Mental Arithmetic and Its Impact on the Development of Mathematical Abilities

Аннотация

, and the capacity to switch quickly between and more complex processes, including numerical different cognitive modes. Table 1 provides a sequence analysis and their transformation into description of key models. abstract representations [1, 7]. Mathematical abilities in this framework are Table 1 – Characteristics of cognitive information processing models in mental arithmetic (compiled by the author based on [2-6, 8, 10]) Model Description Information In theoretical studies, working memory, which has limited capacity and is Theory and critical for temporary information storage and processing, serves as a key Working element of analysis. The corresponding model, proposed by A. Baddeley, Memory considers mental calculations as a dynamic process in which visual and Concepts verbal components integrate into a unified information system. During The American Journal of Social Science and Education Innovations 50 https://www.theamericanjournals.com/index.php/tajssei The American Journal of Social Science and Education Innovations Model Description arithmetic operations, activation of the central executive component is observed, responsible for coordinating and controlling computational activities. Neurocognitive Within neuropsychology, it has been demonstrated that mental arithmetic Approach and processes activate not only the prefrontal cortex, which is responsible for Functional planning and control, but also temporal structures involved in processing Distribution numerical representations. This model highlights two primary pathways for information processing: one oriented towards numerical semantics and the other towards spatial-visual number perception. This dichotomy helps explain how regular mental arithmetic training contributes to the redistribution of neural resources and strengthens inter-cortical connections. The "Mental This approach suggests that the learner visualizes a traditional abacus and Abacus" uses it as an internal model for performing calculations. This method Concept optimizes numerical data processing and forms a stable cognitive strategy that enables manipulation of abstract representations without external aids. Theoretically, this mechanism can be viewed as a manifestation of neuroplasticity, where new informational schemes integrate into existing cognitive structures. and significantly accelerates decision-making. In Next, it is necessary to describe the mechanism by which mental arithmetic influences mathematical theoretical models, this phenomenon is described as a thinking. synergistic effect, where the integration of diverse signals leads to more stable and accurate computation Unlike standard algorithmic memorization, this performance [1, 6, 7]. approach stimulates the development of flexible problem-solving strategies. Regular mental calculation Consider the following examples. If one needs to practice enhances the ability to quickly recognize subtract 12 from 87, a common strategy is to break the patterns and model alternative solutions. This process smaller number into components—here, 12 consists of is characterized by a high degree of adaptability, 10 and 2. Since subtracting 10 from any number is allowing individuals to apply complex information- straightforward, one can first subtract 10 from 87, processing schemes when faced with non-standard yielding 77. Then, subtracting 2 from 77 results in 75. situations. A mental addition method is commonly used when a One of the central mechanisms of mental arithmetic number contains 8 or 9 in the units place. To add 9 to involves transforming abstract numerical concepts into any number, one can first add 10 and then subtract 1. concrete visual structures. During training, learners do As noted by W. Ross and colleagues, children under the not merely perform arithmetic operations but also age of 10 exhibit a greater reliance on counting and visualize numerical relationships, which facilitates cognitive effort in processing numerical information better memory retention and a deeper understanding compared to older children [11]. of mathematical principles. This approach helps avoid In a study involving 52 third-grade students, L. Dawei the fragmentation of traditional methods and fosters a and colleagues used graphical educational aids based holistic perception of numerical relationships. on mental arithmetic strategies and schema theory. Neuroscientific research indicates the active After a 14-day training period, the experimental group involvement of various sensory systems in mental demonstrated significant improvements in speed, calculations. The combination of visual, auditory, and accuracy, and consistency in mental addition and proprioceptive information enables multidimensional subtraction. Both addition and subtraction tests in the data encoding, which reduces the likelihood of errors The American Journal of Social Science and Education Innovations 51 https://www.theamericanjournals.com/index.php/tajssei The American Journal