Secondary School Students Investigating Mathematics

This paper describes a research study to find out the ability of Singapore secondary school students in attempting open investigative tasks. The results show that most high-ability students had no experience in open mathematical investigation and they did not even know how to start. Providing sample problems in the tasks for students to investigate did not seem to help them understand the requirements of the tasks. The implication of these findings on research methodology using paper-and-pencil tests will be discussed. Many school mathematics curricula emphasise the use of mathematical investigation in the teaching and learning of mathematics. For example, the Australian national curriculum states that, “Mathematical investigations can help students to develop mathematical concepts and can also provide them with experience of some of the processes through which mathematical ideas are generated and tested ” (Australian Education Council, 1991, p. 14) and the Cockcroft Report in the United Kingdom stipulates that “mathematics teaching at all levels should include opportunities for … investigational work ” (Cockcroft, 1982, p. 71). In New Zealand, their Mathematics in the New Zealand Curriculum (Ministry of Education of New Zealand, 1992) also stresses the importance of mathematica