The effect of finding relationships, using variables, drawing diagrams and simplification strategies on the development of formulating skills.

Background: formulation serves as a bridge between real-life situations and mathematics, is a critical skill in processes that are crucial for mathematics education, such as problem solving, mathematical literacy, modeling, realistic mathematics education, conceptual thinking, and STEM education, but also emerges as a skill that must be considered for cognitive processes such as cognitive load theory, metacognitive norms, and psychological self-regulation. The fact that most research conducted in the context of formulation remains at a descriptive level and that students are not proficient in this process highlights the need for intervention-based research to develop formulating skills. Methods: in this study, a pre-test-post-test control group quasi-experimental design was chosen to reveal the effect of the Relationships, Using Variables, Drawing Diagrams, and Simplification strategies on the ability to formulate. The participants were 52 tenth-grade students studying at an Anatolian High School in the Marmara Region of Türkiye. Two existing classes at the selected school were randomly assigned to the experimental group ( Results: pre-test scores showed that both groups had similar levels of formulation ability, with no significant difference between them ( Conclusion: the findings show that strategy-based instruction, utilizing relationships, using variables, drawing diagrams, and simplification strategies, significantly improved students' formulating skills. The strategy-based instruction designed within the framework of the Worked Examples approach has positive effects on students' cognitive load management, metacognitive awareness, and problem-solving performance. The research also contributes to the field of educational psychology both theoretically and practically.