Mathematics in Education and Industry

<p><strong>Context and relevance.</strong> Individualization of the learning process is the most important task of modern pedagogy, especially in primary education, where basic mathematical skills are formed. The existing class-lesson system often does not allow to promptly identify and correct individual errors of students. The author's proposed development of an adaptive digital system based on Markov models is aimed at solving this problem. <strong>Objective.</strong> Development of a prototype of a digital educational system to support individualized learning process of mathematics in elementary school. <strong>Hypothesis.</strong> An adaptive system based on Markov processes with discrete states and continuous time can increase the efficiency of individualized learning and improve students' mathematical skills. <strong>Methods and materials.</strong> The study developed a web application that uses Markov processes to assess elementary school students' mathematical knowledge and skills. The system offers tasks with predefined answer choices, captures errors, generates error-appropriate prompts, and adapts task difficulty based on student progress. <strong>Results.</strong> A prototype of a digital system is presented, which allows effectively detecting and correcting typical errors of elementary school students in solving mathematical problems, providing an individualized approach to teaching and reducing the teacher's workload. <strong>Conclusions.</strong> The developed system provides opportunities for increasing individualization of learning and quality of mathematics education in elementary school. Further expansion of the system functionality is recommended, including integration of additional analytical modules and adaptation to other educational subjects and age groups.</p>

Relevance. The relevance of the research is conditioned upon the existence of a contradiction between the predominantly abstract-theoretical nature of the conventional school course of mathematics and the objective need to develop students� skills in the practical application of mathematical knowledge and tools to solve specific applied problems in real-life situations. Purpose. The purpose of the research is to identify and comprehensively justify the role and place of contextual mathematical tasks in the development of students� functional literacy, understood as the ability to apply mathematical knowledge in life situations. Methodology. The study employed methods of historical and comparative analysis, curriculum and educational policy analysis, and the generalization of best practices. Results. The work analyses the historical evolution of advanced national systems of mathematics education from the perspective of integrating the practice-oriented contextual approach into them. It is demonstrated that in many countries there has been a gradual transition to more applied mathematics education through the inclusion of realistic contextual tasks. The high effectiveness of school students solving mathematical problems contextualised in everyday scenarios for developing competence in applying abstract mathematical knowledge and skills in real-life situations has been proved. A set of factors stimulating the introduction of the contextualised approach in mathematics teaching, such as the results of international assessments, has been explored in detail. Conclusions. Key pedagogical, methodological and organisational conditions for the successful implementation of this approach in the school system, including the development of teaching materials, teacher training and assessment tools, are identified. The results expand the understanding of the possibilities of contextual tasks in the development of students� functional literacy, which is significant for the improvement of mathematics education. Keywords: mathematics education; practice-oriented learning; application of knowledge; pedagogical practices; curriculum

<em>PhET Interactive Simulations were initially developed for science learning but have recently gained attention in mathematics education due to their potential to enhance students’ problem-solving skills. This research employs the Systematic Literature Review (SLR) method by collecting, reviewing, and analyzing relevant literature on the use of PhET media to improve mathematical problem-solving skills among elementary school students..</em> <em>PhET media is known as an interactive simulation tool initially developed for science learning, but its use in mathematics education has begun to gain attention.</em><em> This research employs the Systematic Literature Review (SLR) method by collecting, reviewing, and analyzing relevant literature on the use of PhET media to improve mathematical problem-solving skills among elementary school students. The study employs the Systematic Literature Review (SLR) method, systematically collecting, reviewing, and analyzing various relevant literature on the use of PhET media in enhancing mathematical problem-solving skills among elementary school students. PhET media is known as an interactive simulation tool initially developed for science learning, but its use in mathematics education has begun to gain attention. This research employs the Systematic Literature Review (SLR) method by collecting, reviewing, and analyzing relevant literature on the use of PhET media to improve mathematical problem-solving skills among elementary school students. The inclusion criteria consist of journal articles published between 2014 and 2024, focusing on the topic of PhET media and mathematical problem-solving skills in elementary school contexts, and accessible through databases such as Google Scholar, ERIC, and Scopus. The exclusion criteria include articles published before 2014, studies unrelated to mathematics learning or PhET media, and sources that are not peer-reviewed journal articles.The review results indicate that PhET media can increase students' active participation, help visualize abstract mathematical concepts, and encourage the application of more flexible and exploratory problem-solving strategies. The effectiveness of PhET also increases when combined with problem-based or inquiry-based learning approaches. These findings have positive implications for teachers and curriculum developers, suggesting the integration of interactive digital media into the mathematics learning process in elementary schools.</em>

