Introduction :

History:

Mathematics has been regarded as the backbone of human civilization.

History of mathematics is the history of civilization.

Mathematics is the mirror of civilization.

Mathematics has led to the development of various subjects, vocations and technology.

Mathematics is the gate and key to all sciences.

All things are mathematical

Philosophy:

There two schools of thought :

1. Mathematics is discovered ( pure mathematics/abstract mathematics)

Mathematics is a dynamic (in the making) subject (vs static subject) whether it was discovered (ie mathematicians like scientists who form theories/laws/principles from simple ideas/examples, intuition, making conjectures/hunches, through questioning and observations .

eg discovered mathematical concepts such as numbers, relations, functions, ratio, proportion, rate, etc.

OR

Mathematics is invented/created (applied mathematics)

(ie mathematicians like technologists who apply mathematics in solving real life problems) eg invent/create symbols, formulas, methods, heuristics, algorithms, models, strategies etc.

Based on two schools of thought in the philosophy of mathematics, discuss its implications to the teaching and learning maths in the classroom.