We present an experimental research aimed at understanding the potential of the Core Concept (CC), intended as a generative and transdisciplinary element that cyclically recurs in a discipline and has a structuring value for the learning. The study is in tune with recent trends calling for synergies between Mathematics Education and other disciplines, especially for teacher professional development (Bakker, 2021). The CC, as a boundary object between Mathematics Education and Teaching Education, was used as an operative tool in a pedagogical device involving pre-service teachers (PTs); our goal was to explore at what extent the CC fosters the PTs’ evolution of cognitive processes and (re)construction of mathematical meanings. PTs faced a learning path consisting in: solving an arithmetic-algebraic task; reviewing their solution after the introduction of the CC; metacognitively reflecting on the experience done. We collected the PTs’ productions and used the levels of generalization (Radford, 2001) as a theoretical lens to analyze the development of the PTs’ cognitive processes. Our qualitative analysis of the PTs’ solutions, supported by their reflections, allowed us to highlight the role of the CC in favoring the PTs’ transition from the factual level of generalization (operative solution of the task), to the contextual one (emergence of structural regularities as mathematical objects), to the symbolic one (elaboration of mathematical meanings). Moreover, previously unforeseen aspects arose: a dynamic interplay emerged between the CC and the mathematical activity. The CC revealed its value as a structuring and structured element: it gave structure to the learning path, promoting the PTs’ transition towards higher levels of generalization; conversely, it was structured by its instrumental use within the mathematical task. The results have implications for teachers’ education, suggesting to design learning paths based on CC.
Promoting pre-service teachers’ evolution in Radford’s levels of generalization through the Core Concepts
Antonella Montone;
2021-01-01
Abstract
We present an experimental research aimed at understanding the potential of the Core Concept (CC), intended as a generative and transdisciplinary element that cyclically recurs in a discipline and has a structuring value for the learning. The study is in tune with recent trends calling for synergies between Mathematics Education and other disciplines, especially for teacher professional development (Bakker, 2021). The CC, as a boundary object between Mathematics Education and Teaching Education, was used as an operative tool in a pedagogical device involving pre-service teachers (PTs); our goal was to explore at what extent the CC fosters the PTs’ evolution of cognitive processes and (re)construction of mathematical meanings. PTs faced a learning path consisting in: solving an arithmetic-algebraic task; reviewing their solution after the introduction of the CC; metacognitively reflecting on the experience done. We collected the PTs’ productions and used the levels of generalization (Radford, 2001) as a theoretical lens to analyze the development of the PTs’ cognitive processes. Our qualitative analysis of the PTs’ solutions, supported by their reflections, allowed us to highlight the role of the CC in favoring the PTs’ transition from the factual level of generalization (operative solution of the task), to the contextual one (emergence of structural regularities as mathematical objects), to the symbolic one (elaboration of mathematical meanings). Moreover, previously unforeseen aspects arose: a dynamic interplay emerged between the CC and the mathematical activity. The CC revealed its value as a structuring and structured element: it gave structure to the learning path, promoting the PTs’ transition towards higher levels of generalization; conversely, it was structured by its instrumental use within the mathematical task. The results have implications for teachers’ education, suggesting to design learning paths based on CC.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
