Networking theories to study teachers’ semiotic potential awareness of mathematics artifacts: A pilot lesson study

Abstract

Although artifacts bridge mathematical abstract concepts and concrete learning, teachers often lack tools to intentionally leverage their semiotic potential. We addressed this gap by developing and testing teachers’ semiotic potential awareness (Te-SPA) analysis—a preliminary framework for assessing teachers’ awareness of the meaning-making potential of mathematical artifacts. Through action-research across three Italian lower secondary schools (N = 7 teachers), we networked semiotic mediation theory, cultural transposition theory, mathematics teacher’s specialized knowledge model, and lesson study to identify contextual enablers and barriers to semiotic awareness development and examine the feasibility of the Te-SPA instrument. Our preliminary analysis revealed three divergent trajectories of awareness development, teacherprogram alignment emerging as a pivotal factor. While acknowledging the pilot phase’s constraints—limited sample, bounded timeframe, and preliminary validation—we show that the Te-SPA analysis offers a viable approach for future research and design of effective teacher preparation programs centered on intentional artifact use.