Teachers' knowledge of students' mathematical thinking is a growing area of research in mathematics education. The literature has reported plentiful evidence of the interplays between teachers' mathematical knowledge and their knowledge of students' mathematical thinking. The present study builds on this body of work to explain how such interplays…

Piaget's theory of stage structure is synonymous with discussions involving cognitive development. As with any theoretical model, researchers inevitably and rightly seek to affirm and/or contest the elements of the model presented. In this comparative study, students' performance across three hands-on engineering tasks for two distinct student…