研究生: |
蔡欣原 Tsai, Shin-Yuan |
---|---|
論文名稱: |
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 The Impact of Generating Different Visual Representations on Bayesian Inference Problem Solving—2×2 Table and Double Tree Diagram |
指導教授: |
吳昭容
Wu, Chao-Jung |
口試委員: |
吳昭容
Wu, Chao-Jung 林正昌 Lin, Cheng-Chang 林珊如 Lin, San-Ju |
口試日期: | 2024/05/29 |
學位類別: |
碩士 Master |
系所名稱: |
教育心理與輔導學系 Department of Educational Psychology and Counseling |
論文出版年: | 2024 |
畢業學年度: | 112 |
語文別: | 中文 |
論文頁數: | 100 |
中文關鍵詞: | 貝氏推理 、視覺輔助 、問題解決 、學習者生成性繪圖 |
英文關鍵詞: | Bayesian reasoning, visual aids, problem solving, learner-generated drawing |
研究方法: | 實驗設計法 |
DOI URL: | http://doi.org/10.6345/NTNU202400715 |
論文種類: | 學術論文 |
相關次數: | 點閱:61 下載:0 |
分享至: |
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
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 than those 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.
許志農、黃森山、陳清風、廖森游、董涵冬(2010):《普通型高級中學數學4A》。龍騰文化。
游森棚、林延輯、柯建彰、洪士薰、洪育祥、張宮明(2010):《普通型高級中等學校數學4A》。翰林出版。
陳界山(2010):《普通型高級中等學校數學4A》。南一出版。
Barbey, A. K., & Sloman, S. A. (2007). Base-rate respect: From ecological rationality to dual processes. Behavioral and Brain Sciences, 30(3), 241−254. https://doi.org/10.1017/S0140525X07001653
Binder, K., Krauss, S., & Bruckmaier, G. (2015). Effects of visualizing statistical information–an empirical study on tree diagrams and 2× 2 tables. Frontiers in Psychology, 6, Article 1186. https://doi.org/10.3389/fpsyg.2015.01186
Binder, K., Krauss, S., & Wiesner, P. (2020). A new visualization for probabilistic situations containing two binary events: The frequency net. Frontiers in Psychology, 11, Article 750. https://doi.org/10.3389/fpsyg.2020.00750
Binder, K., Krauss, S., Schmidmaier, R., & Braun, L. T. (2021). Natural frequency trees improve diagnostic efficiency in Bayesian reasoning. Advances in Health Sciences Education, 26(3), 847−863. https://doi.org/10.1007/s10459-020-10025-8
Böcherer-Linder, K., & Eichler, A. (2017). The impact of visualizing nested sets: An empirical study on tree diagrams and unit squares. Frontiers in Psychology, 7, Article 2026. https://doi.org/10.3389/fpsyg.2016.02026
Böcherer-Linder, K., & Eichler, A. (2019). How to improve performance in Bayesian inference tasks: A comparison of five visualizations. Frontiers in Psychology, 10, Article 267. https://doi.org/10.3389/fpsyg.2019.00267
Brase, G. L. (2009). Pictorial representations in statistical reasoning. Applied Cognitive Psychology, 23(3), 369–381. https://doi.org/10.1002/acp.1460
Brase, G. L., Cosmides, L., & Tooby, J. (1998). Individuation, counting, and statistical inference: The role of frequency and whole-object representations in judgment under uncertainty. Journal of Experimental Psychology: General, 127(1), 3−21. https://doi.org/10.1037/0096-3445.127.1.3
Brase, G. L., & Hill, W. T. (2015). Good fences make for good neighbors but bad science: a review of what improves Bayesian reasoning and why. Frontiers in Psychology, 6, Article 340. https://doi.org/10.3389/fpsyg.2015.00340
Cheng, L., & Beal, C. R. (2020). Effects of student-generated drawing and imagination on science text reading in a computer-based learning environment. Educational Technology Research and Development, 68, 225−247. https://doi.org/10.1007/s11423-019-09684-1
Cosmides, L., & Tooby, J. (1996). Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty. Cognition, 58(1), 1−73. https://doi.org/10.1016/0010-0277(95)00664-8
Dempster, A. P. (1968). A generalization of Bayesian inference. Journal of the Royal Statistical Society: Series B (Methodological), 30(2), 205−232. https://doi.org/10.1111/j.2517-6161.1968.tb00722.x
Eddy, D. (1982). Probabilistic reasoning in clinical medicine: Problems and opportunities. In D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases (pp. 249−267). Cambridge University Press. https://doi.org/10.1017/CBO9780511809477.019
Eichler, A., Böcherer-Linder, K., & Vogel, M. (2020). Different visualizations cause different strategies when dealing with Bayesian situations. Frontiers in Psychology, 11, Article 1897. https://doi.org/10.3389/fpsyg.2020.01897
