Visualization in Mathematics Learning: Arithmetic Problem-Solving and Student Difficulties

Booth, Rhonda D.L; Thomas, Michael

doi:10.1016/s0732-3123(99)00027-9

Cited by 65 publications

(52 citation statements)

References 15 publications

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“…But this is not the only duality for symbols. When we perceive the symbolisation of an object we may simply have a surface or observational view (Thomas, 2001), but in order to get a mathematical perspective of what it represents we have to interpret what we see using our mathematical schemas (c.f., Booth & Thomas, 2000;Thomas, 2006). This process of interpretation of the symbolisation, or representation, may require us to interact with the figural-concept object (Thomas & Hong, 2001), giving rise to identification of the object's properties, often underlying operational invariants (c.f.…”

Section: Discussionmentioning

confidence: 99%

Student perspectives on equation: The transition from school to university

Godfrey

Thomas

2008

Math Ed Res J

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It has been recognised that many student perspectives on equations and their use of the equals sign have not mirrored those that mathematicians would like to see in tertiary students. This paper tracks transition of understanding of the equals sign by comparing secondary school students' thinking with that of first year university students. We analyse the understanding displayed in terms of properties of the constituent parts of equations, identifying a number of incomplete or pseudoconceptions that are sometimes influenced by representational aspects of the properties, and other times by apparent over-generalisation of a property. A start is made on constructing a framework for understanding of the mathematical equation object that could assist in the transition from school to tertiary mathematics study.

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Section: Discussionmentioning

confidence: 99%

Student perspectives on equation: The transition from school to university

Godfrey

Thomas

2008

Math Ed Res J

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“…Students with lower numerical achievement reported descriptive and idiosyncratic images; they focused on non-mathematical aspects and surface characteristics of visual cues. Visualisation skills, which frequently involve recognition of pattern and structure, are positively correlated with mathematical achievement (Arcavi, 2003;Booth & Thomas, 2000) and analogical reasoning (English, 2004). And psychological research has repeatedly shown that scores on mathematics achievement tests correlate moderately highly with scores on intelligence tests~-which invariably include pattern recognition tasks.…”

mentioning

confidence: 99%

Awareness of pattern and structure in early mathematical development

2009

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“…Spatial skills are also used to manage information on the page or in the mind when performing complex computations (Booth & Thomas, 1999;Wheatley, 1998). Spatial visualisation can be used to solve number and fraction problems (Lean & Clements, 1981).…”

Section: Space and Geometrymentioning

confidence: 99%