The investigation of sixth graders’ conjecturing thinking process for the pattern problem solving.

• Main Author: 鍾雅芳
• Other Authors: 林碧珍
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/95335643858780029220

碩士 === 國立新竹教育大學 === 人資處數理教育研究所 === 101 === To explore how sixth-graders proceed "guessing an unknown conclusion" and "judging the correctness of a proposition", this study was conducted by designing and employing two types of conjecturing questions based on original mathematical question. Six students with different mathematic performance were purposely selected in this study. In addition to observing how students guessed unknown questions, and how they judged the correctness of proposition, 20-30 minute semi-structural interviews were applied, too. With all these efforts, the models of conjecturing thinking process among students with different academically capacity were created. The results show that the repeating conjecturing thinking process for the result-unknown questions is comprised of four steps: observation, conjecture, validation and believing. It was found that high-achieving students tended to skip validating and modifying their guesses due to optimistically confidence. However, the medium-achieving students had more occurrence of validation due to lack of confidence. The low-achieving students were found to rely on observation a lot during the entire process. To the second type of question, judging the correctness of a proposition, validating was found as a starting point to initiate the conjecture process. Among this process, the strategy of observation was usually omitted by students because the proposition was embedded in the question itself already. This study found that mid-achieving and low-achieving students would incline to use observation skills rather than validation, and would often claimed the correctness of the proposition confidently; however low-achieving students were possibly just aware of the false proposition, but failed in correcting the false proposition. In addition, this study found that the “guessing an unknown conclusion” is not always complicated than “"judging the correctness of a proposition” for students. In fact, “judging the correctness of a proposition” is more complicated for students when they encountered with the pattern questions. The associations between conjecturing thinking process, student’s academic achievement, and types of tasks were also confirmed in this study. The formations of conjecture are varied for different achieving students, such as specialization, intuitively observation, expansion, and false analogy. What can be seen through interviews is that specialization and expansion are the most frequent ways that students would like to use. Low-achieving students were more likely to form their conjectures with intuitively observation, expansion; while the technique of specialization was widely used by high-achieving students.