The American Journal of Social Science and Education Innovations
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TYPE
Original Research
PAGE NO.
48-54
10.37547/tajssei/Volume07Issue04-07
OPEN ACCESS
SUBMITED
27 February 2025
ACCEPTED
21 March 2025
PUBLISHED
27 April 2025
VOLUME
Vol.07 Issue 04 2025
CITATION
Natella
Н
orodetska. (2025). Mental Arithmetic and Its Impact on the
Development of Mathematical Abilities. The American Journal of Social
Science and Education Innovations, 7(04), 48
–
54.
https://doi.org/10.37547/tajssei/Volume07Issue04-07
COPYRIGHT
© 2025 Original content from this work may be used under the terms
of the creative commons attributes 4.0 License.
Mental Arithmetic and Its
Impact on the
Development of
Mathematical Abilities
Natella Нorodetska
Master of Pedagogy Director, Neuro Mental Math LLC Leading Expert in
Mental Arithmetic Minnesota, USA
Abstract:
This article examines the influence of mental
arithmetic on the development of mathematical
abilities. This domain represents a fundamental
cognitive function that underpins mathematical
thinking. Over the past decades, interest in this issue
has significantly increased due to advancements in
neuroscience,
psychology,
and
educational
technologies. However, despite extensive research,
unresolved questions remain regarding the neural
mechanisms underlying mental calculations, the impact
of external factors on arithmetic performance, and the
effectiveness of various training methods. The
objective of this study is to systematize contemporary
scientific perspectives on mental arithmetic and its
effects on the development of mathematical abilities. A
review of the literature reveals that researchers employ
a wide range of approaches, from neuroimaging
techniques to cognitive experiments focused on the
role of auditory and visual stimuli. Nonetheless,
scientific
debates
persist
concerning
the
neuropsychological models of mental arithmetic, its
interaction with working memory, and attentional
processes. It is concluded that mental arithmetic is a
complex, multifaceted process influenced by both
individual characteristics and external conditions. The
author’s contribu
tion lies in proposing a conceptual
framework for understanding the impact of mental
arithmetic on the development of mathematical
abilities. These findings will be of interest to
psychologists,
neuroscientists,
educators,
and
developers of mathematical training programs.
Keywords:
cognitive processes, mathematical abilities,
mental arithmetic, neuroscience, numerical cognition,
cognitive training.
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Introduction:
In the current educational landscape,
there is a noticeable and systematic shift from
traditional teaching methods to practices that enhance
cognitive development. Given the increasing focus on
cognitive development and the search for new
approaches to teaching mathematics, mental
arithmetic serves not only as a subject of theoretical
analysis but also as a significant practical tool.
The importance of this topic lies in the need to
reconsider the mechanisms of computational skill
formation within the framework of specific cognitive
training. The core issue addressed in this study is how
the development of mental calculation processes
contributes to structuring mathematical thinking and
optimizing working memory and attention.
In line with this, contemporary researchers aim to
develop models that connect mental arithmetic
practice with neurocognitive mechanisms and abstract
problem-solving strategies. Their work is based on
experimental training, neuropsychological testing, and
an analysis of cognitive performance dynamics.
MATERIALS AND METHODS
Research on mental arithmetic can be categorized into
several groups based on methodological approaches.
The first category focuses on analyzing brain activity
during
arithmetic
operations
using
various
neuroimaging techniques. In the study by F.A. Farahani
et al. [3], functional near-infrared spectroscopy (fNIRS)
with continuous wavelet transformation was used to
identify patterns characteristic of mental calculations.
A similar approach, emphasizing signal complexity, was
applied by A. Ghouse et al. [4] in analyzing the
relationship between mental arithmetic and motor
imagery. D. Ma et al. [8] employed a modified
multiparametric complexity metric to recognize brain
states
during
calculations.
Using
electroencephalography (EEG), K. Kim et al. [6]
examined microstates in the brain depending on the
success of arithmetic operations, while S. Dattola [2]
used electromyography to map active brain regions.
The second category of studies examines the impact of
external and cognitive factors on the effectiveness of
mental calculations. F. Kattner et al. [5] investigated the
influence of background auditory stimuli on accuracy
and processing speed in arithmetic tasks, identifying
the mechanism of auditory distraction. W. Ross et al.
[9] analyzed the role of external numerical
representations in children's mental calculations,
demonstrating that interactive number manipulation
improves computational accuracy. S. Salvaggio et al.
[10] focused on the predictive function of eye
movements during arithmetic operations, suggesting
that visual scanning strategies correlate with
mathematical performance. W. Ross et al. [11]
explored how manipulating external numerical
representations affects children's success in mental
arithmetic. L. Dawei et al. [12] described an
experimental study aimed at improving elementary
students' mental arithmetic abilities through a
structured learning approach.
