This study delved into Terry Borton’s reflective model and 7E instructional model to produce comprehensive and guided tools that fit as observation and reflective tools for enhancing learners’ engagement and outcomes in Mathematics lessons. The aim was to gather insights that can inform strategies to adapt Borton’s model to produce tools to be used to observe and analyse 7E model-based Mathematics lessons to contribute to improved student outcomes. Literature information was used to explore, analyse, and synthesise the study’s related existing theories and models to provide a deeper understanding of constraints and prompt question descriptors to produce 21st-century tools to observe and reflect on a Mathematics lesson. After comparing different prompt question descriptors from different literature and Borton’s model, concise descriptors were retained for educational purposes to be analysed, considering the 7E model phases, to produce the guided tools. As a result, two products. “Classroom Observation-Guided Tool”, which includes a guided tool table with a last column for the observer to write comments during class. This column is used to identify gaps in student engagement and learning practices across the 7E phases, which may have been misused. The “Post-Lesson Discussion Guided Tool”, to make a positive post-lesson discussion session, enabling teachers to identify areas for improvement in student engagement to achieve better outcomes next time. Other researchers can study the applicability of 21st-century observation and reflection-guided tools to other subjects, exploring their long-term impact on teacher professional development to improve overall student achievement across all school subjects.

This qualitative study explored the implementation of Differentiated Instruction (DI) in Philippine multigrade classrooms with the aim of understanding teachers’ experiences, strategies, and challenges, as well as developing a performance appraisal tool. Guided by its specific objectives, the research examined how teachers plan, deliver, and manage differentiated lessons while addressing the diverse learning needs of students across multiple grade levels. Findings revealed that effective DI is rooted in intentional instructional planning, including learner profiling, curriculum mapping, and flexible pacing. Instructional delivery was enriched through the use of thematic and multimodal strategies, ability-based groupings, and contextually relevant teaching aids, although technological access and training remained persistent barriers. Classroom management practices emphasized inclusive routines, peer collaboration, and adaptive learning spaces. Teachers also highlighted the importance of assessment tools and reflective teaching practices in continuously improving instruction. In response to these findings, the study developed the Multigrade Differentiated Instruction Performance Appraisal Tool (MDI-PAT), which synthesizes theoretical frameworks with authentic classroom practices. The MDI-PAT serves as both a self-assessment and professional development guide for multigrade educators, promoting ongoing improvement in DI competencies. The study concludes that enhancing teacher capacities in planning, delivery, assessment, classroom management, and reflective practice is essential for fostering inclusive and effective learning environments in multigrade contexts. The insights and tools presented provide a practical framework for educational stakeholders seeking to enhance multigrade instruction in resource-constrained settings.

The personalization of learning and teaching processes represents an advanced approach to education that adapts content, pace, and teaching methods to the individual needs and preferences of students. This approach relies on analyzing diverse student characteristics, such as their knowledge level, progress, learning style, and interests. Achieving these goals is significantly supported by the use of information and communication technology, which facilitates and enhances the implementation of personalization in technology-enhanced learning (TEL). The primary objective of personalization is to increase student engagement, motivation, and support in achieving learning outcomes through individualized learning paths, real-time progress tracking, and feedback. This systematic literature review examines existing personalization approaches in secondary and higher education, supported by technology. The study investigates their effectiveness and provides recommendations for future research. Results reveal that personalized teaching methods—primarily through recommender systems, adaptive learning platforms, and algorithm-driven models—are effective in tailoring educational experiences by leveraging diverse student data, such as demographics, prior achievements, learning styles, and digital engagement. The review shows a predominant focus on higher education, particularly in subjects related to computer science and digital technologies. Quantitative evaluations complemented by qualitative insights, consistently indicate that personalization enhances content mastery, motivation, and overall satisfaction, with no significant negative effects identified.

Educational researchers, as well as researchers in other disciplines, often work with ordinal data, such as Likert item responses and test item scores. Critical questions arise when researchers attempt to implement statistical models to analyse ordinal data, given that many statistical techniques assume the data analysed to be continuous. Could ordinal data be treated as continuous data, that is, assuming the ordinal data to be continuous and then applying statistical techniques as if analysing continuous data? Why and why not? Focusing on structural equation models (SEMs), particularly confirmatory factor analysis (CFA), this article discusses an ongoing debate on the treatment of ordinal data and reports a short review on the practices of conducting and reporting SEMs, in the context of mathematics education research. The author reviewed 70 publications in mathematics education research that reported a study involving SEMs to analyse ordinal data, but less than half discussed how data were treated or guided readers through the analysis; it is therefore harder to repeat such an analysis and evaluate the results. This article invites methodological discussions on SEMs with ordinal variables in the practices of educational research. Subsequently, a standard for reporting SEMs with ordinal data is proposed, followed by an example. This standard contributes to educational research by enabling researchers (self and others) to evaluate SEMs reported. The example demonstrates, using real-life research data, how two different approaches for analysing ordinal data (as continuous or as a product of discretisation from some continuous distributions) can lead to results that disagree.