Personalized learning assessment for secondary education using a hybrid model of circular intuitionistic fuzzy and Aczel–Alsina bonferroni aggregation operator – Nature

 

Report on a Hybrid Model for Personalized Learning Assessment in Secondary Education

Abstract

The achievement of Personalized Learning (PL) in secondary schools, a key enabler for Sustainable Development Goal 4 (SDG 4: Quality Education), is frequently impeded by the absence of robust, data-driven models capable of managing the inherent uncertainty in student data. While educators strive to tailor lessons to individual needs to promote inclusive and equitable education, measuring the true impact of these efforts remains a significant challenge. This study introduces an innovative decision-making approach, the Circular Intuitionistic Fuzzy Aczel–Alsina Bonferroni means (CIFAABM) aggregation operator, to determine the effectiveness of PL. This model provides a comprehensive and precise method for assessing student progress by integrating multiple data sources and capturing the interrelation between various factors. By integrating the Bonferroni Mean (BM) operator with Aczel–Alsina (A-A) operational rules, this approach offers a realistic framework for evaluating PL strategies. The practical application of this model demonstrates its capacity to optimize learning paths and enhance student engagement, thereby contributing directly to the targets of SDG 4. Through comparative analysis, the model’s effectiveness is validated, offering educators a scalable and empirical decision support framework to improve the accuracy of PL evaluations and advance sustainable educational outcomes.

1.0 Introduction: Aligning Personalized Learning with Sustainable Development Goal 4

The global educational landscape is undergoing a significant transformation, driven by a commitment to achieving Sustainable Development Goal 4 (SDG 4), which aims to ensure inclusive and equitable quality education for all. This evolution has been influenced by cognitive sciences and psychology, emphasizing the importance of individual learning needs. Consequently, Personalized Learning (PL) has emerged as a critical pedagogical strategy. Traditional one-size-fits-all teaching methods often fail to accommodate the diverse learning styles, paces, and interests of students, thereby hindering progress towards SDG 4. PL addresses this by tailoring educational experiences to meet each student’s unique requirements, enhancing learning outcomes and promoting equity.

The rapid advancement of technology has been instrumental in making PL models more effective and scalable. Modern technologies, by utilizing real-time data and analytics, empower educators to customize lesson plans, directly supporting the creation of inclusive learning environments as mandated by SDG 4. The American PL Initiative highlights technology’s role in personalizing education on a large scale. This initiative underscores how technology facilitates the collection and analysis of student data to develop individualized teaching strategies. To fully realize the potential of PL and provide every student with an effective and engaging educational experience, the continued development and integration of these technologies are essential. This study proposes a comprehensive mathematical assessment framework to evaluate PL, ensuring that these innovative strategies align with academic goals and contribute meaningfully to the global education agenda.

1.1 The Challenge of Uncertainty in Educational Data

Decision-making is fundamental to educational strategy. Historically, evaluations relied on concrete values, but the introduction of multiple criteria has made this process more complex. The inherent ambiguity and uncertainty in human learning processes highlighted the limitations of classical set theory. To address this, various fuzzy set theories were introduced, from Zadeh’s Fuzzy Sets (FS) to Atanassov’s Intuitionistic Fuzzy Sets (IFS) and Yager’s q-rung orthopair fuzzy sets (q-ROFSs). More recently, the Circular Intuitionistic Fuzzy Set (CIFS) was introduced to handle data within a circular environment, providing a more comprehensive way for experts to express opinions.

1.2 Advancements in Aggregation Operators for Decision-Making

Aggregation Operators (AOs) are crucial for solving multi-criteria group decision-making (MCGDM) problems. While various operators like Hamacher and Frank have been developed, the Aczél–Alsina (A-A) operator offers superior flexibility in managing imprecise criteria and uncertainty. Concurrently, the Bonferroni Mean (BM) operator is vital for capturing the interactions and interdependencies between criteria. This report addresses a gap in the existing literature by proposing a novel combination of the BM and A-A operators within the CIFS framework. This new operator, the CIFAABM, is specifically designed to provide a more resilient and nuanced decision-making tool for the complex, multi-criteria environment of PL, thereby strengthening the implementation of educational models that support SDG 4.

2.0 Literature Review: Contextualizing Personalized Learning within Sustainable Education

2.1 Overview of Personalized Learning as a Catalyst for SDG 4

Personalized Learning (PL) is an innovative educational approach that adapts teaching strategies to the needs, preferences, and abilities of each student. This student-centered model is crucial for fostering the skills required for success and directly supports the principles of SDG 4 by empowering students to take ownership of their education. By integrating technology, PL environments offer unprecedented opportunities to cater to individual needs through digital tools that enhance information accessibility, promote collaboration, and allow for customized assessments and learning pathways.