The third category of research is dedicated to
developing educational methodologies that enhance
arithmetic thinking. A. Abdul-Rahman [1] compared the
effectiveness of calculations in the time and frequency
domains. Ch.H. Lin [7] proposed game-based methods
built on the concept of the mental number line to
improve children's fundamental mathematical skills.
A review of scientific literature reveals that, despite the
abundance of experimental data, contradictions
remain in the interpretation of cognitive mechanisms
underlying mental arithmetic. For example, studies on
neural activity identify different cortical areas
responsible for arithmetic operations, but definitive
conclusions regarding their interactions have not yet
been reached. Additionally, the impact of external
factors such as visual and auditory environments varies
depending on research methodologies and individual
differences among participants. The long-term effects
of regular mental arithmetic training and its integration
into educational programs also remain insufficiently
explored.
The methodological framework of this study includes
comparison, systematization, content analysis of
scientific publications, synthesis, retrospective analysis,
and generalization.
RESULTS AND DISCUSSIO
n
Referring to the retrospective analysis (Fig. 1), it is
appropriate to note that the origins of mental
arithmetic trace back to methods used in ancient
cultures to develop numerical perception. However, in
modern science, this approach is examined through the
lens of cognitive psychology and information theory.
Unlike traditional algorithmic learning schemes, the
approach discussed in this article relies on a multi-
component integration of visual, auditory, and motor
processes, positioning it as a synthesis of intellectual
training and neuroplasticity.
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Fig. 1. A retrospective of the development of mental arithmetic (compiled by the author based on [2, 4, 10]
This approach represents the systematic execution of
computational operations without the use of physical
tools. It encompasses both basic arithmetic operations
and more complex processes, including numerical
sequence analysis and their transformation into
abstract representations [1, 7].
Mathematical abilities in this framework are
determined not only by the level of proficiency in
computational algorithms but also by the degree of
development in analytical thinking, the ability to
abstract, and the capacity to switch quickly between
different cognitive modes. Table 1 provides a
description of key models.
Table 1
–
Characteristics of cognitive information processing models in mental arithmetic (compiled by the
author based on [2-6, 8, 10])
Model
Description
Information
Theory
and
Working
Memory
Concepts
In theoretical studies, working memory, which has limited capacity and is
critical for temporary information storage and processing, serves as a key
element of analysis. The corresponding model, proposed by A. Baddeley,
considers mental calculations as a dynamic process in which visual and
verbal components integrate into a unified information system. During
1. Ancient era (use of the abacus)
2 Antiquity (formation of numerical systems)
3. Middle Ages (development of arithmetic practices)
4. East Asian tradition (systematization of mental arithmetic)
5. Modern period (integration into educational methods)
6. Digital age (use of innovative simulators)
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Model
Description
arithmetic operations, activation of the central executive component is
observed, responsible for coordinating and controlling computational
activities.
Neurocognitive
Approach
and
Functional
Distribution
Within neuropsychology, it has been demonstrated that mental arithmetic
processes activate not only the prefrontal cortex, which is responsible for
planning and control, but also temporal structures involved in processing
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
Abacus"
Concept
This approach suggests that the learner visualizes a traditional abacus and
uses it as an internal model for performing calculations. This method
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.
Next, it is necessary to describe the mechanism by
which mental arithmetic influences mathematical
thinking.
Unlike standard algorithmic memorization, this
approach stimulates the development of flexible
problem-solving strategies. Regular mental calculation
practice enhances the ability to quickly recognize
patterns and model alternative solutions. This process
is characterized by a high degree of adaptability,
allowing individuals to apply complex information-
processing schemes when faced with non-standard
situations.
One of the central mechanisms of mental arithmetic
involves transforming abstract numerical concepts into
concrete visual structures. During training, learners do
not merely perform arithmetic operations but also
visualize numerical relationships, which facilitates
better memory retention and a deeper understanding
of mathematical principles. This approach helps avoid
the fragmentation of traditional methods and fosters a
holistic perception of numerical relationships.
Neuroscientific
research
indicates
the
active
involvement of various sensory systems in mental
calculations. The combination of visual, auditory, and
proprioceptive information enables multidimensional
data encoding, which reduces the likelihood of errors
and significantly accelerates decision-making. In
theoretical models, this phenomenon is described as a
synergistic effect, where the integration of diverse
signals leads to more stable and accurate computation
performance [1, 6, 7].
Consider the following examples. If one needs to
subtract 12 from 87, a common strategy is to break the
smaller number into components
—
here, 12 consists of
10 and 2. Since subtracting 10 from any number is
straightforward, one can first subtract 10 from 87,
yielding 77. Then, subtracting 2 from 77 results in 75.
A mental addition method is commonly used when a
number contains 8 or 9 in the units place. To add 9 to
any number, one can first add 10 and then subtract 1.
As noted by W. Ross and colleagues, children under the
age of 10 exhibit a greater reliance on counting and
cognitive effort in processing numerical information
compared to older children [11].
In a study involving 52 third-grade students, L. Dawei
and colleagues used graphical educational aids based
on mental arithmetic strategies and schema theory.
