THE ROLE OF DATA CONTEXT AND TASK CONTEXT IN YOUNG CHILDREN'S READING OF DATA REPRESENTATIONS

Authors

  • VIRGINIA KINNEAR Deakin University

Keywords:

Statistics education research, Data context, Case-data tables, Young children, Pictorial representations

Abstract

This paper describes the role of data and task context in young children’s interpretation of and reasoning about data tables. A design-based descriptive study was conducted with fourteen 5-year-old children in their first year of formal schooling. A picture storybook provided the data context for a data modelling activity that focused on interpreting and analysing a data table. The children spontaneously read zero as a data value of interest and explained their interpretation of data using knowledge gleaned from the context of the storybook. Presenting the data pictorially and numerically using the structure of a table supported children’s successful reading and interpretation of the data. The structure and representation of the table facilitated development of statistical reasoning that was unexpected of children as young as 5 years.

References

Asp, G., Dowsey, J., & Hollingsworth, H. (1994). Students’ understanding of pictographs and bar graphs. In G. Bell, B. Wright, N. Leeson & G. Geeke (Eds.), Challenges in mathematics education: Constraints on construction. Proceedings of the 17th Annual Conference of Mathematics Education Research Group of Australasia, Lismore (pp. 57–65).

Bakker, A., & Gravemeijer, K. P. E. (2004). Learning to reason about distribution. In D. Ben-Zvi, & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 147–168). Kluwer Academic Publishers.

Ben-Zvi, D. (2004). Reasoning about variability in comparing distributions. Statistics Education Research Journal 3(2), 42–63.https://doi.org/10.52041/serj.v3i2.547

Ben-Zvi, D., Bakker, A., & Makar, K. (2009). Towards a framework for understanding students’ informal statistical inference and argumentation. In Sixth International Forum for Research on Statistical Reasoning, Thinking and Literacy (SRTL-6). Brisbane.

Bethel, E. (2008). Michael Recycle. Koala Books.

Bethel, E. (2009). Litterbug Doug. Koala Books.

Biehler, R., Frischemeier, D., Reading, C., & Shaughnessy, M. (2018). Reasoning about data. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 139–192). Springer. https://doi.org/10.1007/978-3-319-66195-7_5

Bjorklund, C., & Palmer, H. (2020). Preschoolers’ reasoning about numbers in picture books. Mathematical Thinking and Learning, 22(3), 195–213. https://doi.org/10.1080/10986065.2020.1741334

Boels, L., Bakker, A., Drijvers, P., & Van Dooren, W. (2019). Conceptual difficulties when interpreting histograms: A review. Educational Research Review, 28, Article 100291. https://doi.org/10.1016/j.edurev.2019.100291

Chick, H., Fitzallen, N., & Watson, J. (2018). “Plot 1 is all spread out and Plot 2 is all squished together”: Exemplifying statistical variation with young students. In J. Hunter, P. Perger, & L. Darragh, (Eds.), Making waves, opening spaces. Proceedings of the 41st annual conference of the Mathematics Education Research Group of Australasia, Aukland (pp. 218–225).

Child, L. (2009). Charlie and Lola: Look after your planet. Penguin Books.

Asp, G., Dowsey, J., & Hollingsworth, H. (1994). Students’ understanding of pictographs and bar graphs. In G. Bell, B. Wright, N. Leeson & G. Geeke (Eds.), Challenges in mathematics education: Constraints on construction. Proceedings of the 17th Annual Conference of Mathematics Education Research Group of Australasia, Lismore (pp. 57–65).

Bakker, A., & Gravemeijer, K. P. E. (2004). Learning to reason about distribution. In D. Ben-Zvi, & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 147–168). Kluwer Academic Publishers.

