MTE1501
ASSIGNMENT 4 2025
UNIQUE NO.
DUE DATE: 31 AUGUST 2025
, Mathematics 1 for Teachers
Question 1: Mathematics in Society (20)
1.1 Three views of mathematics (with examples) — 6 marks
Instrumentalist / toolbox view: Math is a set of rules and procedures for getting
answers. Example: Using the standard algorithm to divide 1 236 by 12 to find
how many teams you can make from 1 236 learners.
Platonist view: Math is the discovery of objective, eternal truths that exist “out
there.” Example: Showing that the sum of the angles in any Euclidean triangle is
always 180°, regardless of time/place.
System (human activity) view: Math is a socially created, evolving system of
ideas used to model the world. Example: Choosing a linear model vs. an
exponential model to represent cellphone data usage growth in a class project,
and refining it after testing predictions.
1.2 Ancient contributions — 6 marks
Babylonian: Base-60 place-value system enabling precise astronomy and
timekeeping; solved quadratic problems on clay tablets. Real-world problem:
tracking celestial cycles and dividing time (hours:minutes:seconds).
Egyptian: Unit-fraction methods (e.g., 2/n tables), and practical geometry for
surveying after Nile floods. Problem: fairly re-establishing field boundaries and
grain rations.
African: Early counting bones (e.g., Lebombo/Ishango) and sophisticated
indigenous numeration (e.g., Yoruba base-20) used for trade, calendars, and
rituals. Problem: tracking lunar cycles, inventories, and market exchanges.
1.3 Introducing “math as a cultural human activity” (Grade 4) — 4 marks
Start with artifacts: show photos of tally sticks/rope-stretchers; ask, “Why did
people invent these?”
ASSIGNMENT 4 2025
UNIQUE NO.
DUE DATE: 31 AUGUST 2025
, Mathematics 1 for Teachers
Question 1: Mathematics in Society (20)
1.1 Three views of mathematics (with examples) — 6 marks
Instrumentalist / toolbox view: Math is a set of rules and procedures for getting
answers. Example: Using the standard algorithm to divide 1 236 by 12 to find
how many teams you can make from 1 236 learners.
Platonist view: Math is the discovery of objective, eternal truths that exist “out
there.” Example: Showing that the sum of the angles in any Euclidean triangle is
always 180°, regardless of time/place.
System (human activity) view: Math is a socially created, evolving system of
ideas used to model the world. Example: Choosing a linear model vs. an
exponential model to represent cellphone data usage growth in a class project,
and refining it after testing predictions.
1.2 Ancient contributions — 6 marks
Babylonian: Base-60 place-value system enabling precise astronomy and
timekeeping; solved quadratic problems on clay tablets. Real-world problem:
tracking celestial cycles and dividing time (hours:minutes:seconds).
Egyptian: Unit-fraction methods (e.g., 2/n tables), and practical geometry for
surveying after Nile floods. Problem: fairly re-establishing field boundaries and
grain rations.
African: Early counting bones (e.g., Lebombo/Ishango) and sophisticated
indigenous numeration (e.g., Yoruba base-20) used for trade, calendars, and
rituals. Problem: tracking lunar cycles, inventories, and market exchanges.
1.3 Introducing “math as a cultural human activity” (Grade 4) — 4 marks
Start with artifacts: show photos of tally sticks/rope-stretchers; ask, “Why did
people invent these?”
