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.     

Ecosystems and Biodiversity Research

The common goals and the almost perfect complement of the initiatives taken in parallel at Kunming and at several Max Planck sites could serve as valuable starting points for further promoting the CAS/MPS partnership in all matching areas of ecological research.     

Formale objektorientierte Softwareentwicklung mit FOX{\cal F}{{\scriptstyle{\cal O}{\cal X}}}

Zusammenfassung.   Wir stellen die neue Methode vor, die auf die formale Entwicklung sequentieller, objektorientierter Softwaresysteme abzielt. ist eine synergetische Kombination aus der semiformalen Methode Fusion und der formalen Spezifikationssprache Object-Z. Die Methode unterscheidet ausdrücklich Analyse und Entwurf, um die Komplexit?t und die unterschiedlichen Aufgaben der Softwareentwicklung zu bew?ltigen. In jeder Entwicklungsphase werden Zustands- und Verhaltensspezifikationen in graphischer oder textueller Form erstellt. Wir geben Beweisverpflichtungen an, um zu gew?hrleisten, da? die entwickelten Spezifikationen formal konsistent und vollst?ndig sind, und da? das resultierende System zur Ausgangsspezifikation konform ist. Wir illustrieren die Anwendung von an einem einfachen Beispiel, einem Grapheditor. Eingegangen am 24. Dezember 1996 / Angenommen am 8.10.1997     

Teachers’ dilemmatic decision-making: reconciling coexisting policies of increased student retention and performance

In recent years, many countries within the Organisation for Economic Co-operation and Development have formulated educational policies aimed at providing better education to more students. However, this may be perceived as constituting dilemmatic spaces, where teachers must make efforts to reconcile coexisting political demands in their everyday work. The purpose of this article is to provide insight into how teachers handle coexisting educational policies of increased student retention and performance. Empirical findings from a one-year field study at a Danish vocational school explore how teachers’ decision-making as response to coexisting demands of increased student retention and performance involves the development of various pedagogical approaches to the students: an active ‘caring’ approach, a passive ‘wait until this class is over’ approach, an active ‘vocational gate-keeping’ approach, and a passive ‘wait and see whether they drop out’ approach. Based on the findings, it is argued that the various pedagogical approaches are developed through social negotiations with leaders, students, and other teachers. Moreover, these pedagogical approaches lead to the development of further negotiated, dilemmatic decisions to be made. Thus, a dynamic approach to teachers’ dilemmatic decision-making is proposed.     

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.