Resumen

Systems of linear equations (SLE) comprise a fundamental concept in linear algebra, but there is relatively little research regarding the teaching and learning of SLE, especially students’ conceptions of solutions. It has been shown that solving systems with no or infinitely many solutions tends to be less intuitive for students, pointing to the need for more research on the teaching and learning of the topic. We interviewed two mathematics majors who were also preservice teachers in a paired teaching experiment to see how they reasoned about solutions to SLE in ℝ3. We present findings focused on the progression of students’ reasoning about solutions to SLE through the lens of symbolizing. We document their progression of reasoning as an accumulation of coordinated numeric, algebraic, and graphical meanings and symbolizations for solution sets.