UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Education / Department of Early Childhood Education and Development
⋄
ASSESSMENT 2 – 2026
Emergent Mathematics – EMA1501 – Year Module
⋄
Module Code: EMA1501
Module Name: Emergent Mathematics
Assignment No.: Assessment 2
Due Date: June 2026
Semester: Year Module – 2026
Submitted in partial fulfilment of the requirements for EMA1501
at the University of South Africa.
,UNISA | EMA1501 Emergent Mathematics – Assessment 2
Question 1: Mathematical Concepts in Playground Activities
Case Study
The Dolphin class went to the playground for outdoor playtime. The teacher, Ms
Mokoena, took all 20 learners to the playground. She had a basket with toys. Inside
the basket were 5 balls, 10 skipping ropes, 5 medium tins and 20 wooden blocks. The
children enjoyed playing outdoor games in groups of 5. They had to pick up five differ-
ent sizes of the wooden blocks, put them inside the tin, run with it, jump over all 10
skipping ropes on the ground and put one block next to each group member. They then
had to go back to the starting point by jumping and counting backwards, taking one ball
and throwing it to each group member three times. The children each rotated the activity
in each group.
Question 1.1: Identify Five Mathematical Concepts from the Playground Activity (5
marks)
Q: Analyse any five mathematical concepts that can be developed from the playground activi-
ties.
A:
The following five mathematical concepts emerge directly from the Dolphin class activity
described by Ms Mokoena.
1. Counting and Number Sense. The activity calls on children to count objects in con-
crete, physical ways: 20 learners, 10 skipping ropes, 5 blocks, and throwing the ball three
times each. This direct encounter with number is the foundation of number sense in emer-
gent mathematics (Geist, 2009).
2. Seriation and Ordering (Size Comparison). Learners must pick up five wooden
blocks of different sizes and arrange them. This sorting by size – from smallest to largest
or vice versa – is seriation, a pre-number skill tied to logical reasoning (Clements, Sarama
and DiBiase, 2004).
3. Spatial Sense and Position. Jumping over the ropes, running with the tin, and placing
blocks next to each group member all require children to understand where objects are
Page 1 of 16
,UNISA | EMA1501 Emergent Mathematics – Assessment 2
relative to their bodies and to one another. This concept falls under Space and Shape in
the CAPS Grades R–3 mathematics curriculum (Department of Basic Education, 2011).
4. One-to-One Correspondence. Placing one block next to each group member – one
child, one block – directly practises one-to-one correspondence. This is the most basic
precursor to counting and number conservation (Clements et al., 2004).
5. Backward Counting and Number Patterns. Returning to the starting point by
jumping and counting backwards introduces reverse number sequences. Backward count-
ing builds an understanding of subtraction and number order, which are central to early
arithmetic reasoning (Johnston and Bull, 2022).
Page 2 of 16
,UNISA | EMA1501 Emergent Mathematics – Assessment 2
Question 1.2: Contribution to Logical Thinking in Emergent Mathematics (20 marks)
Q: Explain how each of the mathematical concepts you identified from the case study will
contribute towards logical thinking in emergent mathematics.
A:
Logical thinking in early childhood mathematics is not a separate skill that teachers introduce
in isolation. It grows out of the child’s direct experience with concrete objects, sequences, and
relationships (Inhelder and Piaget, 1958). Each concept from the Dolphin class activity feeds
this growth in a specific, traceable way.
1. Counting and Number Sense
When Ms Mokoena’s learners count the ropes they jump over, count how many times they
throw the ball, or recall that there are 20 children in the class, they are doing far more than
reciting a sequence. They are building cardinality – the understanding that the last number
counted tells you the total. This is a logical operation. A child who understands cardinality
can reason about quantity: "I have thrown the ball twice; I need one more throw." That rea-
soning – recognising a gap between what is and what should be – is the beginning of logical
mathematical thinking (Geist, 2009).
The activity provides the ideal context because counting is embedded in a physical, purposeful
task. Research consistently shows that young children develop number sense more reliably
through real experiences than through drill (Clements et al., 2004). In the Dolphin class, the
counting is not abstract; it is tied to the movement of bodies and objects.
