In contemporary education, increasing attention is paid not only to students’ acquisition of subject knowledge but also to their ability to apply this knowledge in real-life and interdisciplinary contexts. In mathematics education, one of the persistent challenges is students’ difficulty in solving text-based applied problems. These difficulties are particularly evident in tasks requiring mathematical modelling, where students must interpret contextual information, translate it into mathematical language, construct an appropriate model, and justify their solution. Observations from external summative assessment indicate that many students struggle at the analysis and modelling stages, resulting in low performance in applied problem-solving sections.
This action research was conducted to address this issue through the purposeful integration of blended learning approaches. The central research question guiding the study was:
How can students’ analytical skills in finding optimal solutions to applied mathematical problems be developed through the use of blended learning models?
The objectives of the study were to:
Identify key difficulties students face when translating word problems into mathematical models;
Design and implement learning activities using the flipped classroom model combined with problem-based and case-based learning strategies;
Examine how these approaches influence students’ analytical thinking, modelling skills, and engagement in applied mathematics tasks.
The study was conducted with 12 Grade 12 students during the topic “Problems on Finding Maximum and Minimum Using Derivatives,” a section closely linked to external assessments. This topic was selected because it requires higher-order thinking, application of calculus concepts, and integration of knowledge from physics and geometry. Such interdisciplinary contexts provide a meaningful platform for developing analytical and modelling competencies.This topic was selected because it requires higher-order thinking, application of calculus concepts, and integration of knowledge from physics and geometry. Such interdisciplinary contexts provide a meaningful platform for developing analytical and modelling competencies.
The theoretical framework of the research draws on constructivist learning theory, which emphasizes learners’ active role in constructing knowledge through inquiry and reflection. Vygotsky’s concept of the Zone of Proximal Development underpins the collaborative learning design, particularly in group and pair work, where peer interaction supports deeper understanding. In addition, the principles of blended learning and the flipped classroom model informed the instructional design, enabling students to engage with theoretical content independently before class and devote classroom time to analysis, discussion, and problem-solving.
Problem-based learning and the case method were employed to situate mathematical concepts within authentic, real-world contexts. These approaches align with the conference theme “Cognition and Action”, as they bridge cognitive processes and practical application. Through structured questioning, guided inquiry, and reflective discussion, students were encouraged to analyse problem situations, identify key variables, and justify their modelling decisions.
Overall, the research sought to explore how intentional pedagogical design within a blended learning environment can enhance students’ analytical skills and support more meaningful engagement with applied mathematics.

This study employed an action research methodology, allowing systematic reflection on teaching practice while implementing and refining instructional strategies in a real classroom context. Action research was chosen due to its focus on practitioner-led inquiry aimed at improving learning outcomes and addressing context-specific challenges. Participants were Grade 12 students studying calculus as part of the school curriculum.The research was conducted over a sequence of lessons focused on solving applied problems involving maximum and minimum values. Data were collected through classroom observations, analysis of students’ written work, online assessment results, and student reflections. The flipped classroom model served as the core blended learning approach. Prior to lessons, students were provided with theoretical materials, instructional videos, and online resources via digital platforms. This allowed students to familiarize themselves with key concepts independently and at their own pace. Classroom time was then dedicated to higher-order learning activities, including problem analysis, modelling, and discussion. Lessons began with problem-based questions linked to physical or geometric contexts to activate prior knowledge and stimulate inquiry. Question-and-answer strategies were used to assess students’ readiness and understanding, employing probing and guiding questions to support analytical thinking. Group work was organised using the case method, where students analysed different applied problems, identified key information, translated conditions into mathematical expressions, and developed solution algorithms collaboratively. Peer assessment and formative assessment strategies were integral to the methodology. Mark schemes were used during pair work to guide self- and peer-evaluation, enabling students to identify errors and reflect on their reasoning. Online assessment tools such as Teacher Made and Microsoft Forms were used to collect individual performance data efficiently and provide immediate feedback. Qualitative data from observations and reflections were analysed to identify patterns in students’ engagement, analytical processes, and problem-solving approaches. Quantitative data from assessments supported the evaluation of learning outcomes. The cyclical nature of action research allowed ongoing refinement of instructional strategies based on observed challenges and successes.

The expected outcomes of this research include both pedagogical and learner-related improvements. It is anticipated that the integration of blended learning, particularly the flipped classroom model, will enhance students’ preparedness for lessons and allow more effective use of classroom time for analytical and collaborative activities. In terms of student learning, the study is expected to demonstrate improvement in students’ ability to analyse applied problems, identify key information, and construct appropriate mathematical models. Students are also expected to show increased confidence in solving interdisciplinary tasks involving mathematics, physics, and geometry. Enhanced engagement and motivation are anticipated as a result of interactive learning strategies and the use of digital assessment tools. From a pedagogical perspective, the research is expected to provide evidence that combining problem-based learning, case methods, and formative assessment within a blended learning environment supports the development of higher-order thinking skills. The findings may inform teaching practices beyond the immediate context of the study, offering practical strategies for improving applied mathematics instruction. The results of the study are intended to contribute to professional dialogue among educators by highlighting effective approaches to developing analytical skills. The research outcomes may also support the dissemination of best practices through seminars, professional learning communities, and future collaborative research initiatives.

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