Development of a Test Instrument to Assess Mathematical Knowledge of Applicants for a Mathematics Teacher Training Program

Abstract

In line with the fact that many universities have to select the ``right students'' for a teacher training program as the number of student applicants increases and that, according to a ruling by the German Federal Constitutional Court in December 2017, this selection must not be based solely on the university entrance qualification grade, reliable instruments are needed to support university selection processes. With regard to later academic success, subject-specific knowledge tests have a particularly good prognostic validity; for teachers, subject-specific content knowledge is even considered a predictor of professional success. In addition to symbolic, formal and technical (declarative and procedural) knowledge about mathematical content (particularly of lower secondary level), which is predominantly operationalized in most of the mathematics specific tests used at the beginning of study, university lecturers also consider knowledge about process-related skills in arguing and proving, problem solving, modelling and communicating to be essential prerequisites for successful studies. However, there is no empirically proven instrument for the selection of applicants for a mathematics teacher training program that systematically assesses this prior knowledge. The paper therefore discusses the development of a test instrument that operationalizes content- and process-related mathematical prior knowledge for lower secondary level. Key results are: School-related mathematical prior content knowledge of test persons with high school diploma can be reliably and validly assessed in this breadth using tasks in multiple-choice format (being highly objective) as part of a classical paper-pencil test. Such a mathematics test provides differentiated information about content knowledge, which is only rarely explained by school grades or general cognitive abilities. The mathematics test provides a complementary basis for admission decisions and didactical developments of university courses.