2. Seriation and Ordering (Size Comparison)
Choosing five blocks of different sizes and placing them in order requires a child to make re-
peated comparisons. To seriate correctly, the child must hold one comparison in mind ("this
block is bigger than the previous one") while simultaneously checking the next ("but is it
smaller than the next?"). Piaget identified seriation as a direct marker of concrete operational
thinking (Inhelder and Piaget, 1958). It demands the child to coordinate two mental relation-
ships at once, which is exactly what logical reasoning asks.
In the playground context, this happens through the hands and the body. Learners grip the
Page 3 of 16
, UNISA | EMA1501 Emergent Mathematics – Assessment 2
blocks, feel their weight and size, and decide. That sensory engagement is critical because
emergent mathematics must be taught through physical experience before abstract representa-
tion (Geist, 2009). A child who can seriate blocks has the same mental machinery needed later
to order numbers on a number line or arrange fractions from smallest to largest.
3. Spatial Sense and Position
Spatial reasoning is not merely knowing where something is. It is the ability to mentally
track the relationships between objects as those objects – and the child – move through space.
When a learner jumps over ten ropes laid on the ground, the child’s brain is continuously up-
dating a spatial map: how far to the next rope, where to land, how to angle the body. This
mental updating is a form of logical reasoning about dynamic relationships (van Oers, 2010).
The CAPS mathematics curriculum for Grade R places position, direction, and spatial orien-
tation within the Space and Shape content area because these skills underpin later geometric
understanding (Department of Basic Education, 2011). A child who develops strong spatial
reasoning can later interpret diagrams, read maps, understand symmetry, and visualise the
transformation of shapes. All of that rests on the same mental skill being practised when the
Dolphin class jumps over ropes.
4. One-to-One Correspondence
When a learner picks up one block and walks to one group member, places it down, then
moves to the next member and does the same, the child is performing a logical matching
operation. One-to-one correspondence is the logical foundation of counting itself: each object
in one set is paired with exactly one object in another set, and nothing is left over or doubled
up (Clements et al., 2004).
This matters for logical thinking because it teaches the child that quantities can be compared
without counting. If every child has a block next to them, and there are no blocks left over,
the sets are equal. That is a logical deduction – not a guess. A child who grasps this can later
understand equivalence in arithmetic (two groups of the same size are equal) and, much later,
the logic behind algebraic equations. The playground activity builds this without the child
even knowing it is mathematics.
Page 4 of 16
College of Education / Department of Early Childhood Education and Development
⋄
ASSESSMENT 2 – 2026
Emergent Mathematics – EMA1501 – Year Module
⋄
Module Code: EMA1501
Module Name: Emergent Mathematics
Assignment No.: Assessment 2
Due Date: June 2026
Semester: Year Module – 2026
Submitted in partial fulfilment of the requirements for EMA1501
at the University of South Africa.
,UNISA | EMA1501 Emergent Mathematics – Assessment 2
Question 1: Mathematical Concepts in Playground Activities
Case Study
The Dolphin class went to the playground for outdoor playtime. The teacher, Ms
Mokoena, took all 20 learners to the playground. She had a basket with toys. Inside
the basket were 5 balls, 10 skipping ropes, 5 medium tins and 20 wooden blocks. The
children enjoyed playing outdoor games in groups of 5. They had to pick up five differ-
ent sizes of the wooden blocks, put them inside the tin, run with it, jump over all 10
skipping ropes on the ground and put one block next to each group member. They then
had to go back to the starting point by jumping and counting backwards, taking one ball
and throwing it to each group member three times. The children each rotated the activity
in each group.
Question 1.1: Identify Five Mathematical Concepts from the Playground Activity (5
marks)
Q: Analyse any five mathematical concepts that can be developed from the playground activi-
ties.
A:
The following five mathematical concepts emerge directly from the Dolphin class activity
described by Ms Mokoena.
1. Counting and Number Sense. The activity calls on children to count objects in con-
crete, physical ways: 20 learners, 10 skipping ropes, 5 blocks, and throwing the ball three
times each. This direct encounter with number is the foundation of number sense in emer-
gent mathematics (Geist, 2009).
2. Seriation and Ordering (Size Comparison). Learners must pick up five wooden
blocks of different sizes and arrange them. This sorting by size – from smallest to largest
or vice versa – is seriation, a pre-number skill tied to logical reasoning (Clements, Sarama
and DiBiase, 2004).
3. Spatial Sense and Position. Jumping over the ropes, running with the tin, and placing
blocks next to each group member all require children to understand where objects are
Page 1 of 16
,UNISA | EMA1501 Emergent Mathematics – Assessment 2
relative to their bodies and to one another. This concept falls under Space and Shape in
the CAPS Grades R–3 mathematics curriculum (Department of Basic Education, 2011).
