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- Klang, Nina, 1978-, et al.
(författare)
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Mathematical Problem-Solving Through Cooperative Learning-The Importance of Peer Acceptance and Friendships
- 2021
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Ingår i: Frontiers in Education. - : Frontiers Media SA. - 2504-284X. ; 6
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Tidskriftsartikel (refereegranskat)abstract
- Mathematical problem-solving constitutes an important area of mathematics instruction, and there is a need for research on instructional approaches supporting student learning in this area. This study aims to contribute to previous research by studying the effects of an instructional approach of cooperative learning on students' mathematical problem-solving in heterogeneous classrooms in grade five, in which students with special needs are educated alongside with their peers. The intervention combined a cooperative learning approach with instruction in problem-solving strategies including mathematical models of multiplication/division, proportionality, and geometry. The teachers in the experimental group received training in cooperative learning and mathematical problem-solving, and implemented the intervention for 15 weeks. The teachers in the control group received training in mathematical problem-solving and provided instruction as they would usually. Students (269 in the intervention and 312 in the control group) participated in tests of mathematical problem-solving in the areas of multiplication/division, proportionality, and geometry before and after the intervention. The results revealed significant effects of the intervention on student performance in overall problem-solving and problem-solving in geometry. The students who received higher scores on social acceptance and friendships for the pre-test also received higher scores on the selected tests of mathematical problem-solving. Thus, the cooperative learning approach may lead to gains in mathematical problem-solving in heterogeneous classrooms, but social acceptance and friendships may also greatly impact students' results.
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| 2. |
- Kaipainen, Mauri, 1957-, et al.
(författare)
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Analysis and synthesis with a three component inferential system : Augmenting the explanatory scope of conceptual spaces
- 2017
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Ingår i: Artificial Intelligence and Cognition 2016. ; , s. 124-137
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Konferensbidrag (refereegranskat)abstract
- The study introduces a model of analysis and synthesis, respective abductive and deductive reasoning, using the three-component inferential system, which is constituted by a perspective-relative augmentation of Gärdenfors's theory of Conceptual Spaces (CS). A general formulation of Perspective, based on our earlier work, corresponds to prioritization among property dimensions. Instead of assuming one conceptual space as in the CS, a distinction is made between the high-dimensional description of the discourse/domain termed Ontospace, and the two-dimensional perspectival space onto which a Perspectiverelative hierarchical conceptualization is projected, referred to as the Perspectival Space. In this setting, deduction is the inference of Perspective-relative conceptualization of the ontospace, while abduction is the reasoning of the Perspective that accounts for a given conceptualization of the ontospace, given in a form of a target cluster This model is articulated on an abstraction level beyond algorithmic implementation.
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