生成不同視覺輔助對貝氏推理問題解決之影響—2×2表格與雙樹圖

Abstract

正確應用貝氏理論進行推理對大多數的人而言不是一件容易的事。過往研究專注在如何使用視覺輔助協助學生解決貝氏推理問題，且大多數的研究結果都一致地發現題目提供2×2表格對解題有最佳的促進效果。然而在缺乏任何視覺輔助的情境下，人們是否能自行建構視覺輔助來解決問題則仍待更多的探索。本研究根據學習者生成性繪圖理論，假設具有與文字相同線性結構的雙樹圖在繪製時可能會較以往促進效果最佳的2×2表格對受試者的解題更有幫助，故嘗試探討受試者自行繪製雙樹圖或2×2表格時對解決貝氏推理問題的影響。研究招募103位18至35歲的受試者進行貝氏推理測驗，受試者依據接收到的視覺輔助被分為純文字組、2×2表格組以及雙樹圖組。實驗分兩階段進行，每階段包含3題計算題及3題決策題，第一階段兩個視覺輔助組別的題目會提供各自的視覺輔助，第二階段則三組皆為純文字，並要求視覺輔助組別作圖再解題。第一階段結果發現，視覺輔助組別的受試者正確率顯著的高於純文字組；而2×2表格組與雙樹圖組在正確率沒有顯著差異，自評難易度上則是2×2表格組顯著較低。第二階段結果發現，視覺輔助組別的受試者正確率仍高於純文字組，但差異僅達邊緣顯著；2×2表格組與雙樹圖組在正確率上依然沒有顯著差異，且自評難易度也依然是2×2表格組顯著較低；繪圖的正確率上2×2表格組與雙樹圖組之差異未達顯著，並且透過相關性分析發現，正確繪圖的數量與解題的正確率具中度正相關。儘管實驗結果並不支持圖像的線性結構有助於繪圖以及解題的假設，但一來可能與天花板效應有關，因受試者大多就讀國立大學，導致本實驗有極高的解題正確率；二來則可能與受試者對特定視覺輔助的熟悉性有關，本研究並未針對受試者對於各種視覺輔助的熟悉度、熟練度進行控制，若學生對2×2表格更為熟悉，則可能導致雙樹圖圖形結構上的優勢難以凸顯出來。後續研究若能改善上述限制，在受試者的招募上進行額外篩選，將有望更了解視覺輔助對人們進行貝氏推理任務的影響。

Correctly applying Bayesian reasoning is challenging for most people. Previous research has focused on using visual aids to help students solve Bayesian reasoning problems, with most studies consistently finding that providing a 2×2 table in the problem statement offers the best facilitation effect. However, whether individuals can construct their own visual aids to solve problems in the absence of any provided visual aids remains to be further explored. Based on the theory of learner-generated drawing, this study hypothesizes that a double tree diagram, which has a linear structure similar to text, might be more helpful for participants when solving problems compared to the previously most effective 2×2 table. Therefore, this study explores the impact of participants self-drawing double tree diagrams or 2×2 tables on solving Bayesian reasoning problems.The study recruited 103 participants aged 18 to 35 to take a Bayesian reasoning test. Participants were divided into three groups based on the visual aid they received: text-only, 2×2 table, and double tree diagram. The experiment was conducted in two phases, each consisting of three calculation questions and three decision-making questions. In the first phase, the questions for the two visual aid groups included their respective visual aids. In the second phase, all three groups received text-only questions and were asked to draw their visual aids before solving the problems.The results of the first phase showed that the accuracy rates in the visual aid groups were significantly higher thanthose in the text-only group. There was no significant difference in accuracy between the 2×2 table group and the double tree diagram group, but the self-rated difficulty was significantly lower in the 2×2 table group. In the second phase, the accuracy rates of the visual aid groups remained higher than the text-only group, though the difference was only marginally significant. There was still no significant difference in accuracy between the 2×2 table group and the double tree diagram group, and the self-rated difficulty remained significantly lower in the 2×2 table group. The drawing accuracy was not significantly different between the 2×2 table group and the double tree diagram group, and correlation analysis revealed a moderate positive correlation between the number of correct drawings and problem-solving accuracy.Although the experimental results do not support the hypothesis that the linear structure of the diagrams aids in drawing and problem-solving, this may be related to a ceiling effect, as most participants were from national universities, resulting in a extremely high accuracy in this experiment. Additionally, the familiarity with specific visual aids among participants was not controlled in this study; if students are more familiar with 2×2 tables, this might obscure the structural advantages of the double tree diagram. Future research that addresses these limitations and recruits a more diverse sample of participants may provide better insights into the impact of visual aids on Bayesian reasoning tasks.