Misconceptions in the field of probability: An important factor in the performance of elementary education undergraduate preservice teachers in probability situations

Document Type : Research Paper

Authors

Department of mathematics, Faculty of basic sciences, Shahid Rajaee teacher training university, Tehran, Iran

Abstract

The aim of the present study, conducted using a descriptive survey method, is to investigate the understanding, comprehension, and misconceptions of undergraduate preservice teachers in the field of elementary education regarding the topic of probability. The statistical population of this study included all undergraduate preservice teachers in elementary education in three provinces: Tehran, Markazi, and North Khorasan, who were studying in the second semester of the academic year 1401-1402. The study sample consisted of 122 individuals from this population, selected through convenience sampling. In this study, first, the identified misconceptions in the field of probability were studied and categorized. Then, considering the purpose of the research and based on the opinions of a number of experienced teachers, 6 of the most common misconceptions were selected and based on them, test questions were designed or adapted for the sample group. Therefore, the measurement tool in this study was a researcher-made test comprising 10 questions on the topic of probability. The validity of this test was confirmed by a number of mathematics education professors and experienced mathematics teachers. The reliability of the test was examined using Cronbach's alpha method, resulting in a coefficient of 0.7. The findings of the study revealed that all six studied misconceptions were present among the sample group of preservice teachers. These cases, in the order of higher to lower prevalence among preservice teachers, are: 1. Inability to write all possible and desirable states, 2. Representativeness, 3. Lack of understanding the concept of part to part and part to whole, 4. Outcome approach, 5. Lack of understanding of ratio and proportion, and 6. Using intuition (visual effect) in comparison of probability.

Highlights

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 Education, 18, 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 Education, 3, 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

Keywords

Main Subjects

References

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 Education, 18, 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 Education, 3, 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

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History

  • Receive Date: 12 February 2025
  • Revise Date: 17 March 2025
  • Accept Date: 05 May 2025

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