UNIVERSITY OF SOUTH AFRICA
College of Education
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
OPM1501: Orientation to Inter-
mediate Phase Mathematics
Assessment 02 — Semester 1, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
OPM1501
Module Code:
Orientation to Intermediate Phase Mathe-
Module Name:
matics
Assessment 02
Assignment:
116421
Unique Number:
5 June 2026
Due Date:
100
Total Marks:
Submitted in partial fulfilment of the requirements for OPM1501 — UNISA 2026
,UNISA | OPM1501 Assessment 02 – 2026
Question 1: Traditional vs. Constructivist Mathematics Teaching
1.1 Critical Essay: Moving Beyond Traditional Teaching Methods in the Intermediate Phase (Grade
5 Measurement)
Introduction
The teaching of mathematics in South African schools has long been dominated by approaches
that centre the teacher as the sole authority and treat learners as passive receivers of infor-
mation. This essay argues that such approaches are no longer sufficient and that mathemat-
ics teachers, particularly in the Intermediate Phase, must shift toward constructivist methods
that promote genuine engagement and meaningful learning. The focus here is on the teach-
ing and learning of measurement in Grade 5, with reference to personal school experiences,
curriculum documents, and scholarly literature.
Behaviourism and Its Limitations
Behaviourism, as a learning theory, holds that knowledge is transmitted from teacher to learner
through reinforcement and conditioning (Hassad, 2011). In the mathematics classroom, this
translates to the teacher demonstrating a procedure, learners copying it, and assessment
confirming whether the procedure was memorised correctly. During my own Grade 5 school-
ing experience, the teaching of measurement followed exactly this pattern. The teacher would
write a conversion formula on the board, for instance 1 km = 1 000 m, and learners would drill
it through repetitive exercises. There was no discussion about why the metric system works
the way it does, no measuring of actual objects, and certainly no room for asking questions.
The result was that many of us could pass a worksheet on conversions yet had no sense of
what a kilometre actually felt like in real life.
This experience aligns with what researchers have documented at scale. Sibanda (2021)
found that South African Intermediate Phase mathematics teachers frequently gave learn-
ers tests rather than investigative tasks, and that cooperative learning, as required by the
Curriculum and Assessment Policy Statement (CAPS), was largely absent. The behaviourist
tendency to measure output without nurturing understanding is, in many South African class-
rooms, still the default.
Constructivism as an Alternative Paradigm
Constructivism, by contrast, holds that learners actively build knowledge through experience
Page 2 of 24
, UNISA | OPM1501 Assessment 02 – 2026
and reflection rather than receiving it passively (Lerman, 1989). Jean Piaget’s cognitive con-
structivism emphasises that children construct understanding through direct interaction with
their environment, while Vygotsky’s social constructivism adds that learning is shaped by
dialogue and collaboration with peers and more knowledgeable others (Sibanda, 2021). To-
gether, these perspectives suggest that mathematics classrooms should be spaces of active
inquiry, discussion, and problem-solving.
The practical implications are significant. Siemon et al. (2013:111) describe the shift in the
teacher’s role this way: rather than being the sole source of information, the teacher becomes
a member of the knowledge-building community of the classroom, asking provocative ques-
tions and modelling problem-solving. This is a fundamentally different relationship between
teacher, learner, and content.
Key Distinction
Behaviourism vs. Constructivism in a Measurement Lesson: Under a behaviourist
approach, a Grade 5 teacher writes “1 m = 100 cm” on the board and drills conversions.
Under a constructivist approach, learners use rulers to measure classroom objects,
record their findings, and discuss patterns before the teacher introduces formal nota-
tion. The content is the same; the depth of understanding is not.
Applying Constructivism in Grade 5 Measurement
In CAPS, measurement in Grade 5 covers length, mass, capacity, area, and perimeter, all of
which lend themselves naturally to hands-on investigation. A constructivist measurement les-
son might begin with the teacher posing a real problem: “We want to tile the classroom floor.
How many tiles will we need?” Learners would work in groups, estimating and then measur-
ing the dimensions of the floor using metre sticks, recording in centimetres and metres, and
negotiating what “area” means before any formal definition is introduced.
This approach embodies two strategies that are well supported by research. First, the use of
concrete manipulatives and real-world contexts. When learners measure actual objects rather
than abstract numbers on a page, they develop what Siemon et al. (2013) call “measurement
sense”, an intuitive feel for quantity that rote learning cannot produce. Second, collaborative
problem-solving, which reflects Vygotsky’s zone of proximal development: learners working
just beyond their current ability level, with peer support, make connections they would not
make alone (Sibanda, 2021).
