Recently I found that another tutor felt strongly against my core questions checklist method because she claim on her blog that it is rote learning and thus bad.
Before I go on to, here is a definition on rote learning on wikipedia, http://en.wikipedia.org/wiki/Rote_learning.
I will admit to demanding rote learning BUT only under certain circumstances.
First, let's talk about students who started Mathematics tuition with me in Secondary 3. We always attempt to learn by understanding the concepts. I always explain the concepts and how they are applicable. Rote learning is bad when you have sufficent time to learn by understanding. Because students who learn by rote learning without understanding tend to get questions wrong when the phrasing of the questions is changed. As such, the emphasis is on learning concepts and how to apply them when we start in Secondary 3 but with non compulsory "this is how you can always get the questions correct" techniques of approaching questions. So much as that I am always risking students who learn slower (plus I do not wish to pressure the student in Sec 3) failing their examinations. Which is why you won't see "100% passes in all examinations" claim being made by me.Â
Unfortunately, learning solely by understanding take a lot of time and effort on the part of the student. And when you start looking for tuition when you failed your Secondary 4 mid year examinations... it appear there is plenty of time... 5 more months eh? WRONG. You have to spend much of your times on your other subjects. And I will never demand more than 8 hours of effort on Additional and Elementary Maths inclusive of self preparations. 20 weeks it seems... but remember 2 weeks will be lost to your oral, practical examinations and the other subject examinations. Leaving us with 18. Now add another week for rest after the prelims. We are left with 17. 17 weeks will give us only at most 20+ lessons.
 20+ lessons sound a lot right? Look at the number of topics in Additional Mathematics. There are more than 20 topics. Now add in the 30 topics from E Maths... 20+ lessons mean you only get 2 hours of tuition per topic AFTER skipping all the topics that you believe you know in E Maths and the simplest topics in E Maths.
Of that 2 hours, if I spend 1 hour slowly explaining concepts and testing whether you really understood... you think we still got hope bo?
As such, when time is too tight, I will resort to rote learning AFTER a brief 10mins explanation of the concepts (this is in the hope that some of the explanations actually go in as relying on memorising alone will not get you an A most of the time unless your memorisation is super).
When someone come looking for tuition just before or after mid year of Secondary 4, I have 2 choices. Teach by understanding and probably the results will be a C. Teach by hit and run understanding and MORE on recognising patterns and probably the result will be a B3 and hopefully a A2 (if the hit and run concept teaching hit the target or the student already have the concepts but was doing badly). Ask yourself if you are the student or parent, which outcome is preferable to you?
So what's the best way? Start in Sec 3 lah! Then we have plenty of time to learn by understanding and reasoning the steps out one by one before agreeing that the sequence make senses and then memorising the sequence for speed and consistency.
For a Sec 3 student... I will slowly explain the reference angle, behaviour of sine, cosine and tangent in the 4 quadrants, and how finding the reference angle and considering where the angle we are looking for lies in and considering the range of the angle we looking for will allow under to deduce the possible value(s) of the angle we are  to solve for.
But for Sec 4 with 5 months left, I will just give a fast 10mins explanation and if you catch it good. If you don't, too bad. Then we will memorise...
Step 1) Get trigo ratio ready to press in calculator
Step 2) Find reference angle (DO NOT PRESS -VE)
Step 3) Draw ASTC diagram and consider the range/sign
Step 4) Solved.
There! One question which is sure to come out definitely settled within 1hour instead of 2 hours.Â
