Rita Stebler

Every word problem has a solution--the social rationality of mathematical modeling in schools

Abstract The focus of this paper is on sense-making and the use of real-world knowledge in mathematical modeling in schools. Arguments are put forward that classroom word problem solving is more—and also less—than the analysis of subject-matter structures. Students easily “solve” stereotyped, even unsolvable, problems without any regard to the constraints of factual reality. Mathematics learning in schools is inseparable not only from the materials employed, but from the macro- and microcultural web of practices within the social context of schooling. It represents, beyond the insightful activity of ideal problem solving, a type of socio-cognitive skill. The two experiments reported replicate and extend a study by Verschaffel, De Corte, and Lasure (1994). In the first experiment, a list of standard problems that could be solved by straightforward use of arithmetic operations, and a parallel list of problems which were problematic with respect to realistic mathematical modeling, were administered to fourth and fifth graders. In the second experiment, a similar list of problematic problems was presented to seventh graders under three socio-contextual conditions varying in the degree to which the pupils were told or signaled that the problems were more difficult to solve than it seemed at first or that they even could be unsolvable. The result of both studies was that most pupils “solved” a significant part of the unsolvable problems without evincing “realistic reactions”. This overall finding is discussed with respect to three issues: 1. (i) the quality of word problems employed in mathematics education, 2. (ii) the culture of teaching and learning, and 3. (iii) the more general issue of social rationality in school mathematics problem solving.

Individuelle mathematikbezogene Lernunterstützung bei Regelspielen zur Förderung früher Mengen-Zahlen-Kompetenzen im Kindergarten

Anhand von Videoaufnahmen aus 29 Kindergartenklassen wird die individuelle mathematikbezogene Lernunterstutzung durch die Padagogin am Beispiel eines Regelspiels zur Forderung von Mengen- und Zahlenkompetenzen untersucht. Dabei werden die mathematikhaltigen Padagogin-Kind-Interaktionen, die rund 18% der Spieldauer ausmachen, anhand eines sozial-konstruktivistisch begrundeten Modells der Lernunterstutzung eingeschatzt. Es zeigt sich, dass die individuelle mathematische Lernunterstutzung vorwiegend positiv beurteilt wird, dass aber viele Padagoginnen ihr differenziertes Wissen uber den aktuellen Lernstand einzelner Kinder nicht hinreichend nutzen, wenn sie ein Kind in der Spielsituation individuell unterstutzen. Die Ergebnisse werden mit Blick auf den Aufbau fachlicher und didaktischer Kompetenzen fur eine spielbasierte mathematische Forderung im Kindergarten diskutiert.

Learning through play – pedagogy and learning outcomes in early childhood mathematics

ABSTRACT Whilst research underlines the importance of early mathematics in kindergarten, practitioners need effective and innovative approaches to pedagogy. Currently, very different approaches are deployed from an instructional, educator-led approach based on training programmes to a play-based approach. This intervention study examines the effects on the mathematical competency of these two pedagogies. Thirty-five kindergarten educators and 324 six-year-old children were randomly assigned to either a training programme, a play-based approach with card and board games or to the control group. Educators’ views on the interventions were gathered in semi-structured interviews. The results indicate higher learning gains overall for the play-based approach. Differentiated effects were found as tendencies: children with low competencies tend to gain more from training programmes compared to no intervention; children with high competencies gain more from the play-based approach than the training. Educators evaluated the play-based intervention with card and board games as better suited to children’s diverse needs.

Unterricht in altersdurchmischten Grundstufenklassen — ein Schulversuch zur Bildung der 4- bis 7-jährigen Kinder im Kanton Zürich

Unter der Bezeichnung „Projekt Grundstufe“ wird im Kanton Zurich eine neue Schulform erprobt, die zwei Jahre Kindergarten und die erste Klasse der Primarschule zusammenfuhrt. An der Erprobung beteiligen sich auf freiwilliger Basis 27 Schulgemeinden bzw. Schulkreise mit 78 Grundstufenklassen, die mit Be ginn des Schuljahres 2004/2005 in drei Staffeln ins Projekt eingestiegen sind. Der Schulversuch dauert bis August 2012.