To maximize the benefits of PL and its contribution to sustainable education, educators must consider several key facets. These components create a holistic framework for implementing PL effectively.

1. Personalized Learning Policies: Establishing clear guidelines and structures that facilitate the customization of educational experiences, ensuring consistency and alignment with the goals of SDG 4.
2. Small-Group Instruction: Enabling educators to provide more focused and individualized attention, addressing specific student needs and fostering a collaborative learning environment.
3. Project-Based Learning (PBL): Engaging students in real-world projects that demand critical thinking, problem-solving, and teamwork, making learning more relevant and meaningful.
4. Student Mentorship: Providing guidance and support to help students navigate their educational journeys, set goals, and maintain motivation, which is crucial for lifelong learning (a key aspect of SDG 4).
5. Role of Teachers: Shifting the teacher’s role to that of a facilitator who creates tailored learning experiences, assesses progress, and provides continuous feedback.

The proposed CIFAABM operator addresses the challenges of implementing PL by managing the uncertainty and imprecision inherent in student data. It allows for the aggregation of diverse criteria, such as learning styles and engagement levels, providing a sophisticated mathematical approach to enhance decision-making and improve educational outcomes in line with SDG principles.

2.2 Identifying Gaps in Sustainable Educational Frameworks

Despite advancements, significant gaps remain in the literature regarding the assessment of PL models. A comprehensive, data-driven framework is needed to evaluate the efficacy of PL in achieving equitable educational outcomes.

• Lack of Comprehensive Assessment Models: There is a need for robust assessment frameworks utilizing MCGDM methodologies to ensure PL initiatives are grounded in reliable data and aligned with educational objectives, particularly those related to SDG 4.
• Undefined Criteria for Effective Implementation: The specific criteria necessary for the successful implementation of PL models require further investigation. An MCGDM approach can help identify the most critical factors for planning and executing PL strategies.
• Under-analyzed Role of Student Engagement: The impact of student interaction and the learning environment in PL is not sufficiently evaluated. Understanding how engagement affects learning outcomes is vital for creating motivating environments that support inclusive education.

2.3 Research Motivations and Contributions

This research is motivated by the need to bridge these gaps and enhance the effectiveness of PL as a tool for sustainable development. The primary contributions of this study are:

1. The development of a comprehensive framework using the CIFAABM operator to evaluate PL models and identify crucial factors for their implementation, directly supporting SDG 4.
2. An analysis of the role of student involvement in PL, providing insights into how engagement affects learning outcomes and the efficacy of PL strategies.
3. The enhancement of PL experiences through an emphasis on data-driven decisions that address individual student needs, promoting equity and reducing inequalities (SDG 10).
4. An analysis of the impact of learning environments on PL models, highlighting the importance of tailored environments in increasing student engagement.
5. Providing educators with a practical strategy for improving PL practices to ensure they are successful, equitable, and inclusive for all students.

3.0 Methodology: The Circular Intuitionistic Fuzzy Aczel–Alsina Bonferroni Mean (CIFAABM) Operator

This section details the development of the CIFAABM operator, an innovative and reliable aggregation tool created by implementing the foundational concepts of the BM operator and A-A operational rules. This operator serves as a technological innovation (contributing to SDG 9) designed to overcome barriers to quality and inclusive education.

3.1 MCGDM Methodology Based on the Proposed Operator

The Multi-Criteria Group Decision-Making (MCGDM) methodology provides a structured approach to solving complex problems with multiple alternatives and criteria. The process, based on the proposed CIFAABM operator, is as follows:

1. Data Collection: Compute the value of each alternative corresponding to a criterion in the form of a Circular Intuitionistic Fuzzy Number (CIFN).
2. Normalization: Normalize the decision matrix if it contains cost-type criteria. Benefit-type criteria do not require normalization.
3. Data Aggregation: Utilize the proposed CIFAABM operator to accumulate the decision matrices into a single, comprehensive matrix.
4. Alternative Evaluation: Compute the final values for each alternative by utilizing the aggregated decision matrices.
5. Ranking: Calculate the score value for each alternative and rank them to identify the optimal choice that best supports the goals of inclusive and equitable education.

4.0 Assessment of Personalized Learning Systems

The primary objective of this case study is to determine the key components of effective PL models by evaluating several alternatives against criteria essential for achieving SDG 4. The analysis assesses PL models based on their effectiveness, student engagement, adaptability, and overall impact on learning outcomes.

