RESUMEN

BACKGROUND: Many learning methods of mathematical reasoning encourage imitative procedures (algorithmic reasoning, AR) instead of more constructive reasoning processes (creative mathematical reasoning, CMR). Recent research suggest that learning with CMR compared to AR leads to better performance and differential brain activity during a subsequent test. Here, we considered the role of individual differences in cognitive ability in relation to effects of CMR. METHODS: We employed a within-subject intervention (N=72, MAge=18.0) followed by a brain-imaging session (fMRI) one week later. A battery of cognitive tests preceded the intervention. Participants were divided into three cognitive ability groups based on their cognitive score (low, intermediate and high). RESULTS: On mathematical tasks previously practiced with CMR compared to AR we observed better performance, and higher brain activity in key regions for mathematical cognition such as left angular gyrus and left inferior/middle frontal gyrus. The CMR-effects did not interact with cognitive ability, albeit the effects on performance were driven by the intermediate and high cognitive ability groups. CONCLUSIONS: Encouraging pupils to engage in constructive processes when learning mathematical reasoning confers lasting learning effects on brain activation, independent of cognitive ability. However, the lack of a CMR-effect on performance for the low cognitive ability group suggest future studies should focus on individualized learning interventions, allowing more opportunities for effortful struggle with CMR.

Asunto(s)

Mapeo Encefálico , Imagen por Resonancia Magnética , Humanos , Imagen por Resonancia Magnética/métodos , Mapeo Encefálico/métodos , Encéfalo/fisiología , Cognición/fisiología , Solución de Problemas/fisiología

RESUMEN

We here demonstrate common neurocognitive long-term memory effects of active learning that generalize over course subjects (mathematics and vocabulary) by the use of fMRI. One week after active learning, relative to more passive learning, performance and fronto-parietal brain activity was significantly higher during retesting, possibly related to the formation and reactivation of semantic representations. These observations indicate that active learning conditions stimulate common processes that become part of the representations and can be reactivated during retrieval to support performance. Our findings are of broad interest and educational significance related to the emerging consensus of active learning as critical in promoting good long-term retention.

Asunto(s)

Aprendizaje por Asociación/fisiología , Encéfalo/fisiología , Adolescente , Mapeo Encefálico/métodos , Humanos , Lingüística/métodos , Imagen por Resonancia Magnética/métodos , Matemática/métodos , Memoria a Largo Plazo/fisiología , Vocabulario

RESUMEN

In the field of mathematics education, one of the main questions remaining under debate is whether students' development of mathematical reasoning and problem-solving is aided more by solving tasks with given instructions or by solving them without instructions. It has been argued, that providing little or no instruction for a mathematical task generates a mathematical struggle, which can facilitate learning. This view in contrast, tasks in which routine procedures can be applied can lead to mechanical repetition with little or no conceptual understanding. This study contrasts Creative Mathematical Reasoning (CMR), in which students must construct the mathematical method, with Algorithmic Reasoning (AR), in which predetermined methods and procedures on how to solve the task are given. Moreover, measures of fluid intelligence and working memory capacity are included in the analyses alongside the students' math tracks. The results show that practicing with CMR tasks was superior to practicing with AR tasks in terms of students' performance on practiced test tasks and transfer test tasks. Cognitive proficiency was shown to have an effect on students' learning for both CMR and AR learning conditions. However, math tracks (advanced versus a more basic level) showed no significant effect. It is argued that going beyond step-by-step textbook solutions is essential and that students need to be presented with mathematical activities involving a struggle. In the CMR approach, students must focus on the relevant information in order to solve the task, and the characteristics of CMR tasks can guide students to the structural features that are critical for aiding comprehension.