NAME: PHILISIWE MOTHA
STUDENT NO: 12770132
MODULE CODE: MTE1501
ASSIGNMENT NO: 03
DATE: 18 JULY 2023
3.1 LU1: Mathematics in Society
Törner and Grigutsch (1994) considered mathematics as either a toolbox, a system
or a process. The toolbox-view sees mathematics as a set of skills. The system-view
sees mathematics as a logical and rigorous system. The process-view of
mathematics states that it is a constructive problem-solving process (Törner &
Grigutsch (1994). Elaborated mathematical views are as follows:
3.1.1 The toolbox/Instrumentalist view
This view is connected to content-focused teaching where the emphasis is on
performance and learning is seen as passive reception of knowledge. This view
usually falls short of deep understanding, knowledge construction and learners have
no active role in mathematics lessons. As a result, it is not experienced as
interesting. The emphasis is mainly on ensuring the correctness of facts and rules
(Beswick, 2005).
3.1.2 The Platonist view
This view is often connected to an objectivistic worldview. It involves understanding
mathematics as a consistent, connected and objective structure. Mathematical
objects are seen to be real and exist independently of human thinking. Mathematical
statements are objectively true or false, and their truth-value is also seen to be
independent from human understanding. In addition, mathematical knowledge is
seen to be non-empirical. This objectivistic view of knowledge positions the teacher
in the classroom as an explainer and the learning is seen as a reception of
, knowledge. The Platonist view implies content-focused teaching, and the emphasis
is on understanding and learning as an active construction of understanding.
3.1.3 The system view
This view aims to order results into a deductive system and build axiomatic system.
This view is useful in identifying inconsistencies, stated and non-stated assumptions,
and it unifies and simplifies mathematical theories by integrating unrelated
statements, theorems and concepts
3.2 LU2: TEACHING AND LEARNING MATHEMATICS
3.2.1 Activity 3.5
a. The word "natural numbers" is used when referring to counting numbers because
they represent the numbers that naturally occur when counting objects.
b. (a) False – All integers are rational numbers and not irrational
(b) True
(c) True
c. The place value of 2 in 23.61 is Tens
The place value of “3” in 423.658 is Units
The place value of “6” in 23.062 is Hundredths
The place value of “6” in 10.958265 is Hundred thousandths
The place value of “9” in 986 234.8390123 is Millionths
The place value of bold “2” in 986 234.8390123 is Hundred thousand
3.2.2 Activity 3.7 (4)
The diagrammatical placing of two number sets represents real number system. The
natural numbers do not include the number 0 and the smallest number is 1 while the
STUDENT NO: 12770132
MODULE CODE: MTE1501
ASSIGNMENT NO: 03
DATE: 18 JULY 2023
3.1 LU1: Mathematics in Society
Törner and Grigutsch (1994) considered mathematics as either a toolbox, a system
or a process. The toolbox-view sees mathematics as a set of skills. The system-view
sees mathematics as a logical and rigorous system. The process-view of
mathematics states that it is a constructive problem-solving process (Törner &
Grigutsch (1994). Elaborated mathematical views are as follows:
3.1.1 The toolbox/Instrumentalist view
This view is connected to content-focused teaching where the emphasis is on
performance and learning is seen as passive reception of knowledge. This view
usually falls short of deep understanding, knowledge construction and learners have
no active role in mathematics lessons. As a result, it is not experienced as
interesting. The emphasis is mainly on ensuring the correctness of facts and rules
(Beswick, 2005).
3.1.2 The Platonist view
This view is often connected to an objectivistic worldview. It involves understanding
mathematics as a consistent, connected and objective structure. Mathematical
objects are seen to be real and exist independently of human thinking. Mathematical
statements are objectively true or false, and their truth-value is also seen to be
independent from human understanding. In addition, mathematical knowledge is
seen to be non-empirical. This objectivistic view of knowledge positions the teacher
in the classroom as an explainer and the learning is seen as a reception of
, knowledge. The Platonist view implies content-focused teaching, and the emphasis
is on understanding and learning as an active construction of understanding.
3.1.3 The system view
This view aims to order results into a deductive system and build axiomatic system.
This view is useful in identifying inconsistencies, stated and non-stated assumptions,
and it unifies and simplifies mathematical theories by integrating unrelated
statements, theorems and concepts
3.2 LU2: TEACHING AND LEARNING MATHEMATICS
3.2.1 Activity 3.5
a. The word "natural numbers" is used when referring to counting numbers because
they represent the numbers that naturally occur when counting objects.
b. (a) False – All integers are rational numbers and not irrational
(b) True
(c) True
c. The place value of 2 in 23.61 is Tens
The place value of “3” in 423.658 is Units
The place value of “6” in 23.062 is Hundredths
The place value of “6” in 10.958265 is Hundred thousandths
The place value of “9” in 986 234.8390123 is Millionths
The place value of bold “2” in 986 234.8390123 is Hundred thousand
3.2.2 Activity 3.7 (4)
The diagrammatical placing of two number sets represents real number system. The
natural numbers do not include the number 0 and the smallest number is 1 while the
