The Relation between High School Students’ Probability Background and Judgmental Heuristic and Biases

• Main Authors: Jyy-Ling Chen, 陳芷羚
• Other Authors: 譚克平
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/00872444343894589963

碩士 === 國立臺灣師範大學 === 科學教育研究所 === 90 === There are three main purposes of this study. The first one is to find out the level of understanding of the secondary students in Taiwan on fundamental probability concepts. The second purpose is to verify if the five judgmental heuristics and probabilistic misconception, identified by Tversky & Kahneman(1972,1973), Fischbein(1991,1997) and Konold(1989), could also be observed among our secondary students. The third purpose is an attempt to find out if there exists any relation between “probability background” and “judgmental heuristics and probabilistic misconception”. A total of three instruments were developed to achieve these purposes. A total of 673 high school subjects in Taipei were involved in this study. Among them are 163 eighth graders who have not studied the topic of “experimental probability” and 513 tenth graders who have not studied the topic of “classical probability”. The first part of this study focused on how these two groups of students perform on item related to the two basic probability concepts, “independence” and “sample space”. The second part of this study focused on how these two groups of students perform on items related to the five judgmental heuristics and probabilistic misconception, namely, “Representativeness”, “Availability”, “Outcome approach”, “Equiprobability Bias in Compound Event” , “Tossing N dice simultaneously vs Tossing one die N times consecutively”. The third part of this study focused on identifying possible relationship between students’ understanding of probability concepts and the five judgmental biases. In this study, quantitative analysis was the primary means for data analysis. Subsequent qualitative analysis was also pursued in order to supplement the findings. Regarding the three purposes, the following results were obtained: 1. Although the prior knowledge and the sample sizes of senior and junior high subjects are quite different, there are many similar results in the multiple regression analysis for these two groups. Among which, the most predictable variable on the performance of “Equiprobability Bias in Compound Event” by our senior or junior high subjects is “sample space”, in a model that explained 35% of the variance of the dependent variable. the most predictable variable on the performance of “Representativeness” by our senior or junior high subjects is “independence”, in a model that explained 50% of the variance of the dependent variable. The most predictable variable on the performance of “Tossing all at once” by our senior or junior high subjects is “independence”, in a model that explained 20% to 30% of the variance of the dependent variable. 2. Except in the “Availability” subscale, it was found that though many subjects chose the correct options, their reasons given revealed major misunderstanding. 3. In both the quantitative and qualitative analysis, we found that some of the subjects shown the schema-transferred and concept-conflicted performance, which they were not aware of. 4. Some junior high subjects and a few senior high subjects consistently chose the options “can not be predicted” or “ all the same” in many items of this study. Their understanding of probability is far from satisfactory, even though on those occasions when the 2 options were the right answers. Their performances could be attributable to the “Outcome approach” heuristic. 5. Some high school subjects mentioned their past experience of dice-tossing, but that did not help them in choosing the correct items. This phenomenon may be attributable to the “Availibility” heuristic. Besides, some of them hold the idea of “dice-tossing can be controlled by human being”. This phenomenon was very evident in the “Independence” and “Tossing N dice simultaneously vs Tossing one die N times consecutively ”, sub-scales. 6. Some junior high subjects held the idea of “ the same dice(coin), the same probability”, “the same lottery ticket , the same probability” and use the rule, “fair or not” as their probability judgmental critiria. A few subjects held the idea “as long as the problems are related to dice-tossing, the probability of the events are all equal to 1/6” and “as to probability, the more frequencies, the more convincement” and used these as their probability judgmental critiria. These subjects had the same characteristic. They only considered the factor of similarity, and not any other factors. This may be attributable to the “Representativeness” judgmental bias. 7. Some subjects showed heavy signs of “Equiprobability Bias in Compound Event” performance, which verify what was discussed in the literature. After a series of further inquisitions, it was found such performances could be further explainable by the “Outcome approach” and the “Representativeness” judgmental bias.