Skip to main content
SpringerLink
Log in

The role of perceptual similarity, context, and situation when selecting attributes: considerations made by 5–6-year-olds in data modeling environments

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

Classroom data modeling involves posing questions, identifying attributes of phenomena, measuring and structuring these attributes, and then composing, revising, and communicating the outcomes. Selecting attributes is a fundamental component of data modeling, and the considerations made when selecting attributes is the focus of this paper. A teaching experiment involving 2 teacher educators and 25 pre-service teachers (PSTs) was carried out with 24 young children (5–6-year-olds) as part of a 4-day data modeling investigation. Although perceptual features of the data influenced initial approaches to attribute selection, considerations of the problem situation influenced a shift from the perceptual and towards consideration of attributes such as taxonomy, habitat, behavior, and diet. Expertise in the data context (animal kingdom) and ability to collaborate and negotiate within groups supported children in their ability to switch attributes, attend to multiple situations presented by the problem, and modify and extend their categorizations of data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. The children appeared unaware that polar bears are arctic animals and penguins reside in a number of regions (typically the southern hemisphere, sometimes Antarctic, and sometimes residing in tropical islands). They are not all cold weather birds.

References

  • Blair, M., & Somerville, S. C. (2009). The importance of differentiation in young children’s acquisition of expertise. Cognition, 112, 259–280.

    Article  Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer.

    Google Scholar 

  • Chi, M. T. H., & Koeske, R. D. (1983). Network representation of a child’s dinosaur knowledge. Developmental Psychology, 19, 29–39.

    Article  Google Scholar 

  • Cobb, P., McClain, K., & Gravemeijer, K. (2003). Learning about statistical covariation. Cognition and Instruction, 21(1), 1–78.

    Article  Google Scholar 

  • Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interactional analysis. American Educational Research Journal, 29, 573–604.

    Article  Google Scholar 

  • Darmody, M., & Smyth, E. (2012). Exploring school and classroom environments in Irish primary schools. Children, Youth and Environments, 22(1), 178–197.

    Article  Google Scholar 

  • DiSessa, A., Hammer, D., Sherin, B., & Kolpakowski, T. (1991). Inventing graphing: Metarepresentational expertise in children. Journal of Mathematical Behavior, 10(1), 117–160.

    Google Scholar 

  • English, L. D. (2010). Young children’s early modelling with data. Mathematics Education Research Journal, 22(2), 24–47.

    Article  Google Scholar 

  • English, L. D. (2012). Data modelling with first-grade students. Educational Studies in Mathematics, 81, 15–30.

    Article  Google Scholar 

  • Ertle, B., Chokshi, S., & Fernandez, C. (2001). Lesson planning tool. Retrieved November 28 2016, from www.tc.columbia.edu/centers/lessonstudy/doc/Lesson_Planning_Tool.pdf

  • Fletcher-Janzen, E., Strickland, T. L., & Reynolds, C. (2000). Handbook of cross-cultural neuro-psychology. New York: Springer Science & Business Media. https://doi.org/10.1007/978-1-4615- 4219-3

    Book  Google Scholar 

  • Gelman, S. A. (2006). Early conceptual development. In K. McCartney & D. Phillips (Eds.), Blackwell handbook of early childhood development (pp. 149–166). Malden: Blackwell.

    Google Scholar 

  • Gelman, S. A., Chesnick, R., & Waxman, S. R. (2005). Mother-child conversations about pictures and objects: Referring to categories and individuals. Child Development, 76, 1129–1143.

  • Gelman, S. A., & Markman, E. M. (1986). Categories and induction in young children. Cognition, 23, 183–209.

  • Gentner, D., & Namy, L. L. (1999). Comparison in the development of categories. Cognitive Development, 14, 487–513.

    Article  Google Scholar 

  • Hancock, C., Kaput, J. T., & Goldsmith, L. T. (1992). Authentic inquiry with data: Critical barriers to classroom implementation. Educational Psychologist, 27(3), 337–364.

    Article  Google Scholar 

  • Hanner, S., James, E., & Rohlfing, M. (2002). Classification models across grades. In R. Lehrer & L. Schauble (Eds.), Investigating real data in the classroom (pp. 99–117). New York: Teachers College.

    Google Scholar 

  • Hourigan, M., & Leavy, A. M. (2016). Practical problems: Introducing statistics to kindergarteners. Teaching Children Mathematics, 22(5), 283–291.

