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
Objectives and Key Themes
This research study investigates how children learn geometry at all levels of compulsory education. The study is motivated by the researcher's personal difficulties in this area and a perceived under-representation of geometry in the mathematics curriculum. The methodology involves administering five tasks to two students at each key stage (KS1-5), analyzing the results using the Van Hiele model of geometric reasoning, and supplementing this analysis with theoretical frameworks from Vygotsky, Piaget, and Bruner, as well as relevant educational literature and research. A questionnaire was also distributed to mathematics teachers at various levels.
- Children's geometrical reasoning abilities across different age groups.
- Application of the Van Hiele model to assess geometrical understanding.
- The influence of shape orientation on children's drawings.
- Comparison of theoretical frameworks (Vygotsky, Piaget, Bruner) with empirical findings.
- Implications for classroom practice and teaching strategies.
Chapter Summaries
Introduction: This chapter introduces the research study, outlining its aim to investigate how children learn geometry across different key stages (KS1-5) within the compulsory education system. The researcher highlights their personal challenges with geometry and the possible under-representation of the subject within the mathematics curriculum as the primary motivations behind this study. The chapter lays the groundwork for the research by establishing the central question and providing a brief overview of the methodology and approach.
Literature Review: This chapter delves into existing research and theoretical frameworks related to children's learning of geometry. It will likely explore the works of prominent researchers like Vygotsky, Piaget, and Bruner, examining their theories on cognitive development and how they relate to geometrical understanding. The chapter will also synthesize findings from current educational literature and research on geometry education, providing a comprehensive overview of the existing knowledge base before the researcher's own investigation. The synthesis should set the stage for the researcher's own contributions and how they build upon existing work.
Methodology: This chapter outlines the specific methods used in the research study. It describes the design of the five tasks administered to the students, detailing the selection criteria for participants and the specific instructions given. The chapter should clearly explain how the Van Hiele model of geometric reasoning was employed for assessing the children's geometrical abilities. It will also detail the procedure for administering the questionnaire to the mathematics teachers, describing the structure of the questionnaire and the selection process for the participants. A thorough explanation of the data collection process, ensuring transparency and replicability, is expected.
Data Collection: This chapter presents the data collected during the study, which includes the children's responses to the five geometric tasks and the teachers' responses to the questionnaire. The raw data will likely be presented in a structured format, potentially with tables and visualizations. The details presented in this chapter serve as the foundation for the analysis and interpretation that follows in the next chapter. The organization and presentation should ensure clarity and ease of understanding for the reader, facilitating a smooth transition to the next stage of the analysis.
Results: This chapter presents the findings of the study, offering a clear and concise summary of the data analysis. It will likely describe the patterns and trends observed in the children's responses, using the Van Hiele model as a framework for interpreting the results. The chapter will present quantitative and qualitative data, explaining any statistically significant findings and highlighting any important insights. The results will likely show trends in geometrical ability across different age groups and discuss the prevalence of non-prototypical shape orientations in children's drawings. This chapter serves as a bridge between the raw data and the discussion that follows.
Keywords
Geometry education, Van Hiele model, geometric reasoning, children's learning, cognitive development, Vygotsky, Piaget, Bruner, mathematics curriculum, teaching strategies, shape orientation, classroom practice.
Frequently Asked Questions: Comprehensive Language Preview of Geometry Education Research
What is the overall focus of this research study?
This research study investigates how children learn geometry at all levels of compulsory education. It's motivated by the researcher's personal difficulties with geometry and a perceived under-representation of geometry in the mathematics curriculum.
What are the key objectives of the research?
The study aims to analyze children's geometrical reasoning abilities across different age groups, apply the Van Hiele model to assess geometrical understanding, examine the influence of shape orientation on children's drawings, compare theoretical frameworks (Vygotsky, Piaget, Bruner) with empirical findings, and determine implications for classroom practice and teaching strategies.
What methodology was used in this research?
The methodology involved administering five tasks to two students at each key stage (KS1-5). The results were analyzed using the Van Hiele model of geometric reasoning, supplemented by theoretical frameworks from Vygotsky, Piaget, and Bruner, and relevant educational literature. A questionnaire was also distributed to mathematics teachers.
What are the main themes explored in the study?
The study explores children's geometrical reasoning abilities, the application of the Van Hiele model, the influence of shape orientation on drawings, a comparison of theoretical frameworks with empirical findings, and implications for teaching strategies.
Which theoretical frameworks are used to inform the study?
The study utilizes the theoretical frameworks of Vygotsky, Piaget, and Bruner to understand cognitive development in relation to geometrical understanding.
What data was collected in the study?
Data collected includes children's responses to five geometric tasks and teachers' responses to a questionnaire. The raw data is presented in a structured format, potentially with tables and visualizations.
How were the results of the study analyzed?
The results were analyzed using the Van Hiele model of geometric reasoning. Quantitative and qualitative data were presented, highlighting statistically significant findings and important insights.
What are the key findings of the study (in general terms)?
The results likely show trends in geometrical ability across different age groups and discuss the prevalence of non-prototypical shape orientations in children's drawings. Specific details are found in the "Results" chapter.
What are the implications of the study for classroom practice?
The study offers implications for classroom practice and suggests improved teaching strategies based on the findings related to children's geometrical understanding and reasoning abilities.
What are the key words associated with this research?
Geometry education, Van Hiele model, geometric reasoning, children's learning, cognitive development, Vygotsky, Piaget, Bruner, mathematics curriculum, teaching strategies, shape orientation, classroom practice.
What is the structure of the research report?
The report includes an introduction, literature review, methodology, data collection, results, and discussion of results, along with a table of contents and keywords.
- Quote paper
- Sam Curran (Author), 2014, Is The Van Hiele Model Useful in Determining How Children Learn Geometry?, Munich, GRIN Verlag, https://www.grin.com/document/301019
