بدفهمی‌های حوزه احتمال: عاملی مهم در عملکرد دانشجومعلمان دوره کارشناسی رشته آموزش ابتدایی در موقعیت‌های احتمالاتی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه ریاضی، دانشکده علوم پایه، دانشگاه شهید رجایی، تهران، ایران

2 گروه ریاضی، دانشکده علوم پایه، دانشگاه تربیت دبیر شهید رجائی، تهران، ایران

چکیده

هدف پژوهش حاضر که به روش توصیفی از نوع زمینه‌یابی انجام شده، بررسی درک و فهم و بدفهمی‌های دانشجومعلمان دوره کارشناسی رشته آموزش ابتدایی در مبحث احتمال است. جامعه آماری این پژوهش کلیه دانشجومعلمان دوره کارشناسی رشته آموزش ابتدایی در سه استان تهران، مرکزی و خراسان شمالی بودند که در نیم‌سال دوم سال تحصیلی 1402-1401 تحصیل می‌کردند. نمونه مورد ‌مطالعه 122 نفر از افراد جامعه بودند که به عنوان نمونه در در دسترس انتخاب شدند. در این پژوهش، ابتدا بدفهمی‌های شناسایی شده در حوزه احتمال مطالعه و طبقه‌بندی شد. سپس، با توجه به هدف پژوهش و بر اساس نظر تعدادی از معلمان با تجربه، 6 بدفهمی رایج‌تر انتخاب و بر اساس آن‌ها به طراحی یا اقتباس سؤالات آزمون برای گروه نمونه اقدام شد. بنابراین، ابزار اندازه‌گیری در این پژوهش، آزمونی محقق‌ساخته شامل 10 سؤال از مبحث احتمال بود. روایی این آزمون توسط تعدادی از اساتید آموزش ریاضی و معلمان ریاضی مجرب تأیید شد. پایایی این آزمون با روش آلفای کرونباخ مورد بررسی قرار گرفت و ضریب 7/0 به دست آمد. یافته‌های پژوهش نشان داد که هر شش بدفهمی مورد مطالعه در این پژوهش، در بین دانشجومعلمان گروه نمونه وجود داشته است. این موارد به ترتیب میزان شیوع بیشتر به کمتر، در میان دانشجومعلمان، عبارتند از: 1. عدم توانایی نوشتن تمام حالات ممکن و مطلوب، 2. معرف‌بودن، 3. عدم درک مفهوم جزء به جزء و جزء به کل، 4. رویکرد نتیجه، 5. عدم درک نسبت و تناسب و 6. استفاده از شهود (اثر بصری) در مقایسه احتمال.