Ellis, K., Cokely, E., Ghazal, S., & Garcia-Retamero, R. (2014). Do people understand their home HIV test results? Risk literacy and information search. Proceedings of the Human Factors and Ergonomics Society, 2014-January, 1323−1327. http://doi.org/10.1177/1541931214581276
Friederichs, H., Ligges, S., & Weissenstein, A. (2014). Using tree diagrams without numerical values in addition to relative numbers improves students’ numeracy skills: A randomized study in medical education. Medical Decision Making, 34(2), 253−257. https://doi.org/10.1016/j.socscimed.2013.01.034
García‐Retamero, R., & Hoffrage, U. (2013). Visual representation of statistical information improves diagnostic inferences in doctors and their patients. Social Science & Medicine, 83, 27−33. https://doi.org/10.1016/j.socscimed.2013.01.034
Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: Frequency formats. Psychological Review, 102(4), 684−704. https://doi.org/10.1037/0033-295X.102.4.684
Goldstein, D. G., & Gigerenzer, G. (2002). Models of ecological rationality: the recognition heuristic. Psychological Review, 109(1), 75−90. https://doi.org/10.1037/h0092846
Hembree, R. (1992). Experiments and relational studies in problem solving: A meta-analysis. Journal for Research in Mathematics Education, 23(3), 242−273. https://doi.org/10.2307/749120
Hoffrage, U., Gigerenzer, G., Krauss, S., & Martignon, L. (2002). Representation facilitates reasoning: What natural frequencies are and what they are not. Cognition, 84(3), 343−352. https://doi.org/10.1016/S0010-0277(02)00050-1
Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3(3), 430−454. https://doi.org/10.1016/0010-0285(72)90016-3
Khan, A., Breslav, S., Glueck, M., & Hornbæk, K. (2015). Benefits of visualization in the mammography problem. International Journal of Human-Computer Studies, 83, 94−113. https://doi.org/10.1016/j.ijhcs.2015.07.001
Krynski, T. R., & Tenenbaum, J. B. (2007). The role of causality in judgment under uncertainty. Journal of Experimental Psychology: General, 136, 430–450. https://doi.org/10.1037/0096-3445.136.3.430
Kunzelmann, A. K., Binder, K., Fischer, M. R., Reincke, M., Braun, L. T., & Schmidmaier, R. (2022). Improving diagnostic efficiency with frequency double-trees and frequency nets in Bayesian reasoning. MDM Policy & Practice, 7(1), Article 238146832210866. https://doi.org/10.1177/23814683221086623
Mandel, D. R. (2007). Nested sets theory, full stop: Explaining performance on Bayesian inference tasks without dual-systems assumptions. Behavioral and Brain Sciences, 30(3), 275−276. https://doi.org/10.1017/S0140525X07001835
Maries, A., & Singh, C. (2023). Helping students become proficient problem solvers part II: An example from waves. Education Sciences, 13(2), Article 138. https://doi.org/10.1007/BF00132294
Massironi, M. (2001). The psychology of graphic images: Seeing, drawing, communicating. Psychology Press. https://doi.org/10.1068/p3207rvw
Mayer, R. E., Steinhoff, K., Bower, G., & Mars, R. (1995). A generative theory of textbook design: Using annotated illustrations to foster meaningful learning of science text. Educational Technology Research and Development, 43, 31−41. https://doi.org/10.1007/BF02300480
McDowell, M., & Jacobs, P. (2017). Meta-analysis of the effect of natural frequencies on Bayesian reasoning. Psychological Bulletin, 143(12), 1273–1312. https://doi.org/10.1037/bul0000126
Micallef, L., Dragicevic, P., & Fekete, J. D. (2012). Assessing the effect of visualizations on Bayesian reasoning through crowdsourcing. IEEE Transactions on Visualization and Computer Graphics, 18(12), 2536−2545. https://doi.org/10.1109/TVCG.2012.199
Moro, R., Bodanza, G. A., & Freidin, E. (2011). Sets or frequencies? How to help people solve conditional probability problems. Journal of Cognitive Psychology, 23(7), 843−857. https://doi.org/10.1080/20445911.2011.579072
Nikovski, D. (2000). Constructing Bayesian networks for medical diagnosis from incomplete and partially correct statistics. IEEE Transactions on Knowledge and Data Engineering, 12(4), 509−516. https://doi.org/10.1109/69.868904
Ott, B. (2020). Learner-generated graphic representations for word problems: An intervention and evaluation study in grade 3. Educational Studies in Mathematics, 105(1), 91−113. https://doi.org/10.1007/s10649-020-09978-9