4. One-to-One Correspondence. Placing one block next to each group member – one
child, one block – directly practises one-to-one correspondence. This is the most basic
precursor to counting and number conservation (Clements et al., 2004).
5. Backward Counting and Number Patterns. Returning to the starting point by
jumping and counting backwards introduces reverse number sequences. Backward count-
ing builds an understanding of subtraction and number order, which are central to early
arithmetic reasoning (Johnston and Bull, 2022).
Page 2 of 16
,UNISA | EMA1501 Emergent Mathematics – Assessment 2
Question 1.2: Contribution to Logical Thinking in Emergent Mathematics (20 marks)
Q: Explain how each of the mathematical concepts you identified from the case study will
contribute towards logical thinking in emergent mathematics.
A:
Logical thinking in early childhood mathematics is not a separate skill that teachers introduce
in isolation. It grows out of the child’s direct experience with concrete objects, sequences, and
relationships (Inhelder and Piaget, 1958). Each concept from the Dolphin class activity feeds
this growth in a specific, traceable way.
1. Counting and Number Sense
When Ms Mokoena’s learners count the ropes they jump over, count how many times they
throw the ball, or recall that there are 20 children in the class, they are doing far more than
reciting a sequence. They are building cardinality – the understanding that the last number
counted tells you the total. This is a logical operation. A child who understands cardinality
can reason about quantity: "I have thrown the ball twice; I need one more throw." That rea-
soning – recognising a gap between what is and what should be – is the beginning of logical
mathematical thinking (Geist, 2009).
The activity provides the ideal context because counting is embedded in a physical, purposeful
task. Research consistently shows that young children develop number sense more reliably
through real experiences than through drill (Clements et al., 2004). In the Dolphin class, the
counting is not abstract; it is tied to the movement of bodies and objects.
2. Seriation and Ordering (Size Comparison)
Choosing five blocks of different sizes and placing them in order requires a child to make re-
peated comparisons. To seriate correctly, the child must hold one comparison in mind ("this
block is bigger than the previous one") while simultaneously checking the next ("but is it
smaller than the next?"). Piaget identified seriation as a direct marker of concrete operational
thinking (Inhelder and Piaget, 1958). It demands the child to coordinate two mental relation-
ships at once, which is exactly what logical reasoning asks.
In the playground context, this happens through the hands and the body. Learners grip the
Page 3 of 16
, UNISA | EMA1501 Emergent Mathematics – Assessment 2
blocks, feel their weight and size, and decide. That sensory engagement is critical because
emergent mathematics must be taught through physical experience before abstract representa-
tion (Geist, 2009). A child who can seriate blocks has the same mental machinery needed later
to order numbers on a number line or arrange fractions from smallest to largest.
3. Spatial Sense and Position
Spatial reasoning is not merely knowing where something is. It is the ability to mentally
track the relationships between objects as those objects – and the child – move through space.
When a learner jumps over ten ropes laid on the ground, the child’s brain is continuously up-
dating a spatial map: how far to the next rope, where to land, how to angle the body. This
mental updating is a form of logical reasoning about dynamic relationships (van Oers, 2010).
The CAPS mathematics curriculum for Grade R places position, direction, and spatial orien-
tation within the Space and Shape content area because these skills underpin later geometric
understanding (Department of Basic Education, 2011). A child who develops strong spatial
reasoning can later interpret diagrams, read maps, understand symmetry, and visualise the
transformation of shapes. All of that rests on the same mental skill being practised when the
Dolphin class jumps over ropes.
4. One-to-One Correspondence
When a learner picks up one block and walks to one group member, places it down, then
moves to the next member and does the same, the child is performing a logical matching
operation. One-to-one correspondence is the logical foundation of counting itself: each object
in one set is paired with exactly one object in another set, and nothing is left over or doubled
up (Clements et al., 2004).
This matters for logical thinking because it teaches the child that quantities can be compared
without counting. If every child has a block next to them, and there are no blocks left over,
the sets are equal. That is a logical deduction – not a guess. A child who grasps this can later
understand equivalence in arithmetic (two groups of the same size are equal) and, much later,
the logic behind algebraic equations. The playground activity builds this without the child
even knowing it is mathematics.
Page 4 of 16
