What does conceptual study mean

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Teaching concept: conceptual basics


The three examples and the objectives developed by them can be regarded as representative examples to illustrate the conceptual basis of training in the IEEM. These can be briefly characterized by the following three terms.

Process-oriented view of the subject

In the eyes of many people, mathematics is a firmly established system of clearly delimited and emerging terms, rules and procedures that are precisely tailored to specific classes of tasks. Learning mathematics is therefore understood as receiving and reproducing given elements of knowledge and instructions. The IEEM, on the other hand, represents a different understanding of mathematics. Mathematics is not a finished product, but rather forms with learners in the process of searching for connections, abnormalities and appropriate interpretations of mathematical relationships (see example Cenk). In other words, mathematics is the science of patterns.


Competence-oriented view of the learner

Learners are not infrequently viewed by adults as ignorant people who need to be imparted the necessary knowledge. Statements and actions that do not match the adults' expectations are then viewed as incorrect and in need of immediate correction. In contrast, the IEEM propagates a point of view that focuses on the learners with their knowledge and understanding (example Lisa): What could they have thought? What can they do? What are the reasonable grounds for an adult wrong approach?

Out more competence-oriented The otherness of their thinking is not seen as Deficit of the child, but as an authentic form of expression and thus as Difference between children and adults seen.


Subject-oriented view of learning

Lessons are sometimes still understood as a place in which the learning material - the fully organized building of mathematics - is pre-portioned into small learning nibbles, which are then to be conveyed in small steps. In such a lesson, the learners are the objects of instruction. In contrast, an orientation to the learning subjects, to their previous knowledge and skills is absolutely necessary. However, it should not be with subjectcentering be equated. Good math lessons benefit from the productive tension openness and structure. It builds on individually differentiated competencies. At the same time, it is goal-oriented and conceptually sound. Timi, for example, could be encouraged by the teacher to produce further examples with subsequent systematization.



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Conceptual basics

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Closing words by Hans Freudenthal