Using Online Discussion Forums to Develop Teachers' Understanding of Students' Mathematical Thinking
Jeffrey Shih, University of Nevada, Las Vegas, United States
Society for Information Technology & Teacher Education International Conference, in Nashville, Tennessee, USA ISBN 978-1-880094-44-0 Publisher: Association for the Advancement of Computing in Education (AACE), Chesapeake, VA
As part of the Principles and Standards for School Mathematics (NCTM, 2000), the standard for the responsibilities of colleges and universities includes the need for mathematics education faculty to be a part of school-based mathematics communities. "Teacher educators, mathematicians, and practicing teachers working together can create a rich intellectual environment that will promote veteran teachers' growth and demonstrate to new teachers the value of learning communities." (NCTM, 2000) Until recently, the development of these learning communities was accomplished through face-to-face interaction. This paper will describe the use of online discussion forums to help create learning communities that provide professional development for pre- and inservice elementary school teachers in both content and pedagogy reflected in the Principles and Standards for School Mathematics of the National Council of Teachers of Mathematics. With the support of a PT3 mini-grant, this study was designed to create opportunities for pre- and inservice teachers to build their understanding of number, number sense, computation, problem solving and mathematical communication, as they engaged with their colleagues in both monthly and on-line workgroup meetings. Twenty inservice elementary school teachers from an urban, at-risk school participated in the study. The Hispanic population of the school is forty-two percent, while twenty-seven percent of the students participate in English as a Second Language curriculum. Forty-seven percent of the families are in the low-income bracket. Sixty percent of the students fall in the below average or overage group in ability level in mathematics. 35 pre-service teachers enrolled in undergraduate mathematics methods classes also participated in the project. Each month the participating pre- and in-service teachers were given a problem to pose to their class in preparation for the in-person workgroup meeting. The problem provided mathematical focus, an opportunity to examine trajectories of students' understanding, a challenge to teachers' expectations and a way to talk about details of mathematical thinking. Having a problem to pose to their students also immediately engaged the teachers in thinking about the relationship between their children's mathematical thinking and their classroom practice. Posing the problem led teachers to see that their classrooms could be a place that they could learn with their students. Concurrently, the inservice teachers used digital cameras to upload examples of their student work to a private website. As part of their elementary mathematics methods course, preservice teachers examined the students' solution strategies and related them to the NCTM Standards and research-based frameworks of the development of student understanding (Carpenter, et. al., 1999). Threaded on-line discussions between preservice teachers, inservice teachers, a mathematics education professor, a mathematics professor and the principal of the school took place on the web site, focusing on both content and pedagogical issues. These experiences, in addition to visits to inservice teachers' classrooms, enhanced the preservice teachers' undergraduate training and focused them on "real" student work and student learning. All of the participants attended monthly one and a half-hour workgroup meetings. The teachers began the workgroup meeting by filling out a reflection sheet that asked focused questions about their own student work or the examples provided on-line. Discussion of the student work followed for approximately one hour. The discussions were centered on the mathematical strategies evident in the student work. The range of strategies was documented and the discussion focused on how the strategies were mathematically similar or different from one another. The existing research documents the effectiveness of using students' mathematical work to support teacher learning (Franke, Carpenter, Fennema, Ansell & Behrend, 1998; Lehrer & Schauble, 1998; Sherin, 1997). Pedagogical issues were also discussed as they were raised in the workgroups. Each meeting concluded with the teachers summarizing verbally and on paper what they learned during the conversation. As the pre- and inservice teachers developed content knowledge, appropriate pedagogical strategies addressing the process standards of problem solving and mathematical communication within the context of the teachers' classrooms were also modeled. This collaborative effort across elementary schools and universities potentially provides a model for professional development and communication as more classrooms and schools go online. References: Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., Empson, S.B. (1999). Children's Mathematics: Cognitively Guided Instruction. Portsmouth, NH: Heinemann. Franke, M.L., Carpenter, T., Fennema, E., Ansell, E., & Behrend, J. (1998). Understanding teachers' self- sustaining, generative change in the context of professional development. Journal of Teaching and Teacher Education. Lehrer, R. & Schauble, L. (1998). Modeling in mathematics and science. Unpublished manuscript. Wisconsin Center for Educational Research, Madison: Wisconsin. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM. Sherin, M. (April. 1997). When teaching becomes learning. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, IL.
Shih, J. (2002). Using Online Discussion Forums to Develop Teachers' Understanding of Students' Mathematical Thinking. In D. Willis, J. Price & N. Davis (Eds.), Proceedings of SITE 2002--Society for Information Technology & Teacher Education International Conference (pp. 1106-1108). Nashville, Tennessee, USA: Association for the Advancement of Computing in Education (AACE).