Effort is made to construct a PSLE Math Paper that includes questions that no child has ever seen before in order that NO child can answer the questions from EXPERIENCE ALONE. Our 12 year olds MUST use divergent thinking to solve these problems.
Necessarily, to be well-crafted, the PSLE Math paper must be able to differentiate the VERY VERY poor students, from the VERY poor, from the RATHER poor, from the average, from the good... As such, there will be questions in the PSLE Math paper that VERY VERY poor students can solve too. This is because if every question were pitched at good students, the VERY VERY poor students and the VERY poor students would both get zero... and then, the exam is unable to differentiate the VERY VERY poor from the VERY poor.
Hence, a large portion of the PSLE Math paper tests ONLY convergent thinking. "Convergent thinking emphasizes speed, accuracy, and logic and focuses on recognizing the familiar, reapplying learnt techniques, and accumulating stored information." (quoted from here). A large portion of the PSLE Math paper can be perfectly handled if the child gets in enough practice and keeps his Math reflexes well oiled and possesses enough problem-solving templates that he can quickly match what he already knows to the question.
The Need to Be Mentally Ambi-Dextrous
However, the MOST DIFFICULT parts of the he PSLE Math paper tests divergent thinking AND convergent thinking. The most difficult questions require the child to generate many possible solutions (divergent thinking) before homing into one solution and implementing it with accuracy (convergent thinking). To be MERELY good at PSLE Math, you need strong convergent thinking skills. To be EXCELLENT at PSLE Math, you need strong divergent thinking skills and convergent thinking skills.
The thing to note is this. Some research evidence SUGGESTS that...
(1) people good at divergent thinking tend also to be careless and sloppy (though not all careless and sloppy people are good at divergent thinking). Think Steve Jobs when he was a hippie.
(2) people good at convergent thinking tend to be careful (ummm... necessarily so because the very definition of convergent thinking includes accuracy)
In a way it's a little like left hander and right hander. Most people are right handers (let's just say "Convergent Thinkers") and some are left handers (let's just say "Divergent Thinkers"). The only problem is that to do well at the PSLE Math, we need the children to be mentally ambidextrous (i.e., good at BOTH Divergent and Convergent thinking). Little Boy is naturally a divergent thinker. At his most relaxed, he glosses over details and tends to approach issues (not Math papers) from what we have noticed to be STRANGE angles. For example, he questioned "Why do we wear clothes? It wouldn't hurt anybody if we all went about our lives naked. " Another time, he was able to give me a Malthusian perspective on the CRAZY education system we have, without ever having read Malthus. Little Boy is able to see everyday problems from odd angles that generate interesting insights which would never occur to what we like to term more "normal" folks. Listening to my boy chat himself to sleep can be quite interesting.
Unfortunately, Little Boy is also very careless. So, he loses Math marks to carelessness.
How Mood Affects Convergent and Divergent Thinking
Now, it's been many years since Petunia has known the following...
(1) negative mood facilitates convergent thinking (and vice versa. See here.)
(2) positive mood facilitates divergent thinking (and vice versa. See here.)
When I sent Little Boy into a Math exam, I gave him specific instructions to think SAD thoughts. The sad mood helped him with his carelessness (i.e., his convergent thinking improved).
What I did NOT realize was that the sad mood I kept urging him into, interfered with his divergent thinking and ability to quickly see multiple perspectives. In the exam conditions, when a problem appears that is unfamiliar, Little Boy feels anxiety. This locks down EVEN MORE of his capacity for divergent thinking. This lead to the following odd situation. When he got his exam paper back and was able to think under more benign conditions, Little Boy could solve all the problems he could not solve in the exam!!
Therefore, I shall now begin to instruct my son to do PSLE Math Paper 1 with SADNESS in his heart and some tension.... and approach PSLE Math Paper 2's last 4 questions with relaxed levity (hmmm... think of something funny). This sounds like a recipe for bipolar disorder, but never mind... let's try that out in the next week or so and see if it works eh?
Too Much of the Same Practice Drills Reduce Divergent Thinking
What is more, too many practice papers with the same predictable questions, reduce Little Boy's ability to think divergently. He gets locked into the predictable drills and gives predictable answers. I think I've gone overboard in giving him Science practices... even though I don't give him anywhere near as many Science practices as Chinese. He surprised me at the last practice by giving a predictable answer to a cleverly made Science question, with a twist. Since the Science question comprised an interesting twist, the predictable answer was wrong.
This was a pity because Little Boy had in the past been marked wrong for engaging in too much divergent thinking for Science, even though the Teacher agreed that the question was ambiguous and could have more than one answer. However, the answer key didn't have that answer so it was wrong. I taught Little Boy to choose the Expected and Most Predictable answer he was able to generate. He did that for me in the recent cleverly set exam practice... and I had to mark him wrong.
The predictable answer was not the best answer this time, when most other times, it has been.
So... our poor kids. When they go out on the limb and get divergent, they're told that there is only one answer and it must be accurate (i.e., they must do convergent thinking) and when they toe the line and engage in convergent thinking, they're told that they must learn to think (i.e., divergent thinking).
I am hoping that PSLE will be better set and marked than school papers because I AM going to use the next few weeks to prime my son for divergent thinking (which I have unknowingly suppressed for the past few years in order to get the THE right answer that is in Teachers' marking scheme). Thankfully, I still indulge Little Boy's penchant for divergent thinking in non-PSLE areas... and so, it should not be too difficult to get him going there for PSLE.
To begin with, we've stopped doing Science drills and gone over to the library to just borrow any science-related video... just to open his brain to possibilities and stimuli. No more Science drills for us!!
Do MOE's Schools Teach/Test/Reward Divergent Thinking?
Some psychologists have developed cognitive exercises to help the brain learn divergent thinking. I have not observed anything like these in schools. So... my answer will be "no". Our schools don't teach divergent thinking. They expect that if you're smart, you'll naturally know.
The schools DO test divergent thinking. The most difficult questions in the PSLE Math paper test divergent thinking. The inference questions in the PSLE English comprehension paper test divergent thinking. The opinion questions in the PSLE Chinese comprehension paper test divergent thinking. The open-ended Science questions test divergent thinking.
Strong divergent thinkers see things from a DIFFERENT perspective. But their new angle makes sense, can be logically argued and gives insights. There should be multiple correct answers to divergent thinking questions. People should be rewarded for seeing things differently... and still logically... and reasonably.
However, when it comes to marking, schools tend to mark divergent thinking questions as if they were convergent thinking questions. If the answer is so fresh and different, then it must wrong, even if it is perfectly reasonable. If it isn't in the marking guide, it is wrong.
I conclude therefore that schools don't really know how to teach divergent thinking. They don't teach it explicitly. They do test it. And then they mark it according to the norms of convergent thinking. There is a right answer and if your answer doesn't match my marking guide, it is wrong... inaccurate.