دانش محتوایی دانشجومعلمان دوره کارشناسی آموزش ابتدایی از احتمال: عاملی اساسی در تدریس کارآمد مفاهیم احتمالاتی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دبیر آموزش و پرورش

2 گروه ریاضی دانشگاه تربیت دبیر شهید رجایی، ایران، تهران

3 استادیار گروه آموزش و پرورش، دانشگاه علامه طباطبائی، تهران

4 دانشیار گروه آمار، دانشگاه شهید بهشتی، تهران

چکیده

هدف از انجام مطالعه حاضر، بررسی درک دانشجومعلمان دوره کارشناسی آموزش ابتدایی از مفاهیم احتمال است. این پژوهش یک مطالعه توصیفی از نوع زمینه‌یابی است. جامعه آماری، کلیه دانشجومعلمان دوره کارشناسی در رشته آموزش ابتداییِ پردیس‌های دانشگاه فرهنگیان استان مرکزی است که درس ریاضیات پایه را گذرانده‌اند. نمونه آماری شامل 137 دانشجومعلم است که به روش خوشه‌ای انتخاب شدند. ابزار جمع‌آوری داده‌ها، آزمونی محقق‌ساخته، شامل پنج مفهوم احتمالاتیِ فضای نمونه، احتمال وقوع یک پیشامد، عادلانه بودن، مقایسه احتمال‌ها و احتمال شرطی بود. روایی این آزمون توسط سه تن از اعضای هیأت علمی دانشگاه‌های شهر تهران و پایایی آن با روش آلفای کرونباخ مورد تأیید قرار گرفت. به منظور تحلیل و طبقه‌بندی پاسخ‌های ارائه شده، از مدل سولو استفاده شد. این مدل پاسخ‌های ارائه شده به سؤالات ریاضی را در پنج سطح پیش‌روندۀ پیش‌ساختاری، تک‌ساختاری، چندساختاری، رابطه‌ای و انتزاع تعمیم‌یافته، دسته‌بندی می‌کند. نتایج این مطالعه نشان داد که در هر پنج مفهومِ احتمالاتی، کمتر از نصف دانشجومعلمان موفق به ارائه پاسخی کامل در سطح رابطه‌ای شدند. همچنین، تحلیل داده‌ها بر حسب رشته تحصیلی مشارکت‌کنندگان در دوره دبیرستان، حاکی از عملکرد بهتر دانش‌آموختگان رشته‌های ریاضی و فیزیک و علوم تجربی و نیز عملکرد ضعیف‌تر دانش‌آموختگان رشته علوم انسانی است.