Ben-Zvi, D. (2004). Reasoning about variability in comparing distributions. Statistics Education Research Journal 3(2), 42–63.https://doi.org/10.52041/serj.v3i2.547

Ben-Zvi, D., Bakker, A., & Makar, K. (2009). Towards a framework for understanding students’ informal statistical inference and argumentation. In Sixth International Forum for Research on Statistical Reasoning, Thinking and Literacy (SRTL-6). Brisbane.

Bethel, E. (2008). Michael Recycle. Koala Books.

Bethel, E. (2009). Litterbug Doug. Koala Books.

Biehler, R., Frischemeier, D., Reading, C., & Shaughnessy, M. (2018). Reasoning about data. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 139–192). Springer. https://doi.org/10.1007/978-3-319-66195-7_5

Bjorklund, C., & Palmer, H. (2020). Preschoolers’ reasoning about numbers in picture books. Mathematical Thinking and Learning, 22(3), 195–213. https://doi.org/10.1080/10986065.2020.1741334

Boels, L., Bakker, A., Drijvers, P., & Van Dooren, W. (2019). Conceptual difficulties when interpreting histograms: A review. Educational Research Review, 28, Article 100291. https://doi.org/10.1016/j.edurev.2019.100291

Chick, H., Fitzallen, N., & Watson, J. (2018). “Plot 1 is all spread out and Plot 2 is all squished together”: Exemplifying statistical variation with young students. In J. Hunter, P. Perger, & L. Darragh, (Eds.), Making waves, opening spaces. Proceedings of the 41st annual conference of the Mathematics Education Research Group of Australasia, Aukland (pp. 218–225).

Child, L. (2009). Charlie and Lola: Look after your planet. Penguin Books.

Clarke, B., Clarke, D., & Cheeseman, J. (2006). The mathematical knowledge and understanding young children bring to school. Mathematics Education Research Journal, 18(1), 78–103. https://doi.org/10.1007/BF03217430

Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. The American Mathematical Monthly, 104(9), 801-823. https://doi.org/10.2307/2975286

Curcio, F. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics education, 18(5), 382–393. https://doi.org/10.2307/749086

Curcio, F. (2010). Developing data-graph comprehension in Grades K–8 (3rd ed.). National Council of Teachers Mathematics.

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

Downton, A., Cheeseman, J., MacDonald, A., McChesney, J., & Russo, J. (2020). Mathematics learning and education from birth to eight years. In J. Way, C. Attard, J. Anderson, J. Bobis, H. McMaster & K. Cartwright (Eds.), Research in mathematics education in Australasia 2016-2019 (pp. 209–244). Springer. https://doi.org/10.1007/978-981-15-4269-5_9

English, L. D. (2009a). Baxter Brown’s messy room.[Unpublished picture storybook written for ARC Discovery Grant DP 0984178]. Queensland University of Technology.

English, L. D. (2009b). Promoting interdisciplinarity through mathematical modelling. ZDM Mathematics Education, 49(1&2), 161–181. https://doi.org/10.1007/s11858-008-0106-z

English, L. (2012). Data modelling with first-grade students. Educational Studies in Mathematics, 81, 15–30. https://doi.org/10.1007/s10649-011-9377-3

English, L. (2018). Young children’s statistical literacy in modelling with data and chance. In A. Leavy, M. Meletiou-Mavrotheris & E. Paparistodemou (Eds.), Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking (pp. 295–313). Springer. https://doi.org/10.1007/978-981-13-1044-7_17

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 (pp. 239–256). Springer. https://doi.org/10.1007/978-981-13-1044-7_14

Fielding-Wells, J. (2018). Scaffolding statistical inquiries for young children. In A. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds.), Statistics in early childhood and primary education (pp. 109–127). Springer. https://doi.org/10.1007/978-981-13-1044-7_7

Fielding-Wells, J., & Makar, K. (2015). Inferring to a model: Using inquiry-baed argumentation to challenge young children’s expectations of equally likely outcomes. In S. Zieffler, & E. Fry (Eds.), Reasoning about uncertainty: Learning and teaching informal inferential reasoning (pp. 1–28). Catalyst Press.

