JESSM   |  e-ISSN: 2979-9899

Original article | Journal of Educational Studies in Science and Mathematics 2023, Vol. 2(1) 43-71

Novice Elementary Teachers’ Probabilistic and Statistical Reasoning: Addressing Misconceptions

Evans Kofi Hokor, Justice Yawson Mensah & Francisco Rodríguez-Alveal

pp. 43 - 71   |  DOI: https://doi.org/10.29329/jessm.2023.618.3   |  Manu. Number: MANU-2306-13-0004.R1

Published online: December 15, 2023  |   Number of Views: 47  |  Number of Download: 477


Abstract

This study evaluates the probabilistic and statistical reasoning of novice teachers about some basic concepts in statistics. For this purpose, a mixed methodology was used through a quantitative, qualitative approach, in which a non-probabilistic sample of 248 novice teachers was considered. The number consists of 108 men and 140 women from three Colleges of Education. Quantitatively, the study compared the mean reasoning scores of male and female teachers in statistical and probabilistic knowledge using a t-test for independent samples, while qualitatively the comments of the novice teachers were analyzed through content analysis. Among the most relevant findings, there were statistically significant differences between male and female teachers in general statistical and probabilistic reasoning. Likewise, the data provided evidence that novice teachers have equiprobability and representativeness biases. In short, both male and female novice teachers were not able to demonstrate sound reasoning in statistical and probabilistic situations. Professional development programs are needed to support teachers, especially novice ones, in the acquisition of probabilistic and statistical reasoning skills

Keywords: Gender, independent sample t-test, novice teachers, statistics education research, statistics and probability, statistical reasoning


How to Cite this Article?

APA 6th edition
Hokor, E.K., Mensah, J.Y. & Rodríguez-Alveal, F. (2023). Novice Elementary Teachers’ Probabilistic and Statistical Reasoning: Addressing Misconceptions . Journal of Educational Studies in Science and Mathematics, 2(1), 43-71. doi: 10.29329/jessm.2023.618.3

Harvard
Hokor, E., Mensah, J. and Rodríguez-Alveal, F. (2023). Novice Elementary Teachers’ Probabilistic and Statistical Reasoning: Addressing Misconceptions . Journal of Educational Studies in Science and Mathematics, 2(1), pp. 43-71.

Chicago 16th edition
Hokor, Evans Kofi, Justice Yawson Mensah and Francisco Rodríguez-Alveal (2023). "Novice Elementary Teachers’ Probabilistic and Statistical Reasoning: Addressing Misconceptions ". Journal of Educational Studies in Science and Mathematics 2 (1):43-71. doi:10.29329/jessm.2023.618.3.

