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Inquiry pedagogy to promote emerging proportional reasoning in primary students

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Abstract

Proportional reasoning as the capacity to compare situations in relative (multiplicative) rather than absolute (additive) terms is an important outcome of primary school mathematics. Research suggests that students tend to see comparative situations in additive rather than multiplicative terms and this thinking can influence their capacity for proportional reasoning in later years. In this paper, excerpts from a classroom case study of a fourth-grade classroom (students aged 9) are presented as they address an inquiry problem that required proportional reasoning. As the inquiry unfolded, students' additive strategies were progressively seen to shift to proportional thinking to enable them to answer the question that guided their inquiry. In wrestling with the challenges they encountered, their emerging proportional reasoning was supported by the inquiry model used to provide a structure, a classroom culture of inquiry and argumentation, and the proportionality embedded in the problem context.

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Notes

  1. Both teachers had been part of the inquiry study for 5 years.

  2. http://www.qsa.qld.edu.au/downloads/p_10/qcar_el_maths_wow.pdf

  3. Shortly after this unit, the classroom was severely damaged. As a result, some of the research data (including some artefacts, the research notes, and handwritten lesson plans and/or revisions) were destroyed. The details of the research reported in this paper were reconstructed from video, student artefacts and (incomplete) records of lesson plans.

  4. Bratz dolls are similar to Barbie dolls in size but, “are portrayed as teenagers distinguished by large heads and skinny bodies, almond-shaped eyes adorned with eyeshadow, and lush, glossy lips” (Wikipedia)

  5. Students often ignored the 1 in the ratio 1:x and just read the ratio as “x”.

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Acknowledgments

This research was supported by the Australian Research Council (LP0990184; DP120100690), Education Queensland and The University of Queensland. The first author is in receipt of an Australian Postgraduate Award Scholarship and wishes to acknowledge the financial support of the Commonwealth Government.

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Authors and Affiliations

  1. The University of Queensland, School of Education, Social Sciences Bldg, Queensland, QLD, 4072, Australia

    Jill Fielding-Wells, Shelley Dole & Katie Makar

  2. The University of Queensland, Queensland, QLD, 4072, Australia

    Jill Fielding-Wells, Shelley Dole & Katie Makar

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  1. Jill Fielding-Wells
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  2. Shelley Dole
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  3. Katie Makar
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Correspondence to Katie Makar.

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The authors contributed equally to this paper. The order was determined by random device.

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Fielding-Wells, J., Dole, S. & Makar, K. Inquiry pedagogy to promote emerging proportional reasoning in primary students. Math Ed Res J 26, 47–77 (2014). https://doi.org/10.1007/s13394-013-0111-6

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  • DOI: https://doi.org/10.1007/s13394-013-0111-6

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