, PLEASE USE THIS DOCUMENT AS A GUIDE ONLY
Scenario 1: Reflecting on the Mathematics in Society
1. Write a reflective essay discussing the definition of mathematics, its role in society, and how
this perspective influences effective mathematics teaching and learning. Your essay should
demonstrate insight from Units 1 and 2. In your response, be sure to address the following
points.
The Living Essence of Mathematics: From Abstract Truths to a Classroom of Discovery
Introduction
Mathematics, often misunderstood as a rigid collection of rules and formulas, is a dynamic and
creative human activity. As a prospective teacher, my reflection on its nature, historical significance,
and pedagogical implications has fundamentally reshaped my view of what it means to teach and
learn this essential subject. This essay will explore the definition of mathematics, its vital role in
society, and how these perspectives will directly influence my teaching practice, particularly in the
Intermediate Phase. By moving away from rote memorisation towards conceptual understanding, I
aim to foster a classroom where learners actively engage with the beauty and relevance of
mathematics.
What is Mathematics?
Mathematics is far more than a set of procedural rules to be memorised. The instrumentalist or
"toolbox" view, which sees it as an "accumulation of facts, rules and skills to be used in the
pursuance of some external end," is a common but limited perception that often leads to
"follow-the-rules, computation-driven, answer-oriented view of mathematics" (MTE1501, Study
Guide, p. 14-15). In contrast, a richer understanding recognises mathematics as a dynamic discipline.
In this essay, I adopt the view of mathematics as a human activity involving pattern-seeking,
problem-solving, and logical reasoning. Van de Walle's description of mathematics as the "science of
pattern and order" (MTE1501, Study Guide, p. 44) resonates strongly, framing it not as a static body
of knowledge but as an active process of "finding and exploring this regularity or order and then
making sense of it" (MTE1501, Study Guide, p. 44). This perspective transforms the learner from a
passive recipient of knowledge into an active explorer who formulates conjectures and discovers
relationships.
Furthermore, mathematics can be understood through the system view, which "endeavours to order
results into a deductive system" emphasising "the importance of proof and proving in mathematics"
(MTE1501, Study Guide, p. 15). This view highlights how mathematics unifies and simplifies
theories by integrating unrelated statements, theorems, and concepts. Additionally, the Platonist view
presents mathematics as "a static but unified body of certain knowledge" that exists independently of
human thinking (MTE1501, Study Guide, p. 14). However, modern perspectives propose that
"mathematics must be accepted as a human activity" where "mathematical objects are invented or
created by humans" and "arise from activity with already existing mathematical objects, and from the
needs of science and daily life" (MTE1501, Study Guide, p. 17). These varying definitions
collectively demonstrate that mathematics is not merely about memorisation but involves discovery,
creation, and logical reasoning.
Scenario 1: Reflecting on the Mathematics in Society
1. Write a reflective essay discussing the definition of mathematics, its role in society, and how
this perspective influences effective mathematics teaching and learning. Your essay should
demonstrate insight from Units 1 and 2. In your response, be sure to address the following
points.
The Living Essence of Mathematics: From Abstract Truths to a Classroom of Discovery
Introduction
Mathematics, often misunderstood as a rigid collection of rules and formulas, is a dynamic and
creative human activity. As a prospective teacher, my reflection on its nature, historical significance,
and pedagogical implications has fundamentally reshaped my view of what it means to teach and
learn this essential subject. This essay will explore the definition of mathematics, its vital role in
society, and how these perspectives will directly influence my teaching practice, particularly in the
Intermediate Phase. By moving away from rote memorisation towards conceptual understanding, I
aim to foster a classroom where learners actively engage with the beauty and relevance of
mathematics.
What is Mathematics?
Mathematics is far more than a set of procedural rules to be memorised. The instrumentalist or
"toolbox" view, which sees it as an "accumulation of facts, rules and skills to be used in the
pursuance of some external end," is a common but limited perception that often leads to
"follow-the-rules, computation-driven, answer-oriented view of mathematics" (MTE1501, Study
Guide, p. 14-15). In contrast, a richer understanding recognises mathematics as a dynamic discipline.
In this essay, I adopt the view of mathematics as a human activity involving pattern-seeking,
problem-solving, and logical reasoning. Van de Walle's description of mathematics as the "science of
pattern and order" (MTE1501, Study Guide, p. 44) resonates strongly, framing it not as a static body
of knowledge but as an active process of "finding and exploring this regularity or order and then
making sense of it" (MTE1501, Study Guide, p. 44). This perspective transforms the learner from a
passive recipient of knowledge into an active explorer who formulates conjectures and discovers
relationships.
Furthermore, mathematics can be understood through the system view, which "endeavours to order
results into a deductive system" emphasising "the importance of proof and proving in mathematics"
(MTE1501, Study Guide, p. 15). This view highlights how mathematics unifies and simplifies
theories by integrating unrelated statements, theorems, and concepts. Additionally, the Platonist view
presents mathematics as "a static but unified body of certain knowledge" that exists independently of
human thinking (MTE1501, Study Guide, p. 14). However, modern perspectives propose that
"mathematics must be accepted as a human activity" where "mathematical objects are invented or
created by humans" and "arise from activity with already existing mathematical objects, and from the
needs of science and daily life" (MTE1501, Study Guide, p. 17). These varying definitions
collectively demonstrate that mathematics is not merely about memorisation but involves discovery,
creation, and logical reasoning.
