Software implementation of the Monte Carlo method in Maple as a tool for developing computational skills.
DOI:
https://doi.org/10.28925/2311-2409.2025.4415Abstract
The article examines the didactic potential of using the Monte Carlo method within the Maple computer mathematics environment as a means of developing students’ computational skills. It is demonstrated that the software implementation of numerical integration through stochastic methods allows for the effective integration of the content of the courses Numerical Methods and Programming, promoting the development of interdisciplinary competencies, computational thinking, spatial imagination, and skills in critical error analysis.
During the study, a laboratory task was implemented in which students performed the calculation of a double integral using the Monte Carlo method in two ways: by averaging the values of the function over the domain and through the geometric interpretation of the volume under the surface of the function. Both approaches were accompanied by process visualization, which contributed to a better understanding of the method’s essence and the algorithm’s structure.
The use of Maple as a learning tool made it possible to minimize the complexity of algorithm implementation and focus students’ attention on the mathematical and logical content of the problem. The results of pedagogical observation revealed an increase in the substantiation level of students’ actions, an expansion of their ability to independently modify algorithms, and the formation of skills in evaluating the accuracy of results and conducting analytical support for numerical calculations.
The proposed approach is scalable, adaptable to various levels of complexity, and applicable in the training of students in mathematics, engineering, and IT fields. The article also outlines prospects for further research related to the implementation of similar methods in environments such as Python and MATLAB, emphasizing algorithmic thinking and visually oriented learning.
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References
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