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TAKE YOUR PICK (OPTION A or B)
QUESTION 1
3.1 LU1: MATHEMATICS IN SOCIETY
Read section 1.3.1: Defining Mathematics - Provide the differences between the three views
used to outline the mathematics consideration. (10 marks)
In section 1.3.1, mathematics is viewed and defined from three distinct perspectives: Mathematics
as a Science, Mathematics as a Language, and Mathematics as a Process. These views differ
fundamentally in how they perceive the nature and role of mathematics in society and learning.
First, Mathematics as a Science considers mathematics as a body of knowledge characterized by
abstract concepts, precise definitions, and logical reasoning. It emphasizes rigor and proofs,
focusing on discovering truths through deduction and systematic investigation. This view sees
mathematics as universal and independent of culture, highlighting patterns, structures, and
relationships that exist objectively.
QUESTION
Second, 1
Mathematics as a Language focuses on mathematics as a symbolic system for
communication. From this perspective, mathematics is a means of expressing ideas clearly and
3.1 LU1: MATHEMATICS IN SOCIETY
efficiently using symbols, notations, and formulas. This view stresses the importance of
Differences between
understanding the three
the syntax views usedoftomathematical
and semantics outline mathematics consideration
expressions (10)
to convey meaning, solve
problems, and communicate with others within and beyond the mathematical community.
In my study of section 1.3.1, three distinct views emerge regarding the definition of mathematics:
the Platonist view, the problem-solving view, and the cultural/social view.
Firstly, the Platonist view considers mathematics as a body of absolute truths existing
independently of human minds. According to this view, mathematical concepts such as numbers,
shapes, and operations are timeless entities that are merely discovered by humans rather than
invented. For example, the Pythagorean theorem exists whether or not humans know it. This view
focuses on mathematics as fixed, formal, and logical.
Secondly, the problem-solving view regards mathematics as a dynamic human activity involving
creativity, exploration, and invention. Here, mathematics is not seen as an external reality but
Disclaimer:
rather as something constructed by people to solve practical or theoretical problems. For instance,
The materials provided
the creation are intended
of calculus for educational
to address motion and and informational
change purposes only.
reflects mathematics asThey
an evolving tool for
should problem-solving
not be submittedand as original work
innovation. or used in violation of any academic institution's
policies. The buyer is solely responsible for how the materials are used.
, For more assistance and exclusive, unique assignments, contact us on Telegram:
https://t.me/varsity_times
OPTION A
QUESTION 1
3.1 LU1: MATHEMATICS IN SOCIETY
Read section 1.3.1: Defining Mathematics - Provide the differences between the three views
used to outline the mathematics consideration. (10 marks)
In section 1.3.1, mathematics is viewed and defined from three distinct perspectives:
Mathematics as a Science, Mathematics as a Language, and Mathematics as a Process. These
views differ fundamentally in how they perceive the nature and role of mathematics in society
and learning.
First, Mathematics as a Science considers mathematics as a body of knowledge characterized
by abstract concepts, precise definitions, and logical reasoning. It emphasizes rigor and proofs,
focusing on discovering truths through deduction and systematic investigation. This view sees
mathematics as universal and independent of culture, highlighting patterns, structures, and
relationships that exist objectively.
Second, Mathematics as a Language focuses on mathematics as a symbolic system for
communication. From this perspective, mathematics is a means of expressing ideas clearly
and efficiently using symbols, notations, and formulas. This view stresses the importance of
understanding the syntax and semantics of mathematical expressions to convey meaning,
solve problems, and communicate with others within and beyond the mathematical
community.
Third, Mathematics as a Process highlights the dynamic, evolving nature of mathematics. It is
seen as a set of activities and problem-solving processes involving reasoning, exploration,
conjecture, and proof. This perspective values the learning journey, creativity, and thinking
skills developed through doing mathematics rather than only the final results or formulas. It
encourages inquiry, experimentation, and making connections between different ideas.
