Learning of Mathematical Analysis Based on the Integration of Philosophical Analysis and Neurocognitive Findings of Symbolic Mathematics

The main purpose of this paper is to investigate the learning of mathematical analysis based on the integration of philosophical analysis and neurocognitive findings. For this purpose, learning mathematical analysis, as one of the aspects of mathematical thinking, has been studied using learning numerical symbols in children based on the neurophilosophical method. To that end, three observational propositions have been deduced from cognitive neuroscience findings on symbolic mathematics including symbolic learning of numbers changes children's brains and the processing of symbolic numbers; nonsymbolic numbers are heterogeneous and there is a vague, bidirectional connection between them; the symbolic knowledge of numbers plays an important role in the future development of children in higher-level mathematics. Then, based on these three propositions, an attempt has been made to examine the philosophical questions of the research and the challenges related to them.In this paper, we argue that combining symbolic numbers learning with how created numerical symbols and encouraging children to make consistent connections between numerical symbols and their mental meaning and verbal expression can provide the necessary tools for the enrichment of metacognitive abilities namely error detection. However, it is necessary to consider challenges such as how children become acquainted with the theory of evolution concerning cultural issues, the type of strategies needed to improve the relationship between semantic and symbolic understanding of numbers in children, and the level of emphasis on problem-solving processes (which also require symbol-based analysis) in mathematics’ education in Iran to improve children's thinking abilities.