The case of disappearing and reappearing zeros: a disconnection between procedural knowledge and conceptual understanding

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

Abstract

We report on 25 Year 5-6 students’ written responses to two items taken from an assessment of mental computation fluency with multiplication, alongside their reasoning of the strategy they had employed, which may or may not have made use of the associative property. Coding of this interview data revealed four distinct levels of conceptual understanding of the associative property, which teachers could use to inform their planning. The findings reveal the complexity associated with assessing multiplicative mental computational fluency and students’ reliance on procedures often considered by them to be more magical than logical.
Original languageEnglish
Title of host publicationMathematics Education Research: Impacting Practice
Subtitle of host publicationProceedings of the 42nd annual conference of the Mathematics Education Research Group of Australasia
EditorsGregory Hine, Susan Blackley, Audrey Cooke
Place of PublicationAdelaide SA Australia
PublisherMathematics Education Research Group of Australasia
Pages236-243
Number of pages8
Publication statusPublished - 2019

Keywords

  • mathematics education
  • Multiplicative thinking
  • Associative property

Cite this

Downton, A., Russo, J., & Hopkins, S. (2019). The case of disappearing and reappearing zeros: a disconnection between procedural knowledge and conceptual understanding. In G. Hine, S. Blackley, & A. Cooke (Eds.), Mathematics Education Research: Impacting Practice: Proceedings of the 42nd annual conference of the Mathematics Education Research Group of Australasia (pp. 236-243). Adelaide SA Australia: Mathematics Education Research Group of Australasia.
Downton, Ann ; Russo, James ; Hopkins, Sarah. / The case of disappearing and reappearing zeros : a disconnection between procedural knowledge and conceptual understanding. Mathematics Education Research: Impacting Practice: Proceedings of the 42nd annual conference of the Mathematics Education Research Group of Australasia. editor / Gregory Hine ; Susan Blackley ; Audrey Cooke. Adelaide SA Australia : Mathematics Education Research Group of Australasia, 2019. pp. 236-243
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Downton, A, Russo, J & Hopkins, S 2019, The case of disappearing and reappearing zeros: a disconnection between procedural knowledge and conceptual understanding. in G Hine, S Blackley & A Cooke (eds), Mathematics Education Research: Impacting Practice: Proceedings of the 42nd annual conference of the Mathematics Education Research Group of Australasia. Mathematics Education Research Group of Australasia, Adelaide SA Australia, pp. 236-243.

The case of disappearing and reappearing zeros : a disconnection between procedural knowledge and conceptual understanding. / Downton, Ann; Russo, James; Hopkins, Sarah.

Mathematics Education Research: Impacting Practice: Proceedings of the 42nd annual conference of the Mathematics Education Research Group of Australasia. ed. / Gregory Hine; Susan Blackley; Audrey Cooke. Adelaide SA Australia : Mathematics Education Research Group of Australasia, 2019. p. 236-243.

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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Downton A, Russo J, Hopkins S. The case of disappearing and reappearing zeros: a disconnection between procedural knowledge and conceptual understanding. In Hine G, Blackley S, Cooke A, editors, Mathematics Education Research: Impacting Practice: Proceedings of the 42nd annual conference of the Mathematics Education Research Group of Australasia. Adelaide SA Australia: Mathematics Education Research Group of Australasia. 2019. p. 236-243