In summary, the three views differ mainly in emphasis: the scientific view stresses fixed
knowledge and logical structure; the language view stresses communication and symbolism;
, For more assistance and exclusive, unique assignments, contact us on Telegram:
https://t.me/varsity_times
and the process view stresses activity, reasoning, and discovery. Each perspective offers
unique insights into how mathematics is understood and taught in society.
3.2 LU2: TEACHING AND LEARNING MATHEMATICS
3.2.1
Mathematics as a science based on order and pattern. Choose a topic showing knowledge
and understanding of connections across three or more content areas. (10 marks)
One excellent topic that connects multiple content areas within mathematics is "Patterns and
Sequences." This topic naturally bridges the areas of number patterns, algebraic thinking,
geometry, and functions, showing deep interconnectedness.
Patterns and sequences begin with the recognition of regularities in numbers or shapes,
connecting to the content area of number sense and arithmetic because learners identify
numerical increments or relationships between terms. Moving further, algebra is introduced
as learners represent these patterns using variables and formulas, such as the nth term of an
arithmetic sequence, connecting to algebraic expressions and functions.
Additionally, patterns are also found in geometry, for example, in the repetition of shapes,
tessellations, or fractals. Geometric sequences link numerical and spatial understanding,
showing how growth or scaling patterns occur in shapes.
This topic promotes understanding of order and structure by highlighting how predictable
changes occur, reinforcing concepts in data handling when patterns represent real-world
phenomena, and in measurement when geometric or numeric patterns translate to length,
area, or volume.
Therefore, the topic "Patterns and Sequences" demonstrates connections across number
sense, algebra, geometry, and functions, providing a comprehensive learning experience that
encourages critical thinking about how different areas of mathematics interrelate through the
lens of order and pattern.
, For more assistance and exclusive, unique assignments, contact us on Telegram:
https://t.me/varsity_times
3.2.3 LU3: Problem Representation and Number Sentences
a. Problem: There are 7 boxes. Each box contains 5 red apples and 4 green apples. How many
apples are there?
Provide two different representations and two number sentences (expressions). (6 marks)
VarsityTimes
For more assistance and exclusive, unique assignments, contact us on Telegram:
https://t.me/varsity_times
TAKE YOUR PICK (OPTION A or B)
QUESTION 1
3.1 LU1: MATHEMATICS IN SOCIETY
Read section 1.3.1: Defining Mathematics - Provide the differences between the three views
used to outline the mathematics consideration. (10 marks)
In section 1.3.1, mathematics is viewed and defined from three distinct perspectives: Mathematics
as a Science, Mathematics as a Language, and Mathematics as a Process. These views differ
fundamentally in how they perceive the nature and role of mathematics in society and learning.
First, Mathematics as a Science considers mathematics as a body of knowledge characterized by
abstract concepts, precise definitions, and logical reasoning. It emphasizes rigor and proofs,
focusing on discovering truths through deduction and systematic investigation. This view sees
mathematics as universal and independent of culture, highlighting patterns, structures, and
relationships that exist objectively.
QUESTION
Second, 1
Mathematics as a Language focuses on mathematics as a symbolic system for
communication. From this perspective, mathematics is a means of expressing ideas clearly and
3.1 LU1: MATHEMATICS IN SOCIETY
efficiently using symbols, notations, and formulas. This view stresses the importance of
Differences between
understanding the three
the syntax views usedoftomathematical
and semantics outline mathematics consideration
expressions (10)
to convey meaning, solve
problems, and communicate with others within and beyond the mathematical community.
In my study of section 1.3.1, three distinct views emerge regarding the definition of mathematics:
the Platonist view, the problem-solving view, and the cultural/social view.
Firstly, the Platonist view considers mathematics as a body of absolute truths existing
independently of human minds. According to this view, mathematical concepts such as numbers,
shapes, and operations are timeless entities that are merely discovered by humans rather than
invented. For example, the Pythagorean theorem exists whether or not humans know it. This view
focuses on mathematics as fixed, formal, and logical.
