• Education of Primary School Mathematics
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• v.14 no.1
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• pp.13-26
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• 2011

The purpose of this research is to analyze geometrical level and the justification process in the proofs of construction by mathematically gifted elementary students. Justification is one of crucial aspect in geometry learning. However, justification is considered as a difficult domain in geometry due to overemphasizing deductive justification. Therefore, researchers used construction with which the students could reveal their justification processes. We also investigated geometrical thought of the mathematically gifted students based on van Hieles's Theory. We analyzed intellectual of the justification process in geometric construction by the mathematically gifted students. 18 mathematically gifted students showed their justification processes when they were explaining their mathematical reasoning in construction. Also, students used the GSP program in some lessons and at home and tested students' geometric levels using the van Hieles's theory. However, we used pencil and paper worksheets for the analyses. The findings show that the levels of van Hieles's geometric thinking of the most gifted students were on from 2 to 3. In the process of justification, they used cut and paste strategies and also used concrete numbers and recalled the previous learning experience. Most of them did not show original ideas of justification during their proofs. We need to use a more sophisticative tasks and approaches so that we can lead gifted students to produce a more creative thinking.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.1
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• pp.165-184
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• 2013

In order to utilize Sphinx Puzzle in shape education or deductive reasoning, a lesson employing Dienes' six-stage theory of learning mathematics was structured to be applied to students of 6th grade of elementary school. 4 students of 6th grade of elementary school, the researcher's current workplace, were selected as subjects. The academic achievement level of 4 subjects range across top to medium, who are generally enthusiastic and hardworking in learning activities. During the 3 lessons, the researcher played role as the guide and observer, recorded observation, collected activity sheet written by subjects, presentation materials, essays on the experience, interview data, and analyzed them to the detail. A task of finding every possible triangle out of pieces of Sphinx Puzzle was given, and until 6 steps of formalization was set, students' attitude to find a better way of mathematical deduction, especially that of operational thinking and deductive thinking, was carefully observed and analyzed.