Investigating Structures of Knowing within Three Relational Constructs, Leading to Higher-Order Mathematical Thinking

Gregory Alan Scott

Investigating Structures of Knowing within Three Relational Constructs, Leading to Higher-Order Mathematical Thinking

Gregory Alan Scott

School of Education

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

Abstract

This paper considers three constructs that address different, yet complementary perspectives on student mathematical performance. The three constructs are the relationship between procedural and conceptual forms of knowledge by Hiebert and Lefevre (1986), the psychology of mathematical abilities in schoolchildren as researched by Krutetskii (1976), and the developmental construct of the SOLO model as devised by Biggs and Collis (1982, 1991). It will be appreciated how these constructs derive three different viewpoints of 'structures of knowing' in mathematics resulting in the possibility of transitional pathways to higher-order thinking. "In simplest terms, higher-order thinking measures include all intellectual tasks that call for more than information retrieval." (Baker 1990 p.7)

Original language	English
Title of host publication	Bridging the Gap between Ideas and Doing Research: Proceedings of the Inaugural Postgraduate Research Conference
Editors	Terrence Hays, Rafat Hussain
Place of Publication	Deakin West, Australia
Publisher	Australian College of Educators
Pages	349-369
ISBN (Print)	9781920819231
Publication status	Published - 2007
Event	Bridging the Gap between Ideas and Doing Research 2006: Inaugural Postgraduate Research Conference - Armidale, Australia Duration: 8 Aug 2006 → 11 Aug 2006

Conference

Conference	Bridging the Gap between Ideas and Doing Research 2006: Inaugural Postgraduate Research Conference
City	Armidale, Australia
Period	8/08/06 → 11/08/06

Keywords

Mathematics and Numeracy Curriculum and Pedagogy

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https://hdl.handle.net/1959.11/4122

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Scott, Gregory Alan. / Investigating Structures of Knowing within Three Relational Constructs, Leading to Higher-Order Mathematical Thinking. Bridging the Gap between Ideas and Doing Research: Proceedings of the Inaugural Postgraduate Research Conference. editor / Terrence Hays ; Rafat Hussain. Deakin West, Australia : Australian College of Educators, 2007. pp. 349-369

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title = "Investigating Structures of Knowing within Three Relational Constructs, Leading to Higher-Order Mathematical Thinking",

abstract = "This paper considers three constructs that address different, yet complementary perspectives on student mathematical performance. The three constructs are the relationship between procedural and conceptual forms of knowledge by Hiebert and Lefevre (1986), the psychology of mathematical abilities in schoolchildren as researched by Krutetskii (1976), and the developmental construct of the SOLO model as devised by Biggs and Collis (1982, 1991). It will be appreciated how these constructs derive three different viewpoints of 'structures of knowing' in mathematics resulting in the possibility of transitional pathways to higher-order thinking. {"}In simplest terms, higher-order thinking measures include all intellectual tasks that call for more than information retrieval.{"} (Baker 1990 p.7)",

keywords = "Mathematics and Numeracy Curriculum and Pedagogy",

author = "Scott, \{Gregory Alan\}",

year = "2007",

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booktitle = "Bridging the Gap between Ideas and Doing Research: Proceedings of the Inaugural Postgraduate Research Conference",

publisher = "Australian College of Educators",

note = "Bridging the Gap between Ideas and Doing Research 2006: Inaugural Postgraduate Research Conference ; Conference date: 08-08-2006 Through 11-08-2006",

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Scott, GA 2007, Investigating Structures of Knowing within Three Relational Constructs, Leading to Higher-Order Mathematical Thinking. in T Hays & R Hussain (eds), Bridging the Gap between Ideas and Doing Research: Proceedings of the Inaugural Postgraduate Research Conference. Australian College of Educators, Deakin West, Australia, pp. 349-369, Bridging the Gap between Ideas and Doing Research 2006: Inaugural Postgraduate Research Conference, Armidale, Australia, 8/08/06. <https://hdl.handle.net/1959.11/4122>

Investigating Structures of Knowing within Three Relational Constructs, Leading to Higher-Order Mathematical Thinking. / Scott, Gregory Alan.
Bridging the Gap between Ideas and Doing Research: Proceedings of the Inaugural Postgraduate Research Conference. ed. / Terrence Hays; Rafat Hussain. Deakin West, Australia: Australian College of Educators, 2007. p. 349-369.

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

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AB - This paper considers three constructs that address different, yet complementary perspectives on student mathematical performance. The three constructs are the relationship between procedural and conceptual forms of knowledge by Hiebert and Lefevre (1986), the psychology of mathematical abilities in schoolchildren as researched by Krutetskii (1976), and the developmental construct of the SOLO model as devised by Biggs and Collis (1982, 1991). It will be appreciated how these constructs derive three different viewpoints of 'structures of knowing' in mathematics resulting in the possibility of transitional pathways to higher-order thinking. "In simplest terms, higher-order thinking measures include all intellectual tasks that call for more than information retrieval." (Baker 1990 p.7)

KW - Mathematics and Numeracy Curriculum and Pedagogy

UR - http://www.une.edu.au/faculties/professions/Resources/2006proceedings.pdf

UR - http://trove.nla.gov.au/version/38825080

M3 - Conference contribution

SN - 9781920819231

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BT - Bridging the Gap between Ideas and Doing Research: Proceedings of the Inaugural Postgraduate Research Conference

A2 - Hays, Terrence

A2 - Hussain, Rafat

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T2 - Bridging the Gap between Ideas and Doing Research 2006: Inaugural Postgraduate Research Conference

Y2 - 8 August 2006 through 11 August 2006

ER -

Investigating Structures of Knowing within Three Relational Constructs, Leading to Higher-Order Mathematical Thinking

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