AN IMITATION GAME
There is something curious about those we call “math people”, which is the way they can solve problems without learning the “proper way”.
Here is a clip of Nobel Laureate Richard Feynman (who also helped invented the atomic bomb) talking about how he “learned” algebra:
After years of teaching the gifted and empowering the keen and willing, we have "decoded" the fluid skills that make a math person tick.
What are fluid skills?
Fluid such as water can change into the shape of any container it is in. It is a common metaphor to describe one’s adaptability in learning.
The term is coined as such due to its similarity to the concept of “fluid intelligence” in psychometric testing. But we use the word “skills” instead of “intelligence” because we are only interested in the things that can be learned and practised. It embodies the pragmatic side of our teaching philosophy.
The fluid skills have been a game changer for our students. Usually, the effect is first noticed by a parent who has been helping his /her child with math. Here is a testimony from a surprised mum:
"...I would also like to commend Mr Lim for his teaching and method of explanation.
We have been doing challenging math worksheets (not given out by your school) at home and Zachary has been recognising the various types of challenging questions and informing me as he worked on the questions that he had already been taught by Mr Lim on how to tackle those types of questions. I was pleasantly surprised and very relieved that he managed to solve the questions by himself without help from me.
I therefore note a marked improvement in his math and his mathematical reasoning and his ability to somehow identify the appropriate method to be used for a particular question..."
The ability to “somehow identify the appropriate method to be used for a particular question..." is a common trait among "math people". To teach it to our students, we deconstructed it into many small components, each of which is a fluid skill that we can practise deliberately.
To most teachers, a method is just a method for a particular type of question. But to us, every method is taught in the context of a bigger picture, which is to teach our students how to think like a math person. What do math people do when they see a problem for the first time? How do they investigate or solve it informally? If they see the same problem appearing again and again, how do they create or learn a shortcut?
We model excellence. The end result is our students learn both the shortcuts, which are important to become high achievers and also the fluid skills, which ascend their experience to a whole new level.