What lies beneath? Conceptual connectivity underlying whole number arithmetic

Joanne Mulligan; Geoff Woolcott

What lies beneath? Conceptual connectivity underlying whole number arithmetic

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

Abstract

Whole number arithmetic (WNA) is considered central to mathematics in the modern industrialised world. New developments in the cognitive and neurocognitive sciences, however, propose that WNA should be viewed in relation to the domain of mathematics more broadly and the real world interactions from which mathematics have developed. This may require mathematics to be conceptualised as a coherent domain that develops from human interaction, and that is reliant on spatial negotiation of one’s environment. A lens on conceptual connectivity integral to an awareness of spatial pattern and structure, therefore, may offer a more complete picture of the connectivity that underlies WNA. A stronger focus on ‘non numerosity’ attributes of mathematics learning and how they underpin WNA and mathematics more generally is proposed.

Original language	English
Title of host publication	Primary mathematics study on whole numbers
Subtitle of host publication	International Commission on Mathematical Instruction (ICMI) study 23 conference proceedings
Editors	Xuhua Sun, Berinderjeet Kaur, Jarmila Novotná
Place of Publication	Macao, China
Publisher	University of Macau
Pages	220-228
Number of pages	9
ISBN (Print)	9789996510663
Publication status	Published - 2015
Event	International Commission on Mathematical Instruction (23rd : 2015) - Macao, China Duration: 3 Jun 2015 → 7 Jun 2015

Conference

Conference	International Commission on Mathematical Instruction (23rd : 2015)
City	Macao, China
Period	3/06/15 → 7/06/15

Keywords

number
spatial reasoning
structural grouping
whole number arithmetic

Cite this

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title = "What lies beneath? Conceptual connectivity underlying whole number arithmetic",

abstract = "Whole number arithmetic (WNA) is considered central to mathematics in the modern industrialised world. New developments in the cognitive and neurocognitive sciences, however, propose that WNA should be viewed in relation to the domain of mathematics more broadly and the real world interactions from which mathematics have developed. This may require mathematics to be conceptualised as a coherent domain that develops from human interaction, and that is reliant on spatial negotiation of one{\textquoteright}s environment. A lens on conceptual connectivity integral to an awareness of spatial pattern and structure, therefore, may offer a more complete picture of the connectivity that underlies WNA. A stronger focus on {\textquoteleft}non numerosity{\textquoteright} attributes of mathematics learning and how they underpin WNA and mathematics more generally is proposed.",

keywords = "number, spatial reasoning, structural grouping, whole number arithmetic",

author = "Joanne Mulligan and Geoff Woolcott",

year = "2015",

language = "English",

isbn = "9789996510663",

pages = "220--228",

editor = "Xuhua Sun and Berinderjeet Kaur and Jarmila Novotn{\'a}",

booktitle = "Primary mathematics study on whole numbers",

publisher = "University of Macau",

note = "International Commission on Mathematical Instruction (23rd : 2015) ; Conference date: 03-06-2015 Through 07-06-2015",

}

Mulligan, J & Woolcott, G 2015, What lies beneath? Conceptual connectivity underlying whole number arithmetic. in X Sun, B Kaur & J Novotná (eds), Primary mathematics study on whole numbers: International Commission on Mathematical Instruction (ICMI) study 23 conference proceedings. University of Macau, Macao, China, pp. 220-228, International Commission on Mathematical Instruction (23rd : 2015), Macao, China, 3/06/15.

What lies beneath? Conceptual connectivity underlying whole number arithmetic. / Mulligan, Joanne; Woolcott, Geoff.
Primary mathematics study on whole numbers: International Commission on Mathematical Instruction (ICMI) study 23 conference proceedings. ed. / Xuhua Sun; Berinderjeet Kaur; Jarmila Novotná. Macao, China: University of Macau, 2015. p. 220-228.

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

TY - GEN

T1 - What lies beneath? Conceptual connectivity underlying whole number arithmetic

AU - Mulligan, Joanne

AU - Woolcott, Geoff

PY - 2015

Y1 - 2015

N2 - Whole number arithmetic (WNA) is considered central to mathematics in the modern industrialised world. New developments in the cognitive and neurocognitive sciences, however, propose that WNA should be viewed in relation to the domain of mathematics more broadly and the real world interactions from which mathematics have developed. This may require mathematics to be conceptualised as a coherent domain that develops from human interaction, and that is reliant on spatial negotiation of one’s environment. A lens on conceptual connectivity integral to an awareness of spatial pattern and structure, therefore, may offer a more complete picture of the connectivity that underlies WNA. A stronger focus on ‘non numerosity’ attributes of mathematics learning and how they underpin WNA and mathematics more generally is proposed.

AB - Whole number arithmetic (WNA) is considered central to mathematics in the modern industrialised world. New developments in the cognitive and neurocognitive sciences, however, propose that WNA should be viewed in relation to the domain of mathematics more broadly and the real world interactions from which mathematics have developed. This may require mathematics to be conceptualised as a coherent domain that develops from human interaction, and that is reliant on spatial negotiation of one’s environment. A lens on conceptual connectivity integral to an awareness of spatial pattern and structure, therefore, may offer a more complete picture of the connectivity that underlies WNA. A stronger focus on ‘non numerosity’ attributes of mathematics learning and how they underpin WNA and mathematics more generally is proposed.

KW - number

KW - spatial reasoning

KW - structural grouping

KW - whole number arithmetic

M3 - Conference proceeding contribution

SN - 9789996510663

SP - 220

EP - 228

BT - Primary mathematics study on whole numbers

A2 - Sun, Xuhua

A2 - Kaur, Berinderjeet

A2 - Novotná, Jarmila

PB - University of Macau

CY - Macao, China

T2 - International Commission on Mathematical Instruction (23rd : 2015)

Y2 - 3 June 2015 through 7 June 2015

ER -

What lies beneath? Conceptual connectivity underlying whole number arithmetic

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Keywords

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