On Friday, tens of thousands of high school graduates beat the hour of truth nationwide: in the written exam in mathematics, they had to show how well they could handle parabolas, levels in space, and binomial distributions.
Although there is still no central high school in Germany, had many students between Rostock and Garmisch-Partenkirchen solve the same tasks. These came from a pool of tasks shared by several federal states. And possibly these were significantly heavier than in the class exams of previous years. In the meantime, more than 60,000 students have signed an online petition calling for a less stringent assessment of the tasks.
But how hard were the tasks actually? So far, the German Teachers Association sees no signs that the tasks were too complicated. "On the Internet, excitement can be mobilized very quickly, so we should wait and see," said Association President Heinz-Peter Meidinger of the "Rhein-Neckar-Zeitung".
"Comparable to the task of 2018"
Niklas Kellner, high school teacher from Munich, sees it very similar: "It was not an impossible task." Apparently, however, the text lengths would have unsettled some students. "There were fewer standard assignments this year, and the students had to figure it out a bit more."
But that was also wanted. It is about understanding and not so much about solving the same tasks with memorized schemas. "The task from the stochastics was comparable to the task of 2018 except for the more complicated formulations," says the teacher, who also offers tutoring on the Internet and Abi Crash Courses under the name of Mathekellner.
Kellner can understand the displeasure of the students in Bavaria but. Because at least compared to 2018, the tasks were more difficult this year. In the previous year, however, there was also a special feature: After a theft of the examination tasks from a school, some tasks had to be exchanged at short notice - and the new tasks proved to be comparatively easy.
The Bavarian Ministry of Culture explained on SPIEGEL inquiry that it takes the instructions of the students "very seriously". They have launched a request to schools and teachers, said Ministry spokesman Günther Schuster. "We want to gather the data and facts to make an assessment."
SPIEGEL ONLINE has taken a closer look at two of the students' stochastic issues - and explains how they are resolved. More detailed explanations can be found on the youtube channel of Mathekellner.
These are two examples from the task pool used in 2019. Because the schools or school authorities were able to select from this pool, however, the Abitur tasks differ from school to school or from country to country.
Stochastic Task 1
A lottery advertises that every ticket wins. The lots and related prizes can be categorized into three categories called "Danube", "Main" and "Lech". The Lostopf contains four times as many lots in the "Main" category as lots in the "Danube" category.
One ticket costs 1 Euro. The owner of the Losbude pays 8 euros in purchasing for a material prize in the category "Danube", 2 euros in the category "Main" and 20 cent in the category "Lech". Determine how large the share of the Danube lots should be if the owner wants to earn an average of 35 cents per lot.
Stochastic task 2
The owner of the Losbude employs an employee who addresses visitors to the folk festival to encourage them to buy lots. She is dissatisfied with the success rate of the employee.
The owner wants to cut the employee's salary if less than 15 percent of the targeted visitors buy tickets. The salary reduction decision should be made using a significance test based on 100 targeted visitors.
It should be avoided as possible to reduce the employee's salary wrongly. Indicate the corresponding null hypothesis and determine the associated decision rule at the significance level of 10 percent. (Note: There is a second question for this task, which we have omitted here.)