MATHEMATICAL PROCESSES/ACTIVITIES AND ITS RELATION TO TEACHING AND LEARNING

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)