After a 14-day training period, the experimental group
demonstrated significant improvements in speed,
accuracy, and consistency in mental addition and
subtraction. Both addition and subtraction tests in the
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control and experimental groups showed outstanding
effectiveness of schema-based training in terms of
reaction time (RTM) and error rate (ER). Pre-test RTM
scores were nearly identical between the control and
experimental groups, but the reduction in post-test
duration in the experimental group was 1.69 times
greater for addition and 2.34 times greater for
subtraction compared to the control group [12].
The author proposes a conceptual "framework" model
illustrating the influence of mental arithmetic on the
development of mathematical abilities. This model
incorporates several interconnected components (Fig.
2).
Fig. 2. The "framework" of the model of the influence of mental arithmetic on the development of
mathematical abilities (compiled by the author)
The model substantiates the inclusion of mental
arithmetic in educational programs based on a
systematic approach to cognitive skill development.
Methodologically, this implies a shift from mechanistic
repetition of algorithms to the conscious formation of
computational strategies, enabling students to develop
a deeper understanding of mathematical principles and
apply them in new contexts. Particular emphasis is
placed on fostering independent problem analysis
combined with the search for unconventional
solutions.
To analyze the described influence, it is necessary to
establish a set of criteria reflecting both quantitative
and qualitative shifts in cognitive functioning. Among
them, the following stand out:
●
Information processing speed (changes in
reaction time when performing arithmetic tasks serve
as an indicator of cognitive improvement).
●
Depth of visual representation (assessment of
the ability to visualize numerical structures through
specialized tests).
●
Level of strategy adaptability (analysis of
switching between different problem-solving methods
and cognitive flexibility in non-standard situations).
Future research should be oriented toward
interdisciplinary
approaches
that
integrate
neuroscience, cognitive psychology, and pedagogy.
One promising objective is the development of models
that account for individual variations in neural
architecture, facilitating the adaptation of mental
arithmetic methods to the specific cognitive profiles of
learners.
In a theoretical context, the approach discussed in this
article should be viewed as a means of forming adaptive
frameworks capable of adjusting to changes in the
educational environment. Investigating the dynamics
Compo
nents
Neural activation and resource
reallocation
Regular mental arithmetic
practice promotes increased
activity in the prefrontal cortex
and other centers responsible
for numerical processing
Dynamic updating of working
schemes
Learning leads to the creation
of stable mental images that
facilitate rapid operation of
numerical data
Development of integrative
cognitive strategies
Imaginative thinking and
adaptive problem-solving
strategies are enhanced by
multi-channel information
processing
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of neural connections during regular mental
computations will contribute to the creation of
algorithms that optimize the learning process while
considering individual cognitive characteristics.
Integrating data from neuroscience and pedagogy
presents
new
opportunities
for
developing
comprehensive educational programs where mental
arithmetic serves as a central component. This
approach not only enhances the effectiveness of
mathematics education but also stimulates the
development of related functions, including critical
thinking and multitasking ability.
One challenge is the risk of a reductionist approach,
where complex cognitive processes are reduced to
purely neural models. Despite the high potential of
neuroimaging, it is essential to recognize that
computational abilities develop under the influence of
cultural, pedagogical, and individual factors. Thus, a
multi-level analysis is recommended, in which
biological mechanisms are considered in conjunction
with the social and psychological aspects of learning.
Another significant aspect is the development of
metacognitive skills, which help students become
aware of their own thought processes. Mental
arithmetic, by requiring continuous monitoring of
calculations, fosters self-regulation and self-control,
which are crucial components of academic success.
Theoretically, this phenomenon aligns with the concept
of reflective thinking, where awareness of one's
cognitive strategies enables individuals to adjust and
optimize information processing.
A critical analysis of the proposed "framework" model
reveals several limitations associated with the
variability of individual cognitive resources. On the
other hand, its potential lies in the ability to adapt
mental arithmetic techniques to specific educational
and psychological conditions. This opens up prospects
for the development of personalized programs that
emphasize
adaptability
rather
than
universal
applicability, ensuring that instructional methods align
with the unique characteristics of each learner.
CONCLUSIONS
This study attempted to analyze the impact of mental
arithmetic on the development of mathematical
abilities. Models of working memory, neurocognitive
mechanisms,
and
sensory
system
integration
demonstrate that regular training in mental
calculations contributes to the formation of stable
cognitive strategies and the development of visual
thinking.
The development of a comprehensive theoretical
foundation that considers both biological and cultural-
pedagogical factors is a crucial step toward optimizing
educational practices and designing adaptive learning
programs.
The advancement of metacognitive skills, critical
analysis
of
reductionist
approaches,
and
interdisciplinary collaboration appear to be promising
directions for future research.
Thus, mental arithmetic functions not only as a method
for training computational skills but also as a
comprehensive tool that fosters flexible, adaptive, and
profound mathematical thinking.
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