Comparison and Competition of Traditional and Visualized Secondary Mathematics Education Approaches: Random Sampling and Mathematical Models Under Neural Network Approach

Graphic design and image processes have a vital role in information technologies and safe, memorable learning activities, which can meet the need for modern and visual aids in the field of education. In this article, the concepts of comparison and competition have been presented using grades or numbers obtained for two different intelligence quotient (IQ) classes of students. The two classes are categorized as learners having textual (un-visualized) and visualized aids. We use the results and outcomes of the random sampling data of the two classes in the parameters of four different, competitive, two-compartmental mathematical models. One of the compartments is for students who only learn through textual learning, and the other one is for students who have access to visualized text resources. Four of the mathematical models were solved numerically, and their grades were obtained by different iterations using the data of the mean of different random sampling tests taken for thirty months; each sampling involved thirty students. The said data are also drawn by using a neural network approach, showing the fitting curves for all the data, the training data, the validation data, and the testing data with histogram, aggression, mean square error, and absolute error. The obtained dynamics are also compared with neural network dynamics. The results of the scenario pointed out that the best results (determined through high grades) were obtained among the students of visual aid learners, as compared to textual and conventional learners. The visualized resources, constructed within the mathematics syllabus domain, may help to upgrade multidimensional mathematical education and the learning activities of intermediate-level students. For this, the findings of the present study are helpful for education policymakers: there is a directive to focus on visual-based learning, utilizing data from various surveys, profile checks, and questionnaires. Furthermore, the techniques presented in this article will be beneficial for those seeking to build a better understanding of the various methods and ideas related to mathematics education.