The aim of this study is to investigate how children learn Geometry (at all levels of compulsory education) in Mathematics.
This study was chosen because of my difficulties in the area and the possible under-representation of Geometry in the Mathematics Curriculum. Five tasks were given to two students for each Key Stage 1-5 inclusive. These were then analysed using the “Van Hiele model of Geometric” reasoning; which was used to make an assessment of children’s geometrical ability.
The study also draws on theoretical frameworks from eminent researchers like Vygotsky, Piaget and Bruner as well as engaging fully with current educational literature and research. A questionnaire on Geometry was also completed by a variety of primary, secondary and A-level mathematics teachers. It was found that geometrical ability increases with age (although young children can display sophisticated knowledge of shape) and that students mainly drew shapes of a non-prototypical orientation. This has increased my subject knowledge and enhanced my classroom practice and also may have the implication of changing other practitioners’ teaching strategies.
Table of Contents
Introduction
Literature Review
Methodology
Data Collection
Results
Discussion of results
Objective & Topics
The primary objective of this research is to investigate how children learn geometry across all levels of compulsory education, specifically evaluating the utility of the Van Hiele Model of geometric reasoning in assessing children's geometrical abilities. The study addresses the perceived under-representation of geometry in the curriculum and explores how teacher-led strategies influence pupil performance.
- Application and validation of the Van Hiele Model of geometric reasoning.
- Comparative analysis of children's geometrical ability across Key Stages 1-5.
- Investigation of prototypical vs. non-prototypical shape orientation.
- Teacher perspectives on the importance and complexity of teaching geometry.
- Influence of pedagogical strategies on students' spatial skills and geometric conceptualization.
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Literature Review
This literature review will focus on the eminent and recent literature which examines the usefulness of the Van Hiele Model in assessing children’s geometrical ability and theories of how children learn Geometry.
Piaget (1953; 1960; 1967) suggests that a child’s initial geometrical discoveries are topological; that they can recognise the boundary aspect of space and distinguish between open and closed figures from the age of 3. Piaget (1953) suggests this development seems to be formulated during the latter sub stages (tertiary, circular reactions, curiously and novelty) of the formative sensorimotor stage when a child interacts with the world around them and begins to explore the properties of new objects. Bruner (1961, p.21) reaffirms this by proposing that children learn by exploring their surroundings and physical environment.
It could be argued that Bruner (1961, p.23) however places more importance on social learning than Piaget. Vygotsky (1962; 78) implies that children learn in a social constructivist model from More Knowledgeable Others (MKOs) and their peers in a classroom environment. Chazan and Lehrer (2012) suggest this is particularly evident in an interactive classroom setting. This seems to be an underlying criticism of Piaget’s theory of cognitive development: that he fails to recognise the social aspect of learning.
Summary of Chapters
Introduction: This chapter contextualizes the research within current educational challenges, noting the potential under-representation of geometry in mathematics curricula and the researcher's personal motivation for the study.
Literature Review: This section evaluates theories regarding cognitive development and geometrical learning, with a specific focus on the Van Hiele model, Piagetian stages, and social constructivist approaches.
Methodology: The chapter outlines the researcher’s 'peflective' paradigm, utilizing a mixed-methods approach that combines positivist testing with reflective practitioner research.
Data Collection: This section details the systematic sampling of 10 students across Key Stages 1-5 and the administration of five geometrical tasks alongside a teacher questionnaire.
Results: The chapter presents quantitative data derived from the five tasks, including assessments based on Van Hiele levels and statistical analyses of the teacher questionnaire.
Discussion of results: This section interprets the findings, highlighting the pervasive influence of prototypical orientations and discussing the implications for teaching strategies and the practical utility of the Van Hiele model.
Keywords
Geometry, Van Hiele Model, Mathematical Education, Spatial Awareness, Prototypical Images, Cognitive Development, Action Research, Primary Education, Secondary Education, Pedagogical Strategies, Geometric Reasoning, Euclidean Geometry, Teaching Methods, Curriculum Reform, Constructivism.
Frequently Asked Questions
What is the core focus of this research study?
The study examines how children learn geometry throughout compulsory education and assesses whether the Van Hiele Model is a reliable framework for evaluating their geometrical reasoning.
Which key topics does the research explore?
It covers geometric development stages, the influence of teacher-led instruction, the impact of prototypical shape representation on learning, and compares geometric abilities across different student age groups.
What is the primary research question?
The central question is whether the Van Hiele Model of geometric reasoning is useful for determining and assessing how children learn geometry.
What scientific methods were employed?
The author used a mixed-methods approach, combining a positivist paradigm for testing children's geometric ability with a reflective, practitioner-based qualitative analysis of teaching practices and teacher perceptions.
What is covered in the main section of the paper?
The main part of the paper details the theoretical framework, the methodology of the student tasks and teacher questionnaires, a presentation of the resulting data, and a critical discussion of the results in relation to existing literature.
Which keywords characterize this work?
Key terms include Geometry, Van Hiele Model, Spatial Awareness, Cognitive Development, Action Research, and Pedagogical Strategies.
How does the "prototypical orientation" of shapes affect student learning?
The study found that students often struggle to recognize shapes that are not in their typical, teacher-taught orientation, suggesting that current teaching practices may unintentionally limit students' flexible understanding of geometric properties.
What conclusion did the author reach regarding the Van Hiele Model?
The author concludes that the model is a fairly reliable assessment tool that correlates well with the observed geometric performance of students, although it may need to be applied flexibly to account for individual variations in ability.
- Arbeit zitieren
- Sam Curran (Autor:in), 2014, Is The Van Hiele Model Useful in Determining How Children Learn Geometry?, München, GRIN Verlag, https://www.grin.com/document/301019
