Supporting Procedural Flexibility and Conceptual Knowledge in Undergraduate Preservice Elementary Teachers: Conceptual and Relational Use of the Equal Sign

This study investigates the development of pedagogical content knowledge in undergraduate pre-service teachers (UPTs). Recognizing the critical link between strong mathematical understanding and effective mathematics teaching, this exploratory qualitative study utilizes clinical interviews with think-aloud protocols and semi-structured interview techniques. The study explores whether a carefully designed sequence of equations prompts procedural flexibility in UPTs' understanding of mathematical concepts, particularly the equal sign. The provided sequence of problems progressed from a generally standard form equation with an operation on the left and an unknown on the right to less familiar forms; culminating with an equation with unknowns on both sides and no explicit operations. Participants identified the problem set, think-aloud protocol, and interview process as key drivers of change, revealing shifts from purely procedural, to procedural and conceptual approaches. These changes were reflected in some participants’ conceptual understanding of the application of the equal sign from operational, to relational and operational. Findings highlight the distinct roles of procedural practice and discourse in shaping understanding. The research contributes to the development of effective learning experiences for UPTs, ultimately aiming to improve mathematics learning experiences for future teachers and for their students.

Author

• Fair, Kimberlie Sanborn

Identifier

hdl:1920/14736

OAI identifier oai:identifier

oai:MARS:1920/14736