Quotations: Problem-Oriented Teaching and the Importance of Tasks

«If we therefore undertake to let the child capture not only all sub-elements, but also the overall structure of an operational complex, it does not suffice to let the student carry out each single step of the thought himself. He must be led to establish the fundamental (intrinsic) relationships that characterize an operational complex, and only thereafter integrate the partial operations. The child’s exploring therefore needs to be given a framework, which from the very outset is aligned to the whole organization and which confers meaning to all steps that are taken in the course of searching. Now, this power which drives the process of inquiry can be engendered through nothing else but through a problem that is vivid in the student’s thinking.» (1951/1976, 91/92)

«The psychology of Jean Piaget indeed teaches us that a problem constitutes an ‘anticipatory schema’, in other words a schematic outline of an operation that is yet to be found, which belongs to an overall system of operations. This operation structures itself over the course of seeking and exploring and is ultimately clearly structured.» (1951/1976, 92)

«If the child is successfully brought to build up an operation by starting from a clearly identified problem, one can assume that he has not only understood all elements of the new mental act, but also its overall structure.» (1951/1976, 92)

«The task that underlies the student's free inquiry must be of such breadth that it preempts a meaningful operation and is not merely a partial act of thought, whose function within the overall consideration is only known to the teacher, while the student produces good luck answers, in the hope that something meaningful may come out of it.» (1951/1976, 94)

«As soon as the distance between the known old thinking schema and a new operation exceeds a certain limit, the class becomes lost in the course of researching. Hence, the rule for tasks which require independent seeking and researching from the student: Narrowing the breadth of the problem such that the class is able to find the solution itself, but without exceeding the limits of meaningful tasks.» (1951/1976, 94)

«Setting a task in a clear and vivid manner is the indispensable prerequisite for the student’s own seeking and researching.» (1951/1976, 94)

«When one speaks of ‘formation of thought’, one means ‘formation of operations’, and when one speaks of ‘formation of operations’, one means ‘building up operations’. The building up of operations is accomplished over the course of seeking and exploring, and all seeking and exploring arises from a problem.» (1951/1976, 94/95)

«If, when setting a problem, one does not tie in concepts and ideas which the student readily possesses, if the data to start with do not suffice, then the seeking and exploring does not lead to the desired results; one becomes lost, and some students refrain from making any effort.» (1951/1976, 95)

«A problem whose objective is to trigger or discover an operation is always an action schema that can be realized, be it by manipulating concrete objects or with the help of drawings on which students work by reshaping, dividing, transferring them etc.» (1951/1976, 96)

«What shape does a didactic unit take in school practice when the student is personally researching and seeking? As we have seen, it begins with a problem which is posed in the course of practical activities, either in real work in the school garden, workshops and suchlike or with other school work (fictitious problem of practical action). The task is discussed together until it is clear and vivid in the student’s mind. The students then begin to search for the solution themselves.» (1951/1976, 99)

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