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    Effects of Geometers' Sketchpad on spatial ability and achievement in transformation geometry among secondary 2 students in Singapore
    Driven by the IT Master Plan implemented by the local education authority, schools in Singapore have over the recent few years incorporated the use of computers in the classroom, including the integration of relevant software for the teaching and learning of mathematics. Educators extol the huge potential in computers being superior over conventional teaching aids and in the suitability of computer software in encouraging students' exploration as a way of learning Mathematics.

    This study investigated how the use of a common construction programme in different pedagogical settings impacted spatial ability and achievement scores of students within concepts in transformation geometry.

    The subjects were Secondary Two Express stream students from a school with above-average ranking among National schools. Three classes participated in the study. All the classes were taught an instructional module on transformation geometry with the use of the Geometer's Sketchpad. The software was however employed differently in the three classes: In Class A (n = 41), the approach adopted by the teacher was that of guided-inquiry, and the technological use was supportive of the pedagogy - students have hands-on experience with the software to explore and make conjectures; in class C(n - 38), the teachers' predominant role was that of an expositor and the students' role that of knowledge-recipients, and the software was used as a teacher's tool to demonstrate dynamically the properties of motions; Class B (n = 42) was the 'in-between' of Class A and Class C - adopting the pedagogy of guided-inquiry in whole-class discourses with the teacher manipulating objects on the displays on the projected screen what students would for themselves like to do on the computers.

    Pre- and Post-treatment tests were conducted using the Wheatley Spatial Ability Test (WSAT), which is a widely-used instrument in testing students' ability in mental manipulations of planimetric objects. Paired-sample t-tests show highly significant increases between pre- and posttest scores in all the classes. There was no significant difference in the posttest scores between the classes after factoring in differences in the pre-test scores, as analysed using ANCOVA.

    A Motion Geometry Test (MGT) was constructed to test the subjects' level of attainment of National curricula objectives within the topic of 'Motion Geometry' in the syllabus at the end of the intervention period. An F-test indicated that scores from students in Class C were significantly lower than those from the other two classes. There was no significant difference in MGT scores between Class A and Class B.

    One-to-one teacher-student interview sessions were conducted with five selected students from each class to further investigate the strength of concepts learnt during the treatment period. Each student was presented with four on-screen object-image figures and his/her task was to fully describe the possible single transformation for each task; the teacher provided prompts when the student encountered difficulties in proceeding further. Analysis of the teacher-student responses points to higher level concept abstraction found in students from Class A.
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