The purposes of this study were (1) to explore the relationship between mathematics education and the rural context and (2) to determine the usefulness of a social theory of learning (Wenger, 1998) to account for students' participation in advanced high school mathematics courses. Qualitative methods were used to gather data in a small, rural high school in the Pacific Northwest. Data gathered included a student survey, interviews with students and mathematics teachers, observations in mathematics classes, and documents related to the curriculum, the school, and the community. The findings suggest that high school mathematics education is related to the rural context in two ways. First, the small size produces characteristics unique to rural high schools. Specifically, a small number of mathematics teachers has considerable ability to shape the curriculum, instruction, and students' views of mathematics. The mathematics course offerings reflect a college preparatory curriculum with few mathematics electives offered. Students' experiences are quite similar and their beliefs about the nature and usefulness of mathematics are fairly uniform. Second, mathematics education is related to the socioeconomic aspects of a rural community. Students' knowledge of mathematics that is used in adults' work and daily life comes from experiences with parents and community members. The usefulness of mathematics, and advanced high school mathematics specifically, may not be apparent for students living in communities without mathematics-intensive jobs. Rural high school students studying advanced mathematics are likely exceeding the formal mathematical education level of their parents. The findings also indicated that Wenger's notions of identity and three modes of belonging provided a useful framework for understanding whether or not students participated in advanced mathematics classes. Students' participation in advanced math classes was related to their engagement in the day-to-day practice of mathematics education in the classroom, the place their engagement fit within the broader experiences of life in their imagination, and the alignment of their energies.

AI-driven personalised learning is increasingly shaping mathematics education, yet evidence remains fragmented regarding its role in developing learners’ mathematical problem-solving skills. This systematic review examined how AI-driven personalised learning influences students’ mathematical problem-solving skills. A structured search of recent empirical studies (2019–2025) identified 20 eligible investigations, which were analysed thematically. Findings show that AI tools, such as adaptive learning systems, intelligent tutoring systems, and chatbots, can enhance mathematical problem solving by providing tailored feedback, adaptive challenges, and scaffolded support that align with learners’ needs. These benefits were observed across primary, secondary, and tertiary settings, contributing to enhanced conceptual understanding, improved strategic reasoning, and increased learner engagement. At the same time, the review highlights notable variations in effectiveness. Some studies have reported an over-reliance on AI hints, misaligned adaptivity, platform complexity, and limited teacher readiness, which have constrained learners’ development of independent problem-solving skills. Infrastructure disparities and data privacy concerns also emerged as persistent challenges. Despite the growing number of studies on AI in mathematics education, limited systematic evidence exists that focuses specifically on AI-driven personalised learning and its influence on mathematical problem-solving processes. This review addresses this gap by synthesising recent empirical studies and identifying the key mechanisms through which AI personalisation supports or constrains learners’ problem-solving development. In general, the review suggests that AI-driven personalised learning holds meaningful potential for strengthening mathematics instruction when grounded in sound pedagogy and supported by adequate technological and instructional resources. This synthesis contributes evidence-based insights for educators and policymakers aiming to integrate AI responsibly and effectively in mathematics education.

The focus of this study is directed towards the examination of the design, development, and analysis of user feedback for the hyper-casual game known as "Obstacle Run," with the aim of enhancing mathematical skills. A comprehensive analysis of the game's design, mechanics, and user experience is conducted. The primary objective of the game is to foster the improvement of mathematical skills in an enjoyable manner and to provide support for the learning process through straightforward game mechanics. An in-game mechanism, requiring players to engage in solving mathematical calculations and problems, is presented by the game titled "Obstacle Run." Increasing the character count within the game is envisioned as a means to bolster mathematical proficiency. This study meticulously focuses on the detailed examination of this unique game, where game design, mechanics, and mathematical calculations come together. Additionally, an exploration of the potential of gamification within game development and education is carried out. The results have been derived from the testing of the game prototype and the subsequent analysis of player feedback. This research is also regarded as a step towards comprehending the connection between hyper-casual games and mathematics education, with the aim of presenting a novel perspective in this domain. It is to be noted that this study is intended to serve as a valuable guide for game developers and educators alike. Its findings are poised to serve as a significant resource for future game projects and strategies in mathematics education. In conclusion, this study provides a summary of a significant endeavor aimed at elucidating the potential of hyper-casual games, such as "Obstacle Run," in facilitating the development of mathematical skills and exploring the possibilities of gamification in the realm of education.

