| Summary: | 碩士 === 國立新竹教育大學 === 數理教育研究所 === 102 === The conjecturing thinking investigation of sixth student with high mathematics learning achievement – using ratio and ratio number for example.
The investigation is for the exploration the sixth students with high learning achievement for the question of ratio and ratio number to express the conjecture thinking process, and how they propose conjecture, how to valiate conjecture and validate the character of conjecture. To design the question of ratio and ratio number into two type mission of 「judging the correctness of a proposition」、「guessing an unknown conclusion」. We selected five students with high learning achievement to have paper test with forty minutes in the beginning. Then, according to their resolution record, progressing talking with thirty minutes. Collecting the data to analysis the thinking point of student to drawing their model of conjecture thinking process. Analysis their inspection method and to realize the character of student’s conjecture thinking process.
The result of investigation shows the students’model of conjecture thinking process will be repeated with the steps of observation, conjecture, validation, contradiction and believing due to the guidance of tasks.It’s easier to start the conjecture thinking process for judging the correctness of a proposition than guessing an unknown conclusion. Among the tasks of ratio and ratio number with different meaning construction, the students’conjecture thinking process is pretty the same as to each others.The method of conjecture proposed by the students, the intuitively observation is the most frequest used ways. For the validation, the simple example,substituting figures are the most frequent ways. It expresses that it has closly relationship between the resolving mathematic task and the student’s former experience. In validation conjecture, they don’t learn the formal proving method, most of them propose the instance to prove. It also can use the object to validate conjecture to reach the purpose of proof. Among the method of validation, the shows although the students face the same tasks, their thinking is different from each other. To use the different method to achieve the purpose of validation, we know the students can use their familiar method to explore the mathematics.
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