## Developing strong conceptual foundations in mathematical reasoning and problem-solving in algebra through multiple and dynamic representations, and digital manipulatives

This research project associated with the Mathematics & Problem-Solving Model focuses on helping students to develop strong conceptual foundations in mathematical reasoning and problem-solving in algebra. In mathematics, multiple and dynamical representations, digital manipulatives, and graphing calculators, are some of the technologies which are already widely used to improve instruction. A study has shown that students constructed their own messy understanding and bridge their understanding of the model-drawing method taught in primary school with the letter-symbolic method taught in secondary school. Therefore there is a need to help students appreciate the connections between the two methods, the limitations of the model method and the power of letter-symbolic algebra. Through this project, we seek to document the use of digital manipulatives with cognitive and meta-cognitive supports in mathematics learning that improves competence in problem-solving, and that develops dispositions of students towards productive mathematical thinking. Through this project, we contribute to MOE’s Algebra project for 2006 – 2007 by designing and developing two IT-supported modules on Algebra Word Problems and Algebraic Manipulation. We will work with the MOE Mathematics IT Project Committee to develop IT-enabled pedagogy, curriculum, IT tools and resources. An integral part of this effort is to use the tools developed to capture data and further understand the theory and practice of students doing algebraic problem solving.