Das Verständnis von Distributivität im Primarschulunterricht: Welcher instruktionale Weg ist lernwirksam?
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2024
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Doctoral Thesis
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Abstract
Mastering basic arithmetic operations such as multiplication tables is considered an important learning objective worldwide. An understanding of multiplication forms the basis for a great deal of future learning content. The question therefore arises as to how multiplication tables should ideally be taught at school.
From a didactic perspective, great importance is currently attached to the acquisition of the multiplication tables with the help of operational strategies or operational relationships. However, from an empirical perspective, it is not exactly clear how lessons should be designed to support the learning of young pupils.
For this reason, the learning environment (LU) 'PrinziDi' was developed and empirically tested on the basis of theory and empirical research. This forms the heart of this work. The LU 'PrinziDi' focuses on the development of conceptual understanding instead of the development of purely procedural knowledge or pure fact recall in multiplication tables. In contrast to traditional teaching materials, the LU is structured from the outset along the principle of distributivity as a mathematical structure or as a central subject-specific concept and along the corresponding operational strategies. A central task involves the diverse decomposition of a multiplication in the form of point fields in the sense of the part-part-whole concept. The LU also includes various cognitively activating procedures. Particular importance is attached to comparing and generating different solutions. These aspects have not yet been specifically focused on in Swiss teaching materials.
Another cornerstone of this thesis is the investigation of the sequencing of problem solving and instruction. The combination of both approaches (problem solving and instruction) is intended to combine the advantages of both. This draws conclusions from the study by Heinze et al. (2018, 2020), which compared a more teacher-controlled approach with a more student-controlled approach in the context of derived strategies for multi-digit addition/subtraction and, based on the results, proposed, among other things, the investigation of a combination of both approaches.
Some empirical studies have shown that ("student-driven") problem solving BEFORE instruction by the teacher (PS-I, Problem-Solving Followed by Instruction or PF) is more effective for learning than the conventional reverse approach in mathematics (TP, Tell-and-Practice or I-PS), in which the teacher instructs first and the learners only solve corresponding problems AFTER. For young children, however, the corresponding empirical evidence is very limited and contradictory. Here, too, the study should provide further insights.
In a quasi-experimental intervention study in Swiss primary school classes (N = 294, 2nd grade, 7 control classes with traditional teaching vs. 8 intervention classes with the LU 'PrinziDi'), the learning effectiveness of the learning environment 'PrinziDi' and the effects of sequencing (PS-I vs. TP) were examined. The effect of the intervention (4x2 lessons) on various aspects of knowledge (precursor skills, conceptual knowledge, procedural knowledge, procedural flexibility) was examined.
The comparison of control vs. intervention classes showed highly significant effects in conceptual and procedural knowledge as well as procedural flexibility in favor of the intervention classes. This shows that the LU is effective for learning. A comparison of the two intervention conditions (PS-I vs. TP) revealed no significant differences between the two conditions apart from the speed tests (procedural knowledge). In the speed test, however, there were highly significant advantages for the PS-I condition. It can be concluded from these results that younger learners can also benefit from a PS-I condition.
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Examiner : Stern, Elsbeth
Examiner : Heinze, Aiso
Examiner : Staub, Fritz
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ETH Zürich
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03753 - Stern, Elsbeth (ehemalig) / Stern, Elsbeth (former)