Rationale
Much of mathematics that is taught in schools has been focused on practiced skills. According to Kulm (1990), the completion of a large number of exercises in a fixed time period has not only been accepted as a measure of mastery but also as an indication of giftedness and potential for doing advanced work. However, higher order thinking in mathematics is complex and multi-faceted.
The use of open-ended mathematical activities would engage students in a meaningful process of exploring, questioning, investigating, communicating and reflecting on mathematical structures and relationships. This would encourage the students to take a different look at mathematical activities that they usually do, to question their knowledge about mathematics when trying to discover hidden links between different objects, to discover structures and relationships between data, to reason mathematically based on logical inference and to communicate their discoveries through appropriate tools.
The use of open-ended mathematical activities would engage students in a meaningful process of exploring, questioning, investigating, communicating and reflecting on mathematical structures and relationships. This would encourage the students to take a different look at mathematical activities that they usually do, to question their knowledge about mathematics when trying to discover hidden links between different objects, to discover structures and relationships between data, to reason mathematically based on logical inference and to communicate their discoveries through appropriate tools.
Structure
The proposed programme is in line with the twenty-first century skills of exploration and discovery, and application of skills and knowledge. It is a ten-week programme to be conducted as an enrichment class for students in primary four. The target group is primary four students as their workload is relatively lighter in the upper primary classes. The students are also able to conduct independent studies. For each session, there will be a teacher to facilitate discussions and students are free to work in groups or individually.
The plan for the programme and the objectives of each session can be seen in Appendix A. The scope and sequence of the programme can be seen in Appendix B. Before the two presentations in sessions 5 and 10, the students would be guided through self-evaluation of their intellectual traits through the use of Appendix C so that they are more aware of their own thinking processes. The two scheduled presentations would also offer the students a platform from which to showcase their talent and work. It would also help the students to develop their communication, presentation and social skills as these are life-skills.
The plan for the programme and the objectives of each session can be seen in Appendix A. The scope and sequence of the programme can be seen in Appendix B. Before the two presentations in sessions 5 and 10, the students would be guided through self-evaluation of their intellectual traits through the use of Appendix C so that they are more aware of their own thinking processes. The two scheduled presentations would also offer the students a platform from which to showcase their talent and work. It would also help the students to develop their communication, presentation and social skills as these are life-skills.
Objectives
In implementing the programme, opportunities would be created for students and teacher-facilitators to work together to incorporate the six dimensions of a culture of thinking (language of thinking, thinking dispositions, metacognition, attitude, higher order thinking and transfer of knowledge). The objectives would also include:
- provide opportunities for independent or group learning for in-depth study
- provide opportunities for students to make generalizations, analysis and deductions
- provide opportunities for students to showcase their work
- encourage students to have extend their learning by creating new scenarios
- encourage students to plan, monitor, and assessing their learning
- encourage students to reflect on their own thinking (intellectual traits)
