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2020 | Book

Introduction Read chapter Read first chapter

The Impact of Scale on Children’s Spatial Thought

A Quantitative Study for Two Settings in Geometry Education

Author: Cathleen Heil

Publisher: Springer Fachmedien Wiesbaden

Book Series : Studien zur theoretischen und empirischen Forschung in der Mathematikdidaktik

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

In this book, Cathleen Heil addresses the question of how to conceptually understand children’s spatial thought in the context of geometry education. She proposes that in order to help children develop their abilities to successfully grasp and manipulate the spatial relations they experience in their everyday lives, spatial thought should not only be addressed in written or tabletop settings at school. Instead, geometry education should also focus on settings involving real space, such as during reasoning with maps.
In a first part of this book, she theoretically addresses the construct of spatial thought at different scales of space from a cognitive psychological point of view and shows that maps can be rich sources for spatial thinking. In a second part, she proposes how to measure children’s spatial thought in a paper-and-pencil setting and map-based setting in real space. In a third, empirical part, she examines the relations between children’s spatial thought in those two settings both at a manifest and latent level.

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
Space plays an important role in children’s everyday life and behavior since it is subject to their experiences, observations, and activities. Starting in toddlerhood, children explore and interact with the space that surrounds them, first by crawling, then by touching objects of different sizes and shapes and observing their positions and locations in space. Later on, children begin to understand that these objects exist beyond their direct experience by reasoning about them and their visual-spatial characteristics.
Cathleen Heil

Theoretical Background

Frontmatter
Chapter 2. Conceptualizing Spatial Cognition
Abstract
Children have to engage in spatial cognition when they interact with space and especially when they face spatial challenges and problems. Spatial problems “are those that have a significant amount of spatial information in the original presentation of the problem or in the way a person represents it”. As outlined in the introduction, primary children face spatial problems not only in the mathematics classroom but also in their day-to-day experience.
Cathleen Heil
Chapter 3. Understanding Spatial Abilities at Different Scales of Space
Abstract
The previous chapter claimed that scale might indirectly influence spatial behavior by affecting the way how spatial information at different scales of space is processed. In other words, when treating scale not only as a spatial but also as a psychological construct, scale might have an impact on spatial thought, on the conscious reflection on the manipulation of spatial information.
Cathleen Heil
Chapter 4. Reviewing Empirical Findings of Spatial Abilities at Different Scales of Space
Abstract
Chapter 3 described how scale affects the processing of spatial information. It identified possible similarities and qualitative differences in the cognitive processes and operations of small-scale and large-scale spatial abilities.
Cathleen Heil

Empirical Study

Frontmatter
Chapter 5. Design of the Empirical Study
Abstract
Part I presented the theoretical framework of this study. This first chapter of Part II describes the design of the empirical study. Section 5.1 specifies the general research interest of this study by presenting the research questions. Moreover, it describes the research design. Section 5.2 discusses the methodological framework and derives conditions and general methodological specifications for the design of the study. Section 5.3 presents how this study was planned to be conducted with respect to the research questions and the methodological framework.
Cathleen Heil
Chapter 6. Testing Material for Small-Scale Spatial Abilities
Abstract
One contribution of this study was to develop an age-specific paper-and-pencil test involving a set of tasks that measured the construct of small-scale spatial abilities with the two subclasses object-based transformation abilities (OB) and egocentric perspective transformation abilities (EGO).
Cathleen Heil
Chapter 7. Testing Material for Large-Scale Spatial Abilities
Abstract
Another important contribution of this study was the development of an age-specific map-based orientation test involving a set of tasks that measured the construct of large-scale spatial abilities with the two broad subclasses which are survey mapping abilities (SurveyMap) and the abilities to reason about the map-environment-self relation (MapEnvSelf) during map-based navigation in space.
Cathleen Heil
Chapter 8. Additional Testing Material
Abstract
This chapter presents the extra materials that were used in the main study. Section 8.1 describes a tabletop version of the Corsi Block Test that was administered to the children to measure individual differences in visuospatial working memory capacity. Section 8.2 presents a perspective taking test involving manipulable material, the PTSOT-C, that was used to further measure children’s abilities to perform imagined transformations of the self.
Cathleen Heil
Chapter 9. Data Collection
Abstract
The main study was conducted on the campus of Leuphana University, Lüneburg, Germany for 13 days from mid of May to mid of June 2016. The testing period was at the end of the school year, and all school grades had already been reported. Some classes were two weeks before summer break When they attended the testing day in mid of June.
Cathleen Heil

Results and Discussion

Frontmatter
Chapter 10. Children’s Small-Scale Spatial Abilities
Abstract
This chapter presents the empirical results concerning children’s small-scale spatial abilities as measured by the paper-and-pencil test proposed in Chapter Section 10.1. It presents the results concerning the quality of individual measures (Section (Section 10.1), concerning empirically separable latent abilities (Section 10.2), and the role of visuospatial working memory (Section 10.3). Section 10.4. presents the results of the measure PTSOT-C. The final Section Section 10.5 discusses the findings with respect to the literature presented in Part I.
Cathleen Heil
Chapter 11. Children’s Large-Scale Spatial Abilities
Abstract
This chapter presents the empirical results concerning children’s large-scale spatial abilities as measured by the map-based orientation test proposed in Chapter 7. It presents the results concerning the psychometrical quality of individual measures measures, about empirically separable latent abilities, and the role of visuospatial working memory. The final Section 11.4 discusses the findings with respect to the literature presented in Part I.
Cathleen Heil
Chapter 12. Relations Between Children’s Small-Scale and Large-Scale Spatial Abilities
Abstract
This chapter presents the empirical results concerning the relation between children’s small-scale spatial abilities as measured by the paper-and-pencil test and large-scale spatial abilities as measured by the map-based orientation test. In addition, it presents results concerning the role of visuospatial working memory capacity. Section 12.1 presents results of correlation and multiple regression analyses that examined possible relations between both classes of spatial abilities at the manifest level. Section 12.2 presents results of structural equation modeling analyses that examined those relations at the latent level.
Cathleen Heil
Chapter 13. Discussion, Limitations, and Implications
Abstract
Children need to process spatial information perceived in spaces of different sizes in their everyday life. Although geometry education aims to address phenomena of children’s day-to-day experiences, there has been little research on the impact of scale on children’s spatial thought. This study addressed this gap in the literature and examined the effect of scale when it comes to children’s spatial cognition in geometry education and considered to which extent small-scale spatial abilities reflect the same or a different class of spatial abilities than large-scale spatial abilities.
Cathleen Heil
Chapter 14. Conclusion
Abstract
So here I am in the very last chapter of this study. During the last five years, I have been given the chance to explore a set of cognitive abilities, which are both a fascinating and challenging research subject. While conducting research on spatial thought in primary school children, I came to realize how important these abilities are for my own life, for example when I struggled to navigate unknown territory or tried to squeeze furniture into rooms.
Cathleen Heil
Backmatter
Metadata
Title
The Impact of Scale on Children’s Spatial Thought
Author
Cathleen Heil
Copyright Year
2020
Electronic ISBN
978-3-658-32648-7
Print ISBN
978-3-658-32647-0
DOI
https://doi.org/10.1007/978-3-658-32648-7

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