STEM education is a way to promote design process implementation so that students can create solutions using science and mathematics knowledge and skills. This study examined students' STEM learning related to PM 2.5 pollution. In total, 75 grade 12 students from a large school in Bangkok, Thailand, participated in this study, which was collaboratively led by a science teacher, a science educator, a scientist, an engineer, and a mathematics educator. A qualitative methodology was used to analyze students' STEM understanding based on multiple data sources: a post-unit survey, a worksheet, reflective journal entries, and interviews. Seven categories of understanding emerged. Most students mentioned that design was a very important process and that they applied a design process when creating their PM 2.5 detector. Some students indicated the use of science, technology, engineering, and mathematics knowledge in their PM 2.5 detector design. However, most students indicated science and technology as core disciplines for their design; mathematics and engineering were less frequently mentioned among this group of students. More than 50% of the students referred to STEM-related skills, such as entrepreneurship, communication, problem solving, and collaboration, which they used to successfully develop their design. The design-based learning approach was useful in encouraging the students to apply the design process to solve real-world problems. They defined the problems in context or specific situation, collected data, generated alternative ideas, chose the best solution, created and tested a prototype, and evaluated and redesigned the prototype.

Purpose: Mathematics is a compulsory subject in education due to its extensive application in daily life. However, in reality, many students still face difficulties in understanding and learning mathematics. One of the key competencies in mathematics education that students need to master is mathematical communication skills. This study aims to analyze the effect of applying the constructivism approach on the mathematical communication skills of grade VIII students at SMP Negeri 1 Bayang Utara. Method: This study uses a quasi-experimental method with a randomized control group only design. The population in this study is all grade VIII students, and the sampling technique is carried out by saturated samples. The sample consisted of two classes, namely an experimental class that used a constructivist approach and a control class that used conventional learning methods. The research instrument is in the form of an essay test that measures students' mathematical communication skills. Findings: The results showed that the average mathematical communication ability of students in the experimental class (81.67) was higher than that of the control class (71.64). Statistical tests with t-tests showed that there was a significant difference between the two groups at a real level of α = 0.05. This proves that the constructivism approach has a significant positive influence on students' mathematical communication skills. Significance: The results of this study show that the constructivist approach enhances students' mathematical communication skills by encouraging active knowledge construction through interaction and exploration. This helps students convey mathematical ideas more effectively, improving their ability to explain problems clearly and logically. These findings imply that the constructivist approach can support the improvement of mathematical learning outcomes, particularly in communication skills, which are essential for developing critical thinking and problem-solving abilities.

Written mathematical communication skills are an important concern in mathematics education. One way to assess these skills is by presenting students with open-ended problems. This study examines differences in written mathematical communication skills based on gender. The purpose of this study is to describe students’ written mathematical communication skills in solving open-ended problems from a gender perspective. The research employed a descriptive qualitative approach, with participants consisting of Grade VIII students from SMPN 2 Pamekasan, categorized into low, medium, and high levels of written mathematical communication skills. Data were collected through open-ended problem-solving tests to analyze students’ written mathematical communication based on gender. The findings indicate that: (1) students in the low-ability category were unable to fully meet the indicators, with both males and females scoring 58; (2) students in the medium-ability category were moderately able to meet the indicators, with both males and females scoring 75; and (3) students in the high-ability category demonstrated strong performance in meeting the indicators, with males scoring 83 and females 100. These results suggest that high-ability students are more effective in meeting the indicators of written mathematical communication, with observable differences based on gender. Female students tend to excel in written narratives, whereas male students show greater strength in visualization. Students with low and medium abilities still require support in notation, image proportion, and written explanations.

