We believe teaching for understanding begins with the development of a few essential orientations. Teachers must have an appreciation for student-centered mathematics teaching, valuing an approach that builds on student thinking. In addition, teachers must appreciate the complexity of students’ mathematical thinking and ideas. Once these orientations are in place we can attend to student thinking in ways that draw inferences about their understanding (Carpenter, Fennema, Peterson & Carey, 1988; Ma, 1999) and use those inferences to further probe, uncover and extend the complexities of student thinking. We contend this is possible through the value of “why.” Asking “why?” when teaching mathematics has benefits for both students and teachers.
Guarino, Jody; Sykes, Marie; and Santagata, Rossella
"The Value of Why for Student and Teacher Learning,"
Networks: An Online Journal for Teacher Research: