| Summary: | 碩士 === 國立中興大學 === 應用數學系所 === 103 === This study aims to explore the learning performance and mis-interpretation of seniors from industrial high schools, who with their prior knowledge had studied the units of “Decoding the Confidence Interval and Confidence Level.” According to the literature review, it is known that students’ prior knowledge for Confidence Interval(CI) is mainly the Normal Distribution(ND).
The study is designed to analyze the responses to the test questions item by item. The subjects are 123 senior students recruited from industrial high schools in Taipei. Based on students’ previous performance and researches on the related literature, two concepts “Normal Distribution and Confidence Interval” were formed, three to four test goals were set up, and the test was designed. To diagnose the students’ perception, the researcher completed the formal final edition of the test by selecting special items from the related literature and by revising certain items after discussion with experts.
Analyzed quantatively, the results are stated as follows:
1. On the concept of ND, the average correct answer rates are 60.2%, 48.8%, and 57.7% respectively. And those on the concept of CI are 58.5%, 28.9%, 48.8%, and 29.8% respectively.
2. According to the over 20% wrong answers rates, the results are (i) on the ND concept, there are 39.8%of the students, who did not correctly apply their experience laws to the question items. 51.2% of the students did not correctly calculate the average and sample standard deviation and 42.3 % of the students did not correctly judge the relationship among the standard deviations in the graphs of the ND concept. (ii) On the test of CI concept, 71.2% of the students did not correctly interpret the poll results and do some inference of the related statistics. 51.2% of the students could not recognize the graphs in the CI, which were revised after changing the Confidence Level. 70.2% of the students did not figure out the interrelationship among sample amount, Confidence Interval, and Confidence Level.
3. The cognitive errors of each test goal:
(i)The misconception of the concept of ND test: (1) Students used the formula of population standard deviation to obtain the sample standard deviation. (2) Students thought that the standard deviation of the wide-and-short type is smaller than that of the narrow-and-long type.
(ii)The misconception of the concept of CI test: (1) 95% of the Confidence Level is the rate. (2) 95% of the Confidence Level is the probability. (3) The narrow CI is more correct. (4) The CI would be longer from larger sampling. (5) The higher correct answer rate, the more samplings.
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