MTE1501
ASSIGNMENT 4 2025
DUE: 31 AUGUST 2025
SEMESTER 2 2025
, MTE1501 ASSIGNMENT 4 2025
DUE 31 AUGUST 2025
Question 1: Mathematics in Society (20 marks)
1.1 Define mathematics using the three views presented in your study guide
(instrumentalist/toolbox, Platonist, and system view). Provide one real-life or classroom
example to illustrate each view. (6 marks)
Instrumentalist / Toolbox view
Mathematics is a set of facts, rules and skills used as tools to achieve some external end
(e.g. arithmetic to solve everyday problems). Example: teaching learners column addition
and using it to add shopping items or to calculate totals for a classroom bake sale.
(Learning Unit 1, 1.3; instrumentalist/toolbox view). (Unit 1, 1.3, p.2)
Platonist view
Mathematics is a static, unified body of knowledge; mathematical objects exist
independently of human thought and statements are objectively true or false. Example:
showing Grade 8 learners that the sum of interior angles of a triangle is 180° as an
immutable fact to be discovered (focus on the truth of the statement, not only procedure).
(Unit 1, 1.3; Platonist view). (Unit 1, 1.3, p.3)
System view
Mathematics is an ordered, deductive system (axioms, proofs, theorems) where building a
consistent axiomatic structure and proving results is central. Example: in a classroom
investigation, learners explore simple axioms for arithmetic (e.g. commutativity of addition)
and construct short proofs or reasoned arguments showing consequences of those axioms.
(Unit 1, 1.3; system view). (Unit 1, 1.3, p.3–4)
1 1
, Question 1.2 - One mathematical contribution from each civilisation and the real-world
problem it solved (6 marks)
Babylonian
Sexagesimal place-value system and practical algebra/astronomy.
Contribution: development of a base-60 (sexagesimal) place-value number system and
methods to solve quadratic problems; also astronomical calculations used to keep the
calendar. Real-world problem solved: maintaining an accurate calendar and scheduling
irrigation cycles (necessary for agriculture and the irrigation system). (Unit 1, 1.5.2, p.6–7)
Egyptian
Measurement and mensuration for land re-establishment and calendar.
Contribution: practical arithmetic and mensuration techniques (measuring areas, re-
establishing land boundaries). Real-world problem solved: after Nile floods, farmers needed to
re-establish fields and boundaries and calculate areas for taxation and land use — this drove
development of measuring techniques and simple arithmetic. (Unit 1, 1.5.2, p.6)
African (early southern African artefact evidence)
Tallying/counting artefacts such as notched bones e.g. Lebombo bone.
Contribution: early tally devices indicating systematic counting (possible lunar/month tallies).
Real-world problem solved: tracking recurring natural cycles (for example, lunar months or
seasonal/ritual counts) or keeping simple counts for resources/rituals an early form of record-
keeping. (See discussion about early counting and cultural origins of mathematics; Unit 1,
1.5.1 and question prompt). (Unit 1, 1.5.1, p.6)
Question 1.3 How to introduce “mathematics as a cultural human activity” to Grade 4
Short lesson plan idea (Grade 4, 20–30 minutes):
Hook (5 min): Show learners a picture of the Lebombo bone (or describe 29 notches) and ask:
“Why might people long ago make notches on a bone?”
2 2
ASSIGNMENT 4 2025
DUE: 31 AUGUST 2025
SEMESTER 2 2025
, MTE1501 ASSIGNMENT 4 2025
DUE 31 AUGUST 2025
Question 1: Mathematics in Society (20 marks)
1.1 Define mathematics using the three views presented in your study guide
(instrumentalist/toolbox, Platonist, and system view). Provide one real-life or classroom
example to illustrate each view. (6 marks)
Instrumentalist / Toolbox view
Mathematics is a set of facts, rules and skills used as tools to achieve some external end
(e.g. arithmetic to solve everyday problems). Example: teaching learners column addition
and using it to add shopping items or to calculate totals for a classroom bake sale.
(Learning Unit 1, 1.3; instrumentalist/toolbox view). (Unit 1, 1.3, p.2)
Platonist view
Mathematics is a static, unified body of knowledge; mathematical objects exist
independently of human thought and statements are objectively true or false. Example:
showing Grade 8 learners that the sum of interior angles of a triangle is 180° as an
immutable fact to be discovered (focus on the truth of the statement, not only procedure).
(Unit 1, 1.3; Platonist view). (Unit 1, 1.3, p.3)
System view
Mathematics is an ordered, deductive system (axioms, proofs, theorems) where building a
consistent axiomatic structure and proving results is central. Example: in a classroom
investigation, learners explore simple axioms for arithmetic (e.g. commutativity of addition)
and construct short proofs or reasoned arguments showing consequences of those axioms.
(Unit 1, 1.3; system view). (Unit 1, 1.3, p.3–4)
1 1
, Question 1.2 - One mathematical contribution from each civilisation and the real-world
problem it solved (6 marks)
Babylonian
Sexagesimal place-value system and practical algebra/astronomy.
Contribution: development of a base-60 (sexagesimal) place-value number system and
methods to solve quadratic problems; also astronomical calculations used to keep the
calendar. Real-world problem solved: maintaining an accurate calendar and scheduling
irrigation cycles (necessary for agriculture and the irrigation system). (Unit 1, 1.5.2, p.6–7)
Egyptian
Measurement and mensuration for land re-establishment and calendar.
Contribution: practical arithmetic and mensuration techniques (measuring areas, re-
establishing land boundaries). Real-world problem solved: after Nile floods, farmers needed to
re-establish fields and boundaries and calculate areas for taxation and land use — this drove
development of measuring techniques and simple arithmetic. (Unit 1, 1.5.2, p.6)
African (early southern African artefact evidence)
Tallying/counting artefacts such as notched bones e.g. Lebombo bone.
Contribution: early tally devices indicating systematic counting (possible lunar/month tallies).
Real-world problem solved: tracking recurring natural cycles (for example, lunar months or
seasonal/ritual counts) or keeping simple counts for resources/rituals an early form of record-
keeping. (See discussion about early counting and cultural origins of mathematics; Unit 1,
1.5.1 and question prompt). (Unit 1, 1.5.1, p.6)
Question 1.3 How to introduce “mathematics as a cultural human activity” to Grade 4
Short lesson plan idea (Grade 4, 20–30 minutes):
Hook (5 min): Show learners a picture of the Lebombo bone (or describe 29 notches) and ask:
“Why might people long ago make notches on a bone?”
2 2
