Constructing slope conceptualizations: Physical, geometrical, and algebraic

The concept of slope constitutes a fundamental component of the discourse surrounding linear equations. A subset of students frequently interprets slope merely as an algebraic ratio. This particular context fosters a superficial understanding of slope, as these students typically resort to mechanical memorization of the slope formula. The intent of this research endeavor is to enhance a holistic understanding of the slope concept: physically, geometrically, algebraically; through the deployment of realistic teaching activities. Two students are participants in this research endeavor. The research group initiated a series of questions aimed at assessing their comprehension by delivering a total of six activities, which were systematically designed using the emergent modeling framework central to the educational design principles of Realistic Mathematics Education (RME). These activities are structured to facilitate the students' understanding of the fundamental concept of slope, transitioning from physical properties, through geometric ratios, to algebraic ratios. Subsequent to the investigations and the interviews conducted, the researchers deduce that the utilization of realistic activities significantly enhances students' comprehension of the foundational concept of slope: physical, geometric, algebraic.