YOUNG CHILDREN’S PROBABILISTIC AND STATISTICAL REASONING IN THE CONTEXT OF INFORMAL STATISTICAL INFERENCE
DOI:
https://doi.org/10.52041/serj.v22i2.434Keywords:
Statistics education research, Probabilistic reasoning, Statistical thinking, Informal statistical inference, Bar graphs, RandomnessAbstract
This paper reports the statistical and probabilistic reasoning of young children in terms of randomness, variability, and data representations in the context of informal inferential reasoning (IIR). Using the IIR approach, a task was designed and conducted one-on-one with 28 children aged 5 to 6 years old, in a case study setting. The researcher used a voice recorder during interviews, took photos, and recorded field notes. The data were analyzed according to the principles of informal inferential reasoning, which are generalizing beyond the data, using data as evidence for generalizing, and using probabilistic language whilst being aware of uncertainty. The findings indicate that young children are capable of making informal inferences from a sample space, describing event probability, and constructing bar graph and pie chart data representations.
References
Argün, Z., Arikan, A., Bulut, S., & Sriraman, B. (2010). A brief history of mathematics education in Turkey: K-12 mathematics curricula. ZDM Mathematics Education, 42(5), 429–441. https://doi.org/10.1007/s11858-010-0250-0
Batanero, C., Arteaga, P., & Gea, M. M. (2018). Statistical graphs in Spanish textbooks and diagnostic tests for 6–8-year-old children. In A. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds.), Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking (pp. 163–180). Springer. https://doi.org/10.1007/978-981-13-1044-7_10
Ben-Zvi, D. (2018). Foreword. In A. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds.), Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking (pp. vii–viii). Springer.
Ben-Zvi, D., & Sharett-Amir, Y. (2005). How do primary school students begin to reason about distributions? In M. Pfannkuch (Ed.), Reasoning about distribution: A collection of current research studies. Proceedings of the fourth international research forum on statistical reasoning, thinking, and literacy (SRTL-4), Auckland, New Zealand (pp. 2–7).
Borovcnik, M. (2011). Strengthening the role of probability within statistics curricula. In C. Batanero, G. Burrill & C. Reading (Eds.) Teaching statistics in school mathematics: Challenges for teaching and teacher education (pp. 71-83). Springer. https://doi.org/10.1007/978-94-007-1131-0_11
Borovcnik, M. G., & Bentz, H. J. (1991). Empirical research in understanding probability. In R. Kapadia & M. Borovcnik (Eds.) Chance encounters: Probability in education (pp. 73–105). Kluwer Academic Publishers. https://doi.org/10.1007/978-94-011-3532-0_3
diSessa, A. A. (2004). Metarepresentation: Native competence and targets for instruction. Cognition and Instruction, 22(3), 293-331. https://doi.org/10.1207/s1532690xci2203_2
English, L. D. (1993). Children’s strategies for solving two- and three-stage combinatorial problems. Journal for Research in Mathematics Education, 24(3), 255–273. https://doi.org/10.5951/jresematheduc.24.3.0255
Estrella, S. (2018). Data representations in early statistics: Data sense, meta-representational competence and transnumeration. In A. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds), Statistics in early childhood and primary education. Early mathematics learning and development (pp. 239–256). Springer. https://doi.org/10.1007/978-981-13-1044-7_14
Fischbein, E., & Schnarch, D. (1997). Brief report: The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education, 28(1), 96–105. https://doi.org/10.5951/jresematheduc.28.1.0096
Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124–158. https://doi.org/10.2307/749671
Greer, B. (2014). Commentary on perspective II: Psychology. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (pp. 299–309). Springer. https://doi.org/10.1007/978-94-007-7155-0_16
Groth, R. E., Austin, J. W., Naumann, M., & Rickards, M. (2021). Toward a theoretical structure to characterize early probabilistic thinking. Mathematics Education Research Journal, 33(2), 241–261. https://doi.org/10.1007/s13394-019-00287-w
Kazak, S., & Leavy, A. M. (2018). Emergent reasoning about uncertainty in primary school children with a focus on subjective probability. In A. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds.), Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking (pp. 37–54). Springer. https://doi.org/10.1007/978-981-13-1044-7_3
Langrall, C., Nisbet, S., & Mooney, E. (2006). The interplay between students’ statistical knowledge and context knowledge in analyzing data. In A. Rossman & B. Chance (Eds.), Working cooperatively in statistics education. Proceedings of the Seventh International Conference on Teaching Statistics (ICOTS7), Salvador, Brazil. https://iase-web.org/documents/papers/icots7/2A3_LANG.pdf?1402524964
Leavy, A. (2008). An examination of the role of statistical investigation in supporting the development of young children’s statistical reasoning. In O. Saracho & B. Spodek (Eds.), Contemporary perspectives on mathematics in early childhood education (pp. 215–232). Information Age Publishing.
