Creativity: Pedagogical Moves in a Generative Classroom

• In Event: Learning Mathematics Through Networked Classroom Activities: 10 Years of Progress?

Abstract

This paper reports on research by the Generative Activities in Singapore (GenSing) (Davis, 2009) project to increase understanding of the pedagogical moves teachers make to foster creativity. GenSing is a four-year design study focused on students’ developing understanding of function-based algebra using generative, network-based activities and the types of pedagogical practices needed to foster deep understanding.
For the GenSing project, a 12-week curricular unit composed of 10 different Generative Activities covering the algebra components of the Secondary 1 syllabus was implemented in all Secondary 1 classes at the research site. The curricular activities were created using the principles of generative design (Stroup, Ares, Hurford, & Lesh, 2007), incorporating function-based algebra (Kaput, 1995) and facilitated by the use of a classroom network (Roschelle, Penuel, & Abrahamson, 2004; Stroup et al., 2002). Our earlier studies found that the generative function-based approach to teaching algebraic concepts has the potential to improve students’ understanding of the structural aspects of introductory algebraic concepts (Stroup, Carmona, & Davis, 2005).
We created a number of software visualization tools that transform the student-created digital artifacts from the various generative activities into representations that give insight into different facets of student activity. In one activity, students are challenged to find expressions equivalent to y=2x. Using handheld devices connected to a classroom network, students enter their expressions and submit them to the public group display. The Spiral Visualizer uses this data to create a visualization depicting unique functions submitted, whether the student-generated expression is correct, and other information. The visualization gives a strong sense that something very different occurred in Mr. Tan’s and Mr. Lee’s (pseudonyms) classrooms, even thought the student population in the two classes is quite similar.
We have been investigating the types of pedagogical moves used by teachers that foster creativity in student engagement in generative activities (in the example, “creativity” is defined as the wealth and variety of representations of functions equivalent to 2x). Using detailed field notes and video analyses of the pedagogical moves made by teachers during the time period covered by the spiral, we identify a variety of pedagogical moves and their role in fostering or inhibiting the diversity of responses in the group display. For example, two of the key moves used by Mr. Tan were: (1) Asking students to “surprise him” and (2) Highlighting and discussing different expressions in the display space. In the paper, we will present links between particular activities, pedagogical moves and related student creativity.

Author

• Sarah M. Davis, National Institute of Education - Nanyang Technological University