Ideas of early division prior to formal instruction

Jill Cheeseman; Ann Downton; Anne Roche

Ideas of early division prior to formal instruction

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

Abstract

Often young children develop ideas of mathematics before they formally meet them at school. Such is the case with early counting concepts. However, little is known about children’s early ideas of division. The study reported here investigated the ideas of 114 children (5-6-years old) before they had received any formal instruction about division in their first year at school. A pencil and paper test comprising worded problems with diagrams was read aloud by the teacher. We analysed children’s drawings on the diagrams. Results indicate that 74% of children could conceive of at least one division situation prior to any instruction. Some children (20%) could interpret quotitive and partitive division problems. Children drawing on diagrams can provide evidence of their conceptual interpretation of division problems.

Original language	English
Title of host publication	Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education, 2022
Editors	Ceneida Fernández, Salvador Llinares, Ángel Gutiérrez, Núria Planas
Place of Publication	Alicante Spain
Publisher	Psychology of Mathematics Education (PME)
Pages	131-138
Number of pages	8
Volume	2
ISBN (Electronic)	9788413021751
ISBN (Print)	9788413021768
Publication status	Published - 2022
Event	Annual Conference of the International Group for the Psychology of Mathematics Education 2022: Mathematics education research supporting practice: Empowering the future - University of Alicante, Alicante, Spain Duration: 18 Jul 2022 → 23 Jul 2022 Conference number: 45th https://web.ua.es/pme45/

Publication series

Name	Proceedings of the International Group for the Psychology of Mathematics Education
Volume	2
ISSN (Print)	0771-100X
ISSN (Electronic)	2790-3648

Conference

Conference	Annual Conference of the International Group for the Psychology of Mathematics Education 2022
Abbreviated title	PME 2022
Country/Territory	Spain
City	Alicante
Period	18/07/22 → 23/07/22
Internet address	https://web.ua.es/pme45/

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https://web.ua.es/en/pme45/documents/proceedings-pme-45-vol2.pdf

Cite this

Cheeseman, J., Downton, A., & Roche, A. (2022). Ideas of early division prior to formal instruction. In C. Fernández, S. Llinares, Á. Gutiérrez, & N. Planas (Eds.), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education, 2022 (Vol. 2, pp. 131-138). (Proceedings of the International Group for the Psychology of Mathematics Education; Vol. 2). Psychology of Mathematics Education (PME). https://web.ua.es/en/pme45/documents/proceedings-pme-45-vol2.pdf

Cheeseman, Jill ; Downton, Ann ; Roche, Anne. / Ideas of early division prior to formal instruction. Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education, 2022. editor / Ceneida Fernández ; Salvador Llinares ; Ángel Gutiérrez ; Núria Planas. Vol. 2 Alicante Spain : Psychology of Mathematics Education (PME), 2022. pp. 131-138 (Proceedings of the International Group for the Psychology of Mathematics Education).

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title = "Ideas of early division prior to formal instruction",

abstract = "Often young children develop ideas of mathematics before they formally meet them at school. Such is the case with early counting concepts. However, little is known about children{\textquoteright}s early ideas of division. The study reported here investigated the ideas of 114 children (5-6-years old) before they had received any formal instruction about division in their first year at school. A pencil and paper test comprising worded problems with diagrams was read aloud by the teacher. We analysed children{\textquoteright}s drawings on the diagrams. Results indicate that 74% of children could conceive of at least one division situation prior to any instruction. Some children (20%) could interpret quotitive and partitive division problems. Children drawing on diagrams can provide evidence of their conceptual interpretation of division problems.",

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editor = "Ceneida Fern{\'a}ndez and Salvador Llinares and {\'A}ngel Guti{\'e}rrez and N{\'u}ria Planas",

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Cheeseman, J , Downton, A & Roche, A 2022, Ideas of early division prior to formal instruction. in C Fernández, S Llinares, Á Gutiérrez & N Planas (eds), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education, 2022. vol. 2, Proceedings of the International Group for the Psychology of Mathematics Education, vol. 2, Psychology of Mathematics Education (PME), Alicante Spain, pp. 131-138, Annual Conference of the International Group for the Psychology of Mathematics Education 2022, Alicante, Spain, 18/07/22. <https://web.ua.es/en/pme45/documents/proceedings-pme-45-vol2.pdf>

Ideas of early division prior to formal instruction. / Cheeseman, Jill ; Downton, Ann; Roche, Anne.
Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education, 2022. ed. / Ceneida Fernández; Salvador Llinares; Ángel Gutiérrez; Núria Planas. Vol. 2 Alicante Spain: Psychology of Mathematics Education (PME), 2022. p. 131-138 (Proceedings of the International Group for the Psychology of Mathematics Education; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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AB - Often young children develop ideas of mathematics before they formally meet them at school. Such is the case with early counting concepts. However, little is known about children’s early ideas of division. The study reported here investigated the ideas of 114 children (5-6-years old) before they had received any formal instruction about division in their first year at school. A pencil and paper test comprising worded problems with diagrams was read aloud by the teacher. We analysed children’s drawings on the diagrams. Results indicate that 74% of children could conceive of at least one division situation prior to any instruction. Some children (20%) could interpret quotitive and partitive division problems. Children drawing on diagrams can provide evidence of their conceptual interpretation of division problems.

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Cheeseman J , Downton A, Roche A. Ideas of early division prior to formal instruction. In Fernández C, Llinares S, Gutiérrez Á, Planas N, editors, Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education, 2022. Vol. 2. Alicante Spain: Psychology of Mathematics Education (PME). 2022. p. 131-138. (Proceedings of the International Group for the Psychology of Mathematics Education).

Ideas of early division prior to formal instruction

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