This paper examines arithmetic thinking, the integration of AI-powered mathematics solvers, and AI platforms. Arithmetic thinking encompasses understanding mathematical concepts, demonstrating flexibility by solving problems using multiple methods, developing number sense through the application of arithmetic properties and the hierarchy of operations, and justifying solutions through logical reasoning. While traditional math solvers assist in obtaining answers to arithmetic problems, they often fail to explain the rationale behind a particular solution. The procedural steps they provide typically illustrate how to solve a problem but do not foster the development of arithmetic thinking. In contrast, many AI platforms not only offer procedural methods for solving arithmetic problems but also engage students in deeper conceptual understanding. When students input questions into AI chatbots and request explanations for arithmetic solutions, these systems can provide clear reasoning grounded in arithmetic concepts. Consequently, AI has the potential to significantly enhance arithmetic thinking. The involvement of educators and researchers in the development and integration of AI in educational contexts can contribute meaningfully to this advancement, particularly in promoting the understanding and application of arithmetic thinking.
AI and Advanced Mathematical Software Role in Shaping High School Students' Arithmetic Thinking
Jose Marti STEM Academy, Union City, NJ, USA
Abstract
This paper examines arithmetic thinking, the integration of AI-powered mathematics solvers, and AI platforms. Arithmetic thinking encompasses understanding mathematical concepts, demonstrating flexibility by solving problems using multiple methods, developing number sense through the application of arithmetic properties and the hierarchy of operations, and justifying solutions through logical reasoning. While traditional math solvers assist in obtaining answers to arithmetic problems, they often fail to explain the rationale behind a particular solution. The procedural steps they provide typically illustrate how to solve a problem but do not foster the development of arithmetic thinking. In contrast, many AI platforms not only offer procedural methods for solving arithmetic problems but also engage students in deeper conceptual understanding. When students input questions into AI chatbots and request explanations for arithmetic solutions, these systems can provide clear reasoning grounded in arithmetic concepts. Consequently, AI has the potential to significantly enhance arithmetic thinking. The involvement of educators and researchers in the development and integration of AI in educational contexts can contribute meaningfully to this advancement, particularly in promoting the understanding and application of arithmetic thinking.
Keywords: Arithmetic, Arithmetic Thinking; AI platforms; Math Solver; Conceptual Knowledge.
1. Introduction
The first section of this paper introduces several key subtopics, including the definition of arithmetic thinking, the influence of AI and mathematical solvers on arithmetic and arithmetic thinking, and the research questions guiding the study. Together, these components establish a foundation for examining how technology supports students’ mathematical development.
This paper centers on the role of artificial intelligence (AI) in shaping students’ arithmetic thinking. As AI tools and advanced mathematical solvers become increasingly integrated into educational settings, they have the potential to influence how students understand numerical relationships, apply operations, and engage in problem-solving. By exploring these connections, the paper aims to highlight both the opportunities and challenges AI presents in supporting meaningful mathematical learning.
2. Method
2.1 Context of AI in Education
To understand AI more clearly, it is important to recognize that artificial intelligence can be categorized into different types based on its capabilities and functionalities (GeeksforGeeks, 2025). Within AI research, three widely recognized levels of artificial intelligence are described: Artificial Narrow Intelligence (ANI) , Artificial General Intelligence (AGI), and Artificial Superintelligence (ASI) .
Currently, only ANI exists in practical, real-world applications, while AGI and ASI remain theoretical and undeveloped. For this reason, when discussing AI in educational contexts, we are specifically referring to ANI , as it includes the tools and systems actively used in classrooms today. The distinctions among ANI, AGI, and ASI are summarized in Table 1 .
Table 1. The three types of artificial intelligence, where ANI is commonly called AI
Illustrations are not included in the reading sample
(Source: modification from ChatGPT, 2025)
AI in secondary education is expanding rapidly due to its significant benefits. However, effective implementation requires school districts to move through three key phases: awareness , adoption, and evolution. These phases mirror the complex and hierarchical structures found in both AI systems and educational institutions, each of which evolves dynamically throughout the learning and integration process (Ouyang & Jiao, 2021). Figure 1 illustrates these three phases that educators should consider before integrating AI into their school districts—particularly within the high school mathematics curriculum.
Abbildung in dieser Leseprobe nicht enthaltenFigure 1. Three phases of AI in education: Ignite AI, Implement AI, and Infuse AI. The figure is modified from the webinar DA District Administration- presenter Giancarlo Brotto (Brotto, 2025).
