Pre-service mathematics teachers’ understanding of conditional probability in the context of the COVID-19 pandemic

Franka Miriam Brückler 1 * , Željka Milin Šipuš 1
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1 Department of Mathematics, Faculty of Science, University of Zagreb, Zagreb, CROATIA
* Corresponding Author
EUR J SCI MATH ED, Volume 11, Issue 1, pp. 89-104. https://doi.org/10.30935/scimath/12436
Published Online: 08 September 2022, Published: 01 January 2023
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ABSTRACT

During the last two years, the COVID-19 pandemic had a secondary effect of increased media content loaded with mathematical, often probabilistic information (and misinformation). Our exploratory study investigates the probabilistic intuitions, misconceptions, biases, and fallacies in conditional probability reasoning of mathematics teacher candidates in the context of the pandemic. The pre-service mathematics teachers who participated in our study were given a questionnaire with five contextual conditional probability problems, all formulated similarly to media statements often encountered when discussing the COVID-19 pandemic. Our findings confirm the previous findings on biases and fallacies related to conditional probability problems with a social context. They were also indicative of several types of errors (both numerical and logical) as more common than expected. Our results also reveal that pre-service mathematics teachers apparently separate the content learned in the classroom from the application of the knowledge in critical examination of the information to which they are daily exposed by the media.
Keywords: conditional probability, context of a probability problem, pre-service mathematics teachers, COVID-19 pandemic, media in teaching of probability and statistics

CITATION

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. https://doi.org/10.30935/scimath/12436

