DEVELOPING DATA SENSE: MAKING INFERENCES FROM VARIABILITY IN TSUNAMIS AT PRIMARY SCHOOL

Authors

  • SOLEDAD ESTRELLA Pontifical Catholic University of Valparaiso
  • ANDREA VERGARA Catholic University of Maule
  • ORLANDO GONZÁLEZ Assumption University

DOI:

https://doi.org/10.52041/serj.v20i2.413

Keywords:

Statistics education research, Data sense, Statistical variability, Data representations, Lesson study

Abstract

In order to study the manifestation of data sense and identify ways of thinking about variability in authentically realistic problems in a group of Chilean fifth-grade students, a lesson plan was designed and implemented, within the framework of statistical literacy and using the “lesson study” modality, in which students were urged to make inferences based on the analysis of data corresponding to the tsunami that struck the Chilean coast in 2010. This article focuses on the qualitative study of the data representations produced by two groups of students during the implementation of the lesson plan. The analysis of the behavior of the tsunami carried out by the students led them to work simultaneously with nominal qualitative, ordinal qualitative, discrete quantitative, and continuous quantitative variables; to create new variables; to construct representations of data (multiple bar graphs and frequency tables); and to make inferences based on the data. We conclude that the use of an authentic context and the construction of their own representations promoted data sense in students and facilitated the development of their statistical thinking, through which they were able to recognize, describe, and explain the variability of the phenomenon.

Abstract: Spanish

Con el propósito de estudiar la manifestación del sentido del dato e identificar las formas de razonar la variabilidad en problemas auténticamente realistas en un grupo de estudiantes chilenos de quinto grado de primaria, se diseñó e implementó un plan de clases, en el marco de alfabetización estadística y bajo la modalidad “lesson study”, en el que se instó a los estudiantes a hacer inferencias a partir del análisis de los datos correspondientes al tsunami que azotó la costa de Chile en 2010. Este artículo se centra en el estudio cualitativo de las representaciones de datos producidas por dos grupos de estudiantes durante la implementación del plan de clases. El análisis del comportamiento de los datos del tsunami realizado por los estudiantes los llevó a trabajar simultáneamente con variables cualitativas nominales, cualitativas ordinales, cuantitativas discretas y cuantitativas continuas; crear nuevas variables; elaborar representaciones de datos (gráfico de barras múltiples y tabla de frecuencias); y hacer inferencias basadas en los datos. Se concluye que el uso de un contexto auténtico y la construcción de representaciones propias, promovieron en los estudiantes el sentido del dato y facilitaron el desarrollo de su pensamiento estadístico, pudiendo reconocer, describir y explicar la variabilidad del fenómeno.

References

Arnold, P. (2008). Developing new statistical content knowledge with secondary school mathematics teachers. Joint ICMI/IASE study: Teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study, 18, 1–6.

Chan, S., & Ismail, Z. (2013). Assessing misconceptions in reasoning about variability among high school students. Procedia-Social and Behavioral Sciences, 93, 1478–1483.

Dierdorp, A., Bakker, A., Ben-Zvi, D., & Makar, K. (2017). Secondary students’ considerations of variability in measurement activities based on authentic practices. Statistics Education Research Journal, 16(2), 397–418.

Ekol, G., & Sinclair, N. (2016). Undergraduate students’ conceptions of variability in a dynamic computer-based environment. In D. Ben-Zvi & K. Makar (Eds.), The teaching and learning of statistics (pp. 193–203). Springer

English, L., & Watson, J. (2018). Modelling with authentic data in sixth grade. ZDM, 50(1-2), 103–115.

Estrella, S. (2017). Enseñar estadística para alfabetizar estadísticamente y desarrollar el razonamiento estadístico [Teaching statistics to statistically literate and develop statistical reasoning]. In A. Salcedo (Ed.), Alternativas Pedagógicas para la Educación Matemática del Siglo XXI (pp. 173–194). Centro de Investigaciones Educativas, Universidad Central de Venezuela.

Estrella, S. (2018). Data representations in early statistics: Data sense, meta-representational competence and transnumeration. In A. Leavy, M. Meletiou, & E. Paparistodemou (Eds.), Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking (pp. 239–256). Springer.

Estrella, S., Mena, A., & Olfos, R. (2018). Lesson study in Chile: A very promising but still uncertain path. In M. Quaresma, C. Winsløw, S. Clivaz, J. Pedro da Ponte, A. Ní Shúilleabháin, A. Takahashi (Eds.), Mathematics lesson study around the world: Theoretical and methodological issues (pp. 105–122). Springer.

Estrella, S., & Olfos, R. (2012). La taxonomía de comprensión gráfica de Curcio a través del gráfico de Minard: Una clase en séptimo grado [Curcio’s taxonomy of graphical comprehension through Minard´s graph: A class in the seventh grade]. Revista Educación Matemática, 24(2), 119–129.

Estrella, S., Olfos, R., & Morales, S. (2014). What can we learn from natural disasters to prevent loss of life in the future? In J. W. Lott & C. J. Lott (Eds.), Lessons learned from across the world: PreK–8 (pp. 66–71). National Council of Mathematics Teachers.

