Computer-Supported Math Discourse Among Teachers and Students

This full research-and-development project designs, develops and tests an interrelated system of technological, pedagogical and analytic components to provide a range of opportunities for middleand high-school students to engage in significant mathematical discourse (DR K-12 challenge 2); it catalyzes and supports these opportunities by enhancing the ability of in-service teachers to engage in, appreciate and foster math-problem-exploration and math-discourse skills in their students (DR K-12 challenge 3). The project addresses the core STEM discipline of mathematics by motivating the identification, comprehension and enjoyment of mathematical discourse skills through socially interactive, collaborative learning experiences involving pedagogically organized series of stimulating, skill-appropriate problems using computer-based visualization/exploration and small-group math-problem discussion. The project’s design-based-research approach crafts a socio-technical educational model to provide a comprehensive, practical package of tools and techniques for classroom teachers and students, which integrates and refines a number of mutually supportive components: (a) Innovative technology: A custom, open-source virtual learning environment that integrates synchronous and asynchronous media with the first multi-user dynamic-math-visualization application. (b) Curricular resources: Problem-based learning topics in specific areas of mathematics designed to help teachers tune rich math problems to local texts or curriculum and to guide student exploration. (c) In-service teacher professional development: Practicing teachers in online masters programs are mentored to understand and model the innovative technologies and pedagogies by doing collaborative problem posing/exploring/solving and engaging in collaborative reflection on the math discourse in their logged interactions. (d) Middleand high-school students: The teachers introduce the model, technology and resources into their classrooms. The project builds on and integrates previous work of the PIs, including: the discourse-analysisbased theory of group cognition (Stahl, 2006); the Virtual Math Teams learning environment developed, analyzed and evaluated in (Stahl, 2009b); curricular materials and dynamic math visualization software of GeoGebra, adapted to flexible multi-user collaborative learning; online professional development and online mentoring of in-service math teachers at the Math Forum and at the Drexel and Rutgers-Newark schools of education; and the adaptation of conversation analysis to text-based chat interaction analysis, designed to highlight how collaborative problem solving or group knowledge building takes place. The project adapts components that have been explored, prototyped, or piloted by the PIs to classroom use. Project key personnel and Advisory Committee members bring expertise and experience in educational software R&D; math problem-set adaptation, dissemination and mentoring; in-service math teacher training; online math resources, collaborative learning, problem-based learning and dynamic math; design-based educational research management and evaluation; theory of knowledge building in small groups and in online communities. They also bring opportunities for national deployment and scaling up. Intellectual merit. This project integrates leading-edge cyber-learning-environment technology incorporating innovative collaborative math exploration tools with educational approaches based on current directions in the learning sciences. It approaches this through a systematic iterative process of coevolving the technology and curricular resources in the context of engaging, reflective collaborativelearning experiences of significant mathematical discourse by in-service teachers and their students. It thereby advances theory, technology and practice within real-world educational settings to forge a coherent research-based approach to math education appropriate to today’s challenges and potentials. Broader impact. The project designs, tests, integrates, evaluates and disseminates technology, curricular resources, pedagogical methods and analytic tools for use in math-teacher professionaldevelopment programs, classrooms of math students, home-schooling networks, online schools and the Math Forum community (over three million visits per month). Project results will support the use of math exploration technology within collaborative math-discourse approaches at diverse schools nationally through their spread to in-service teacher-training programs and services—bringing practical cyberlearning of math to at-risk and isolated math students. It documents the potential impact on both teachers and students of this computer-supported math-discourse approach quantitatively and qualitatively.