Mathematical problem solving is central to mathematics learning. It involves the acquisition and application of mathematics concepts and skills in a wide range of situations, including non-routine, open-ended and real-world problems.
The development of mathematical problem solving ability is dependent on five interrelated components, namely, Concepts, Skills, Processes, Attitudes and Metacognition.
[Source: http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-secondary.pdf ]
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About the Geometry strand in the syllabus and
the Intuitive-Experimental Approach
Geometry is the study of geometric figures, their properties and relationships. Measurement includes mensuration and trigonometry. It involves the practical aspects of mathematics and solving of real-world problems. Both are important domain for students to develop their power of spatial visualisation and reasoning skills.
According to van Hiele’s theory of geometric development, students progress through hierarchical levels of thought in geometry. For example, initially, students identify and reason about shapes by visual perception such as recognising rectangles as door shapes. At the next level, they can describe and recognise geometric shapes by their properties. Subsequently,
at the informal deduction level, they can classify figures and give informal arguments to justify their classification, for example, they are able to justify that a square is a special rectangle. After this stage, students begin to work with deductive reasoning and are able to proceed to formal proof.
The intuitive-experimental approach is proposed for the teaching and
learning of geometry. It involves providing students with informal and handson learning experiences which allow students to make sense of their
learning. The concepts are introduced visually, experientially, inductively
and then deductively.
At the primary level, students have learnt geometry through working with
concrete models and manipulatives. At the secondary level, they use
dynamic geometry software such as the Geometer’s Sketchpad to construct
and manipulate geometric objects (points, lines, triangles etc) and to explore
geometric properties and relationships. They can investigate patterns, make
conjectures and draw conclusions. In this way, they are actively involved in
learning geometry.
[Source: A Guide to Teaching and Learning of O-level Mathematics 2007, First Edition, Mar 2006. © Copyright 2006 Curriculum Planning and Development Division]
