Skip to main content

Young Children’s Reasoning Through Data Exploration

  • Chapter
  • First Online:
Forging Connections in Early Mathematics Teaching and Learning

Abstract

This chapter follows the progress of nine high-ability Year 1 Australian students as they develop reasoning skills through data exploration and analysis. The students used self-portraits drawn by child artists in Kindergarten and Year 3 to develop a rule-based classification model. Students tested their model on larger sets of self-portraits and developed their own illustrations to support the rule-based model. Seven of the nine students demonstrated advanced mathematical reasoning through their analysis of the test findings to inform their judgements regarding the strengths and weaknesses of the model. Students demonstrated this reasoning through graphical representations, reflective statements and two-way tables. These findings demonstrate the potential of rule-based model building and data analysis to extend the mathematical experiences of mathematically gifted young children.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Activities sourced from the Critical Thinking Company (Parks & Black, 1997).

References

  • Clements, D., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York, NY: Routledge.

    Google Scholar 

  • Diezmann, C. M., & Watters, J. (1998). Thinking by young children during argumentation: Use of evidence and logic. In Thinking processes: Going beyond the surface curriculum (pp. 115–134).

    Google Scholar 

  • English, L. (2010). Young children’s early modelling with data. Mathematics Education Research Journal, 22(2), 24–47. doi:10.1007/BF03217564.

    Article  Google Scholar 

  • English, L. (2012). Data modelling with first-grade students. Educational Studies in Mathematics, 81(1), 15–30.

    Article  Google Scholar 

  • English, L. (2013). Reconceptualizing statistical learning in the early years. In L. English & J. Mulligan (Eds.), Reconceptualizing early mathematics learning (pp. 67–82). New York: Springer.

    Chapter  Google Scholar 

  • Gopnik, A. (2012). Scientific thinking in young children: Theoretical advances, empirical research, and policy implications. Science, 337, 1623–1627.

    Article  Google Scholar 

  • Harrison, C. (2005). Young gifted children: Their search for complexity and connection. Exeter, NSW: Inscript Publishing.

    Google Scholar 

  • Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence: An essay on the construction of formal operational structures. New York: Basic Books.

    Book  Google Scholar 

  • Kinnear, V. (2013). Young children’s statistical reasoning: A tale of two contexts. Ph.D. Queensland University of Technology, Brisbane, QLD.

    Google Scholar 

  • Leavy, A. (2008). An examination of the role of statistical investigation in supporting the development of young children’s statistical reasoning. In O. N. Saracho & B. Spodek (Eds.), Contemporary perspectives on mathematics in early childhood education (pp. 215–232). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Lehrer, R., & Schauble, L. (2000). Inventing data structures for representational purposes: Elementary grade students’ classification models. Mathematical Thinking and Learning, 1–2, 51–74. doi:10.1207/S15327833MTL0202_3.

    Article  Google Scholar 

  • Lesh, R. A., & Carmona, G. (2003). Piagetian conceptual systems and models for mathematizing everyday experiences. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 71–96). Mahwah, N.J.: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lesh, R. A., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5, 109–129.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • Meletiou-Mavrotheris, M., & Paparistodemou, E. (2015). Developing students’ reasoning about samples and sampling in the context of informal inferences. Educational Studies in Mathematics, 88(3), 385–404. doi:10.1007/S10649-014-9551-5.

    Article  Google Scholar 

  • Morsanyi, K., Divine, A., Nobes, A., & Szucs, D. (2013). The link between logic, mathematics and imagination: Evidence from children with developmental dyscalculia and mathematically gifted children. Developmental Science, 16(4), 542–553. doi:10.1111/desc.12048.

    Article  Google Scholar 

  • Mulligan, J. (2015). Moving beyond basic numeracy: Data modeling in the early years of schooling. ZDM Mathematics Education, 47, 653–663.

    Article  Google Scholar 

  • Mulligan, J., Hodge, K., Mitchelmore, M., & English, L. (2013). Tracking structural development through data modelling in highly able grade 1 students. In V. Steinle, L. Ball, & C. Bardini (Eds.), Proceeding of the 36th annual conference of the mathematics education research group of Australasia (pp. 530–536). Melbourne, Vic: MERGA.

    Google Scholar 

  • Mulligan, J., Mitchelmore, M., & Stephanaou, A. (2015). Pattern and Structure Assessment: an assessment program for early mathematics (F-2) Response Booklets F. 1, 2. Camperdown, VIC: Australian Council for Educational Research.

    Google Scholar 

  • Parks, S., & Black, H. (1997). Building thinking skills® book 1. Pacific Grove, CA: Critical Thinking Company.

    Google Scholar 

  • Raven, J., Raven, J. C., & Court, J. H. (1998). Manual for Raven’s progressive matrices and vocabulary scales (Vol. 2). San Antonio, TX: Pearson.

    Google Scholar 

  • Thom, J. S., & McGarvey, L. M. (2015). The act and artefact of drawing(s): Observing geometric thinking with, in, and through children’s drawings. ZDM: The International Journal on Mathematics Education, 47(3), 465–481. doi:10.1007/s11858-015-0697-0.

    Article  Google Scholar 

  • Zawojewski, J. S. (2010). Problem solving versus modeling. In R. A. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford, Modeling students’ mathematical modeling competencies (pp. 237–244). New York: Springer. doi:10.1007/978-1-4419-0561-1.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gabrielle Oslington .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Oslington, G., Mulligan, J.T., Van Bergen, P. (2018). Young Children’s Reasoning Through Data Exploration. In: Kinnear, V., Lai, M., Muir, T. (eds) Forging Connections in Early Mathematics Teaching and Learning. Early Mathematics Learning and Development. Springer, Singapore. https://doi.org/10.1007/978-981-10-7153-9_11

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-7153-9_11

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-7151-5

  • Online ISBN: 978-981-10-7153-9

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics