Research on the mechanism of the validation of mathematics argumentation

• Main Authors: Ye,Ming Da, 葉明達
• Other Authors: Leou Shian
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/61404653290836870176

博士 === 國立高雄師範大學 === 科學教育研究所 === 93 === Mathematics proof is an indispensable tool to promote the understanding of mathematics. Along with the development of reading comprehension theory, reading and writing are becoming to be regarded as different aspects of one unified process. Similarly, In the process of proof constructing, the problem solver must repeatedly read partial argument that he wrote before to obtain the logic consistency. In the process of argumentation validating, the validater possibly need to construct the assistant proof to check the reasoning correctness. Validation and proof construction can be seen as different aspects of a single process, and mathematics argumentation validation has therefore prompted another way to learn mathematics proof. The purpose of this research is to discuss the cognitive mechanism of mathematics argumentation validating and the thinking connotation. The subjects are eight second-grade senior high students, four mathematics masters, and two mathematicians. This research analyzes the validating protocol by thinking aloud method, interviewing, and questionnaires. Furthermore, the periodical validating processes of two mathematicians were used to confirm the preceding result. The main findings and results are as follows: When case students validate, there are two kinds of mechanism of mathematics argumentation validation, which are "the text with obvious proof framework" and " the text without obvious proof framework. But high validating performance students’ knowledge structure, strategies and accepted criteria are different from those of low validating performance students. The outlines of mathematicians’ validating processes are similar to students’, but the quality of inspecting is different. There are sixteen kinds of difficulties in students’ validating processes. They happened in different stages and also possibly have cause and effect relationship. Some high performance students have reached "the macro validity comprehension level". Although the majority of case students hold positive attitude to the help of validation, only minority of them can foster validation habit. To sum up, the thinking model of mathematics argumentation validation raised in this research is not only a mechanism based on actual observation data, but also is an integrated model that contains knowledge, strategy and affection. But the results from students’ interview also support the fact that validation can be learned. This conclusion may provide references to mathematics argumentation teaching and the following researches.