九年級學生在機率教學前後誤用機率判斷偏誤之差異探討

Abstract

本研究的目的為研究國中九年級學生在學習機率單元前後，對於機率概念的了解與代表性偏誤、可利用性偏誤Kahneman&Tversky(1974)）及結果取向判斷偏誤(Konold1989)的異同。主要採量的分析，以自訂的問卷評量工具對受試者進行筆試。研究之樣本為學過國小簡單機率的國中九年級學生，問卷實施的方式為筆試，研究過程設計了前測、後測兩份試卷，並在施測前進行預試來評估試題信度、效度。前測問卷施測目的在探討學生在教學前利用常識、直觀來解題所可能造成的機率偏誤。教學過後也進行後測問卷的施測，並利用前後兩次施測的結果，探討國中生在教學前後機率判斷偏誤上的差異性。本研究之對象為中學九年級學生，共148位學生來進行施測，研究者依學生數學分組教學之成績，分為高分群、中間群、低分群，依據性別和分群兩個變項來進行分析。分析結果發現：\n1.性別變項無顯著差異，故教學過程中不用特別考慮性別差異。\n2.分群分析結果如下：\n(1)結果取向\n 在一次投擲問題中，前、後測問卷分析結果發現，中、高分群前後測整體表現皆無偏誤的比例較低分群來的少。\n(2)代表性偏誤\n 在代表性偏誤中的正時近效應與負時近效應的問題中，低分群在前、後測仍犯有偏誤比中、高分群前後測都犯有偏誤的比例來的高。而改變樣本空間問題中，中、高分群在前、後測皆沒有偏誤的比比例較低分群高。複合樣本問題中探討代表性偏誤，低分群在前、後測仍然有偏誤的比例較中、高分群前、後測犯有偏誤高。\n(3)可利用性偏誤\n 三群在前、後測的綜合表現並無顯著差異。

The study aims to explore the differences of judgmental heuristic and biases on representativeness, availability (Kahneman &Tversky, 1974) and outcome approach (Konold, 1989) in terms of comprehension of probability concepts by ninth graders before and after studying the subject. The results are based on a quantitative analysis of the data collected from two sets of paper-and-pencil self-designed questionnaires. Pre-test questionnaire is meant to explore students’ potential probability biases when they work out the problems based on their previous knowledge and intuition prior to any instruction, while post-test questionnaire is conducted after instruction. The subjects in our experiment are composed of one hundred and forty-eight ninth graders who have only learned some basic probability concepts in primary school, and are classified into high-, mid- and low-scorer groups based on their previous academic performance. \nThe findings suggest that:\n1. Gender effect is not significantly different, so there is no need to pay attention to the gender difference in teaching process. \n2. The results of analyses for different groups are listed in what follows. \n(1) Outcome approach:\nIn the problem of tossing a coin, the results of pre-test and post-test indicate that the proportion of subjects who are without biases is higher in mid- and high-scorers than that of low-scorers. \n(2) Representativeness bias:\nIn the problem of positive recency effect and negative recency effect, the proportion of committing biases is higher in low-scorers than that of mid- and high-scorers in both pre- and post-tests.\nIn the problem of changes in sample spaces, the proportion of lack of biases is higher in mid- and high-scorers than that of low-scorers. \nIn the composite-event problem that deals with representative biases, the proportion of committing biases among low-scorers is higher than that of mid- and high-scorers in both pre- and post-tests.\n(3) Availability bias:\nThere is no significant difference in the overall performance of pre- and post-tests among the three groups.