I witnessed this contrast as a learner. A relief teacher once brought a set of scales into class
Page 3 of 24
College of Education
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
OPM1501: Orientation to Inter-
mediate Phase Mathematics
Assessment 02 — Semester 1, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
OPM1501
Module Code:
Orientation to Intermediate Phase Mathe-
Module Name:
matics
Assessment 02
Assignment:
116421
Unique Number:
5 June 2026
Due Date:
100
Total Marks:
Submitted in partial fulfilment of the requirements for OPM1501 — UNISA 2026
,UNISA | OPM1501 Assessment 02 – 2026
Question 1: Traditional vs. Constructivist Mathematics Teaching
1.1 Critical Essay: Moving Beyond Traditional Teaching Methods in the Intermediate Phase (Grade
5 Measurement)
Introduction
The teaching of mathematics in South African schools has long been dominated by approaches
that centre the teacher as the sole authority and treat learners as passive receivers of infor-
mation. This essay argues that such approaches are no longer sufficient and that mathemat-
ics teachers, particularly in the Intermediate Phase, must shift toward constructivist methods
that promote genuine engagement and meaningful learning. The focus here is on the teach-
ing and learning of measurement in Grade 5, with reference to personal school experiences,
curriculum documents, and scholarly literature.
Behaviourism and Its Limitations
Behaviourism, as a learning theory, holds that knowledge is transmitted from teacher to learner
through reinforcement and conditioning (Hassad, 2011). In the mathematics classroom, this
translates to the teacher demonstrating a procedure, learners copying it, and assessment
confirming whether the procedure was memorised correctly. During my own Grade 5 school-
ing experience, the teaching of measurement followed exactly this pattern. The teacher would
write a conversion formula on the board, for instance 1 km = 1 000 m, and learners would drill
it through repetitive exercises. There was no discussion about why the metric system works
the way it does, no measuring of actual objects, and certainly no room for asking questions.
The result was that many of us could pass a worksheet on conversions yet had no sense of
what a kilometre actually felt like in real life.
This experience aligns with what researchers have documented at scale. Sibanda (2021)
found that South African Intermediate Phase mathematics teachers frequently gave learn-
ers tests rather than investigative tasks, and that cooperative learning, as required by the
Curriculum and Assessment Policy Statement (CAPS), was largely absent. The behaviourist
tendency to measure output without nurturing understanding is, in many South African class-
rooms, still the default.
Constructivism as an Alternative Paradigm
Constructivism, by contrast, holds that learners actively build knowledge through experience
Page 2 of 24
, UNISA | OPM1501 Assessment 02 – 2026
and reflection rather than receiving it passively (Lerman, 1989). Jean Piaget’s cognitive con-
structivism emphasises that children construct understanding through direct interaction with
their environment, while Vygotsky’s social constructivism adds that learning is shaped by
dialogue and collaboration with peers and more knowledgeable others (Sibanda, 2021). To-
gether, these perspectives suggest that mathematics classrooms should be spaces of active
inquiry, discussion, and problem-solving.
The practical implications are significant. Siemon et al. (2013:111) describe the shift in the
teacher’s role this way: rather than being the sole source of information, the teacher becomes
a member of the knowledge-building community of the classroom, asking provocative ques-
tions and modelling problem-solving. This is a fundamentally different relationship between
teacher, learner, and content.
Key Distinction
Behaviourism vs. Constructivism in a Measurement Lesson: Under a behaviourist
approach, a Grade 5 teacher writes “1 m = 100 cm” on the board and drills conversions.
Under a constructivist approach, learners use rulers to measure classroom objects,
record their findings, and discuss patterns before the teacher introduces formal nota-
tion. The content is the same; the depth of understanding is not.
Applying Constructivism in Grade 5 Measurement
In CAPS, measurement in Grade 5 covers length, mass, capacity, area, and perimeter, all of
which lend themselves naturally to hands-on investigation. A constructivist measurement les-
son might begin with the teacher posing a real problem: “We want to tile the classroom floor.
How many tiles will we need?” Learners would work in groups, estimating and then measur-
ing the dimensions of the floor using metre sticks, recording in centimetres and metres, and
negotiating what “area” means before any formal definition is introduced.
This approach embodies two strategies that are well supported by research. First, the use of
concrete manipulatives and real-world contexts. When learners measure actual objects rather
than abstract numbers on a page, they develop what Siemon et al. (2013) call “measurement
sense”, an intuitive feel for quantity that rote learning cannot produce. Second, collaborative
problem-solving, which reflects Vygotsky’s zone of proximal development: learners working
just beyond their current ability level, with peer support, make connections they would not
make alone (Sibanda, 2021).
I witnessed this contrast as a learner. A relief teacher once brought a set of scales into class
Page 3 of 24