Fielding, J., & Makar, K. (2022). Challenging conceptual understanding in a complex system: supporting young students to address extended mathematical inquiry problems. Instructional Science, 50, 35–61. https://doi.org/10.1007/s11251-021-09564-3

Frischemeier, D. (2019). Primary school students’ reasoning when comparing groups using modal clumps, medians, and hatplots. Mathematics Education Research Journal, 31, 485–505. https://doi.org/10.1007/s13394-019-00261-6

Frischemeier, D. (2020). Building statisticians at an early age: Statistical projects exploring meaningful data in primary school. Statistics Education Research Journal, 19(1), 39–56. https://doi.org/10.52041/serj.v19i1.118

Friel, S. N., Bright, G. W., & Curcio, F. R. (1997). Understanding students’ understanding of graphs. Mathematics Teaching in the Middle School, 3(3), 224–227. https://doi.org/10.5951/MTMS.3.3.0224

Friel, S. N., Bright, G. W., & Curcio, F. R. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional applications. Journal for Research in Mathematics Education, 32(2), 124–158. https://doi.org/10.2307/749671

Gal, I. (2005). Statistical literacy. In D. Ben-Zvi, & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 47–78). Kluwer Academic Publishers. https://doi.org/10.1007/1-4020-2278-6_3

Garfield, J. B., & Ben-Zvi, D. (2007). How students learn statistics revisited: A current review of research on teaching and learning statistics. International Statistical Review, 75(3), 372–296. doi: 10.1111/j.1751-5823.2007.00029.x

Gervasoni, A., & Perry, B. (2015). Children’s mathematical knowledge prior to school and implications for transition. In B. Perry, A. MacDonald, & A. Gervasoni (Eds.), Mathematics and transititon to school: International perspectives. Springer. https://doi.org/10.1007/978-981-287-215-9_4

Gil, E., & Ben-Zvi, D. (2011). Explanations and context in the emergence of student’s informal inferential reasoning. Mathematical Thinking and Learning, 13(1&2), 87–108. https://doi.org/ 10.1080/10986065.2011.538295

Kinnear, V. (2013). Young children’s statistical reasoning: A tale of two contexts.[Doctoral dissertation, Queensland University of Technology].

Kinnear, V. (2018). Initiating interest in statistical problems: The role of picture storybooks. In A. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds.), Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking (pp. 183–199). Springer. https://doi.org/10.1007/978-981-13-1044-7_11

Konold, C., Finzer, W., & Kreetong, K. (2017). Modeling as a core component of structuring data. Statistics Education Research Journal, 16(2), 191–212. https://doi.org/10.52041/serj.v16i2.190

Konold, C., Higgins, T., Khalil, K., & Russell, S. J. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305–325. https://doi.org/10.1007/s10649-013-9529-8

Langrall, C., Jansem, S., Nisbet, S., & Mooney, E. (2011). The role of context expertise when comparing data. Mathematical Thinking and Learning 13(1&2), 47–67. https://doi.org/10.1080/10986065.2011.538620

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.

Leavy, A., & Hourigan, M. (2016). Crime scenes and msytery players! Using driving questions to support the development of statistical literacy. Teaching Statistics 13(1), 29–35. https://doi.org/10.1111/12088

Leavy, A. M., & Hourigan, M. (2018). Inscriptional capacities of young children engaged in statistical investigations. In A. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou, (Eds). Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking. Springer. https://doi.org/10.1007/978-981-13-1044-7

Leavy, A., & Hourigan, M. (2019). Expanding the focus of early years mathematics education: Statistics and probability. In O. N. Saracho (Ed.), Handbook of research on the education of young children (pp. 99–112). Routledge. https://doi.org/10.4324/9780429442827-7

Leavy, A., & Hourigan, M. (2021). Data modelling and informal inferential reasoning: Instances of early mathematical modelling. In J. M. Suh, M. Wickstrom, & L. D. English (Eds.), Exploring mathematical modeling with young learners (p. 67–93). Springer. https://doi.org/10.1007/978-3-030-63900-6_4

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. https://doi.org/10.1007/978-3-319-66195-7_7

Lehrer, R., & Schauble, L. (2002). Children’s work with data. In R. Lehrer, & L. Schauble (Eds.), Investigating real data in the classroom: Expanding children’s understanding of math and science (pp. 1–26). Teachers College Press.