Paivio, A. (1991). Dual coding theory: Retrospect and current status. Canadian Journal of Psychology/Revue Canadienne de Psychologie, 45(3), 255−287. https://doi.org/10.1037/h0084295
Rellensmann, J., Schukajlow, S., Blomberg, J., & Leopold, C. (2022). Effects of drawing instructions and strategic knowledge on mathematical modeling performance: Mediated by the use of the drawing strategy. Applied Cognitive Psychology, 36(2), 402−417. https://doi.org/10.1002/acp.3930
Robinson, A., Keller, L. R., & del Campo, C. (2022). Building insights on true positives vs. false positives: Bayes’ rule. Decision Sciences Journal of Innovative Education, 20(4), 224−234. https://doi.org/10.1111/dsji.12265
Schnotz, W., & Bannert, M. (2003). Construction and interference in learning from multiple representation. Learning and Instruction, 13(2), 141−156. https://doi.org/10.1016/S0959-4752(02)00017-8
Sirota, M., Kostovičová, L., & Juanchich, M. (2014). The effect of iconicity of visual displays on statistical reasoning: Evidence in favor of the null hypothesis. Psychonomic Bulletin & Review, 21, 961−968. https://doi.org/10.3758/s13423-013-0555-4
Sloman, S. A., Over, D., Slovak, L., & Stibel, J. M. (2003). Frequency illusions and other fallacies. Organizational Behavior and Human Decision Processes, 91(2), 296−309. https://doi.org/10.1016/S0749-5978(03)00021-9
Sturm, A., & Eichler, A. (2014, July). Students’ beliefs about the benefit of statistical knowledge when perceiving information through daily media. In Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9), Flagstaff, AZ: Sustainability in Statistics Education. International Statistical Institute. https://doi.org/10.52041/SRAP.05105
Todd, P. M., & Gigerenzer, G. (2007). Environments that make us smart: Ecological rationality. Current Directions in Psychological Science, 16(3), 167−171. https://doi.org/10.1111/j.1467-8721.2007.00497.x
Tolsberg, K., Põldre, S., & Kikas, E. (2022). Learner-generated drawing as a learning strategy. The effect of teacher-guided intervention program “Learning with Understanding” on composing drawings in math word problems in the primary grades. Frontiers in Education, 7, Article 962067. https://doi.org/10.3389/feduc.2022.962067
Van De Schoot, R., Winter, S. D., Ryan, O., Zondervan-Zwijnenburg, M., & Depaoli, S. (2017). A systematic review of Bayesian articles in psychology: The last 25 years. Psychological Methods, 22(2), 217−239. https://doi.org/10.1037/met0000100.supp
Van Meter, P., & Garner, J. (2005). The promise and practice of learner-generated drawing: Literature review and synthesis. Educational Psychology Review, 17, 285−325. https://doi.org/10.1007/s10648-005-8136-3
Vignal, M., & Wilcox, B. R. (2022). Investigating unprompted and prompted diagrams generated by physics majors during problem solving. Physical Review Physics Education Research, 18(1),1−19. https://doi.org/10.1103/PhysRevPhysEducRes.18.010104
Yamagishi, K. (2003). Facilitating normative judgments of conditional probability: Frequency or nested sets?. Experimental psychology, 50(2), 97−106. https://doi.org/10.1026//1618-3169.50.2.97
Zhang, Y., Guo, X., Pi, Z., & Yang, J. (2021). Learning by drawing in STEM: A meta-analysis. Paper presentation at 2021 Tenth International Conference of Educational Innovation through Technology (EITT), Chongqing, China. https://doi.org/10.1109/EITT53287.2021.00025
Zellner, A. (1983). Applications of Bayesian analysis in econometrics. Journal of the Royal Statistical Society. Series D (The Statistician), 32(1/2), 23−34. https://doi.org/10.2307/2987589
Zhao, F., Schnotz, W., Wagner, I., & Gaschler, R. (2020). Texts and pictures serve different functions in conjoint mental model construction and adaptation. Memory & Cognition, 48, 69−82. https://doi.org/10.3758/s13421-019-00962-0
Zikmund-Fisher, B. J., Witteman, H. O., Dickson, M., Fuhrel-Forbis, A., Kahn, V. C., Exe, N. L., & Fagerlin, A. (2014). Blocks, ovals, or people? Icon type affects risk perceptions and recall of pictographs. Medical Decision Making, 34(4), 443−453. https://doi.org/10.1177/0272989X13511706