One of the indicators telling a teacher whether a pupil understands the subject matter is the pupil’s ability to come up with new,original solving procedures when solving a new problem.
But this is something a teacher cannot teach directly. He/she can expect this approach from their pupils, he/she can ask for it, support them in it but he/she cannot teach it (Sarrazy and
Novotná, 2013). This is one of the key concepts of didactics of mathematics, the didactical contract and paradoxes connected to it (Brousseau, 1997).
One of the indicators telling a teacher whether a pupil understands the subject matter is the pupil’s ability to come up with new,original solving procedures when solving a new problem.But this is something a teacher cannot teach directly. He/she can expect this approach from their pupils, he/she can ask for it, support them in it but he/she cannot teach it (Sarrazy andNovotná, 2013). This is one of the key concepts of didactics of mathematics, the didactical contract and paradoxes connected to it (Brousseau, 1997).
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