Lehrer, R., Kim, M. J., & Schauble, L. (2007). Supporting the development of conceptions of statistics by engaging students in measuring and modeling variability. International Journal of Computers for Mathematical Learning, 12(3), 195–216. https://doi.org/10.1007/s10758-007-9122-2
Lopes, C. E., & Cox, D. (2018). The impact of culturally responsive teaching on statistical and probabilistic learning of elementary children. In A. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds.), Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking (pp. 75–88). Springer. https://doi.org/10.1007/978-981-13-1044-7_5
Makar, K. (2018). Theorising links between context and structure to introduce powerful statistical ideas in the early years. In A. Leavy, M. Meletiou-Mavrotheris & E. Paparistodemou (Eds.), Statistics in early childhood and primary education (pp. 3–20). Springer. https://doi.org./10.1007/978-981-13-1044-7_1
Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1). 82–105. https://doi.org/10.52041/serj.v8i1.457
McPhee, D., & Makar, K. (2018). Early childhood experiences in informal inferential statistics using an inquiry approach. In M. A. Sorto, A. White & L. Guyot (Eds.), Looking back, looking forward. Proceedings of the Tenth International Conference on Teaching Statistics (ICOTS10), Kyoto, Japan. https://iase-web.org/icots/10/proceedings/pdfs/ICOTS10_4B1.pdf?1531364263
Moore, D. S. (1990). Uncertainty. In L. A. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 95–137). National Academy Press.
Nikiforidou, Z. (2018). Probabilistic thinking and young children: theory and pedagogy. In A. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds.), Statistics in early childhood and primary education (pp. 21–34). Singapore. https:doi.org/10.1007/978-981-13-1044-7_2
Patton, M. Q. (2014). Qualitative research and evaluation methods: Integrating theory and practice. SAGE Publications.
Perry, B., & Dockett, S. (2008). Young children’s access to powerful mathematical ideas. Handbook of international research in mathematics education (pp. 81–112). Routledge.
Piaget, J., & Inhelder, B. (1975). The origin of the idea of chance in children (translated by L. Leake, Jr., P. Burrell & H. D. Fischbein). W. W. Norton.
Reading, C., & Shaughnessy, J. M. (2004). Reasoning about variation. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 201–226). Springer. https://doi.org/10.1007/1-4020-2278-6_9
Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 465–494). Macmillan.
Shaughnessy, M. (2010). Statistics for all: The flip side of quantitative reasoning. National Council of Teachers of Mathematics.
Sorto, M. A. (2006). Identifying content knowledge for teaching statistics. In A. Rossman & B. Chance (Eds.), Working cooperatively in statistics education. Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil. http://www.stat.auckland.ac.nz/~iase/publications/17/C130.pdf
Spence, I., & Krizel, P. (1994). Children’s perception of proportion in graphs. Child Development, 65(4), 1193–1213. https://doi.org/10.1111/j.1467-8624.1994.tb00812.x
Watson, J. M. (2009). The influence of variation and expectation on the developing awareness of distribution. Statistics Education Research Journal, 8(1), 32–61. https://doi.org/10.52041/serj.v8i1.456
Watson, J. M., & Fitzallen, N. (September 19, 2019). Building understanding of randomness from ideas about variation and expectation. Statistics Teacher. https://www.statisticsteacher.org/2019/09/19/building-understanding-of-randomness-from-ideas-about-variation-and-expectation/
Watson, J., Fitzallen, N., Fielding-Wells, J., & Madden, S. (2018). The practice of statistics. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 105-137). Springer. https://doi.org/10.1007/978-3-319-66195-7_4
Watson, J. M., & Moritz, J. B. (2000). Developing concepts of sampling. Journal for Research in Mathematics Education, 31(1), 44–70. https://doi.org/10.2307/749819
Yin, R. K. (2014). Case study research: Design and methods (Vol. 5). SAGE Publications.
Zieffler, A., Garfield, J. B., Delmas, R., & Reading, C. (2008). A framework to support research on informal inferential reasoning. Statistics Education Research Journal, 7(2), 40–58. https://doi.org/10.52041/serj.v7i2.469