4.1 Alternatives and Criteria for Evaluation

Five key PL models (alternatives) were selected for this analysis:

• A1: Fully Personalized Learning System
• A2: Partially Semi-Personalized Learning System
• A3: Hybrid Personalized Learning System
• A4: Teacher-Led Personalized Learning System
• A5: Technology Integration Personalized Learning System

These alternatives were evaluated against four interdependent criteria crucial for fostering quality education:

• P1: Individualized Learning Path
• P2: Competency-Based Progression
• P3: Teacher Facilitation
• P4: Collaborative Learning

The interdependence of these criteria justifies the use of the Bonferroni Mean within the CIFAABM operator, as it accurately reflects the synergistic relationships between factors like teacher support and individualized paths. This allows for a more nuanced and accurate representation of each learning model’s overall effectiveness in promoting sustainable educational goals.

4.2 Results of the Assessment

Following the five-step MCGDM methodology, data was collected, aggregated, and evaluated. The score values for each alternative were calculated to determine their ranking. The results indicated that the Technology Integration PL System (A5) was the most effective model among the alternatives considered. This finding underscores the critical role of technology in creating scalable and effective personalized learning environments that can advance the objectives of SDG 4.

5.0 Comparative Analysis and Discussion

To validate the effectiveness of the proposed CIFAABM operator, a comparative analysis was conducted against existing aggregation operators, including IFS, CIFBM, and CIFAA. The analysis reveals that prior approaches are often insufficient as they fail to capture the complex relationships between attributive values in educational settings.

5.1 Superiority of the CIFAABM Operator

The CIFAABM operator demonstrates superior and more stable performance, particularly in analyzing the non-linear interdependencies of criteria. Unlike traditional operators that may not capture the practical dynamics of PL environments, the CIFAABM operator effectively manages the vagueness and imprecision inherent in educational data. This leads to a more dependable and correct selection of PL models, thereby enhancing the quality and efficacy of educational strategies aligned with SDG 4. The superiority of the model lies not in the magnitude of its final score, but in its capacity to reveal nuanced interdependencies and provide consistent, realistic rankings.

5.2 Practical Implications for Educators

The CIFAABM operator offers significant practical implications for educators striving to implement PL and contribute to SDG 4:

• It can be used to identify diverse learning preferences and participation levels, enabling teachers to design lessons that meet individual student needs.
• It helps develop contextualized learning models that adapt to student capabilities and challenges by leveraging the operator’s ability to handle interconnected skills.
• It informs decisions regarding curriculum materials and pedagogical approaches for students with diverse learning abilities.
• It supports the creation of customized evaluation criteria that reflect individual student progress, moving beyond standardized testing to foster a more equitable assessment culture.

6.0 Conclusion

This report introduced the CIFAABM operator as a robust solution for improving the assessment of Personalized Learning models, a critical component in the pursuit of Sustainable Development Goal 4. By effectively managing the uncertainty and interdependence of criteria in educational data, the CIFAABM operator enhances the accuracy of decision-making. The findings confirm that this operator is not only effective in identifying the most suitable PL model but is also stable and reliable across different scenarios. This research provides educators and decision-makers with a powerful tool to enhance PL environments and advance the global agenda for inclusive and equitable quality education.

6.1 Advantages of the Proposed Model

• The MCGDM approach ensures a comprehensive assessment of PL models by considering multiple criteria.
• The technique offers versatility and flexibility, allowing it to be tailored to diverse educational settings and priorities.
• The use of data analytics improves the accuracy and effectiveness of the evaluation, leading to more reliable conclusions.
• The findings support the implementation of highly personalized systems that can significantly boost student engagement and learning outcomes, contributing to SDG 4 and SDG 10.

6.2 Limitations and Future Directions

While the proposed model is versatile, its implementation may require significant customization for different educational contexts. The accuracy of the evaluation depends on the quality of available data, and its computational complexity could pose challenges for scalability. Future research could focus on integrating the CIFAABM operator with artificial intelligence and machine learning to create dynamic models that adapt to learners’ needs in real-time. The model could also be extended to other educational settings, such as higher education and vocational training, and compared with other advanced aggregation operators to further refine its application in solving complex decision-making problems in education. Such advancements will continue to extend the scalability and utility of PL models in diverse educational contexts, furthering the mission of the Sustainable Development Goals.

Analysis of Sustainable Development Goals in the Article

1. Which SDGs are addressed or connected to the issues highlighted in the article?

The article primarily addresses issues related to Sustainable Development Goal 4 (SDG 4): Quality Education. The entire focus of the research is on improving the effectiveness of education, specifically at the secondary school level, through personalized learning (PL). The study aims to create a more effective, inclusive, and data-driven educational experience, which is the core mission of SDG 4.

