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Mathematical thinking encompasses both formal deduction and semantic interpretation. Distinct formal shapes of mathematical statements form a foundation for syntactic conceptions of logical entailment, while mathematical cognition relies on quasi-empirical concept formation and knowledge acquisition. This work specifically examines the roles of semantic and syntactic aspects in mathematical reasoning within predicate logic and elementary algebra. An experimental framework is established to systematically differentiate between semantic and syntactic forms of mathematical thinking. Psychologically, both levels of processing are crucial in various mathematical reasoning types, yet their interrelation remains unclear. Important connections are revealed through everyday language, facilitating meaningful transitions between different descriptive levels and integrating multiple processing forms into a cohesive network of conceptual strategies. The findings are discussed concerning educational concepts and epistemological issues. Semantic perspectives indicate that, alongside traditional formal tools, empiristic methodologies in mathematics should also be acknowledged. The developed tools aim to enhance understanding of the fundamental modalities of mathematical reasoning, highlighting the richness and complexity of the processes involved.
Buchkauf
Semantic and syntactic levels of mathematical thinking and learning, Hermann Rodenhausen
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- Erscheinungsdatum
- 2009
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