The image illustrates the three phases of AI integration in education. Phase one involves raising awareness of AI’s role in mathematics and preparing school districts to evaluate its potential benefits and challenges. According to Ding et al. (2024), developing teachers’ AI literacy is essential for achieving readiness. In phase two , AI begins to enhance instruction and learning by supporting classroom practices and improving access to adaptive tools. Phase three emphasizes using AI not only to increase efficiency but also to transform education in meaningful ways—what Mollick, as cited in Bylin (2025), describes as “doing better things.” With intentional implementation and thoughtful adaptation, AI can significantly improve teaching and learning outcomes. The accompanying table highlights leading AI math solvers that support this transformation, particularly in strengthening students’ arithmetic thinking.
Table 2. Describes several of the top math solvers powered by AI for high school students.
Illustrations are not included in the reading sample
(Source: modification from Gemini, 2025)
Illustrations are not included in the reading sample
Figure 2. Main key components of the arithmetic thinking
2.2 Key Components of Arithmetic Thinking
Although there is no single, universally accepted definition, the academic literature generally conceptualizes arithmetic thinking as the capacity to understand numerical structures, recognize relationships among quantities, and apply this understanding to reason through problems rather than merely execute computational procedures. In essence, arithmetic thinking constitutes a foundational dimension of mathematics, encompassing both numerical operations and the relational properties that underlie them. Moreover, as illustrated in Figure 2 - Algebraic Thinking - the construct of algebraic thinking is understood to include the comprehension of mathematical concepts, strategic flexibility, problem-solving proficiency, numerical sense-making, and the capacity to justify arithmetic reasoning.
2.3 Application of AI in Arithmetic Thinking
Arithmetic, a fundamental branch of mathematics taught from the elementary level through college-level introductory courses, primarily emphasizes procedural skills such as computation and the application of the order of operations. Students frequently encounter difficulty when engaging with more complex tasks, such as operating on complex fractions (often referred to as “double fractions”). AI-powered mathematics solvers can provide support by generating step-by-step solutions to such problems. However, these tools - grounded in artificial narrow intelligence (ANI)—generally lack the capacity to articulate the underlying reasoning behind their procedures unless explicitly prompted. Consequently, while these systems can reinforce procedural fluency, they do not inherently cultivate deeper forms of arithmetic thinking.
Thus, the effective integration of AI as a cognitive partner in arithmetic education requires intentional questioning and pedagogical guidance to shift learners’ focus from obtaining answers to developing meaningful mathematical understanding. The following example illustrates the process of solving a complex fraction using Symbolab, a math solver powered by ANI.
Solve the double fraction: Illustrations are not included in the reading sample
Symbolab - Solution: Illustrations are not included in the reading sample
Symbolab provides step-by-step solutions for arithmetic problems, incorporating both symbolic and numerical explanations to support learning (AIChief, 2025). However, its primary focus is often on procedural execution rather than the underlying mathematical reasoning.
For instance, while the tool might correctly solve a problem and yield as the answer, it typically does not provide an explanation for why this is the case. In contrast, Gemini emphasizes the critical importance of understanding the order of operations (commonly known as PEMDAS/BODMAS). This foundational knowledge is essential for developing true arithmetic thinking that extends beyond mere procedural accuracy.
● Parentheses / Brackets
● Exponents / Orders
● Multiplication and Division (from left to right)
● Addition and Subtraction (from left to right)
Common arithmetic operations encompass addition, subtraction, multiplication, and division, along with more advanced operations like exponentiation, roots, and logarithms.
When these operations involve variables, they align closely with the principles of algebra. For example, the concept that any non-zero number raised to the power of zero equals one is a core mathematical rule . Encouraging robust arithmetic thinking promotes the exploration of the rationale supporting such fundamental rules (ChiliMath, n.d.).
Illustrations are not included in the reading sample
Figure 3. The process of dividing fractions, respectively utilizing double fractions through math solver powered by AI - Symbolab.
ChatGPT: Let's explore why a number to the power of 0 is equal to 1 from a purely arithmetic perspective — without relying too heavily on abstract rules or algebra. We'll use just numbers and patterns, as illustrated in Figure 2.
Illustrations are not included in the reading sample
Figure 4. Reasoning why a number raised to the zero power results in one in pure arithmetic perspective.
By interacting judiciously with AI, students can realize significant educational benefits. For example, when students encounter difficulties with an arithmetic problem, they can request an in-depth explanation rather than just the final answer. Instead of simply requesting the solution from a standard math solver, students are encouraged to upload a clear photo of the problem to a vetted AI tool and specifically ask for an explanation of the methodology or the rationale for applying a particular rule (Almond, 2025). Following this guided interaction, students should critically analyze the entire solution to achieve a comprehensive understanding of the arithmetic example.
