Maths tutorials have been a whole lot of fun so far; my tutors have been most willing to share their experiences. We learnt many new teaching methods/strategies to introduce the same old math topics to students in more engaging ways and I'm really looking forward to putting all these strategies to use soon.
Before I go any further, I just want to say that the learning of mathematics these days is vastly different from what we were exposed to in the past; instead of focusing as much on rote memorization (that was very much how we learnt about maths back then, wasn't it?), the focus is now on the development of students' process skills which will come in useful in problem-solving. Instead of learning mathematics in an isolated contexts, students are now exposed to problems that are more relatable to their daily lives so that learning will become much more meaningful for them.
Also, instead of diving head-first into abstract representations of mathematical concepts these days, teachers let students play and explore with 'concrete' math-learning materials (that's where the fun begins) before using pictures to represent them and finally moving on to the abstract representation.
Here are some of the 'concrete' materials that we've been learning to make use of in our tutorials:
DIY unit-cube and cuboids that I used for one of my micro-teaching sessions; making 2D representations of 3D-models on isometric dot paper (P5).
Tangram pieces in the shape of a crane; something that we were required to fold when Grandfather Tang's story was being read (P2).
Tangram square.
Coloured counters to reveal patterns when counting.
Coloured wooden blocks; surface area.
3 corners from the same triangle; proof that interior angles of a triangle add up to 180degrees.
Geometric strips; teaching properties of figures (e.g. parallelogram, rhombus, etc)
There are more, but I think the ones that I've shown up there are enough to prove my point.
The other point of this entry is really for me to rant.
I'm getting increasingly irritable by some of the comments that people make about primary school mathematics like "maths problems are getting too difficult these days, I only learnt this in primary (insert appropriate level) back then", or "workbooks like to make things complicated for simple calculations; e.g. add in redundant steps, it's so confusing!", or "don't know if the kids are being tested on their English abilities or mathematical understanding"; people who have not been pedagogically-trained but think they know better.
Debunking these comments:
"maths problems are getting too difficult these days, I only learnt this in primary (insert appropriate level) back then"
以前警察穿短裤.
I'm sorry that you think math problems are getting tougher (it's true, at least for people like me who've gone through the older ways of learning) these days but times have changed (and so has the syllabus; not all though) and we need to keep up with these changes - that's the politically correct thing to say, of course. In order to keep up with the global pace and develop our students into critical and creative young people able to generate alternative solutions for an old problem instead of following the previous solution blindly (i.e. do for the sake of doing, without understanding), we cannot continue with the old rote memorization way of learning where students just do drill-and-practice sums all the time.
These 'difficult' problems have been identified by many education researchers as useful in helping young students develop essential thinking and processing skills that will greatly aid them in problem-solving, and have not been presented to students just because teachers enjoy watching students (and parents too, for this matter) stumble on them.
"workbooks like to make things complicated for simple calculations; e.g. add in redundant steps, it's so confusing!"
Build the foundation/basis for more advanced thinking in children. Over the course of our education, we have come to become so good with the basics (or at least we think we are) and have absolutely no problems with simple operations (e.g. addition, subtraction, etc). Process of learning/acquisition may seem to have come very naturally to us, but I can assure you otherwise; it came along together with the countless drill-and-practice exercises that we've completed back then. Forget that students thinking and our thinking (as adults) are at very different levels/stages, in terms of processing capabilities, and we assume that they think the same way as we do. But that is not the case. They need lots of scaffolding (step-by-step instructions/guide) to progress from one level to the next. We see redundant steps in workbooks, children see a step-by-step guide.
Why not simply use the rote memorization method, it worked okay for us, so it must work okay for the kids these days too, you may say. Because in the past, it was mainly just doing without understanding. Example, can you explain why must we 'bring' the '3' up to '7' when we do our working for 76 X 6? Are you thinking something along the line of "because that's how I've always been doing it" or "because that was what I was taught?" Not understanding, blindly following. The answer that I was looking for should actually be related to the concept of Place Values and Regrouping.
Spend more time now to spend less time in future.
The steps are not redundant; can present to students alternative ways of deriving a solution, and over time, students will learn to judge for themselves which are the most efficient/effective ones.
"don't know if the kids are being tested on their English abilities or mathematical understanding"
I have mixed feelings about this. On one hand, I definitely agree that language used in problems posed to students should be within their language competencies so that they are able to understand what the question/problem is talking about. On the other, I do not seem any harm in stretching our students slightly beyond their abilities across the curriculum because learning should not take place in isolation, i.e. what is learnt in English class should not just be relevant during English lessons, but should come in useful in subjects across the curriculum. It really does make a good opportunity for teachers to teach students new vocabulary. That said, I absolutely do not agree with using language in maths problems to 'trick' students; or using it to have the same effect for other subjects within the curriculum.
The worst thing parents/tutors can do is to tell children that "these steps are stupid/useless" and insist on your way of doing things. Here we are, trying so hard to build up positive attitudes towards mathematics in children and by saying the negative things you do about math teaching and learning, you've just successfully destroyed whatever we've tried to construct.
And yes, it makes me very upset :(
End of rant.
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