Responsibility for German eucation system lies primarily with the states while the federal government only has a minor role. Optional kindergarten education is provided for all children between three and six years old, after which school attendance is compulsory for nine or ten years. In Germany, students are graded on a scale of one through six, one being high and six being very low, or failing. Home-schooling is not permitted in any of the German Bundesländer except if a child is suffering from some illness that makes it impossible for him or her to attend school. There are also rare cases where foreign families living for a short time in Germany have been granted exemption from compulsory schooling to homeschool their children in their own language. Primary education usually lasts for four years (6 in Berlin) and public schools are not stratified at this stage. In contrast, secondary education includes four types of schools based on a pupil's ability as determined by teacher recommendations: the Gymnasium includes the most gifted children and prepares students for university studies; the Realschule has a broader range of emphasis for intermediary students; the Hauptschule prepares pupils for vocational education, and the Gesamtschule or comprehensive school combines the three approaches. There are also Förderschulen (schools for the mentally challenged and physically challenged). One in 21 students attends a Förderschule In order to enter a university, high school students are required to take the Abitur examination, however students possessing a diploma from a vocational school may also apply to enter. A special system of apprenticeship called Duale Ausbildung allows pupils in vocational training to learn in a company as well as in a state-run school. Although Germany has had a history of a strong educational system, recent PISA student assessments demonstrated a weakness in certain subjects. In the test of 43 countries in the year 2000, Germany ranked 21st in reading and 20th in both mathematics and the natural sciences, prompting calls for reform.