In Germany the university entrance qualification is acquired by successfully passing the academic high school exit examination (Abitur). An important function of centrally organized high school exit examinations is to guarantee the comparability of graduations. This so called ‘comparability function’ of school certifications (Kühn, 2010) especially gained importance in Germany, since the PISA-Studies revealed that the comparability of graduations is not necessarily given in the German school system. (Blossfeld et al., 2011; Marzano & Heflebower, 2011). Therefore, the federal states of Germany - except for one - shifted from a decentral to a central organization of the examination system. This examination is centrally organized in 15 out of the 16 federal states of Germany. Only in one federal state the examination tasks are still compiled by the teachers.

Nevertheless, the assessment of these central examinations is still done by the course teachers, based on previously centrally defined criteria and sample solutions with a given scale of maximum points to be achieved. The examination procedure can thus be characterized as a half-standardized achievement test.

Previous studies have shown that teachers use diverse criteria and evaluation scales for assigning grades to written tests (Ingenkamp 1997; Schrader & Helmke 2001). The study presented in this paper therefore focuses on the inspection of the validity of the half-standardized achievement test procedure. For this purpose the examination tasks and the results of the central high school exit examinations in mathematics for the federal state of North-Rhine-Westphalia are compared to those of the standardized pre-university TIMSS-test (Baumert et al., 2000; Mullis et al., 1998). The pre-university TIMSS-test has been chosen to grasp the quality of the central high school exit examinations by comparing its results with the results of the written A-level examination in mathematics. The TIMSS-test is supposed to serve this function as it holds a very high curricular validity which has been once more reaffirmed in the context of the presented study itself.

Baumert, J., Bos, W., & Watermann, R. (2000). Fachleistungen im voruniversitären Mathematik- und Physikunterricht im internationalen Vergleich. In J. Baumert (Ed.). TIMSS/III. Dritte internationale Mathematik- und Naturwissenschaftsstudie – mathematische und naturwissenschaftliche Bildung am Ende der Schullaufbahn, (pp. 129–180). Opladen: Leske + Budrich. Blossfeld, H.-P.,Bos, W.,Daniel, H.-P.,Hannover, B.,Lenzen, D., & Prenzel, M. (2011). Gemeinsames Kernabitur. Zur Sicherung von nationalen Bildungsstandards und fairem Hochschulzugang. Münster: Waxmann. Bond, T. G., & Fox C. M. (2010): Applying the Rasch model. Fundamental measurement in the human sciences. Mahwah, NJ: Lawrence Erlbaum. Ingenkamp, K. (Hg.) (1997): Die Fragwürdigkeit der Zensurengebung. 9. Aufl. Weinheim: Beltz. Kühn, S. M. (2010). Steuerung und Innovation durch Abschlussprüfungen? Wiesbaden: VS Verlag. Marzano, R. J., & Heflebower, T. (2011). Grades that show what students know. Educational Leadership 69 (3), 34–39. Mullis, I.V., Martin, M.O., Beaton, A.E. et. al. (1998).Mathematics and science achievement in the final year of secondary school. IEA's Third International Mathematics and Science Study (TIMSS).Chestnut Hill and Boston College. Schrader, F.-W., & Helmke, A. (2001). Alltägliche Leistungsbeurteilung durch Lehrer. In F. E. Weinert (Hg.): Leistungsmessungen in Schulen. Weinheim: Beltz, S. 45–58.