In any competitive environment, Chess tournament, Wimbledon final, Maths exam… The difference between the champ and the just good enough has sometimes little to do with intrinsic abilities but something more subtle: the immersion in an inner world made of sophisticated recipes that mimic the outer reality close to perfection and allowing you to solve any riddle posed by the given challenge.
Some people call this a system, or following processes, or inventing your personal circuit. We, at North Delta College, call this “having a Method”.
We will explain to the reader, in this Methodology Blog, why having a Method is first critical if you are aiming high in Maths and second has nothing to do with being a Robot!!
- What is a Method?
A method is a corpus of techniques that are set and allowing the practitioner to use established recipes to solve a given range of problems.
The method is not the final answer to the problem but certainly permits if you are stuck in your learning curve in some areas of Maths to unlock the bottleneck, and get back your feet to the ground.
The method will generally be made of steps to be followed and principles to be applied in a practical setup and hence allowing you to supplement your Maths skills by ready-made processes that might seem arbitrary at first sight, but absolutely instrumental in gaining, later on, new insights.
- Welcome to the Machine
Let us give an example.
Example: John is trying to add 2 vectors but is absolutely lost when he attempts to do so, although he fully understands what a vector means.
His tutor comes with the following recipe to help him.
- Label the first vector u and the second vector v and identify their starting and endpoints to both.
- Take the second vector v and translate it so that its starting point merges with the endpoint of the first vector u.
- Join the triangle. Call the third side x.
- The vector w= u+v is precisely the vector starting where u started and ending at the other extremity of x!!
To make sure he grasps the mechanism behind the construction, the tutor imposes on John 9 exercises split in 3 drilling sessions plus homeworks.
After 2 weeks, John feels he has stretched his brain in a curious way but that ultimately, he has reached where he wanted.
- Methods & Maths Ambitions
Any Maths teacher will remind you of the following fact: Methods are critical in Maths!!
They are the path that takes you to the ascending lift when Maths are considered as a purely societal object. Good grades, good universities, high position in the Maths hierarchy, and even few research problems…
Methods shouldn’t be confused with real intelligence, however they are the vital tools that differentiate the amateur from the star, GCSE level Maths with A level Maths and higher, the simply curious mind with the accomplished dedicated scientist.
- Methodic or Robotic?
However the question remains.
Let us go back to section 2. Have I not become a robot trying to learn that recipe? Is it still brain work when my mind has to work like inside a clock and follow a number of prescribed rules by someone else with 0 personal involvement?
Let us answer by another question.
Do you know any other way of understanding the major discoveries made by Descartes, Newton or Pascal than first unfolding what they were trying to convey…
Hence that extra effort, that extra pain is necessary…
Besides, being methodic is not a sign of mental closedness, but rather a manifestation that your ambitions are real. Indeed, Any significant effort in adult life requires being methodic!!
- What is the difference between a Method and an Algorithm?
Moreover, Methods should not be confused with Algorithms. Algorithms are indeed brain-dead and are meant for a processing unit (calculator, computer…)
Methods are a slightly more subtle concept which is also more universal as Methods are not limited to maths.
Methods send a very powerful signal to the brain, indicating the need for a lifestyle change. From tentative to transformative. From amateurism to real action. From touristic tendencies to indigenous expertise on your subject.
So, ladies and gentlemen, Welcome to the Machine.
For a journey that will bring you new dimensions.
To discover another facet of your real potential
Hence Methods are fundamental and completely under-emphasised in modern maths teaching.
To, my A-level student-reader: Were you conscious of the technical existence of this notion? Or were you studying maths blissfully unaware that the A+ student has a secret tendency that you could explore too! With some guidance of course….