    Google Scholar 

  • Johnson, K. E., & Mervis, C. B. (1994). Microgenetic analysis of first steps in children’s acquisition of expertise on shorebirds. Developmental Psychology, 30, 418–435.

    Article  Google Scholar 

  • Kinnear, V. (2013). Young children’s statistical reasoning: A tale of two contexts (Unpublished doctoral dissertation). Queensland University of Technology, Brisbane, Australia.

  • Kinnear, V., & Clarke, J. (2016). Young children’s abductive reasoning about data. In Proceedings of the 13th International Congress on Mathematical Education. Hamburg, July 24–31. Retrieved from http://icme13.org/files/ICME13-Programme356_low36.pdf

  • Leavy, A. M. (2015). Looking at practice: Revealing the knowledge demands of teaching data handling in the primary classroom. Mathematics Education Research Journal, 27(3), 283–309. https://doi.org/10.1007/s13394-014-0138-3

    Article  Google Scholar 

  • Leavy, A. M., & Hourigan, M. (2015). Motivating inquiry in statistics and probability in the primary classroom. Teaching Statistics, 37(2), 41–47. https://doi.org/10.1111/test.12062

    Google Scholar 

  • Leavy, A. M., & Hourigan, M. (2016a). Crime scenes and mystery players! Using interesting contexts and driving questions to support the development of statistical literacy. Teaching Statistics, 38(1), 29–35. https://doi.org/10.1111/test.12088

  • Leavy, A. M., & Hourigan, M. (2016b). Using lesson study to support knowledge development in initial teacher education: Insights from early number classrooms. Teaching and Teacher Education, 57, 161–175. https://doi.org/10.1016/j.tate.2016.04.002

  • 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, 195–216.

    Article  Google Scholar 

  • Lehrer, R., & Schauble, L. (2000). Inventing data structures for representational purposes: Elementary grade students’ classification models. Mathematical Thinking and Learning, 21(1&2), 51–74.

    Article  Google Scholar 

  • Lehrer, R., & Schauble, L. (2007). Contrasting emerging conceptions of distribution in contexts of error and natural variation. In M. C. Lovett & P. Shah (Eds.), Thinking with data (pp. 149–176). New York: Taylor & Francis.

    Google Scholar 

  • Lesh, R., & Doerr, H. M. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematics teaching, learning, and problem solving. Mahwah: Lawrence Erlbaum Associates, Inc..

    Google Scholar 

  • Lesh, R., & Kelly, A. (2000). Multitiered teaching experiments. In A. Kelly & R. Lesh (Eds.), Research design in mathematics and science education (pp. 197–230). Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lesh, R., & Lehrer, R. (2003). Mathematical learning. In W. Reynolds & G. Miller (Eds.), Comprehensive handbook of psychology  (Vol. 7, pp. 357–390). New York: John Wiley.

  • Paparistodemou, E., & Meletiou-Mavrotheris, M. (2008). Enhancing reasoning about statistical inference in 8 year-old students. Statistics Education Research Journal, 7(2), 83–106.

    Google Scholar 

  • Petersen, L. A., & McNeil, N. M. (2013). Effects of perceptually rich manipulatives on preschoolers’ counting performance: Established knowledge counts. Child Development, 84(3), 1020–1033.

    Article  Google Scholar 

  • Samuelson, L. K., & Smith, L. B. (2005). They call it like they see it: Spontaneous naming and attention to shape. Developmental Science, 8, 182–198.

    Article  Google Scholar 

  • Uzzell, B. P., Ponton, M., & Ardila, A. (Eds.). (2013). International handbook of cross-cultural neuropsychology. Mahwah: Lawrence Erlbaum.

  • Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry (with discussion). International Statistical Review, 67(3), 223–265.

    Article  Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge the work of all reviewers and editors of this manuscript who invested their time and energy in providing insightful and constructive feedback on earlier versions of this paper.

Funding

The research was supported by a faculty seed-funding grant [SF16-101] from Mary Immaculate College.

Author information

Authors and Affiliations

  1. Department of Language, Literacy and Mathematics Education, Mary Immaculate College, University of Limerick, South Circular Road, Limerick, Ireland

    Aisling Leavy & Mairead Hourigan

Authors
  1. Aisling Leavy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mairead Hourigan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aisling Leavy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Leavy, A., Hourigan, M. The role of perceptual similarity, context, and situation when selecting attributes: considerations made by 5–6-year-olds in data modeling environments. Educ Stud Math 97, 163–183 (2018). https://doi.org/10.1007/s10649-017-9791-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-017-9791-2

Keywords

Search

Navigation