Secondly, the problem-solving view regards mathematics as a dynamic human activity involving
creativity, exploration, and invention. Here, mathematics is not seen as an external reality but
Disclaimer:
rather as something constructed by people to solve practical or theoretical problems. For instance,
The materials provided
the creation are intended
of calculus for educational
to address motion and and informational
change purposes only.
reflects mathematics asThey
an evolving tool for
should problem-solving
not be submittedand as original work
innovation. or used in violation of any academic institution's
policies. The buyer is solely responsible for how the materials are used.
, For more assistance and exclusive, unique assignments, contact us on Telegram:
https://t.me/varsity_times
OPTION A
QUESTION 1
3.1 LU1: MATHEMATICS IN SOCIETY
Read section 1.3.1: Defining Mathematics - Provide the differences between the three views
used to outline the mathematics consideration. (10 marks)
In section 1.3.1, mathematics is viewed and defined from three distinct perspectives:
Mathematics as a Science, Mathematics as a Language, and Mathematics as a Process. These
views differ fundamentally in how they perceive the nature and role of mathematics in society
and learning.
First, Mathematics as a Science considers mathematics as a body of knowledge characterized
by abstract concepts, precise definitions, and logical reasoning. It emphasizes rigor and proofs,
focusing on discovering truths through deduction and systematic investigation. This view sees
mathematics as universal and independent of culture, highlighting patterns, structures, and
relationships that exist objectively.
Second, Mathematics as a Language focuses on mathematics as a symbolic system for
communication. From this perspective, mathematics is a means of expressing ideas clearly
and efficiently using symbols, notations, and formulas. This view stresses the importance of
understanding the syntax and semantics of mathematical expressions to convey meaning,
solve problems, and communicate with others within and beyond the mathematical
community.
Third, Mathematics as a Process highlights the dynamic, evolving nature of mathematics. It is
seen as a set of activities and problem-solving processes involving reasoning, exploration,
conjecture, and proof. This perspective values the learning journey, creativity, and thinking
skills developed through doing mathematics rather than only the final results or formulas. It
encourages inquiry, experimentation, and making connections between different ideas.
In summary, the three views differ mainly in emphasis: the scientific view stresses fixed
knowledge and logical structure; the language view stresses communication and symbolism;
, For more assistance and exclusive, unique assignments, contact us on Telegram:
https://t.me/varsity_times
and the process view stresses activity, reasoning, and discovery. Each perspective offers
unique insights into how mathematics is understood and taught in society.
3.2 LU2: TEACHING AND LEARNING MATHEMATICS
3.2.1
Mathematics as a science based on order and pattern. Choose a topic showing knowledge
and understanding of connections across three or more content areas. (10 marks)
One excellent topic that connects multiple content areas within mathematics is "Patterns and
Sequences." This topic naturally bridges the areas of number patterns, algebraic thinking,
geometry, and functions, showing deep interconnectedness.
Patterns and sequences begin with the recognition of regularities in numbers or shapes,
connecting to the content area of number sense and arithmetic because learners identify
numerical increments or relationships between terms. Moving further, algebra is introduced
as learners represent these patterns using variables and formulas, such as the nth term of an
arithmetic sequence, connecting to algebraic expressions and functions.
Additionally, patterns are also found in geometry, for example, in the repetition of shapes,
tessellations, or fractals. Geometric sequences link numerical and spatial understanding,
showing how growth or scaling patterns occur in shapes.
This topic promotes understanding of order and structure by highlighting how predictable
changes occur, reinforcing concepts in data handling when patterns represent real-world
phenomena, and in measurement when geometric or numeric patterns translate to length,
area, or volume.
Therefore, the topic "Patterns and Sequences" demonstrates connections across number
sense, algebra, geometry, and functions, providing a comprehensive learning experience that
encourages critical thinking about how different areas of mathematics interrelate through the
lens of order and pattern.
, For more assistance and exclusive, unique assignments, contact us on Telegram:
https://t.me/varsity_times
3.2.3 LU3: Problem Representation and Number Sentences
a. Problem: There are 7 boxes. Each box contains 5 red apples and 4 green apples. How many
apples are there?
Provide two different representations and two number sentences (expressions). (6 marks)
