권성룡 Kwon Seong Lyong
DOI: JANT Vol.7(No.2) 85-99, 2003
In this paper, firstly examined various proofs types that cover informal empirical justifications by Balacheff, Miyazaki, and Harel & Sowder and Tall. Using these theoretical frameworks, justification activities by 5th graders were analyzed and several conclusions were drawn as follow: 1) Children in 5th grade could justify using various proofs types and method ranged from external proofs schemes by Harel & Sowder to thought experiment by Balacheff. This implies that children in elementary school can justify various mathematical statements of ideas for themselves. To improve children`s proving abilities, rich experience for justifying should be provided. 2) Activities that make conjectures from cases then justify should be given to students in order to develop a sense of necessity of formal proof. 3) Children have to understand the meaning and usage of mathematical symbol to advance to formal deductive proofs. 4) New theoretical framework is needed to be established to provide a framework for research on elementary school children`s justification activities. Research on proof mainly focused on the type of proof in terms of reasoning and activities involved. But proof types are also influenced by the tasks given. In elementary school, tasks that require physical activities or examples are provided. To develop students` various proof types, tasks that require various justification methods should be provided. 5) Children`s justification type were influenced not only by development level but also by the concept they had. 6) Justification activities provide useful situation that assess students` mathematical understanding. 7) Teachers` understanding toward role of proof(verification, explanation, communication, discovery, systematization) should be the starting point of proof activities.