An Adaptive Cognitive Probability Distortion Model for Modelling Student Teachers' Probabilistic Reasoning: Mathematical Formulation and MATLAB Implementation

Author

Dharam Pal Guleria, Dr. Ramandeep Kaur

Abstract

 Mathematical modelling offers a specific Framework for representing probabilistic reasoning under uncertain situations by integrating computational and cognitive principles. Existing studies on probability education and randomness have largely depended on empirical observation to analyse misconceptions, providing specific investigation and theoretical mechanisms for analysing how cognitive biases support probabilistic judgement. The study provides an Adaptive Cognitive Probability Distortion Model (ACPDM), which involves formal probabilistic reasoning, heuristic reasoning and dynamic learning practices within a mathematical framework. The proposed model involves Bayesian belief updating, Markov cognitive state transition and weighted probability estimation to cover changes regarding probability reasoning throughout the reasoning tasks. Additionally, the mathematical formulation is supported through computational application and analytical support, empowering systematic analysis of learning patterns and biased behaviour. The proposed framework supports a foundation for predictive modelling of probabilistic reasoning and acknowledges a computational approach for analysing cognitive processes along with mathematical education.

Keywords

Adaptive Cognitive Probability Distortion Model, Bayesian Inference, Cognitive Modelling, Markov Chains, Mathematical Modelling, Probability Theory, MATLAB Simulation, Probabilistic Reasoning

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References

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