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3.1 LU1: MATHEMATICS IN SOCIETY
3.1.1. Read section 1.3.1: Defining Mathematics - in your study guide and provide the differences
between the three views used to outline the mathematics consideration.
The Toolbox/Instrumentalist View
This view defines mathematics as a set of practical tools—rules, procedures, and techniques used to
solve real-world problems. It focuses heavily on performance, where learners are expected to
memorise and apply formulas and methods without necessarily understanding the underlying
concepts. Teaching in this context tends to be content-driven, prioritising accuracy and correct
answers over conceptual depth. As a result, learners often become passive recipients of knowledge,
simply following steps rather than engaging with the subject meaningfully. This approach can limit
opportunities for deeper understanding and can make mathematics feel rigid or disconnected from
real thinking.
The Platonist View
The Platonist view presents mathematics as a fixed, objective, and interconnected body of
knowledge. It suggests that mathematical truths exist independently of human thought and are
discovered rather than invented. This perspective sees mathematical objects as timeless and
unchanging, with statements considered either true or false regardless of human perception. In
teaching, this view supports a more structured and explanatory approach, where the teacher imparts
knowledge while also encouraging students to actively engage in building understanding. Unlike the
instrumentalist view, it leans toward deeper comprehension, seeing learning as an active process of
uncovering the inherent truths of mathematics.
The System View
The system view approaches mathematics as a logical and deductive structure. Its main aim is to
build an ordered system of knowledge through formal reasoning and proof. This perspective
emphasises the importance of constructing and working within axiomatic systems, where
conclusions are logically derived from agreed-upon premises. It allows for the identification of
inconsistencies and helps unify various branches of mathematics by connecting different ideas under
a common framework. Teaching from this viewpoint focuses on the development of reasoning and
proof skills, encouraging learners to understand how mathematical concepts are interrelated within a
broader system.
3.1 LU1: MATHEMATICS IN SOCIETY
3.1.1. Read section 1.3.1: Defining Mathematics - in your study guide and provide the differences
between the three views used to outline the mathematics consideration.
The Toolbox/Instrumentalist View
This view defines mathematics as a set of practical tools—rules, procedures, and techniques used to
solve real-world problems. It focuses heavily on performance, where learners are expected to
memorise and apply formulas and methods without necessarily understanding the underlying
concepts. Teaching in this context tends to be content-driven, prioritising accuracy and correct
answers over conceptual depth. As a result, learners often become passive recipients of knowledge,
simply following steps rather than engaging with the subject meaningfully. This approach can limit
opportunities for deeper understanding and can make mathematics feel rigid or disconnected from
real thinking.
The Platonist View
The Platonist view presents mathematics as a fixed, objective, and interconnected body of
knowledge. It suggests that mathematical truths exist independently of human thought and are
discovered rather than invented. This perspective sees mathematical objects as timeless and
unchanging, with statements considered either true or false regardless of human perception. In
teaching, this view supports a more structured and explanatory approach, where the teacher imparts
knowledge while also encouraging students to actively engage in building understanding. Unlike the
instrumentalist view, it leans toward deeper comprehension, seeing learning as an active process of
uncovering the inherent truths of mathematics.
The System View
The system view approaches mathematics as a logical and deductive structure. Its main aim is to
build an ordered system of knowledge through formal reasoning and proof. This perspective
emphasises the importance of constructing and working within axiomatic systems, where
conclusions are logically derived from agreed-upon premises. It allows for the identification of
inconsistencies and helps unify various branches of mathematics by connecting different ideas under
a common framework. Teaching from this viewpoint focuses on the development of reasoning and
proof skills, encouraging learners to understand how mathematical concepts are interrelated within a
broader system.
