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STAGES OF DEVELOPING GEOMETRIC CONCEPTS IN PRIMARY SCHOOL
PUPILS
Palvanbaeva Nigora
2nd-year student, Faculty of Primary Education
Ajiniyoz Nukus State Pedagogical Institute
Abstract:
This article explores the stages of developing geometric concepts in primary
school pupils, emphasizing the importance of age-appropriate methods, visual aids, and
hands-on activities. The study highlights the critical role of early mathematics education in
building a foundation for spatial thinking, problem-solving, and logical reasoning. As Piaget
(1952) suggests, cognitive development occurs in stages, and geometry provides a
foundation for more abstract mathematical reasoning. By understanding how children
gradually comprehend geometry, teachers can better structure lessons and learning
experiences that foster deep understanding and long-term retention.
Keywords:
Primary education, geometric concepts, geometric thinking, Piaget, van Hiele,
pedagogical approaches, visualization, analytical thinking, hands-on learning, Uzbek
pedagogy, teaching methodology, geometric shapes, mathematics education, student
development, digital tools, traditional teaching methods.
Introduction
Geometry is a fundamental branch of mathematics that begins to take shape in early
childhood education. For primary school students, geometry is not merely about shapes and
lines—it is an essential tool to develop spatial awareness, visual reasoning, and logical
thinking. As Clements & Sarama (2007) argue, early exposure to geometric concepts is
crucial for laying the groundwork for later mathematical learning. The process of learning
geometry at a young age requires carefully structured pedagogical approaches that
correspond with children's cognitive development. This paper outlines the stages through
which young learners acquire geometric understanding and proposes strategies for effective
instruction in each stage.
Theoretical Background
Piaget’s theory of cognitive development and van Hiele’s model of geometric thinking are
foundational in understanding how children learn geometry. According to Piaget, children
move from concrete operational to formal operational stages, where their abstract thinking
abilities improve (Piaget, 1952). Van Hiele identified five levels of geometric thought:
Visualization, Analysis, Informal Deduction, Deduction, and Rigor. According to van Hiele
(1986), most primary school students are at the Visualization and Analysis levels.
Recognizing these levels helps educators align their teaching with students’ cognitive
readiness.
In the context of Uzbekistan, local researchers have conducted studies on the development
of geometric thinking in primary school pupils. According to M. Tursunov (2010), primary
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school pupils in Uzbekistan also pass through similar stages in their understanding of
geometry. However, Uzbek pedagogical approaches emphasize the integration of cultural
and historical elements into the teaching of geometry. For example, Uzbek educators, like R.
Muminov (2015), argue that local educational practices often rely on hands-on learning and
visual representation, aligning with van Hiele’s concept of visualization. Muminov further
suggests that, while foreign models focus on the abstract development of geometry, in
Uzbekistan, there is a stronger emphasis on students’ engagement with geometric shapes
through tangible objects such as models of famous Uzbek architectural structures.
Furthermore, the methodological differences between Western and Uzbek pedagogical
approaches are also notable in the integration of traditional teaching tools. While foreign
models like those suggested by Clements & Sarama (2007) emphasize digital tools and
software to enhance geometric learning, in Uzbekistan, traditional tools such as geometric
sets and board activities are still widely used in classrooms. According to A. Rasulova
(2019), these traditional methods provide a more direct connection between students and
their environment, enabling a deeper and more personal understanding of geometry.
Thus, while both foreign and Uzbek pedagogical models agree on the importance of visual
aids and hands-on activities, Uzbek educators often incorporate local cultural elements into
the learning process, which provides a unique aspect to the teaching of geometry in primary
schools.
Stages of Developing Geometric Concepts
1. Recognition (Visualization)
At this stage, students recognize shapes based on their overall appearance, not their
properties. As van Hiele (1986) notes, at the Visualization level, children are able to identify
shapes like squares and circles without understanding the underlying geometric properties.
Teaching at this level should include visual aids, drawing activities, and real-life examples.
2. Description (Analysis)
Pupils begin to notice properties such as the number of sides, angles, and symmetry.
According to Clements & Sarama (2007), children’s ability to describe shapes based on
properties emerges in the early elementary years. Activities that involve sorting, classifying,
and comparing shapes are beneficial here.
3. Informal Deduction
Children start to understand relationships between shapes. For example, they can realize that
all squares are rectangles, but not all rectangles are squares. As Clements & Sarama (2007)
highlight, this understanding is crucial for developing higher-order thinking in geometry.
Introducing shape hierarchies and using diagrams helps facilitate this understanding.
4. Concrete Modeling
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Using physical objects or manipulatives, students can build and explore shapes. This hands-
on experience reinforces abstract concepts through tactile learning and helps in connecting
visual perception with geometric language. As van Hiele (1986) suggests, concrete modeling
provides the foundation for abstract geometric thinking.
5. Integration and Application
Students apply their knowledge of shapes to solve problems, such as identifying shapes in
their environment, measuring perimeters, or drawing shapes to fit given criteria. This stage
is essential for transitioning from rote learning to meaningful application. According to
NCTM (2000), problem-solving is a key skill that geometry instruction should cultivate in
young learners.
Effective Methods and Tools
Use of Visual Aids: Pictures, charts, and interactive whiteboards help students visualize
shapes and their properties.
Manipulatives: Tangrams, pattern blocks, and 3D models offer tactile experiences that make
abstract concepts concrete.
Digital Tools: Geometry software or educational apps allow dynamic interaction and
exploration.
Storytelling and Art: Integrating geometric shapes into stories or drawings engages students
and encourages creative thinking.
Games and Puzzles: These motivate learners while strengthening spatial reasoning and
shape recognition.
Conclusion
Understanding the stages of geometric concept development in primary pupils allows
educators to provide targeted instruction that aligns with their students’ cognitive abilities. A
blend of visual, tactile, and digital methods enhances geometric learning and lays the
foundation for future mathematical success. Teachers play a vital role in guiding children
through each stage, ensuring a gradual and deep understanding of geometry. As Piaget (1952)
emphasizes, early exposure to abstract thinking in mathematics paves the way for success in
later stages of education.
References
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2.
Van Hiele, P. M. (1986). Structure and Insight: A Theory of Learning in Geometry.
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3.
Tursunov, M. (2010). Geometric Thinking in Primary School Pupils: A Comparative
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