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Open-Ended Tasks

Imagination does not mean conceiving entirely anew, but doing something from existing things.
Thomas Mann

adenauer This monument stands at Bundeskanzlerplatz in Bonn. It shows the head of Konrad Adenauer, who was the first Chancellor of the Federal Republic of Germany between 1949 and 1963.

What would be the size of a corresponding life-size monument of Adenauer on the same scale?

Explain your ideas to your group mates.

Present your ideas and results as a group to your classmates.

Picture source: GA archives
Task according to: HERGET; JAHNKE; KROLL, productive tasks for teaching mathematics at secondary level I

What are open-ended tasks?

A task is open if it does not lead in small steps to a certain result that not just gives a solution or a way to reach a solution. But it's not merely the task which determines whether it is open-ended or closed. It is also and in particular, the phases of teaching that develop in the context of the task.

Closed tasks can lead to open-ended ones when

  • information is omitted,
  • initial conditions are changed,
  • a task is reversed,
  • many or all possible solutions can be sought and
  • the approach can be justified

You can find here additional material for information and use in teaching:

W. Herget (2001), A picture conveys more than a 1000 words ... Measuring, Estimating, Thinking - many ways, many answers (PDF, 4 MB)

W. Herget, D. Scholz, A different kind of task - from the newspaper, Kallmeyer, 1998