The Contribution of the New Technologies to Learning Mathematics

Objective: The benefits of computational thinking have become an increasingly acknowledged and popular subject of investigation among researchers. This research aims to gather detail and comprehensive information regarding the learning of computational thinking skills in mathematics at various educational levels through a systematic literature review approach. Methods: With a focus on education level, instructional media, mathematics content, and the components of computational thinking addressed by previous researchers, this paper applied the PRISMA Systematic Review Protocol to offer a comprehensive synthesis of sixteen empirical studies retrieved from the Scopus database on the implementation of computational thinking in mathematics education. Findings: Most research on fostering computational thinking in mathematics education is concentrated at the elementary and junior high school. To optimize the development of computational thinking in mathematics, teachers should be reminded of strategies to support students, particularly through activities involving simulations using various instructional media. Examples of such media include programming platforms, visualization tools, and interactive simulations and games. Number operations and geometry are the mathematical content most widely used for fostering computational thinking. Algorithmic thinking, a crucial component in fostering computational thinking among elementary school students, helps them develop a strong foundation for understanding higher mathematical concepts. Conclusion: A systematic review of computational thinking in learning mathematics at the various education level is conducted in this study. The chosen studies were systematically analyzed for the advancement of computational thinking in learning mathematics to provide new an insight information for educators and stakeholders. Keywords: computational thinking, mathematics, systematic literature review. DOI: http://dx.doi.org/10.23960/jpmipa/v25i1.pp34-52

New forms of mathematical knowledge are growing in importance for mathematics and education, including tacit knowledge; knowledge of particulars, language and rhetoric in mathematics. These developments also include a recognition of the philosophical import of the social context of mathematics, and are part of the diminished domination of the field by absolutist philosophies. From an epistemological perspective, all knowledge must have a warrant and it is argued in the paper that tacit knowledge is validated by public performance and demonstration. This enables a parallel to be drawn between the justification of knowledge, and the assessment of learning. An important factor in the warranting of knowledge is the means of communicating it convincingly in written form, i.e., the rhetoric of mathematics. Skemp’s concept of ‘logical understanding’ anticipates the significance of tacit rhetorical knowledge in school mathematics. School mathematics has a range of rhetorical styles, and when one is used appropriately it indicates to the teacher the level of a student’s understanding. The paper highlights the import of attending to rhetoric and the range of rhetorical styles in school mathematics, and the need for explicit instruction in the area.

The purpose of this community service is to build an understanding of the importance of imagination in enhancing mathematical communication in early childhood. Through the storytelling method, this training activity aims to provide insights to the teachers at Ibn Khawarizm Kindergarten on how to utilize storytelling in mathematics education. Before the training, 20 participants were given a pre-test to assess their initial understanding of their pedagogical knowledge, while a post-test was administered after the training to evaluate the changes. The pre-test results showed that participants had a limited understanding of the application of storytelling in mathematics teaching, with an average score of 60%. After the training, there was a significant improvement in participants' abilities, with post-test scores reaching 85% for understanding basic mathematical concepts and 80% for the ability to integrate storytelling into teaching. Participants' confidence in teaching mathematics using creative methods also increased from 65% in the pre-test to 92% in the post-test. The impact of this training is expected to enhance teachers' mathematical communication skills, which will, in turn, influence the development of mathematical communication skills in children in the classroom.

Teaching mathematics in an EFL context at higher education; before, during and after the COVID-19 pandemic: a comparative study

A person who can think critically in mathematics means having a high level of ability and is a fundamental ability that students must have to learn mathematics. The research aims to determine the influence of understanding the ARIAS model on students' critical thinking skills in terms of learning style. This type of research is quasi-experimental with a post-test nonequivalent control group design. The research population is a student majoring in mathematics education at Bina Bangsa University, then selected two classes as research subjects. The acquisition of data from mathematical critical thinking skills tests and learning style questionnaires was then processed with the ANOVA (Analysis of Variance) test. The results showed a significant difference in mathematical necessary thinking skills between students and ARIAS learning and ordinary learning and judging from students' learning styles. There was a substantial difference in mathematical critical thinking skills. Furthermore, it is known that there is an interaction between the type of learning and its learning style towards students' mathematical necessary thinking skills.