2. 4 Enhanced Engagement and Motivation in Arithmetic with Technology
There are various types of educational videos, including presentation videos, webinars, animations, interactive videos, whiteboard animations, micro-videos, and others (Pllana, 2022). YouTube videos, as illustrated in Figure 7, often feature topics such as matchstick riddles that involve arithmetic. These puzzles actively engage viewers and foster arithmetic thinking, particularly when they incorporate mathematical equations and number transformations. Such informal learning environments support visual learners and encourage the practical application of arithmetic reasoning. Moreover, visual examples serve to illustrate key components of arithmetic thinking, as detailed in Figure 2.
Illustrations are not included in the reading sample
Figure 5. YouTube videos with matchstick puzzles - visual arithmetic modified figures from MindYourOpinion (n. d.) and Simply Logic (n. d).
3. Findings
● AI acts as a "thinker" that helps students understand and explain conceptual knowledge in arithmetic.
● Advanced mathematical solvers assist students with computations in arithmetic.
● Applying key components of arithmetic thinking skills helps students gain a deeper understanding of conceptual knowledge.
● AI platforms function as thinkers in understanding and explaining arithmetic, while mathematical solvers serve as computational executors.
● Combining AI platforms with advanced mathematical solvers enhances students' learning outcomes in arithmetic.
3. 1 Difference Between Arithmetic and Arithmetic Thinking
In short, the difference between arithmetic and arithmetic thinking: arithmetic is calculating, while arithmetic thinking is reasoning. Arithmetic and arithmetic reasoning are not the same; arithmetic is the content that contains the procedures such as 3 + 6 = 9, multiplications, long division, or operating with fractions. Arithmetic thinking deals more with reasoning, understanding concepts, justifying answers, analyzing an arithmetic problem from different angles. Their difference in greater details is described in ten different aspects in Table 3.
Table 3. The difference between arithmetic and arithmetic thinking
Illustrations are not included in the reading sample
(Source: modification from ChatGPT, 2025)
4. Discussion
Common arithmetic operations—addition, subtraction, multiplication, and division—are fundamental to math learning, with advanced operations like exponentiation, roots, and logarithms extending this knowledge. When variables enter the picture, these operations become part of algebraic reasoning, linking arithmetic and algebra. Pllana and Baez emphasize that understanding these concepts deeply supports arithmetic thinking rather than mere memorization. For example, the rule that any number raised to the zero power equals one invites deeper exploration: “Why does this hold true?” As Baez et al. (2025) notes, AI tools can guide students through these patterns and explanations, helping them understand that the zero exponent emerges logically from the properties of exponents. Pllana et al. (2024) stresses that promoting this kind of reasoning is crucial for developing flexible problem-solving skills, making arithmetic thinking richer and more meaningful beyond simple computation.
AI has a complex but transformative role in shaping high school students’ arithmetic thinking. Chatbot-based AI platforms and math solvers can help students bridge conceptual and procedural knowledge, but their effectiveness depends on how students use them. For instance, Symbolab offers step-by-step solutions, aiding understanding, while Mathway often just gives final answers. Tools like Wolfram Alpha provide deeper insights for more complex problems.
Choosing the right AI tools and using them wisely can significantly enhance learning (conceptual knowledge). While AI offers personalized feedback and support, including free tools like ChatGPT, students must engage in critically analyzing steps, asking follow-up questions, and avoiding passive copying. This active approach promotes genuine arithmetic thinking.
To fully benefit, both students and teachers must use AI thoughtfully in conjunction with advanced math solvers powered by AI, encouraging exploration and understanding rather than rote learning. As AI technology advances, newer tools will address current limitations, making learning more accessible, inclusive, and effective. Overall, informed and strategic use of AI holds great potential to improve how arithmetic is taught and learned.
5. Conclusion
This study highlights the distinctive yet complementary roles of AI platforms and advanced mathematical solvers in developing arithmetic thinking. While traditional arithmetic focuses on procedural calculations, arithmetic thinking emphasizes reasoning, conceptual understanding, and flexible problem-solving strategies. AI platforms function as cognitive "thinkers," guiding students in understanding, explaining, and justifying arithmetic concepts, whereas advanced mathematical solvers primarily serve as computational executors, efficiently performing calculations.
The integration of AI platforms with sophisticated math solvers has been shown to enhance students’ learning outcomes by bridging the gap between procedural fluency and conceptual reasoning. By actively engaging with AI tools, students can explore multiple solution strategies, develop number sense, and deepen their understanding of arithmetic principles. Importantly, the effective use of AI requires thoughtful interaction: students must critically analyze steps, pose follow-up questions, and avoid passive reliance on automated answers.
Overall, the strategic incorporation of AI in arithmetic instruction can transform learning from rote computation to meaningful reasoning. When combined with educator guidance, AI has the potential to foster flexible, conceptually grounded arithmetic thinking, equipping students with skills that extend beyond mere calculation and preparing them for more advanced mathematical reasoning.
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