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Use of Dot Paper to Enhance Learning (for Classes I VIII)


Heiles (1958) proposed that there are 5 levels of thought at which we can discuss, learn and teach geometry. At level 0 the students perceive figures by their appearance as a whole. When they call a figure a square, they react to the total figure and not to its specific properties such as all its angles are right angles and all its sides have equal lengths. At level 1, students are able to analyse figures and see such properties. They are also able to identify figures by their properties. That is a figure that has all its sides of equal lengths and all its angles right angles is a square. They still do not see relations between figures e.g. a square is a rectangle. At level 2 the students begin to see relationship between figures e.g. a rectangle is a parallelogram. At level 3, they can follow proof of theorems and they can develop sequence of statements to deduce one statement from another. Level 4 is the most rigorous level at which students have deep understanding of mathematical structures and are able to justify statement made about structures. Instruction in Geometry to be effective should be based on student’s level of thinking. It besides enriching their thinking at that level should move them towards next level. In this paper we suggest some activities using dot or Geo paper that can be used for enrichment at levels 1 and 2 and would help in preparing students for high school geometry. A 5 × 5 dot paper given in Appendix 1, a larger one in Appendix 2, circular dot paper is given in Appendix 3 and an isometric or triangle dot paper is given in Appendix 4. These can be photocopied for use in class. These will also enhance understanding of concepts, communication and reasoning in geometry. Some opportunities are provided for exploration of ideas. We have restricted activities to 2005 syllabus of NCERT for classes I -VIII. Teachers can choose activities appropriate for their class.

Paper contributed by Harinder Mahajan (nee Nanda)

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