References
  1. Amir, G. S., & Williams, J. S. (1999). Cultural Influences on Children’s Probabilistic Thinking. Journal of Mathematical Behavior, 18(1), 85-107. [Google Scholar]
  2. Anway, D., & Bennett, E. (2004, August 1-4). Common misconceptions in probability among students in an elementary statistics class. [Paper presentation]. Artiste Roundtable Conference on Assessment in Statistics held at Lawrence University. http://www.rossmanchance.com/artist/proceedings/AnwayBennett.pdf  [Google Scholar]
  3. Aseeri, M. M. Y. (2015). The Reality of Professional Development of Mathematics and Science Teachers at Elementary Schools in Najran, Saudi Arabia. Journal of Education and Practice, 6(23) [Google Scholar]
  4. Belova, N. & Zowada, C. (2020). Innovating Higher Education via Game-Based Learning on Misconceptions. Education Sciences, 10, 221. https://doi:10.3390/educsci10090221 [Google Scholar] [Crossref] 
  5. Creswell, J. W. (2012). Educational research: Planning, conducting and evaluating quantitative and qualitative research (3rd ed.). Boston, MA: Pearson Education, Inc.  [Google Scholar]
  6. Creswell, J. W. (2014). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (4th ed.,). United States: SAGE Publication, Inc. [Google Scholar]
  7. Damişman, S. & Tanişh, D. (2017). Examination of Mathematics Teachers’ Pedagogical Content Knowledge of Probability. Malaysian Online Journal of Educational Sciences, 5(2). [Google Scholar]
  8. delMas, R. (2004). A comparison of mathematical and statistical reasoning. In D. Ben-Zevi & J.Garfield (Eds.), The Challenge of Developing Statistical Literacy, Reasoning and Thinking (pp. 79-95). Dordrecht, The Netherlands: Kluwer Academic Press. [Google Scholar]
  9. Estrada, A. & Batanero, C. (2020). Prospective Primary School Teachers’ Attitudes towards Probability and its Teaching. International Electronic Journal of Mathematics Education, 15(1), em0559. https://doi.org/10.29333/iejme [Google Scholar] [Crossref] 
  10. Garfield, J. (2003). Assessing Statistical reasoning. Statistics Education Research Journal, 2(1), 22-38. http://fehps.une.edu.au/serj  [Google Scholar]
  11. Garfield, J. & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Dordrecht, The Netherlands: Springer. [Google Scholar]
  12. Garfield, J. & Gal. I. (1999). Teaching and Assessing Statistical Reasoning.  In L. V. Stiff & F. R. Curcio (Eds.), Developing Mathematical Reasoning in Grades K-12: 1999 Yearbook (pp.207-219). Reston, VA: Nation Council of Mathematics Teachers [Google Scholar]
  13. Gómez-Torres, E., Batanero, C. & Contreras, C. D. J. M. (2016). Developing a questionnaire to assess the probability Content Knowledge of prospective primary school teachers. Statistics Education Research Journal, 15(2), 197- 215. [Google Scholar]
  14. Gürbüz, R., Birgin, O., & Çatlıoğlu, H. (2012). Comparing the probability-related misconceptions of pupils at different education levels.  Croatian Journal of Education, 14 (2/2012), 307-357. [Google Scholar]
  15. Groth, R. E. (2017). Developing Statistical Knowledge for Teaching during Design-Based Research. Statistics Education Research Journal, 16(2), 376-396.  http://iase-web.org/Publications.php?p=SERJ  [Google Scholar]
  16. Groth, R. (2007). Research commentary: toward a conceptualization of statistical knowledge for teaching. Journal for Research in Mathematics Education, 38(5), p. 427-437. [Google Scholar]
  17. Henriques, A. & Oliveira, H. (2013). Prospective Teacher’s Statistical Knowledge for Teaching When Analysing Classroom Episodes. In A. M. Lindmeier & A. Heinze (Eds.). Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, 3, 41-48. Kiel, Germany: PME [Google Scholar]
  18. Hirsch, L. S., & O’Donnell, A. M. (2001). Representativeness in statistical reasoning: Identifying and assessing misconceptions. Journal of Statistics Education, 9(2), 96-105. https://doi.org/10.1080/10691898.2001.11910655  [Google Scholar] [Crossref] 
  19. Hokor, E. K. (2023). Probabilistic thinking for life: The decision-making ability of professionals in uncertain situations. International Journal of Studies in Education and Science (IJSES), 4(1), 31-54. https://doi.org/10.46328/ijses.44  [Google Scholar] [Crossref] 
  20. Hokor, E. K. (2022). Integration of critical thinking and reasoning skills into lessons through block factor game for finding factors of a number. Journal of Mathematics and Science Teacher, 2(2), em010. https://doi.org/10.29333/mathsciteacher/12188  [Google Scholar] [Crossref] 
  21. Hokor, E. K. (2020). Pre-Service Teachers’ Probabilistic Reasoning in Constructivist Classroom. Pedagogical Research, 5(2), em0053. https://doi.org/10.29333/pr/7838 [Google Scholar] [Crossref] 
