††††††††††† Electronic Proceedings of the 12th Asian Technology Conference in Mathematics



            Abstract for 12767

            Designing Web-based Cognitive Tools to Enhance Teaching and Learning

            of Mathematical Problem Solving

            Authors: Luis Tirtasanjaya Lioe, Yanping Fang, Kai Fai Ho

            Affiliations: Centre for Research in Pedagogy and Practice, National

            Institute of Education, Singapore, Centre for Research in Pedagogy

            and Practice, and Curriculum Teaching Unit, National Institute of

            Education, Singapore., Centre for Research in Pedagogy and Practice,

            National Institute of Education, Singapore.



            Many researchers and cognitive scientists have been exploring

            effective professional development for teachers that offers

            flexibility of time and a continuity to ensure successful transfer

            of learning to teachersí daily practices (Ball and Cohen, 1996;

            Hapgood, Palincsar, Kucan, Gelpi-Lomangino, & Khasnabis, 2005). This

            paper reports on a large research project which aims at building

            web-based cognitive tools for teacher professional development in

            the area of mathematical problem solving (MPS) in upper primary and

            lower secondary schools in Singapore. To this end, we draw on a rich

            variety of classroom data to design web-based cognitive tools, such

            as video cases of teachersí practices, studentsí problem solving

            processes (Boaler and Humphreys, 2005) and a databank of

            mathematical problems. The video cases of teaching practices aim to

            initiate, through guided discussion forums, a peer-sharing and

            peer-learning among participant-teachers, while the video cases of

            studentsí pair work aim to open discussions among the teachers on

            studentsí challenges in solving problems and ways to help students  


            overcome them. Over time, such on-line discussions will be able to

            build a virtual community of learners (Gee, 2003) through

            interactive technologies and digital media as teachers pose

            questions, analyze data, consider different perspectives, and apply

            new knowledge to their own teaching practice (Baildon & Fang, 2007).

            Meanwhile, our databank of problems, with wide variety of contexts,

            rich problem types and multiple solution approaches (Foong, 2002;

            Frobisher, 1994), serves as a resource to support problem solving

            activities in classrooms as well as scaffold cognitive processes of

            various problem-solving strategies. The development of these

            web-based cognitive tools involves iterative process of improving

            and evaluation based on feedback from teachers as users. This paper

            will highlight the design and implementation processes of these

            cognitive tools as well as the research implications for teachersí

            professional learning.




            Baildon, M. & Fang, Y.P. (2007). A*Star Project Grant Proposal

            (Science and Engineering Research Council, SERC)/Agency for Science,

            Technology & Research (A*STAR), Singapore


            Ball, D., & Cohen, D.K. (1999). Developing practice, developing

            practitioners: Toward a practice-based theory of professional

            education. In L. Darling-Hammond & G. Skyyes (Eds.). Teaching as the

            learning profession: Handbook of policy and practice (pp. 3-32). San

            Fransisco: Jossey-Bass.


            Boaler, J. & Humphreys, C. (2005). Connecting mathematical ideas:

            middle school video cases to support teaching and learning.

            Heinemann, Portsmouth, NH.


            Foong, P. Y. (2002). The role of problems to enhance pedagogical

            practices in the Singapore mathematics classroom. The Mathematics

            Educator, 6(2), 15-31.


            Frobisher, L. (1994). Problems, investigations and an investigative

            approach. In A. Orton & G. Wain (Eds.), Issues in Teaching

            Mathematics (pp.150-173). London: Cassell.


            Gee, J. P.(2003). What Video Games Have to Teach Us About Learning

            and Literacy. New York: Palgrave McMillan.


            Hapgoof, S., Palincsar, A.S., Kucan, L., Gelpi-Lomangino, A., &

            Khasnabis, D. (2005). Investigating a new measure of teachersí

            pedagogical content knowledge for teaching informal text

            comprehension. Paper presented at the annual meeting of the American

            Educational Research Association.