Conceptualizing algebraic connections: Honoring voices from future mathematics teachers and the instructors who teach them

Beginning teachers benefit from preparation emphasizing supporting students with diverse needs and developing deeper understandings of algebraic connections. Our study aims to explore how instructors in secondary preparation programs and mathematics preservice teachers (M-PSTs) conceptualize and enact algebraic connections in required courses. Our dataset comprises instructor interviews and course materials from 48 courses across five universities, and 10 focus group interviews involving 37 M-PSTs. Employing constant comparison method, we analyzed data by creating a coding system for algebraic connections. Our findings highlight varying perspectives of M-PSTs and instructors related to encounters with algebraic connections, emphasis of algebraic connection types by both groups, and types emphasized as main objectives of courses in five secondary mathematics teacher education programs. We describe nine algebraic connection themes that were identified in this investigation. We discuss emergent implications for curriculum development, instructional practices, and foundational algebraic concepts in teacher preparation programs.