The sum itself is the front of the tapestry. The real math sits at the back where the yarns are sewn.
The current teaching and assessment system focus mainly on the forefront.
4IR thinking in mathematics means that the sum is first devised before it is done. For this there are thinking tools to discover concepts and patterns. There are other thinking tools to analyse facts and processes, others to synthesize them.
There are thinking tools to discover the hierarchy of operations, others to compare and contrast steps, others to distinguish the whole from parts, others to discover cause and effect, others to find analogies and others to sequence steps. There are tools to discover and foresee mistakes.
Thinking tools may sound like a new higher-grade subject. It is not. We were born with thinking tools. Children can be equipped with this from an early age. School leavers should be thinking fit and not memorizing fit.
The proof is in the pudding. The list is long.
This is feedback from a grade 7 math teacher who has equipped her children with thinking tools:
“The average of my three math classes was usually between 55% and 58%.
This year (2019) the average of the final exams set by the department is 72%.”