کلیدواژه‌ها

موضوعات


Arican, M., & Kuzu, O. (2020). Diagnosing preservice teachers’ understanding of statistics and probability: Developing a test for cognitive assessment. International Journal of Science and Mathematics Education18, 771-790.
Azimpour, Sohrab and Vahedi, Hossein (2021). Misunderstandings among elementary school students regarding probability. Quarterly Journal of  Research in Mathematics Education, 2(3), 109-116. [Persian]
Bakhshalizadeh, Shahrnaz and Boroujerdian, Naser (2017). Identifying common misconceptions of fourth grade elementary school students in the content area of ​​geometry and measuring and comparing their performance with the average performance at the international level. Journal of Educational Innovations, 16(64), 101-126. [Persian]
Batanero, C., & Borovcnik, M. (2016). Statistics and probability in high school. Springer.
Batanero, C., Chernoff, E. J., Engel, J., Lee, H. S., & Sánchez, E. (2016). Research on teaching and learning probability (p. 33). Springer Nature.
Batanero, C., & Diaz, C. (2012). Training school teachers to teach probability: Reflections and challenges. Chilean Journal of Statistics, 3(1), 3–13.
Chernoff, E. J., & Sriraman B. (2014) (Eds.). Probabilistic thinking: Presenting plural perspectives. Springer.
DeTemple, D. W., Long, C. T., & Millman, R. S. (2015). Mathematical reasoning for elementary school teachers. Pearson Education.
Dollard, C. (2011). Preservice elementary teachers and the fundamentals of probability. Statistics Education Research Journal, 10(2), 27-47.
Doosti, Malihe; Reyhani, Ebrahim (2015). Identifying misunderstandings, strategies, and reasoning of sixth grade students in solving fraction problems. Quarterly Journal of Research in Education, 4(4), 41-59. [Persian]
Fischbein, E., & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal of Research in Mathematics Education, 28(1), 96–105.
Goya, Zahra and Hessam, Abdullah (2005). The role of schema in the formation of students' mathematical misunderstandings. Journal of Mathematical Education Development, 22(82), 4-15. [Persian]
Higher Education Development and Planning Council. (2020). Curriculum for the Bachelor's Degree in Elementary Education. [Persian]
Hirsch, L.S., & O’Donnell, A.M. (2001). Representativeness in statistical reasoning: Identifying and assessing misconceptions. Journal of Statistics Education, 9(2), 96-105.
Hokor, E. K. (2020). Pre-Service Teachers' Probabilistic Reasoning in Constructivist Classroom. Pedagogical Research, 5(2), em0053.
Jahanipour, Ruhollah (1998). Probability/ Fatemi Publications. [Persian]
Jones, D. L., & Tarr, J. E. (2007). An examination of the levels of cogitive demand required by probability tasks in middle grades mathematics textbooks. Statistics Education Research Journal, 6(2), 4-27.
Kahaki Ali, Reyhani Ebrahim and Bahrami Samani Ehsan (2019). Assessment of understanding and understanding of Eighth Grade Students of Probability. Andishe 2019; 24 (1) :57-80 [Persian]
Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6(1), 59–98.
Konold, C., Pollatsek, A.,Well, A., Lohmeier, J., & Lipson, A. (1993). Inconsistencies in students’ reasoning about probability. Journal for Research in Mathematics Education, 24(5), 392–414.
Kvatinsky, T., & Even, R. (2002). Framework for teacher knowledge and understanding about probability. In Proceedings of the Sixth International Conference on Teaching Statistics (CD). Cape Town, South Africa: International Statistical Institute.
Lee, H. S., Sanei, H., Famularo, L., Masters, J., Bradshaw, L., & Schellman, M. (2023). Validating a concept inventory for measuring students’ probabilistic reasoning: The case of reasoning within the context of a raffle. The Journal of Mathematical Behavior, 71, 101081.
Li, J. (2000). Chinese students' understanding of probability (Doctoral dissertation).
Li, J., & Mendoza Pereira, L. (2002). Misconceptions in probability. In Proceedings of the sixth international conference on teaching statistics, Developing a statistically literate society.
Michael, J., (2002). Misconceptions-What students think they know. Advances in physiology education. 26 (1), 4-6.
Mirzaeian, Javad (2020). Investigating the understanding and comprehension of 11th grade mathematics students about probability and its misunderstanding. Master's thesis in Mathematics Education, Saveh Institute of Higher Education, Science and Technology. [Persian]
Nabbout-Cheiban, M. (2017). Intuitive thinking and misconceptions of independent events: A case study of US and French pre-service teachers. International Journal of Research in Undergraduate Mathematics Education3, 255-282.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, Reston, VA:National Council of Teachers of Mathematics.
Odafe, V. U. (2011). Pre-Service Teachers' Conceptions of Probability. PRIMUS, 21(7), 592-605.
Olivier, A. (1989). Handling pupils’ misconceptions. Pythagoras, 21, 10-19.
Rabbani, Sanaz (2014). Students' conceptual errors in conditional probability. Master's thesis in mathematics education, Shahid Rajaee University. [Persian]
Rezaei, Mani (2012). Characteristics of Syntactic Thinking and Its Place in School Curriculum, Iranian Journal of Curriculum Studies, 26, 33-58. [Persian]
Secretariat of the Supreme Council of Education. (2012). National Curriculum of the Islamic Republic of Iran. Tehran: Ministry of Education Publications. [Persian]
Stohl, H. (2005). Probability in teacher education and development. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning, 297–324, Springer.
Tversky, A., & Kaheman, D. (1974). Judgment under uncertainty: heuristics and biases. Science, 185, 1124–1131