UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Education
⋄
ASSESSMENT 02
Semester 1, 2026
⋄
Module Code: OPM1501
Module Name: Orientation to Intermediate Phase Mathe-
matics
Assignment No.: 02
Due Date: 5 June 2026
Semester: Semester 1, 2026
Unique Number: 116421
Submitted in partial fulfilment of the requirements for OPM1501
at the University of South Africa.
,UNISA | OPM1501 Assignment 02 – 2026
Question 1: Moving Beyond Traditional Mathematics Teaching
1.1 Critical Essay: Teaching Measurement in the Intermediate Phase
Introduction
The idea that teachers should stop relying on traditional methods in favour of approaches
that foster genuine engagement is one that deserves more than surface agreement. It asks
teachers to rethink what learning actually is, and to be honest about what has not been work-
ing. In South Africa, where Intermediate Phase learners continue to perform poorly in math-
ematics assessments, this question carries real urgency. At its core, the debate is between
two competing theories of how knowledge is formed: behaviourism, which held the field for
much of the twentieth century, and constructivism, which has since emerged as the more
defensible alternative.
Behaviourism versus Constructivism: Two Different Views of the Learner
Behaviourism positions the teacher as the source of knowledge and the learner as a passive
receiver. Learning, under this view, is a matter of stimulus and response: the teacher demon-
strates a procedure, the learner repeats it, and correct repetition is rewarded. In a traditional
Grade 5 measurement lesson, this might look like the teacher writing the formula for perime-
ter on the board, working through two examples, and then issuing twenty similar sums as
consolidation. The learners who remember the formula perform well; those who do not are
marked wrong and left behind. There is no investigation, no discussion, no connection to lived
experience.
The problem with this model is not that it produces no results at all. Rote repetition does
embed certain facts. The deeper problem is that it produces fragile knowledge. As Lerman
(1989, cited in Lerman, 1989) observed, traditional mathematics teaching centred on formula
memorisation is insufficient for promoting lasting conceptual understanding. Learners who
have memorised the formula for area may still be unable to recognise an area problem in a
different context, because they were never asked to understand what area means.
Constructivism offers a fundamentally different picture. Drawing on the work of Piaget and
Vygotsky, it argues that learners do not receive knowledge; they build it. Each new concept
must be connected to what the learner already knows, and that connection is made through
Page 1 of 21
, UNISA | OPM1501 Assignment 02 – 2026
active engagement, problem-solving, and reflection (Bada and Olusegun, 2015). Vygotsky
adds the social dimension: learning happens through interaction with more capable peers
and teachers within the learner’s Zone of Proximal Development. This means that conversa-
tion, collaborative tasks, and carefully scaffolded questions are not luxuries in a mathematics
classroom; they are the actual mechanism of learning.
Key Distinction
Behaviourism treats learning as passive reception, rewarding correct repetition of
demonstrated procedures.
Constructivism treats learning as active construction, where the learner builds new
understanding by connecting it to prior knowledge through exploration and dialogue.
Applying Constructivism to the Teaching of Measurement in Grade 5
Measurement is one of the most naturally constructivist-friendly topics in the Intermediate
Phase curriculum. It connects directly to real objects, real spaces, and real decisions. A Grade
5 learner can hold a ruler, walk the perimeter of the classroom, compare the area of two book
covers, or estimate the capacity of a water bottle. This is not possible with abstract number
theory. The tragedy is that most learners encounter measurement as a set of formulas to be
copied and applied, which strips the topic of precisely the qualities that make it accessible.
A constructivist lesson on measuring perimeter would look quite different. The teacher might
begin by placing the learners in groups and handing each group a different irregular shape
cut from cardboard. Without giving any formula, the teacher asks: “How would you find the
total distance around your shape?” Some groups will use string, others will count tiles, and
others will attempt to add the side lengths. This is productive struggle. The teacher circulates,
asks probing questions, and withholds the answer. After the exploration, groups share their
strategies. The class arrives collectively at the idea of adding all side lengths, and the formal
notation follows as a record of what they already discovered. This is what research on con-
structivist teaching in measurement describes as effective: integrating real-world contexts,
hands-on activities, and group work to build understanding rather than transmit it (Ahmad et
al., 2020).
I remember a Grade 6 lesson in my own schooling where the teacher showed us how to calcu-
late the area of a rectangle, wrote the formula on the board, and gave us thirty practice sums.
