, PLEASE USE THIS DOCUMENT AS A GUIDE ONLY
Question 1
1. In OPM1501, we emphasise that Mathematics teachers should stop relying on traditional
teaching methods and adopt approaches that will foster learner engagement and meaningful
learning experiences.
1.1. Write a 1000-word essay in which you critically demonstrate your understanding of the
above statement. Focus on the teaching and learning of measurement in any grade in the
Intermediate Phase.
Moving Beyond Traditional Teaching – A Constructivist Approach to Measurement in the
Intermediate Phase
The statement that mathematics teachers should abandon traditional teaching methods in favour of
approaches that foster learner engagement and meaningful learning is not merely a pedagogical
suggestion; it is a necessity for developing mathematical proficiency. The OPM1501 study guide
explicitly critiques the traditional view where “the teacher ‘tells’ learners about or explains a
mathematical concept… Learners then practice the method and rely upon the teacher to tell them the
correct answers” (OPM1501, 2020: 2). This essay critically demonstrates my understanding of this
shift, focusing on the teaching and learning of measurement in the Intermediate Phase. By
juxtaposing constructivism with behaviourism and applying constructivist principles to measurement,
I will argue that only through active engagement can learners truly understand measurable attributes,
rather than merely memorising formulas.
Description of Constructivism vs. Behaviourism and Practical Implications
To understand the shift, one must first contrast two learning theories: behaviourism and
constructivism. Behaviourism, which underpins traditional “teach-by-telling” approaches, views the
learner as a passive recipient. Knowledge is transmitted from teacher to student, who is expected to
reproduce it accurately. Learning is measured by observable changes in behaviour, such as correctly
performing a routine algorithm. The study guide warns that this approach “produces a
follow-the-rules, computation-driven, answer-oriented view of mathematics” (OPM1501, 2020: 2).
In a behaviourist measurement lesson, a teacher would state, “The area of a rectangle is length times
breadth,” write the formula on the board, and have learners complete 20 similar problems. The focus
is on procedural fluency and correct answers, not understanding why the formula works.
In contrast, constructivism, based largely on Piaget’s work, posits that learners are “creators of their
own knowledge” (OPM1501, 2020: 4). Knowledge cannot be passively absorbed; it must be actively
constructed by integrating new experiences into existing mental schemas. Two key processes are
assimilation (using an existing schema to understand a new experience) and accommodation
(altering existing schemas when new ideas do not fit) (OPM1501, 2020: 4-5). A constructivist
teacher facilitates exploration, encourages conjecture, and values the process over the final answer.
The practical implications are profound: lessons must begin where the learners are, use hands-on
materials, promote discussion, and present problems before teaching rules. The teacher’s role shifts
from “sage on the stage” to “guide on the side,” asking thought-provoking questions rather than
providing immediate solutions (OPM1501, 2020: 23-24).
Question 1
1. In OPM1501, we emphasise that Mathematics teachers should stop relying on traditional
teaching methods and adopt approaches that will foster learner engagement and meaningful
learning experiences.
1.1. Write a 1000-word essay in which you critically demonstrate your understanding of the
above statement. Focus on the teaching and learning of measurement in any grade in the
Intermediate Phase.
Moving Beyond Traditional Teaching – A Constructivist Approach to Measurement in the
Intermediate Phase
The statement that mathematics teachers should abandon traditional teaching methods in favour of
approaches that foster learner engagement and meaningful learning is not merely a pedagogical
suggestion; it is a necessity for developing mathematical proficiency. The OPM1501 study guide
explicitly critiques the traditional view where “the teacher ‘tells’ learners about or explains a
mathematical concept… Learners then practice the method and rely upon the teacher to tell them the
correct answers” (OPM1501, 2020: 2). This essay critically demonstrates my understanding of this
shift, focusing on the teaching and learning of measurement in the Intermediate Phase. By
juxtaposing constructivism with behaviourism and applying constructivist principles to measurement,
I will argue that only through active engagement can learners truly understand measurable attributes,
rather than merely memorising formulas.
Description of Constructivism vs. Behaviourism and Practical Implications
To understand the shift, one must first contrast two learning theories: behaviourism and
constructivism. Behaviourism, which underpins traditional “teach-by-telling” approaches, views the
learner as a passive recipient. Knowledge is transmitted from teacher to student, who is expected to
reproduce it accurately. Learning is measured by observable changes in behaviour, such as correctly
performing a routine algorithm. The study guide warns that this approach “produces a
follow-the-rules, computation-driven, answer-oriented view of mathematics” (OPM1501, 2020: 2).
In a behaviourist measurement lesson, a teacher would state, “The area of a rectangle is length times
breadth,” write the formula on the board, and have learners complete 20 similar problems. The focus
is on procedural fluency and correct answers, not understanding why the formula works.
In contrast, constructivism, based largely on Piaget’s work, posits that learners are “creators of their
own knowledge” (OPM1501, 2020: 4). Knowledge cannot be passively absorbed; it must be actively
constructed by integrating new experiences into existing mental schemas. Two key processes are
assimilation (using an existing schema to understand a new experience) and accommodation
(altering existing schemas when new ideas do not fit) (OPM1501, 2020: 4-5). A constructivist
teacher facilitates exploration, encourages conjecture, and values the process over the final answer.
The practical implications are profound: lessons must begin where the learners are, use hands-on
materials, promote discussion, and present problems before teaching rules. The teacher’s role shifts
from “sage on the stage” to “guide on the side,” asking thought-provoking questions rather than
providing immediate solutions (OPM1501, 2020: 23-24).
