GenSing 2: Pedagogy, Content and Teacher Tools in the Generative Classroom, a GenSing Project
To function in the 21st century students need deep conceptual understanding of mathematics, specifically algebra as it is the gatekeeper to higher-level mathematics. Research in mathematics education has shown that educational environments in which students engage in mathematics as mathematicians, sharing and discussing ideas, fosters this deeper understanding (Boaler, 1998, 2002; Lampert, 1990, 2001). An approach that shifts the focus from procedural computation with its emphasis on right and wrong to an emphasis on ideas and structure, requires a change in the pedagogical practices of the classroom (Lampert, 1990). Traditional algebraic instruction has students arriving at Secondary 3 and 4 with only a computation understanding of algebraic topics. It has created students without robust conceptual connections between the different algebraic representations of graph, expression and table. Successful models of instruction in algebra have employed a focus on multiple representations and Generative Design principles as the basis of instruction (Kaput, 1995, 1998; Stroup, Ares, Hurford, & Lesh, 2007; Stroup & Davis, 2005; Stroup et al., 2002). My initial research work, GenSing Pilot and GenSing1, has extended these design principles to mathematics classrooms here in Singapore (Davis, 2007). Both point to the effectiveness of a focus on "powerful mathematical ideas" and new styles of interaction, but more research is needed to fully understand and mine the potential of this new type of instruction.
Building on the foundation of two years of site based research in Singapore, the GenSing 2 (Generative Activities in Singapore) Project will study the use of a classroom network technology to enact a function-based algebra curriculum created with a pedagogy based on generative design. The study will explore how this curriculum-pedagogy-technology intersection impacts students’ conceptual understanding and effects meaningful change in teacher’s pedagogical practices. Further, the proposed work will develop software visualization tools that permit teachers to utilize the data created by these activities in new forms of formative assessment.
This project will broaden curricular activities, applications and classroom management tools in the Singaporean school system affording powerful methods for teachers to enhance mathematics understanding. Sustainable curricula-packages along with long-term, continuous professional development tools for use with technology-enriched curricula in math learning and pedagogy will be developed and integrated at the Secondary level. The technology demands engaged student learning and inclusion, allowing for high student interactivity and social agency along with ongoing formative assessment.