An integrated cognitive mathematical technological framework for calculator assisted higher order thinking skills instruction in secondary mathematics

Abstract

This paper presents the Integrated Cognitive Mathematical Technological (ICMT) Framework, a sort of theoretical model meant to cultivate Higher-Order Thinking Skills (HOTS) in secondary mathematics education, by using scientific calculators in a strategic way. The framework tries to fill a critical gap you often see in existing literature, because it combines three components normally handled separately: Piaget’s theory on formal operational reasoning, Mason’s mathematical thinking processes (Specialising, Generalising, Conjecturing, Convincing), and calculator technology as a cognitive instrument. It targets Malaysian Form 4 students (aged 15–16) and addresses continuing performance gaps shown in PISA and TIMSS, plus the fact that calculators still are not used enough in classrooms. In practice, the framework is operationalized through an instructional sequence focusing on quadratic functions, along with process-based assessment criteria. It was developed via a systematic theoretical synthesis method (Jabareen, 2009), and it connects educational psychology, mathematics teaching approaches, and technology integration. The paper also covers what the framework cannot fully cover, including limitations and potential risks when calculators are integrated into learning, and it explains future directions for empirical validation. Overall, the ICMT Framework supports a sustainable and more equitable route for turning national educational policies into actual classroom routines, and it could possibly be adapted across different cultural contexts.