In NSW selective school literature, they talk about higher order thinking. However every one wonders "How high is high enough?" To understand this we can refer to Bloom's taxonomy of knowledge for a clear picture. We generally know that "knowing" is just the start and would be at the bottom. We also know that creating new knowledge (or invent) is the highest and it is at the top. There are 6 levels in Bloom's taxanomy of knowledge, and most students only work at level 1 and 2 from the bottom. But the selective test questions are mainly positioned at the top 2 levels with very few questions at the 3rd level from the top. This is why most top students only score between 65%-75% and the above average students only score about 40% - 50%. If we account for the effect of multiple choice which already give students 25% chance to get something right, the average students only ever get about 10%-15% right to get about 35% in these tests. That is very little for the average students.
This also explains why private schools consider writing as the most important area for English. It is because a good writing work is a right at the top 2 levels of Bloom's taxanomy where the writer create/invent/put things together for a purpose. Students have to have the right ideas and also have enough command of grammar and words to put express their "creative" ideas. Certainly, there are a lot of students who write badly and barely operate at level 2-3 from the bottom. It is very easy to see the loose ideas that don't come together.
When a teacher (or parent) teaches kids, they have to be aware of the order too. One very common mistake is to attempt to make the kids think at the 2nd level from the top (Evaluate level) when they are only at the 1st or 2nd level from the bottom. In all problem solving questions, the answer is at the 2nd level from the top (Evaluate), yet students generally struggle at 4th or 5th level from the top. Good teachers know how to check for students' prior knowledge to find out what level they are at and only teach at 1 level higher than where they are to take them up 1 level each time. Failing to do this, students will have to try to remember the solution. This is what we call "rote" learning. This is learning by remembering only and one cannot apply the knowledge in slightly different situation as there is no real understanding.
So if you attempt to teach kids (or any one), you must start from where the person is for a particular topic and work the way up to the top. There is no short cut!
What they do at tutoring colleges' trials is drilling work where students get to do a lot of questions so they become familiar and can do them quickly in exam condition. This is only effective when the students already operate at the top 2 levels of Bloom's taxonomy. They already can evaluate and create therefore they only need better speed. The majority of students only at the bottom 3 levels so they cannot solve the problems. Parents just hope that they get to remember the solutions (by rote) and get lucky when there are very similar questions in the exams. This is why the majority of students who have done 10000 questions cannot score better than the smarter ones who only do 1000.
Having said all that, the majority of students who enter top 10 selective schools barely operate at the "Evaluate level". This is why they still benefit from doing at least 5000 questions to win places in these schools! This is why on Mathemafix, the ones who get similar scores by doing less will end up getting higher results. But the ones who are really smart but they do only about 2000 questions (and have unstable scores) also score lower. At the level of top 10 selective schools, one cannot do very little or come from low intelligence and still get a chance. There must be a bit of both.
Here is an excellent Youtube video on Bloom's taxonomy. https://www.youtube.com/watch?v=KGXANN3MUsg
Today the revised Bloom's taxonomy is mostly used as it makes more sense to put Synthesis at the top over Evaluation. The word Synthesis is hard to understand. So they change it to Creating. This makes perfect sense as you cannot really create anything new (that is of any value) without understanding. At the synthesis/creating level, you actually create new things or new knowledge from what you have at hand.
Bloom's taxonomy (Remembering, Understanding, Analyzing, Applying, Evaluating, Creating). In the old thinking we have (Learning, Practicing, Working), so we can map the old to the new as Learning = Remembering + Understanding + Analyzing, Practicing = Applying + Evaluating, Working = Creating
It looks like the new Bloom's taxonomy is more detailed and refined than what people know for thousands of years before. It is based on cognitive psychology which is a very modern learning area.
What parents can do to help their kids is to expose them to higher order thinking all the times at home. Get them to think. Don't feed them with answers before they get a chance to think. Ask them leading questions rather than telling them before they even start to think. We tend to avoid wasting time by telling kids directly, but this actually stops them from thinking.
Example: Higher order thinking is like this.
"Why do plants need the Sun to grow?" asked Vincent.
"Well, it is a bit like how your mum needs energy to cook your food. Think about it. Google a bit about it if you like." replied Dad.
Don't spit it out.
"The plants get energy from sunlight to make food for themselves."
This would be spoon-feeding and won't encourage higher order thinking! This encourages rote-learning to save time.
More on Bloom's taxonomy
List of action verbs at different levels: http://www.cte.cornell.edu/documents/Assessment%20-%20Blooms%20Taxonomy%20Action%20Verbs.pdf
By using the verbs at the correct level, one can help kids to use correct level of thinking. So it is a BIG learning job for parents too!