Lehrer, R., & Schauble, L. (2004). Modeling variation through distribution. American Education Research Journal, 41(3), 635-679. https://doi.org/10.3102/0028312041003635

Lehrer, R., & Schauble, L. (2005). Developing modeling and argument in the elementary grades. In T. Romberg, T. Carpenter, & F. Dremock (Eds.). Understanding mathematics and science matters (pp. 29-53). Lawrence Erlbaum Associates.

Lesh, R., Caylor, E., Gupta, S., & Middleton, J. A. (2008). A science need: Designing tasks to engage students in modelling complex data. Educational Studies in Mathematics, 68(2), 113–130. https://doi.org/10.1007/s10649-008-9118-4

Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning and problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching (pp. 3-33). Lawrence Erlbaum Associates.

Lesh, R., & Lehrer, R. (2000). Iterative refinement cycles for videotape analyses of conceptual change. In A. E. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 665–708). Lawrence Erlbaum.

Makar, K. (2016). Developing young children’s emergent inferential practices in statistics. Mathematical Thinking and Learning, 18(1), 1–24. https://doi.org/10.1080/10986065.2016.1107820

Makar, K. (2018). Theorising links between context and structure to introduce powerful statistical ideas in the early years. In A. M. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou(Eds). Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking (pp. 3–20). Springer. https://doi.org/10.1007/978-981-13-1044-7_1

Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1&2), 152–173. https://doi.org/10.1080/10986065.2011.538301

Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistical Education Research Journal, 8(1), 82–105. https://doi.org/10.52041/serj.v8i1.457

Masnick, A. M., Klahr, D., & Morris, B. J. (2007). Separating signal from noise: Children’s understanding of error and variability in experimental outcomes. In M. C. Lovett, & P. Shah (Eds.), Thinking with data (pp. 3–26). Lawrence Erlbaum.

Mooney, E., Langrall, C., & Nesbit, S. (2006). Developing a model to describe the use of contextual knowledge in data explorations. In A. Rossman & B. Chance (Eds.), Working cooperatively in statistics education. Proceedings of the 7th International Conference on Teaching Statistics (ICOTS7), Salvador, Brazil. http://iase-web.org/documents/papers/icots7/2A4_MOON.pdf?1402524964

Moore, D. S. (2006). The basic practice of statistics. W. H. Freeman.

Mulligan, J. (2015). Moving beyond basic numeracy: Data modeling in the early years of schooling. ZDM Mathematics Education, 47(4), 653–663. https://doi.org/10.1007/s11858-015-0687-2

Mulligan, J. T. (2022). Pathways to early mathematical thinking in kindergarten: The pattern and structure mathematics awareness program. In A. Sharif-Rasslan, & D. Hassidov (Eds.), Special issues in early childhood mathematics education research (pp. 155–170). Brill Publishing. https://doi:10.1163/9789004510685_007

Mulligan, J., English, L., & Oslington, G. (2020). Supporting early mathematical development through a ‘pattern and structure’ intervention program. ZDM Mathematics Education, 52(4), 663–676. https://doi.org/10.1007/s11858-020-01147-9

Munzner, T. (2014). Visualization analysis and design. CRC Press.

