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Visuospatial Reasoning: An Ecocultural Perspective for Space, Geometry and Measurement Education

Kay Owens
Publisher: 
Springer
Publication Date: 
2014
Number of Pages: 
377
Format: 
Hardcover
Series: 
Mathematics Education Library
Price: 
129.00
ISBN: 
9783319024622
Category: 
Monograph
[Reviewed by
Tom Schulte
, on
06/14/2015
]

Drawn on first-hand and reported field interactions with elementary mathematics students from Papua New Guinea (PNG) and other First Nations, this work is aimed at mathematics educators looking to develop culturally aware curricula and classroom approaches to teaching fundamentals in algebra and geometry. The author does not present suggestions or sample curricula, but rather identifies key landmarks on the topography of cultural influences in learning mathematics. This often runs into a fascinating minutiae of language elements, such as considering how adverbs like “over”, “here”, and “there” are considered in the Navajo, Maori, or PNG mind. While not completely stating a psychology of linguistically and culturally influenced visuospatial reasoning, this is what is being described: how the minds of specific cultures interpret mathematical ideas as pointers on how to present them effectively. This is done through an overview of available research and the author’s own experiences. Many images, some in color, of arts, crafts, and construction in various communities add to the text.

Cultural differences in learning, describing, and understanding geometric and algebraic topics may be substantial. This is a clearly supported and central tenet of the text. In the complex learning process, the author focuses largely on how language interprets and specifies both measuring space and locating within space. This often involves providing relevant background on the languages touched on. This core problem to be solved is stated by the author in various ways, such as “Area measurement is a particularly problematic issue if visuospatial reasoning from ecocultural contexts is not incorporated into the learning.” In breaking down the atoms of such tasks and the language to express them, the author takes us to places like Wiradjuri, NSW, Australia where “4 can be expressed bula bula, or bungu, or magu” as an example of a culture with multiple frame words in its counting system. (The Tolai language offers even deeper complexities.) What are the implications of teaching the area of plane figures to young minds from a culture with a 4-, 8-, or 10-cycle system ornamented with gesture and morpheme combinations depending on what is being counted and when (during a ceremony?) or why? The author points out what should be considered before entering the classroom and cites the relevant papers for an “enthnographic” approach to an effective pedagogy in elementary mathematics.


Tom Schulte prepares students of the wonderfully diverse Oakland Community College community for calculus.

Introduction: Visuospatial reasoning in context

Visuospatial reasoning in 20th century psychology-based studies

Changing Perspective: sociocultural elaboration

Place, culture, language, and visuospatial reasoning

Visuospatial reasoning in cultural activities in Papua New Guinea

Visuospatial reasoning in other cultures

The impact of an ecocultural perspective of visuospatial reasoning on mathematics education

The importance of an ecocultural perspective for Indigenous and transcultural education

Visuospatial reasoning in contexts with digital technology

An ecocultural perspective on visuospatial reasoning in geometry and measurement education

Appendices

Dummy View - NOT TO BE DELETED