کلیدواژه‌ها

موضوعات


Adeniji, S. M., Baker, P., & Schmude, M. (2022). Structure of the Observed Learning Outcomes (SOLO) model: A mixed-method systematic review of research in mathematics education. EURASIA Journal of Mathematics, Science and Technology Education, 18(6), 1-17.
Alonso-Castaño, M., Alonso, P., Mellone, M., & Rodríguez-Muñiz, L. J. (2021). What Mathematical Knowledge Do Prospective Teachers Reveal When Creating and Solving a Probability Problem? Mathematics, 9(24), 1-16.
Álvarez-Arroyo, R., Batanero, C., & Gea, M. M. (2024). Probabilistic literacy and reasoning of prospective secondary school teachers when interpreting media news. ZDM–Mathematics Education, 1-14.‏
Ang, L. H., & Shahrill, M. (2014). Identifying students’ specific misconceptions in learning probability. International Journal of Probability and Statistics, 3(2), 23-29.
Batanero, C. (2022). Training teachers to teach probability: A promising research area. Canadian Journal of Science, Mathematics and Technology Education, 22(3), 729-734.‏
Batanero, C., & Álvarez-Arroyo, R. (2024). Teaching and learning of probability. ZDM–Mathematics Education, 56(1), 5-17.‏
Batanero, C., Chernoff, E. J., Engel, J., Lee, H. S., & Sánchez, E. (2016). Research on teaching and learning probability (pp. 1–33). Springer Nature.‏
Batanero, C., & Diaz, C. (2012). Training school teachers to teach probability: Reflections and challenges. Chilean Journal of Statistics, 3(1), 3–13.
Biggs J, Collis K (1982) Evaluating the quality of learning: the SOLO taxonomy. Academic, New York.
Biggs, J & Collis, K (1991). Multimodal learning and the quality of intelligent behavior. Intelligence: Reconceptualization and measurement, 57-76.
Biggs, J & Tang, C (2011). Teaching for Quality Learning at University. Open University Press. United Kingdom.
Borovcnik, M., & Kapadia, R. (2018). Reasoning with risk: Teaching probability and risk as twin concepts. In C. Batanero & E. Chernoff (Eds.), Teaching and learning stochastics. Advances in probability education research (pp. 3–22). Springer
Brückler, F. M., & Milin Šipuš, Ž. (2023). Pre-service mathematics teachers’ understanding of conditional probability in the context of the COVID-19 pandemic. European Journal of Science and Mathematics Education, 11(1), 89-104.
Denton, D. (2023). Preparing preservice teachers to teach probability and statistics to early learners: A systematic review. Statistics Education Research Journal, 22(2), 14-14.‏
Dollard, C. (2011). Preservice elementary teachers and the fundamentals of probability. Statistics Education Research Journal, 10(2), 27-47.‏
Eskandari, M., Reyhani, E., & Izadi, M. (2024). The probability concept in elementary mathematics textbooks: An analytical look at the concepts and tasks' cognitive demand levels. A new approach to children's education quarterly, Articles in Press, Accepted Manuscript, Available Online from 14 July 2024). [Persian]
Eskandari, M., Reyhani, E., Rahimi, Z., & Bahrami Samani, E. (2023). An Analysis of Iranian Junior High School Mathematics Textbooks Based on Different Interpretations of Probability. Journal of Curriculum Research. 13(1), 31-55. [Persian]
Gandhi, H. (2022). Thirty-One Teachers’ Epistemic Beliefs as They Worked with Random Generators: an Explorative Study. Canadian Journal of Science, Mathematics and Technology Education, 22(3), 645–658.‏
Gómez-Torres E., Díaz C., Contreras J.M., Ortiz J.J. (2018) Prospective Teachers’ Probabilistic Reasoning in the Context of Sampling. In: Batanero C., Chernoff E. (eds) Teaching and Learning Stochastics. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-72871-1_20
Higher Council of Education, Ministry of Education, Educational Research and Planning Organization. National curriculum of the Islamic Republic of Iran (2013). [Persian]
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for research in mathematics education, 39(4), 372-400.‏
Hourigan, M., & Leavy, A. M. (2020). Pre-service teachers’ understanding of probabilistic fairness: Analysis of decisions around task design. International journal of mathematical education in science and technology, 51(7), 997-1019.‏
Kaedi, F. (2017). Evaluating the content knowledge and the pedagogical content knowledge’s grade of preservice mathematics teachers of Farhangian university in probability. (Unpublished masterʼs thesis). Farhangian University, shahid Chamran Campus. [Persian]
Kahaki, A., Reihani, I., & Bahrami Samani, E. (2019). Examining 8th students' understanding of probability. Statistical Thinking. 47, 57-80. [Persian]
Kazak, S., & Leavy, A. (2022). The emerging interplay between subjective and objective notions of probability in young children. Canadian Journal of Science, Mathematics and Technology Education, 22(3), 538-557.‏
Kurt, G. & Coşkuntuncel, O. (2020). Assessment of elementary mathematics teachers’ probability content knowledge in terms of different meanings of probability. Turkish Journal of Computer and Mathematics Education, 11(3), 706-732.
Huerta P.M. (2018). Preparing Teachers for Teaching Probability Through Problem Solving. In: Batanero C., Chernoff E. (eds) Teaching and Learning Stochastics. ICME-13 Monographs. Springer, Cham.
Ministry of Science, Research and Technology, Higher Education Development and Planning Council (Farhangian University). Primary education curriculum (2019). [Persian]
Mooney, E. S., Langrall, C. W., & Hertel, J. T. (2014). A practitional perspective on probabilistic thinking models and frameworks. Probabilistic thinking: Presenting plural perspectives, 495-507.‏
Paparistodemou, E., & Meletiou-Mavrotheris, M. (2018). Teachers’ reflection on challenges for teaching probability in the early years. In A. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds.), Statistics in early childhood and primary education supporting early statistical and probabilistic thinking (pp. 201–215). Singapore: Springer.
Park, M.J., & Lee, E. (2018). Korean Preservice Elementary Teachers’ Abilities to Identify Equiprobability Bias and Teaching Strategies. International Journal of Science and Mathematics Education, 1-19.
Pegg, J. (2018). Structure of the Observed Learning Outcome (SOLO) Model. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham
Pegg, J., & Tall, D. (2005). The fundamental cycle of concept construction underlying various theoretical frameworks. ZDM, 37(6), 468-475.
Savard, A. (2014). Developing probabilistic thinking: What about people’s conceptions? Probabilistic thinking: Presenting plural perspectives, 283-298.
Shamel, N.(2023). Students’ Misconceptions in Conditional Probability. Unpublished masterʼs thesis). Shahid Rajaee Teacher Training University, Faculty of Science Branch. [Persian]
Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational Research, 15(3), 4–14.
Stohl H. (2005). Probability in Teacher Education and Development. In Jones G.A. (Ed.), Exploring Probability in School: Challenges for Teaching and Learning (pp. 345-366). Springer.