An Overview of Strategies for Conceptualizing Derivative and their Applications in Daily Life for Secondary-Level Mathematics Students

Abstract

Derivative is a foundational concept in calculus but can be challenging for secondary students to grasp conceptually. This paper provides an overview of research-backed strategies for developing a strong conceptual understanding of derivative. Visual and intuitive approaches are discussed, such as relating the derivative to real-world contexts involving speed, growth, and modeling phenomena. The importance of multiple linked representations and building connections between graphical, numeric, verbal and symbolic perspectives is emphasized. Strategies for motivating learning through real-world applications and simulations relating concepts to students' lives are outlined. Procedural expertise and conceptual mastery are cultivated together. The benefits of a conceptual learning, problem solving abilities, and STEM-related fields are noted. Curricular recommendations focus on conceptual exploration prior to formal definitions. Thus, the paper highlights best practices for conceptualizing derivative through visual-intuitive, multi-representational and application-based approaches to promote flexible, adaptive understanding and lay the groundwork for calculus success.