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Sunday March 5, 2006

Tool to explain properties of cubes and cuboids


IT’S called Phase-based Manipulative and Geometer's Sketchpad Instructional Activities (PMGSIA), but despite its mouthful of a name, it’s been basically designed for a simple task: to help students in a particular aspect of their schoolwork. 

At Booth No 33 during last week’s Malaysia Technology Expo, Chew Cheng Meng (pic), who conceptualised the system as part of his PhD studies in Universiti Malaya's Faculty of Education under the supervision of Assoc Prof Dr Noraini Idris, explained the components, how it worked, and its target audience. 

“It’s meant for students in Form 1, and specific for Chapter 12 of solid geometry. It’s to help them understand the properties of cubes and cuboids,” Chew explained. 

The PMGSIA has four components: models of cubes (which students will make themselves), a CD containing the Geometer’s Sketchpad Instructional Activities, an activity book for the student, and a teacher’s book that contains the lesson plans and answers. 

The activities comprise two learning periods (Learning Period 1 and 2) each consisting of five phases especially designed to enable students to get from knowing the basic properties of cubes and cuboids (Level 1) to knowing how to review and summarise relationships between cubes and cuboids (Level 3). 

Learning Period 1 comprises seven 40-minute lessons and 14 phase-based manipulative instructional activities. Learning Period 2 also comprises seven 40-minute lessons and 14 phase-based manipulative and Geometer’s Sketchpad instructional activities. 

“Learning starts from the very basic, which is to find out what the students know about cubes and cuboids. Some of them don’t even know what a cube is,” said Chew, who considers solid geometry in Form 1 an important component of the five-year secondary mathematics curriculum. 

“It’s the foundational chapter. It provides a rich source of visualisation for understanding basic mathematic concepts, provides continued growth and power in logical reasoning, and is the foundation for study of science, engineering, and architecture, among others,” he said. 

“It also enables students to appreciate the importance and beauty of maths through its cultural and aesthetic values.” 

Chew cited the reported poor performance of Malaysian students in compulsory solid geometry as the basis for designing the system. 

The performance of Malaysian students in compulsory solid geometry questions in Maths Paper 2 PMR and SPM exams is constantly in the weak category, as indicated in the SPM performance reports of 2001, 2002 and 2003. 

“Only 39% of overall candidates could answer the questions,” Chew said. 

In addition, he said, the Third International Mathematics and Science Study Report (Oct 1998) said Malaysian Form 2 students performed poorly in geometry at the highest international benchmark. 

(The performance of 5,500 Malaysian students was reviewed during the survey for the report.) 

“We were rated at 22, which is below the international average. For the medium benchmark, Malaysian students did okay,” said Chew, who is studying under a fellowship from Universiti Sains Malaysia. 

He has carried out a pilot study of the PMGSIA among 60 pupils and found the results encouraging. 

“It enabled the students to attain Level 3 thinking about cubes and cuboids, and enhanced their achievement in content knowledge of solid geometry,” he said. 

“The students also had positive opinions about the activities as they could understand better the properties of and relationships between cubes and cuboids.” 

“It’s a dynamic programme and students can play around with it. It is also cheap and can be recycled,” he added.

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