An explorative study on designing tool-based task in the teaching of school mathematics

This 36 months project aims to explore teaching approaches for school mathematics with mathematics teachers designing teaching tasks making use of concrete tools and manipulatives. In traditional Hong Kong school mathematics classrooms, the teaching and learning of mathematics mainly follow a teacher-centred approach. Teachers often present known abstract mathematical facts to students that are symbolic in nature, and students use these facts to solve problems. Even though this approach may be effective to enable students to prepare for examination and can be conducive to train students’ thinking, it does not motivate students to realize that mathematics can actually be experienced personally through handling of concrete objects and that abstract ideas can be acquired through an inquiry process. Research has shown that mathematical experiences can be mediated through tools and tools are commonly considered as resources susceptible of enhancing the teaching-learning activity. We interpret tools here as physical or virtual objects that have the potential to mediate between mathematical experience and mathematical understanding. For examples, wooden unit blocks or abacus-like tool helps children develop arithmetic, and interactive ICT platforms enhance students’ understanding of geometry. Through designing teaching and learning tasks with appropriate integration of tools, students are opened to learning environments where they can experience and make sense of abstract mathematical concepts. Using tools in the teaching and learning of mathematics has been shown to greatly empower students’ mathematical ability. In this connection, teachers play a complex and critical role to exploit the pedagogical potentials of the tools. Therefore, the starting point of exploration should focus on how teachers design tool-based teaching tasks. This project is grounded on teaching and learning theories of tool mediation and task design. Selected Hong Kong primary and secondary mathematics teachers will be engaged in workshops, lesson planning and trial teachings with appropriately chosen tools to design teaching and learning tasks. It aims to develop a tool-based mathematics task design model that is practical for teachers to use and serves as a frame for theoretical study. Currently the Hong Kong New Senior Secondary Mathematics Curriculum is under review and one area of discussion is on how to design assessment task to be used for teaching and learning. Hopefully this project will contribute to this area of discussion.