The processes of mathematics are the thinking activities associated with doing mathematics:-

Basic activities :

1. counting - dealing with quantities/numbers and it grows becomes arithmetic, algebra (generalization of

arithmetic), number theory, statistics, probablity , decision science, acturial science, risk management

so on...

2. measuring - dealing with length, area, volume,etc and it grows becomes geometry, trigonometry, so on...

3. finding relationships between variables- dealing with variables and it grows becomes algebra,

calculus, so on...

More advanced activities :

1. Mathematical modelling

- the process of developing/designing/

constructing/formulating a mathematical model from real

world/everyday life/natural phenomena/word problems (heat,light,

energy, waves etc) to become mathematical models (in the form of equations, functions, graphs, tables etc)

eg Newton's law motion, F=ma

Boyle's law PV=c

Plans and elevations, earth as sphere, bearing etc

2. Searching for patterns

Maths is the study of patterns of various kinds in

- numbers (patterns of numbers- odd, even,prime

numbers, arithmetic, geometric progressions etc),

- shapes (patterns of shapes- transformations -

translation, reflection and rotation,

geometrical patterns etc )

-relationships ( form of functions and

graphs- sine,cosine curves ; probability as a pattern of

chances etc)

Other related activities include classifying/categorization, symbolizing, abstracting, defining,assuming

conjecturing, applying, collecting data, reasoning (inductively and deductively), proving, number sense

estimation, data handling, recognising and representing relationship mathematically etc..

(ie the process of mathematical thinking)

The products of mathematics are the results of mathematical thinking and activities include definition of concepts (defined concepts), postulates (eg a line can be drawn between any two points), methods for solving problems, rules, formulas, theorems, mathematical models etc

(ie the product of mathematical thought)