  22. Hokor, E. K., Apawu, J., Owusu-Ansah, N. A., & Agormor, S. (2022). Preservice Teachers’ Misconceptions in Reasoning about Probabilistic Situations. Pedagogical Research, 7(1), em0112. https://doi.org/10.29333/pr/11441  [Google Scholar] [Crossref] 
  23. Hokor, E. K. & Sedofia, J. (2021). Developing Probabilistic Reasoning in Preservice Teachers: Comparing the Learner-centered and Teacher-centered Approaches of Teaching. International Journal of Studies in Education and Science (IJSES), 2(2), 120-145. [Google Scholar]
  24. Huerta, P. (2020). Hipótesis y conjeturas en el desarrollo del pensamiento estocástico: retos para su enseñanza y en la formación de profesores.  Revista Latinoamericana de Investigación en Matemática Educativa, 23(1), 79-102. https://doi.org/10.12802/relime.20.2313  [Google Scholar] [Crossref] 
  25. 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. https://DOI:10.2307/749150  [Google Scholar]
  26. Krippendorf, K. (1997). Metodología de análisis de contenido. Teoría y práctica. Paidós [Google Scholar]
  27. Liu, H. & Garfield, J. B. (2002). Sex Differences in Statistical Reasoning. Bulletin of Educational Psychology, 34(1), 123-138.  [Google Scholar]
  28. Martin, N., Hughes, J., & Fugelsang, J. (2017). The Roles of Experience, Sex, and Individual Differences in Statistical Reasoning. Statistics Education Research Journal, 16(2).  http://iase-web.org/Publications.php?p=SERJ  [Google Scholar]
  29. McMillan, J. & Schumacher, S. (2011).  Investigación educativa.  Madrid: Pearson-Adisson Wesley. [Google Scholar]
  30. Ministry of Education, (2019a). Mathematics Curriculum for Primary Schools (Basic 1 - 3). Accra: National Council for Curriculum and Assessment [NaCCA].   [Google Scholar]
  31. Ministry of Education, (2019b). Mathematics Curriculum for Primary Schools (Basic 4 - 6). Accra: National Council for Curriculum and Assessment [NaCCA]. [Google Scholar]
  32. Ortiz, C. V. & Alsina, Á. (2019). Intuitive Ideas about Chance and Probability in Children from 4 to 6 Years Old. Acta Scientiae, Canoas, 21(3), 131-154. https://DOI:10.17648/acta.scientiae.v21iss3id5215   [Google Scholar]
  33. Ozmen, Z. M. & Baki, A. (2021). Statistics Instructors’ Perceptions of Statistics Literacy in Different Undergraduate Programs. International Journal of Research in Education and Science, 7(3), 852-871. https://doi.org/10.46328/ijres.1817 [Google Scholar] [Crossref] 
  34. Ubilla, F. M., Vásquez, C., Rojas, F., & Gorgorió, N. (2021). Santiago – Villarrica – Barcelona: The Statistical Investigative Cycle in Primary Education Teacher Training. Statistics Education Research Journal, 20(2). https://DOI:10.52041/serj.v20i2.392  [Google Scholar]
  35. University of Cape Coast, (2021). College-Based Teacher Professional Learning Manuel (Unpublished Mathematics Curriculum for Level 300), College of Education Studies School of educational Development and Outreach Institute of education [Google Scholar]
  36. Paul, M. & Hlanganipai, N. (2014). The nature of misconceptions and cognitive obstacles faced by secondary school mathematics students in understanding probability: A case study of selected Polokwame secondary schools. Mediterranean Journal of Social Sciences, 5(8), 2039-9340. https://doi.org/10.5901/mjss.2014.v5n8p446  [Google Scholar] [Crossref] 
  37. Rodriguez-Alveal, F., Diaz-Levicoy, D., & Aguerrea, M. (2022). Literacy and probabilistic thinking in pre-service and in-service mathematics teachers. Uniciencia, 36(1), 1-16. https://doi.org/10.15359/ru.36-1.22  [Google Scholar] [Crossref] 
  38. Rodríguez-Alveal, F., Aguerrea, M., & Díaz-Levicoy, D. (2022). El concepto aleatoriedad en los libros de texto chilenos de educación primaria. Acta Scientiae. 25(1), 1-27. https://doi.org/10.17648/acta.scientiae.6974   [Google Scholar] [Crossref] 
  39. Schram, C. M. (1996). A Meta-Analysis of Sex Differences in Applied Statistics Achievement. Journal of Educational and Behavioral Statistics, 21(1), 55-77. [Google Scholar]
  40. Sharma, S. (2016). Probability from a socio-cultural perspective. Statistics Education Research Journal, 15(2), 126-144. http://iase-web.org/Publications.php?p=SERJ  [Google Scholar]
  41. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi:10.3102/1001318X015002004  [Google Scholar] [Crossref] 
  42. Slama, R., Moussapour, R., Benoit, G., Anderson, N., & Reich, J. (2021). The Future of Math Teacher Professional Learning. United States: Teaching Systems LAB   [Google Scholar]
  43. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. [Google Scholar]