I could do those sums by the end of the lesson. A week later, when we encountered a word
Page 2 of 21
College of Education
⋄
ASSESSMENT 02
Semester 1, 2026
⋄
Module Code: OPM1501
Module Name: Orientation to Intermediate Phase Mathe-
matics
Assignment No.: 02
Due Date: 5 June 2026
Semester: Semester 1, 2026
Unique Number: 116421
Submitted in partial fulfilment of the requirements for OPM1501
at the University of South Africa.
,UNISA | OPM1501 Assignment 02 – 2026
Question 1: Moving Beyond Traditional Mathematics Teaching
1.1 Critical Essay: Teaching Measurement in the Intermediate Phase
Introduction
The idea that teachers should stop relying on traditional methods in favour of approaches
that foster genuine engagement is one that deserves more than surface agreement. It asks
teachers to rethink what learning actually is, and to be honest about what has not been work-
ing. In South Africa, where Intermediate Phase learners continue to perform poorly in math-
ematics assessments, this question carries real urgency. At its core, the debate is between
two competing theories of how knowledge is formed: behaviourism, which held the field for
much of the twentieth century, and constructivism, which has since emerged as the more
defensible alternative.
Behaviourism versus Constructivism: Two Different Views of the Learner
Behaviourism positions the teacher as the source of knowledge and the learner as a passive
receiver. Learning, under this view, is a matter of stimulus and response: the teacher demon-
strates a procedure, the learner repeats it, and correct repetition is rewarded. In a traditional
Grade 5 measurement lesson, this might look like the teacher writing the formula for perime-
ter on the board, working through two examples, and then issuing twenty similar sums as
consolidation. The learners who remember the formula perform well; those who do not are
marked wrong and left behind. There is no investigation, no discussion, no connection to lived
experience.
The problem with this model is not that it produces no results at all. Rote repetition does
embed certain facts. The deeper problem is that it produces fragile knowledge. As Lerman
(1989, cited in Lerman, 1989) observed, traditional mathematics teaching centred on formula
memorisation is insufficient for promoting lasting conceptual understanding. Learners who
have memorised the formula for area may still be unable to recognise an area problem in a
different context, because they were never asked to understand what area means.
Constructivism offers a fundamentally different picture. Drawing on the work of Piaget and
Vygotsky, it argues that learners do not receive knowledge; they build it. Each new concept
must be connected to what the learner already knows, and that connection is made through
Page 1 of 21
, UNISA | OPM1501 Assignment 02 – 2026
active engagement, problem-solving, and reflection (Bada and Olusegun, 2015). Vygotsky
adds the social dimension: learning happens through interaction with more capable peers
and teachers within the learner’s Zone of Proximal Development. This means that conversa-
tion, collaborative tasks, and carefully scaffolded questions are not luxuries in a mathematics
classroom; they are the actual mechanism of learning.
Key Distinction
Behaviourism treats learning as passive reception, rewarding correct repetition of
demonstrated procedures.
Constructivism treats learning as active construction, where the learner builds new
understanding by connecting it to prior knowledge through exploration and dialogue.
Applying Constructivism to the Teaching of Measurement in Grade 5
Measurement is one of the most naturally constructivist-friendly topics in the Intermediate
Phase curriculum. It connects directly to real objects, real spaces, and real decisions. A Grade
5 learner can hold a ruler, walk the perimeter of the classroom, compare the area of two book
covers, or estimate the capacity of a water bottle. This is not possible with abstract number
theory. The tragedy is that most learners encounter measurement as a set of formulas to be
copied and applied, which strips the topic of precisely the qualities that make it accessible.
A constructivist lesson on measuring perimeter would look quite different. The teacher might
begin by placing the learners in groups and handing each group a different irregular shape
cut from cardboard. Without giving any formula, the teacher asks: “How would you find the
total distance around your shape?” Some groups will use string, others will count tiles, and
others will attempt to add the side lengths. This is productive struggle. The teacher circulates,
asks probing questions, and withholds the answer. After the exploration, groups share their
strategies. The class arrives collectively at the idea of adding all side lengths, and the formal
notation follows as a record of what they already discovered. This is what research on con-
structivist teaching in measurement describes as effective: integrating real-world contexts,
hands-on activities, and group work to build understanding rather than transmit it (Ahmad et
al., 2020).
I remember a Grade 6 lesson in my own schooling where the teacher showed us how to calcu-
late the area of a rectangle, wrote the formula on the board, and gave us thirty practice sums.
I could do those sums by the end of the lesson. A week later, when we encountered a word
Page 2 of 21
