Teachers' Conceptions And Constructions Of Pedagogical Representations In Teaching Arithmetic Average

This study examined twelve inexperienced and eleven experienced teachers' constructions of and conceptions about pedagogical representations for teaching arithmetic average. The teachers were asked to generate appropriate pedagogical representations as well as predict and evaluate the uses of different representations for solving problems involving the arithmetic average. The experienced teachers were able to predict a variety of representations as well as errors that are recognized as common among middle-school students, while the inexperienced teachers used algebraic representations almost exclusively. Additionally, the inexperienced teachers tended to value algebraic solutions over guess-and-check or visual drawing solutions, more so than did the experienced teachers. However, the differences in the experienced and inexperienced teachers' abilities to predict and evaluate the use of different representations were not clearly evident in their generation of pedagogical representations in a lesson plan context.