Estrella, S., Olfos, R., Morales, S., & Vidal-Szabó, P. (2017). Argumentaciones de estudiantes de primaria sobre representaciones externas de datos: componentes lógicas, numéricas y geométricas. [Arguments of primary school students on external representations of data: logical, numerical and geometric components] RELIME, Revista Latinoamericana de Investigación en Matemática Educativa, 20(3), 345–370.

Estrella, S., Zakaryan, D., Olfos, R., & Espinoza, G. (2020). How teachers learn to maintain the cognitive demand of tasks through lesson study. Journal of Mathematics Teacher Education, 23(3), 293–310.

Friel, S., Bright, G., Frierson, D., & Kader, G. (1997). A framework for assessing knowledge and learning in statistics (K–8). In I. Gal & J. Garfield (Eds.), The assessment challenge in statistics education (pp. 55–63). IOS Press.

Gal, I. (2004). Adults’ statistical literacy: Meanings, components, responsibilities. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 47–78). Kluwer.

Gal, I. (2005). Towards “probability literacy” for all citizens: Building blocks and instructional dilemmas. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 39–63). Springer.

Garfield, J. (1993). Teaching statistics using small-group cooperative learning. Journal of Statistics Education, 1(1). http://ww2.amstat.org/publications/jse/v1n1/garfield.html.

Garfield, J., Le, L., Zieffler, A., & Ben-Zvi, D. (2015). Developing students’ reasoning about samples and sampling variability as a path to expert statistical thinking. Educational Studies in Mathematics, 88(3), 327–342.

Inzunsa-Cazares, S. (2016). Razonamiento de estudiantes universitarios sobre variabilidad e intervalos de confianza en un contexto inferencial informal. [University students´ reasoning on variability and confidence intervals in an informal inferential context] In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 969-983). The University of Arizona.

Isoda, M., & Olfos, R. (2009). El enfoque de resolución de problemas en la enseñanza de la matemática a partir del estudio de clases. [The problem-solving approach in the teaching of mathematics from the classroom] Ediciones Universitarias de Valparaíso, Pontificia Universidad Católica de Valparaíso.

Isoda, M., Chitmun, S., & Gonzalez, O. (2018). Japanese and Thai senior high school mathematics teachers’ knowledge of variability. Statistics Education Research Journal, 17(2), 196–215. https://doi.org/10.52041/serj.v17i2.166

Konold, C., Higgins, T., Russell, S., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305–325.

Langrall, C., Nisbet, S., Mooney, E., & Jansem, S. (2011). The role of context expertise when comparing data. Mathematical Thinking and Learning, 13(1–2), 47–67.

Lehrer, R., & English, L. (2018). Introducing children to modeling variability. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 229-260). Springer.

Lehrer, R., Kim, M., & 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.

Lovett, J. N., & Lee, H. S. (2018). Preservice secondary mathematics teachers’ statistical knowledge: A snapshot of strengths and weaknesses. Journal of Statistics Education, 26(3), 214–222.

Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105.

McIntosh, A., Reys, B., Reys, R., Bana, J., & Farrell, B. (1997). Number sense in school mathematics: Student performance in four countries. Mathematics, Science & Technology Education Centre, Edith Cowan University.

Ministerio de Educación de Chile. (2018). Matemática. In Bases Curriculares Primero a Sexto Básico (pp. 214–261). MINEDUC.

Pfannkuch, M., & Ben-Zvi, D. (2011). Developing teachers’ statistical thinking. In C. Batanero, G. Burrill & C. Reading (Eds.), Teaching statistics in school mathematics-challenges for teaching and teacher education (pp. 323–333). Springer.

Pfannkuch, M., & Wild, C. (2004). Towards an understanding of statistical thinking. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 17–46). Springer.

Pfannkuch, M., Arnold, P., & Wild, C. (2015). What I see is not quite the way it really is: Students’ emergent reasoning about sampling variability. Educational Studies in Mathematics, 88(3), 343–360.

Phan, H. (2012). A sociocultural perspective of learning: Developing a new theoretical tenet. Paper presented at the Joint Australian Association for Research in Education and Asia-Pacific Educational Research Association Conference (AARE-APERA 2012) World Education Research Association (WERA) Focal Meeting, Sydney, New South Wales, December 2–6.

Shaughnessy, M. (2007). Research on statistics’ reasoning and learning. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 957–1009). Information Age Publishers.

Shaughnessy, M., & Pfannkuch, M. (2002). How faithful is old faithful? Statistical thinking: A story of variation and prediction. Mathematics Teacher, 95(4), 252–259.

Smith, C., Fitzallen, N., Watson, J., & Wright, S. (2019). The practice of statistics for STEM: Primary students and pre-service primary teachers exploring variation in seed dispersal. Teaching Science, 65(1), 38–47.

Snee, R. (1993). What's missing in statistical education? The American Statistician, 47(2), 149–154.

Torok, R., & Watson, J. (2000). Development of the concept of statistical variation: An exploratory study. Mathematics Education Research Journal, 12(2), 147–169.

Watson, J. (2016). Linking science and statistics: Curriculum expectations in three countries. International Journal of Science and Mathematics Education, 15(6), 1057–1073.

Published

2021-12-25