MTE1501
Assignment 4
Due 31 August 2025
,Mathematics 1 for Teachers
Question 1: Mathematics in Society (20 marks)
1.1 Three Perspectives on Mathematics (6 marks)
Mathematics can be understood from different philosophical perspectives:
Instrumentalist / “toolbox” view
In this perspective, mathematics is regarded as a set of rules, methods, and
formulas used to solve practical problems. The focus is not on meaning or
underlying concepts, but on applying learned techniques.
Example: A Grade 6 learner uses long division to determine how many groups of
12 can be made from 1 236 learners. The calculation is purely mechanical,
aimed at getting the correct numerical answer.
Platonist perspective
Here, mathematics is seen as a discovery of eternal truths that exist outside
human experience. According to this view, mathematical facts are universal,
timeless, and independent of culture.
Example: Proving that the interior angles of every Euclidean triangle always sum
to 180°, irrespective of culture, time, or human invention. This truth exists
whether or not humans recognize it.
Mathematics as a human activity (systemic view)
This interpretation views mathematics as a dynamic, cultural activity created by
humans to understand, explain, and structure the world. Mathematics evolves
with society and adapts to new needs.
Example: Learners investigate whether cellphone data usage is better
represented by a linear function or an exponential function. They then refine their
model based on the observed patterns, showing mathematics as an evolving tool
for sense-making.
, 1.2 Contributions of Ancient Civilisations (6 marks)
Babylonians
They developed a base-60 positional number system, which allowed them to
make highly sophisticated astronomical observations.
Application: Division of hours into minutes and seconds, and recording planetary
and lunar cycles – a practice still in use today.
Egyptians
They made extensive use of geometry in measuring land and resources,
particularly after the Nile River flooded. Their mathematics was largely practical,
focusing on fractions and measurement.
Application: Surveyors used geometry to re-establish farmland boundaries and to
calculate the distribution of harvested grain.
African societies
Archaeological evidence, such as the Lebombo and Ishango bones, shows that
early African societies kept tally marks to count lunar cycles. Other cultures, such
as the Yoruba, developed base-20 counting systems.
Application: These systems were applied in trade, timekeeping (calendars), ritual
organisation, and recording astronomical observations.
1.3 Teaching “Mathematics as a Cultural Human Activity” in Grade 4 (4 marks)
A teacher could introduce learners to mathematics as a human invention by designing a
culturally rich activity:
1. Show pictures of ancient tools such as tally sticks, the Lebombo bone, or rope-
stretchers. Ask learners: “Why do you think people created these tools? What
problems were they solving?”
2. Organize stations where learners rotate between number systems – writing
numbers 1–30 in Roman numerals, Zulu/Yoruba numerals, and modern base-10.
Assignment 4
Due 31 August 2025
,Mathematics 1 for Teachers
Question 1: Mathematics in Society (20 marks)
1.1 Three Perspectives on Mathematics (6 marks)
Mathematics can be understood from different philosophical perspectives:
Instrumentalist / “toolbox” view
In this perspective, mathematics is regarded as a set of rules, methods, and
formulas used to solve practical problems. The focus is not on meaning or
underlying concepts, but on applying learned techniques.
Example: A Grade 6 learner uses long division to determine how many groups of
12 can be made from 1 236 learners. The calculation is purely mechanical,
aimed at getting the correct numerical answer.
Platonist perspective
Here, mathematics is seen as a discovery of eternal truths that exist outside
human experience. According to this view, mathematical facts are universal,
timeless, and independent of culture.
Example: Proving that the interior angles of every Euclidean triangle always sum
to 180°, irrespective of culture, time, or human invention. This truth exists
whether or not humans recognize it.
Mathematics as a human activity (systemic view)
This interpretation views mathematics as a dynamic, cultural activity created by
humans to understand, explain, and structure the world. Mathematics evolves
with society and adapts to new needs.
Example: Learners investigate whether cellphone data usage is better
represented by a linear function or an exponential function. They then refine their
model based on the observed patterns, showing mathematics as an evolving tool
for sense-making.
, 1.2 Contributions of Ancient Civilisations (6 marks)
Babylonians
They developed a base-60 positional number system, which allowed them to
make highly sophisticated astronomical observations.
Application: Division of hours into minutes and seconds, and recording planetary
and lunar cycles – a practice still in use today.
Egyptians
They made extensive use of geometry in measuring land and resources,
particularly after the Nile River flooded. Their mathematics was largely practical,
focusing on fractions and measurement.
Application: Surveyors used geometry to re-establish farmland boundaries and to
calculate the distribution of harvested grain.
African societies
Archaeological evidence, such as the Lebombo and Ishango bones, shows that
early African societies kept tally marks to count lunar cycles. Other cultures, such
as the Yoruba, developed base-20 counting systems.
Application: These systems were applied in trade, timekeeping (calendars), ritual
organisation, and recording astronomical observations.
1.3 Teaching “Mathematics as a Cultural Human Activity” in Grade 4 (4 marks)
A teacher could introduce learners to mathematics as a human invention by designing a
culturally rich activity:
1. Show pictures of ancient tools such as tally sticks, the Lebombo bone, or rope-
stretchers. Ask learners: “Why do you think people created these tools? What
problems were they solving?”
2. Organize stations where learners rotate between number systems – writing
numbers 1–30 in Roman numerals, Zulu/Yoruba numerals, and modern base-10.
