Just finished marking the class test on Partial fractions & Indices for this class. My Gosh! Only 11 pupils out of 28 passed the test with 6 gotten borderline fail and the rest failed terribly. Those who failed had no recollection of what the 3 cases in Partial fractions are as shown in their workings. They could not even write down the general form for each cases! Considering questions on Partial fractions are rather standard, obviously many of the pupils did not bother to study for the test at all. It was quite disheartening as I have spent so much time trying to ensure that pupils were able to follow what were being taught in class so much so that not enough time for me to do revision for mid year exams with them.
The 2nd question was crafted such that the general form was given to them and yet many can only do up to performing long division to convert the given algebraic fraction into the sum of a polynomial and a proper fraction and could not continue correctly from there. Problems that most pupils had were basically algebra. They could not express the fractional equations into polynomial identities, eg. "(x^2-8x+44)/[(x+2)(x+2)^2]=A/(x+2) + B/(x-2) + C/(x-2)^2" after simplifying became "x^2-8x+44=A(x+2)^2 + B(x-2) + C(x-2)^2" or x^2-8x+44) =A(x-2)(x-2)^2 + B(x+2)(x-2)^2 + C(x+2)(x-2)".
The 3rd and 4th questions were on Indices. These 2 questions showed that even some of the better pupils could not obtain the answers correctly. This showed that the class did not grasp the concept of Indices well. This is always the case. Pupils "hate" Indices as they can get confused easily. Need to target their foundation in E Math Indices then. I tried explaining again how the laws of Indices arrived and pupils were able to understand. What they lack of is how to apply the laws of Indices and especially when they are given more complicated expressions to simplify. Guess I will have to discuss with the Sec 3 Math teachers to think of a better way to help pupils master the skills required in Indices. Maybe drill & practice would still be a better strategy to train them in doing Indices?
sounds like disheartening outcomes for all the hard work.
ReplyDeleteWhether drill will be better is still dependent on how the pupils learn best.
Some may understand and apply better when they "derive" the formulae. Others simply need to memorise.
Some need to remember patterns and steps.
We are hard pressed to find some method that will work for most, and that method may not exist as each of them need to learn differently.
Maybe the drill & practice can work for most, after having given he "derived" method and other pattern or step methods.
The moral of the story is "never give up".
Take heart and press on!