• SDG 4: Quality Education: The article’s central theme is the assessment and enhancement of personalized learning in secondary schools to “improve student performance” and “enhance learning outcomes.” It directly tackles the challenge of tailoring education to meet “the unique needs of each student,” which aligns with the goal of providing quality and equitable education for all. The text explicitly states that the goal is to lead to a “more successful and inclusive educational experience.”
• SDG 9: Industry, Innovation, and Infrastructure: While a secondary connection, the article is relevant to SDG 9, particularly its emphasis on innovation and technology. The study introduces an “innovative and novel decision-making approach” and highlights how “Technology’s rapid advancement has become game-changing” for personalized learning. This focus on developing and integrating new technologies to improve educational systems connects to the broader goal of fostering innovation.

2. What specific targets under those SDGs can be identified based on the article’s content?

Based on the article’s focus, several specific targets under SDG 4 can be identified:

1. Target 4.1: Ensure that all girls and boys complete free, equitable and quality primary and secondary education leading to relevant and effective learning outcomes.
   • Explanation: The article is explicitly set in the context of “secondary schools” and is motivated by the fact that personalized learning “does not always lead to improved student performance.” The entire study is designed to develop a framework to better assess and “enhance learning outcomes,” which is the central aim of this target. The proposed model seeks to provide a “more comprehensive and precise way to assess student progress.”
2. Target 4.5: Eliminate gender disparities in education and ensure equal access to all levels of education… for the vulnerable.
   • Explanation: The article emphasizes making personalized learning “equitable and effective for all learners.” It acknowledges that conventional teaching overlooks “the unique needs and individual specifications of each student” and that PL should cater to learners with “varied learning styles, speeds, and interests.” The stated contribution is to assist teachers in improving PL practices to be “successful, equitable, and inclusive to all students,” directly aligning with the principle of equal access and inclusivity.
3. Target 4.a: Build and upgrade education facilities that are… inclusive and effective learning environments for all.
   • Explanation: The article identifies the “learning environment” as a critical component for successful PL implementation. One of the research gaps it aims to fill is that the “significance of student interaction and learning environment in PL approaches is not appropriately analyzed.” The study contributes by analyzing the “impact of learning environments on PL models, emphasizing the importance of tailored learning environments in increasing student engagement and learning results.”
4. Target 4.c: Substantially increase the supply of qualified teachers…
   • Explanation: While not about increasing the number of teachers, this target also concerns improving teacher qualifications and support. The article directly supports educators by providing a “scalable and empirical decision support framework” and “robust assessment frameworks that enable teachers to effectively evaluate various facets of PL.” By giving teachers better tools for “data-driven decision-making,” the study aims to enhance their capacity to deliver quality, personalized education effectively.

3. Are there any indicators mentioned or implied in the article that can be used to measure progress towards the identified targets?

Yes, the article mentions and implies several indicators that can be used to measure progress towards the identified targets:

• For Target 4.1 (Effective learning outcomes):
  • Indicator: Student performance and learning outcomes. The article repeatedly mentions “improved student performance,” “learning outcomes,” and “student progress” as the ultimate goals of effective personalized learning. The proposed CIFAABM model is a tool designed specifically to “assess student progress” more accurately.
• For Target 4.5 (Equitable and inclusive education):
  • Indicator: Adaptability to individual student needs. The article implies that a key measure of equity is the system’s ability to cater to “individual learning needs and differences,” “varied learning styles, speeds, and interests.” The effectiveness of “individualized learning paths” is a core criterion in the study’s assessment model.
• For Target 4.a (Effective learning environments):
  • Indicator: Student engagement and enthusiasm. The article identifies “student engagement” and “student enthusiasm” as crucial factors for evaluation. It states that a comprehensive assessment framework must evaluate factors like “student engagement” and that effective PL strategies should “elevate… student enthusiasm.”
• For Target 4.c (Support for teachers):
  • Indicator: Availability and use of data-driven decision-making tools. The article’s main contribution is a “data-driven decision support framework” for educators. The development, adoption, and effectiveness of such tools for teachers to “enhance teaching strategies” and “optimize personalized learning paths” serve as a clear indicator of progress in supporting them.

4. Summary Table of SDGs, Targets, and Indicators

SDGs	Targets	Indicators Identified in the Article
SDG 4: Quality Education	4.1 Ensure quality secondary education leading to effective learning outcomes.	Improved student performance Enhanced learning outcomes Accurate assessment of student progress
SDG 4: Quality Education	4.5 Ensure equal access and inclusive education for all learners.	Effectiveness of individualized learning paths Adaptability to varied learning styles, speeds, and interests Inclusivity of PL practices for all students
SDG 4: Quality Education	4.a Provide inclusive and effective learning environments.	Levels of student engagement Measures of student enthusiasm Effectiveness of tailored learning environments
SDG 4: Quality Education	4.c Increase the supply of qualified and supported teachers.	Development of robust assessment frameworks for teachers Use of data-driven decision support tools by educators Enhanced teaching strategies based on model outputs

Source: nature.com