforced contributions of government. If government retreats even more the future from investing an adequate share of total revenue in the science community and higher education at large, this social sub-sector will need to look for alternative funding sources. Industry as contractor (naturally paying for the goods and services delivered by the higher education sector) may be one source. The third sector, known to many of the institutions of higher education for centuries, should be another. In the highly competitive environment of the future loyalties and other benign attitudes are no longer to be taken for granted, not even by alma mater. Therefore, higher education should invest some time and talents, as well as some ECUs in order to come to terms with this sector and to get a better share from its grant-making capacities. The opportunities are there.     

Szenario-basierter Systemtest von Software-Produktfamilien

Zusammenfassung In der Produktfamilienentwicklung werden durch zwei Entwicklungsprozesse, Domain und Application Engineering, zun"achst wiederverwendbare Entwicklungsartefakte produziert, um diese anschlie?end zur Konstruktion von kundenspezifischen Applikationen einzusetzen. Die Wiederverwendbarkeit wird durch die explizite Definition der Variabilit"at der geplanten Applikationen einer Produktfamilie erzielt. Diese proaktive Wiederverwendung ist bisher in den konstruktiven Entwicklungsphasen realisiert, jedoch noch nicht im Test. Mit ScenTED (Scen_ario based TE_st Case D_erivation) wird in diesem Beitrag eine wiederverwendungsorientierte Technik zur Testfallerstellung f"ur den Systemtest, dem Test eines ausf"uhrbaren Systems gegen spezifizierte Use-Cases, von Produktfamilien vorgestellt. ScenTED basiert auf zwei Kernideen: der Erhaltung der Variabilit"at in Testf"allen und der Szenario-basierten Verfeinerung der Testf"alle. Durch die Erhaltung der Variabilit"at wird die Wiederverwendbarkeit von Testf"allen gesichert; die Szenario-basierte Verfeinerung erm"oglicht Nachvollziehbarkeit durch die durchg"angige Nutzung von Szenarien. In diesem Beitrag wird die ScenTED-Technik an einem Beispiel erl"autert und Erfahrungen aus dem industriellen Einsatz diskutiert.

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Product family engineering consists of two development processes: Domain engineering and application engineering. Reuseable artefacts are created in the domain engineering process. These artefacts are used for the creation of customer specific applications during the application engineering process. Reusability is achieved with the explicit definition of variability that specifies the potential applications of the product family. The proactive reuse has been realized in the construnction phases of the development process, but not within the test phases. We propose ScenTED (Scen_ario based TE_st Case D_erivation) for the creation of reusable test cases for a use case based system testing in product family engineering. ScenTED has two key ideas: The first is the preservation of variability in test cases and the second idea is the scenario-based refinement of test cases. The preservation of variability ensures the reusability of test cases. The scenario-based refinement enables the traceability from requirements to test cases. We present the ScenTED technique in this article with an example and discuss an industrial case study.

CR Subject Classification D2.5