Katrin Löwen

Aufgaben im COACTIV-Projekt: Zeugnisse des kognitiven Aktivierungspotentials im deutschen Mathematikunterricht

ZusammenfassungIm Rahmen des DFG-Projekts «Professionswissen von Lehrkräften, kognitiv aktivierender Mathematikunterricht und die Entwicklung von mathematischer Kompetenz» (kurz: COACTIV) wurden die Mathematiklehrkräfte, deren Klassen an den PISA-Erhebungen 2003 und 2004 teilnahmen, befragt und getestet. Um die Qualität der im deutschen Mathematikunterricht gegen Ende der Sekundarstufe I eingesetzten Aufgaben zu untersuchen, wurden von diesen Lehrkräften Mathematikaufgaben eingesammelt, die sie in ihren Klassen (Jahrgangsstufe 9 und 10) im Schuljahr 2003/2004 verwendet hatten (im Unterricht, in Klassenarbeiten oder in Hausaufgaben). Diese Aufgaben (ca. 45.000) wurden anhand eines in COACTIV entwickelten Klassifikationsschemas beurteilt. Dabei sollte der Frage nachgegangen werden, welches Potential diese Aufgaben fur Lerngelegenheiten im Mathematikunterricht bieten. In diesem Beitrag werden die wichtigsten Kategorien des Klassifikationsschemas vorgestellt und ausgewählte Ergebnisse berichtet.AbstractIn the context of the DFG-funded project “Professional Knowledge of Teachers, Cognitively Activating Instruction, and the Development of Students’ Mathematical Competence” (COACTIV), the mathematics teachers whose classes participated in the 2003/2004 longitudinal component of the PISA assessment in Germany were surveyed and tested. To provide insights into the quality of the tasks implemented in German mathematics classrooms toward the end of secondary level I, the teachers were also asked to submit the examinations, tests, and homework assignments they had set for their 9th and 10th grade classes in the 2003/2004 school year. All tasks (approx. 45,000) were then coded according to a classification scheme developed specifically for COACTIV. The objective was to investigate the potential of these tasks to provide learning opportunities in the mathematics classroom. This article presents the major categories of the classification scheme and reports selected findings.

Task Analysis in COACTIV: Examining the Potential for Cognitive Activation in German Mathematics Classrooms

Although COACTIV did not gather data directly by means of classroom observation, it nevertheless provided concrete insights into the mathematics instruction provided, by reconstructing learning situations at the task level. Specifically, the tasks actually assigned by the COACTIV teachers were analyzed as documents of mathematics instruction, being classified according to a newly developed classification system with a focus on the potential for cognitive activation. The structure and scope of this classification system are presented in this chapter. As a complement to the self-report measures discussed in Chap. 6, the tasks submitted by the COACTIV teachers provide real, “objective” evidence of the content of mathematics instruction at the end of lower secondary education in Germany. The results presented in Chap. 6 and in this chapter support each other in indicating that mathematics instruction in Germany tends to offer little potential for cognitive activation. Yet, as Chap. 9 shows, exposure to more cognitively demanding tasks has positive effects on student learning gains. On the meta-level, our findings provide evidence for the theoretical argument that the tasks administered play a key role in promoting students’ mathematical learning—and that tasks are thus indeed suitable indicators of cognitive activation in the classroom.

The COACTIV Research Program: Methodological Framework

This chapter provides the methodological background for all analyses reported in this book, describing the various studies that constitute the COACTIV research program. The first main study in the program was the COACTIV study, which laid the theoretical and empirical foundations for the COACTIV research program. In this study, aspects of the professional competence of a sample of 372 secondary school mathematics teachers were assessed using questionnaires, tests, and task analyses. An important feature of this study was its embedding in the 2003 PISA student assessment, which made it possible to investigate effects of teacher competence on instructional quality and student-related outcomes. This first main study was complemented by several smaller validation studies. The second main study, COACTIV-R, used a longitudinal design to investigate 856 teacher candidates during the practical induction phase of preservice teacher education in Germany over the course of 1 year. The third main study, BilWiss, investigates the nonsubject-specific general educational knowledge of a sample of more than 3,000 teacher candidates immediately after completion of the university-based phase of teacher education. The chapter provides information on the designs, samples, and instruments of these studies.