REFERENCES

  • Bar-Hillel, M. (1983). The base-rate fallacy controversy. In R. W. Scholz (Ed.), Decision making under uncertainty (pp. 39-61). Elsevier. https://doi.org/10.1016/S0166-4115(08)62193-7
  • Batanero, C., Chernoff, E. J., Engel, J., Lee, H. S., & Sánchez, E. (2016). Research on teaching and learning probability. Springer. https://doi.org/10.1007/978-3-319-31625-3
  • Batanero, C., Contreras, J. M., Díaz, C., & Sánchez, E. (2015). Prospective teachers’ semiotic conflicts in computing probabilities from a two-way table. International Electronic Journal of Mathematics Education, 10(1), 3-16. https://doi.org/10.29333/iejme/288
  • Borovcnik, M., & Peard, R. (1996). Probability. in A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 239-288). Kluwer. https://doi.org/10.1007/978-94-009-1465-0
  • Bursali, G. G., & Ozdemir, B. G. (2019). Instructional explanations of mathematics teachers and preservice teachers on misconceptions: The subject of probability. Journal of Computer and Education Research, 7(14), 642-672. https://doi.org/10.18009/jcer.639384
  • Carles, M., & Huerta, M. P. (2007). Conditional probability problems and contexts. The diagnostic test context. In D. Pitta-Panzati, & G. Philippou (Eds.), Proceedings of the 5th Congress of the European Society for Research in Mathematics Education (pp. 702-711).
  • Chevallard, Y., & Sensevy, G. (2014). Anthropological approaches in mathematics education, French perspectives. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 38-43). Springer. https://doi.org/10.1007/978-94-007-4978-8_9
  • Di Martino, P., & Zan, R. (2015). The construct of attitude in mathematics education. In B. Pepin, & B. Roesken-Winter (Eds.), From beliefs to dynamic affect systems in mathematics education: Exploring a mosaic of relationships and interactions (pp. 51-72). Springer. https://doi.org/10.1007/978-3-319-06808-4_3
  • Díaz, C., & Batanero, C. (2008). Students’ biases in conditional probability reasoning. In Proceedings of the IASE—ICME 11 2008 (pp. 1-11).
  • Díaz, C., & Batanero, C. (2009). University students’ knowledge and biases in conditional probability reasoning. International Electronic Journal of Mathematics Education, 4(3), 131-162. https://doi.org/10.29333/iejme/234
  • Díaz, C., & Fuente, I. D. L. (2007). Assessing students’ difficulties with conditional probability and Bayesian reasoning. International Electronic Journal of Mathematics Education, 2(3), 128-148. https://doi.org/10.29333/iejme/180
  • Estrada, A., & Batanero, C. D. (2006). Computing probabilities from two way tables: An exploratory study with future teachers. In A. Rossman, & B. Chance (Eds.), ICOTS 7 conference proceedings.
  • Estrada, A., & Batanero, C. D. (2020). Prospective primary school teachers’ attitudes towards probability and its teaching. International Electronic Journal of Mathematics Education, 15(1), 1-14. https://doi.org/10.29333/iejme/5941
  • Estrada, A., Batanero, C., & Díaz, C. (2018). Exploring teachers’ attitudes towards probability and its teaching. In C. Batanero, & E. Chernoff (Eds.), Teaching and learning stochastics: Advances in probability education research (pp. 313-332). Springer. https://doi.org/10.1007/978-3-319-72871-1_18
  • Falk, R. (1986). Conditional probabilities: Insights and difficulties. In R. Davidson, & J. Swift (Eds.), Proceedings of the 2nd International Conference on Teaching Statistics (pp. 292-297). International Statistical Institute.
  • Falk, R. (1989). Inference under uncertainty via conditional probabilities. In R. Morris (Ed.), Studies in mathematics education: The teaching of statistics (pp. 175-184). UNESCO.
  • Feller, W. (1968). An introduction to probability theory and its applications. John Wiley and Sons.
  • Fischbein, E. (1987). Intuition in science and mathematics. An educational approach. Reidel.
  • Fischbein, E. (1999). Psychology and mathematics education. Mathematical Thinking and Learning, 1, 47-58. https://doi.org/10.1207/s15327833mtl0101_2
  • Fischbein, E., & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? An exploratory research study. Educational Studies in Mathematics, 15(1), 1-24. https://doi.org/10.1007/BF00380436
  • Fischbein, E., & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education, 28(1), 96-105. https://doi.org/10.2307/749665
  • Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Reidel.
  • Gal, I. (2002). Adult’s statistical literacy. Meanings, components, responsibilities. International Statistical Review, 70(1), 1-25. https://doi.org/10.2307/1403713
  • Gómez-Chacón, I. (2000) Affective influences in the knowledge of mathematics. Educational Studies in Mathematics, 43(2), 149-168. https://doi.org/10.1023/A:1017518812079
  • Goméz-Torres, E., Batanero, C., & Díaz, C. (2016). Developing a questionnaire to assess the probability content knowledge of prospective primary school teachers. Statistics Education Research Journal, 15(2), 197-215. https://doi.org/10.52041/serj.v15i2.248
  • Greer, B. (2001). Understanding probabilistic thinking: The legacy of Efraim Fischbein. Educational Studies in Mathematics, 45(1), 15-33. https://doi.org/10.1023/A:1013801623755
  • Hokor, E. K. (2020). Pre-service teachers’ probabilistic reasoning in constructivist classroom. Pedagogical Research, 5(2), 1-9. https://doi.org/10.29333/pr/7838
  • Jones, G. A. (2005). Exploring probability in school. Challenges for teaching and learning. Springer. https://doi.org/10.1007/b105829
  • Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1997). A framework for assessing and nurturing young children’s thinking in probability. Educational Studies in Mathematics, 32(2), 101-125. https://doi.org/10.1023/A:1002981520728
  • Kus, M., & Cakiroglu, E. (2020). Prospective mathematics teachers’ critical thinking processes about scientific research: Newspaper article example. Turkish Journal of Education, 9(1), 22-45. https://doi.org/10.19128/turje.605456
  • Lonjedo Vicent, M. A., Huerta Palau, M. P., & Fariña, M. C. (2012). Conditional probability problems in textbooks–an example from Spain. Revista Latinoamericana de Investigación en Matemática Educativa [Latin American Journal of Research in Educational Mathematics], 15(3), 319-337.
  • Martignon, L., & Wassner, C. (2002). Teaching decision making and statistical thinking with natural frequencies. In B. Phillips (Ed.), Developing a statistically literate society: Proceedings of the sixth international conference on teaching statistics, South Africa. International Statistical Institute. https://www.stat.auckland.ac.nz/~iase/publications/1/10_52_ma.pdf
  • Muñiz-Rodríguez, L., Rodríguez-Muñiz, L. J., & Alsina, Á. (2020). Deficits in the statistical and probabilistic literacy of citizens: Effects in a world in crisis. Mathematics, 8(11), 1872. https://doi.org/10.3390/math8111872
  • Nilsson, P., Blomberg, P., & Ärlebäck, J. B. (2014). Exploring realistic Bayesian modeling situations. In K. Makar, B. de Sousa, & R. Gould (Eds.), Sustainability in statistics education: Proceedings of the 9th International Conference on Teaching Statistics. International Statistical Institute. https://iase-web.org/icots/9/proceedings/pdfs/ICOTS9_6A3_NILSSON.pdf
  • Olgun, B., & Isiksal-Bostan, M. (2019). The influence of the context of conditional probability problems on probabilistic thinking: A case study with teacher candidates. In Proceedings of the 11th Congress of the European Society for Research in Mathematics Education. Utrecht University. https://hal.archives-ouvertes.fr/hal-02412821
  • Ozen, M. (2013). Investigation of pre-service mathematics teachers’ critical thinking processes through statistical and probabilistic knowledge in the context of popular media texts [Master’s thesis, Middle East Technical University].
  • Philipp, R. A. (2007). Mathematics teachers’ beliefs and affects. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257-315). Information Age Publishing & National Council of Teachers of Mathematics.
  • Ruz, F., Chance, B., Medina, E., & Contreras, J. M. (2021). Content knowledge and attitudes towards stochastics and its teaching in pre-service Chilean mathematics teachers. Statistics Education Research Journal, 20, 1. https://doi.org/10.52041/serj.v20i1.100
  • Segarra, J., & Julià, C. (2022). Mathematics teaching efficacy belief and attitude of pre-service teachers and academic achievement. European Journal of Science and Mathematics Education, 10(1), 1-14. https://doi.org/10.30935/scimath/11381
  • Stohl, H. (2005). Probability in teacher education and development. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 345-366). Springer. https://doi.org/10.1007/0-387-24530-8_15
  • Tarr, J. E., & Jones, G. A. (1997). A framework for assessing middle school students’ thinking in conditional probability and independence. Mathematics Education Research Journal, 9, 39-59. https://doi.org/10.1007/BF03217301
  • Tversky, A., & Kahneman, D. (1982). Judgements of and by representativeness. In D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases (pp. 84-98). Cambridge University Press. https://doi.org/10.1017/CBO9780511809477.007
  • Watson, J. (1995). Conditional probability: Its place in the mathematics curriculum. The Mathematics Teacher, 88(1), 12-17. https://doi.org/10.5951/MT.88.1.0012
  • Watson, J. (1997). Assessing statistical thinking using the media. In I. Gal, & J. B. Garfield (Eds.), The assessment challenge in statistics education (pp. 107-121). International Statistical Institute/IOS Press.
  • Yohe, S. (2020, August 15). How good are COVID-19 (SARS-CoV-2) diagnostic PCR tests. College of American Pathologists. https://www.cap.org/member-resources/articles/how-good-are-covid-19-sars-cov-2-diagnostic-pcr-tests