Traditionally maths is taught as steps that must be followed. Each type of sum has its own sets of steps or recipes that must be followed. When maths is seen as steps and recipes, it relates more to home economics that to mathematical thinking.
The Thinking Tools approach see maths as a tapestry with a neat front end and a back end where loose threads are knotted and tied together which is the side where the real maths hides. Most education systems are woven (excuse the pun) to the near front end of the sum. For example, they teach their learners to multiply 99 x 49 to write the 49 under the 99 and start multiplying 9 with 9 and carry the 8 if the 81 over, etc until the sum is done. This Thinking Tools learner will immediately 'see' that 100 x 50 which gives 5000 and then deduct the undercalculation, which is 149, from the 5000 which results in 4851.
For Thinking Tools learners, certain numbers have a deeper meaning because they are special numbers. 45 is a special number because 4 of them provides a rectangle and a square. Rectangles and squares again lay the basis for the back end of multiplication, while learning the front end of multiplication tables leads to meaningless repetition and memorisation. Squares are the backbone of standard parabola.
Each kind of sum, from an easy word sum to a parabola has its own back end.
The discovery of the real backend maths led to relating doing sums with parachute jumping. This led to the coining of the PILOT CHUTE concept which is a lesson planning protocol that empowers learners to determine what to do, identify red flag warnings and establish how to tackle the problem before jumping into the deep end and running the risk not to succeed. All new extra classes are guided by a pilot chute for the specific sum.
This protocol provides learners with a safe launching pad to prevent from falling into a non-intentional learning pit. It also enables learners to establish their own learning 'position' in space and time enabling them to determine their point of departure, destination, designing a metacognitive plan, take action, remediate mistakes and record their progress. This enables learners to become CRITICAL THINKERS and self-regulated learners.
Do you want to be teacher of steps and recipes?
OR
Do you want to be empowered to enable learners to discover how the back end of the sum works which becomes cemented in their problem-solving DNA?
Do you want your child to depend on steps and recipes when writing tests and exams?
OR
Do you want your child to be able to grasp and figure out the loose ends and string them in a meaningful pattern which opens the sum like a pomegranate?