Oslington, G., Mulligan, J., & Van Bergen, P. (2018). Young children’s reasoning through data exploration. In V. Kinnear, M. Y. Lai, & T. Muir (Ed.), Forging connections in early mathematics teaching and learning (pp. 191–212). Springer. https://doi.org/10.1007/978-981-10-7153-9_11

Oslington, G., Mulligan, J., & Van Bergen, P. (2020). Third-graders’ predictive reasoning strategies. Educational Studies in Mathematics, 104(1), 5–24. https://doi.org/10.1007/s10649-020-09949-0

Pfannkuch, M. (2011). The role of context in developing informal statistical inferential reasoning: A classroom study. Mathematical Thinking and Learning, 13(1&2), 27–46. https://doi.org/ 10.1080/10986065.2011.538302

Pfannkuch, M., Ben-Zvi, D., & Budgett, S. (2018). Innovations in statistical modeling to connect data, chance and context. ZDM Mathematics Education, 50(7), 1113–1123 https://doi.org/10.1007/s11858-018-0989-2

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). Kluwer Academic Publishers. https://doi.org/10.1007/1-4020-2278-6_2

Reading, C. (2009). Cognitive development of informal inferential reasoning. 57th Session of the International Statistical Institute - Statistics: Our past, present & future, Durban, South Africa.

Schaeffer, R. L. (2006). Statistics and mathematics: On making a happy marriage. In G. Burrill (Ed.), Thinking and reasoning with data and chance: Sixty-eighth NCTM yearbook (pp. 309–321). National Council of Teachers of Mathematics.

Shaughnessy, J. M. (2007). Research on statistics learning and reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 957–1010). National Council of Teachers of Mathematics.

Suh, J. M., English, L. D., & Wickstrom, M. (Eds.). (2021). Exploring mathematical modeling with young learners. Springer. https://doi.org/10.1007/978-3-030-63900-6

van den Heuvel-Panhuizen, M., Iliada E., & Robitzsch, A. (2016). Effects of reading picture books on kindergartners’ mathematics performance. Educational Psychology, 36(2), 323–346. https://doi.org/10.1080/01443410.2014.963029

van den Heuvel-Panhuizen, M., & van den Boogaard, S. (2008). Picture books as an impetus for kindergarteners’ mathematical thinking. Mathematical Thinking and Learning, 10, 34–373. https://doi.org/10.1080/10986060802425539

Watson, J. (2006). Statistical literacy at school: growth and goals. Lawrence Erlbaum.

Watson, J. (2018). Variation and expectation for six-year-olds. (pp. 55–73). In A. M. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds), Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking (pp. 3–20). Springer. https://doi.org/10.1007/978-981-13-1044-7_4

Watson, J., & Fitzallen, N. (2021). What sense do children make of “data” by Year 3? In Y. H. Leong, B. Kaur, B. H. Choy, J. B. W. Yeo, & S. L. Chin (Eds.), Excellence in mathematics education: Foundations and pathways. Proceedings of the 43rd annual conference of the Mathematics Education Research Group of Australasia, Singapore (pp. 409–416).

Watson, J., & Moritz, J. (2001). Development of reasoning associated with pictographs: Representing, interpreting, and predicting. Educational Studies in Mathematics, 48(1), 47–81. https://doi.org/10.1023/A:1015594414565

Wild, C., & Pfannkuch, M. (1998). What is statistical thinking? Proceedings of the 5th International Conference on Teaching Statistics (ICOTS5), Singapore. http://www.stat.auckland.ac.nz/~iase/publications/2/Topic3c.pdf

Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical inquiry. International Statistical Review, 67(3), 223–248. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x

Wild, C., Utts, J., & Horton, N. (2018). What is statistics? In D. Ben-Zvi, K. Makar, J. Garfield (Eds.), International handbook of research in statistics education (pp. 5–36). Springer. https://doi.org/10.1007/978-3-319-66195-7_1

Zieffler, A., Fry, E., & Garfield, J. (2018). What is statistics education? In D. Ben-Zvi, K. Makar, J. Garfield (Eds.), International handbook of research in statistics education (pp. 71–99). Springer. https://doi.org/10.1007/978-3-319-66195-7_2

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2023-07-31

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Early Statistical and Probabilistic Thinking