TY - BOOK
T1 - The Impact of Scale on Children’s Spatial Thought
T2 - A Quantitative Study for Two Settings in Geometry Education
AU - Heil, Cathleen
N1 - Publisher Copyright:
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2020.
PY - 2020
Y1 - 2020
N2 - Children’s thought about space is influenced by their abilities to perceive, encode, and mentally manipulate spatial relations they experience and explore in everyday life. Geometry education in primary school aims to support children as they organize those experiences at an abstract level and develop cognitive abilities to consciously manipulate spatial information in different spatial settings, that is, their spatial abilities. Many studies have investigated children’s abilities to mentally manipulate spatial relations in tabletop settings but not those required when the self is located or moving in real space. Addressing this gap in the literature, this study proposes map-based spatial tasks in real space and examines the relations of individual differences in the corresponding underlying cognitive abilities used to solve spatial tasks at both scales of space, small-scale and large-scale spatial abilities, in greater detail. Using a correlational study design, this study investigates the relation between performances of 240 fourth graders on a mid-sized German university completing paper-based tasks in a classroom setting and map-based orientation tasks in a real space setting. The former test consisted of a subset of tasks that required the children to mentally manipulate object-based transformations and another asking the children to transform the imagined self. The latter test mimicked the practical use of maps such as indicating the direction toward unseen locations, finding one’s position and viewing direction on the map, or navigating toward a predefined goal. The test also included tasks without a map that required the children to make inferences on directions to landmarks from survey knowledge acquired during movement in space. Descriptive results revealed that paper-and-pencil tasks requiring multistep mental transformations of abstract and complex spatial information were appropriate means to measure individual differences in children’s performances reflecting small-scale spatial abilities. Moreover, maps were found to be potentially powerful cognitive tools for teachers and researchers to stimulate and measure children’s spatial thought in real space. By comparing different models in confirmatory factor analyses, the study showed that at both scales of space, spatial abilities should not be treated as an undifferentiated construct but rather be understood as multidimensional. The results suggested that a two-factor model distinguishing between object manipulation and perspective transformation abilities might be an option to model small-scale spatial abilities. They also confirmed a three-factor model distinguishing between the abilities to make inferences on directions from survey knowledge and two subclasses of map use, namely the abilities to transform information from the map to the referent space, comprehension abilities, and the ones to use information from the referent space to reason about spatial locations on the map, production abilities. The results of multivariate statistical analyses at the manifest and latent level indicated that children’s spatial abilities at both scales of space are partially but not fully related. These results specify the degree of overlap between subclasses of small-scale and subclasses of large-scale spatial abilities, clarify the role of visuospatial working memory as a mediator when it comes to relations with abilities to use a map in real space, and emphasize the predictive role of particular spatial tasks. The results provide new insights regarding the similarities and differences between both classes of spatial abilities. The findings of this study contribute to the literature in the study of spatial thought in mathematics education and provide empirical evidence for the development of pedagogical interventions both in geometry education and beyond.
AB - Children’s thought about space is influenced by their abilities to perceive, encode, and mentally manipulate spatial relations they experience and explore in everyday life. Geometry education in primary school aims to support children as they organize those experiences at an abstract level and develop cognitive abilities to consciously manipulate spatial information in different spatial settings, that is, their spatial abilities. Many studies have investigated children’s abilities to mentally manipulate spatial relations in tabletop settings but not those required when the self is located or moving in real space. Addressing this gap in the literature, this study proposes map-based spatial tasks in real space and examines the relations of individual differences in the corresponding underlying cognitive abilities used to solve spatial tasks at both scales of space, small-scale and large-scale spatial abilities, in greater detail. Using a correlational study design, this study investigates the relation between performances of 240 fourth graders on a mid-sized German university completing paper-based tasks in a classroom setting and map-based orientation tasks in a real space setting. The former test consisted of a subset of tasks that required the children to mentally manipulate object-based transformations and another asking the children to transform the imagined self. The latter test mimicked the practical use of maps such as indicating the direction toward unseen locations, finding one’s position and viewing direction on the map, or navigating toward a predefined goal. The test also included tasks without a map that required the children to make inferences on directions to landmarks from survey knowledge acquired during movement in space. Descriptive results revealed that paper-and-pencil tasks requiring multistep mental transformations of abstract and complex spatial information were appropriate means to measure individual differences in children’s performances reflecting small-scale spatial abilities. Moreover, maps were found to be potentially powerful cognitive tools for teachers and researchers to stimulate and measure children’s spatial thought in real space. By comparing different models in confirmatory factor analyses, the study showed that at both scales of space, spatial abilities should not be treated as an undifferentiated construct but rather be understood as multidimensional. The results suggested that a two-factor model distinguishing between object manipulation and perspective transformation abilities might be an option to model small-scale spatial abilities. They also confirmed a three-factor model distinguishing between the abilities to make inferences on directions from survey knowledge and two subclasses of map use, namely the abilities to transform information from the map to the referent space, comprehension abilities, and the ones to use information from the referent space to reason about spatial locations on the map, production abilities. The results of multivariate statistical analyses at the manifest and latent level indicated that children’s spatial abilities at both scales of space are partially but not fully related. These results specify the degree of overlap between subclasses of small-scale and subclasses of large-scale spatial abilities, clarify the role of visuospatial working memory as a mediator when it comes to relations with abilities to use a map in real space, and emphasize the predictive role of particular spatial tasks. The results provide new insights regarding the similarities and differences between both classes of spatial abilities. The findings of this study contribute to the literature in the study of spatial thought in mathematics education and provide empirical evidence for the development of pedagogical interventions both in geometry education and beyond.
KW - Map Reading
KW - Mathematics Education
KW - Primary Education
KW - Spatial Abilities
KW - Structural Equation Modeling
KW - Educational science
UR - https://www.scopus.com/pages/publications/105036869144
U2 - 10.1007/978-3-658-32648-7
DO - 10.1007/978-3-658-32648-7
M3 - Book
SN - 978-3-658-32647-0
VL - Part F6037
T3 - Studien zur theoretischen und empirischen Forschung in der Mathematikdidaktik
BT - The Impact of Scale on Children’s Spatial Thought
PB - Springer Verlag
CY - Wiesbaden
ER -