HED4813
ASSIGNMENT 2 2025
UNIQUE NO. 147511
DUE DATE: 2 SEPTEMBER 2025
,Question 1
Introduction
Jean Piaget’s theory of cognitive development has had a profound impact on
educational psychology and pedagogy worldwide, shaping how teachers understand
children’s intellectual growth. Piaget identified four universal and sequential stages of
cognitive development—sensorimotor, preoperational, concrete operational, and formal
operational—that describe how children construct knowledge and adapt to their
environment (Piaget, 1972). Each stage is characterised by distinctive ways of thinking,
reasoning, and problem-solving, which directly influence how children engage with
mathematics. In the South African context, where classrooms are diverse in terms of
language, culture, and socio-economic background, understanding Piaget’s theory
provides educators with a framework for designing appropriate, differentiated, and
developmentally sensitive mathematics instruction (Donald, Lazarus & Lolwana, 2014).
This essay critically discusses Piaget’s four stages of cognitive development, their
impact on mathematical understanding, and relevant classroom strategies. It also
reflects on the implications for curriculum design and differentiated instruction in South
African schools, where challenges such as large class sizes, resource disparities, and
multilingualism demand pedagogical flexibility.
1. Piaget’s Stages of Cognitive Development
1.1 Sensorimotor Stage (0–2 years)
Characteristics: Infants learn primarily through sensory experiences and motor
activities. Cognitive development is driven by reflexes, trial-and-error learning,
and the gradual emergence of object permanence—the understanding that
objects continue to exist even when not visible (Piaget, 1952).
Key processes: Sensory exploration, imitation, and basic cause-and-effect
reasoning.
, 1.2 Preoperational Stage (2–7 years)
Characteristics: Children develop symbolic thought, enabling them to use
words, drawings, and play to represent objects. However, their thinking is
egocentric, intuitive, and dominated by perception rather than logic (Woolfolk,
2019). They struggle with conservation tasks and reversibility.
Key processes: Rapid language development, symbolic play, and imagination.
1.3 Concrete Operational Stage (7–11 years)
Characteristics: Logical thinking emerges, but it is restricted to concrete and
tangible objects. Children grasp conservation, classification, seriation, and
reversibility. They can perform mental operations on real objects but struggle with
abstract or hypothetical concepts (Piaget, 1972).
Key processes: Improved logical reasoning, problem-solving with manipulatives,
decentration (ability to see multiple perspectives).
1.4 Formal Operational Stage (11 years onwards)
Characteristics: Learners can think abstractly, reason hypothetically, and use
deductive logic. They can manipulate symbols without concrete referents,
formulate hypotheses, and consider multiple variables simultaneously (Flavell,
1985).
Key processes: Hypothetical-deductive reasoning, abstract thought, systematic
problem-solving.
2. Application to Mathematics Learning
2.1 Sensorimotor Stage and Mathematics
At this stage, mathematics learning is indirect. Infants begin to understand basic
concepts of quantity and spatial awareness through play and interaction. For example,
grasping two blocks versus one introduces early numeracy foundations (Baroody,
2004). Object permanence supports the idea that “three apples” remain constant even if
ASSIGNMENT 2 2025
UNIQUE NO. 147511
DUE DATE: 2 SEPTEMBER 2025
,Question 1
Introduction
Jean Piaget’s theory of cognitive development has had a profound impact on
educational psychology and pedagogy worldwide, shaping how teachers understand
children’s intellectual growth. Piaget identified four universal and sequential stages of
cognitive development—sensorimotor, preoperational, concrete operational, and formal
operational—that describe how children construct knowledge and adapt to their
environment (Piaget, 1972). Each stage is characterised by distinctive ways of thinking,
reasoning, and problem-solving, which directly influence how children engage with
mathematics. In the South African context, where classrooms are diverse in terms of
language, culture, and socio-economic background, understanding Piaget’s theory
provides educators with a framework for designing appropriate, differentiated, and
developmentally sensitive mathematics instruction (Donald, Lazarus & Lolwana, 2014).
This essay critically discusses Piaget’s four stages of cognitive development, their
impact on mathematical understanding, and relevant classroom strategies. It also
reflects on the implications for curriculum design and differentiated instruction in South
African schools, where challenges such as large class sizes, resource disparities, and
multilingualism demand pedagogical flexibility.
1. Piaget’s Stages of Cognitive Development
1.1 Sensorimotor Stage (0–2 years)
Characteristics: Infants learn primarily through sensory experiences and motor
activities. Cognitive development is driven by reflexes, trial-and-error learning,
and the gradual emergence of object permanence—the understanding that
objects continue to exist even when not visible (Piaget, 1952).
Key processes: Sensory exploration, imitation, and basic cause-and-effect
reasoning.
, 1.2 Preoperational Stage (2–7 years)
Characteristics: Children develop symbolic thought, enabling them to use
words, drawings, and play to represent objects. However, their thinking is
egocentric, intuitive, and dominated by perception rather than logic (Woolfolk,
2019). They struggle with conservation tasks and reversibility.
Key processes: Rapid language development, symbolic play, and imagination.
1.3 Concrete Operational Stage (7–11 years)
Characteristics: Logical thinking emerges, but it is restricted to concrete and
tangible objects. Children grasp conservation, classification, seriation, and
reversibility. They can perform mental operations on real objects but struggle with
abstract or hypothetical concepts (Piaget, 1972).
Key processes: Improved logical reasoning, problem-solving with manipulatives,
decentration (ability to see multiple perspectives).
1.4 Formal Operational Stage (11 years onwards)
Characteristics: Learners can think abstractly, reason hypothetically, and use
deductive logic. They can manipulate symbols without concrete referents,
formulate hypotheses, and consider multiple variables simultaneously (Flavell,
1985).
Key processes: Hypothetical-deductive reasoning, abstract thought, systematic
problem-solving.
2. Application to Mathematics Learning
2.1 Sensorimotor Stage and Mathematics
At this stage, mathematics learning is indirect. Infants begin to understand basic
concepts of quantity and spatial awareness through play and interaction. For example,
grasping two blocks versus one introduces early numeracy foundations (Baroody,
2004). Object permanence supports the idea that “three apples” remain constant even if
