ngalinh wrote:
I.e., you're busying yourself with trying to "classify" things -- subgroup data, "classic" pattern, etc. -- instead of actually thinking about the situation described in the problem.
Those kinds of thoughts should always be backups, to be used only if you are completely confused by the situation described in the passage.
You seem to know every corner in students' mind. :(
Nah, I've just taught many different things, to many different ages of students. One thing I've learned, in general, is that
terminology/classification kills understanding.
In other words, as soon as there are "names" or "labels" that people can stick on things, they just stop trying to
understand those things. Instead, it just becomes a game of slapping meaningless labels on things.
As an example, the concept of losing/gaining electrons, from elementary chemistry, is very simple. Honestly it's something that a six- or seven-year-old would have very little trouble understanding. (An electron is "minus one". If you add that, you are minus one. If you take it away, you are plus one.)
But, as soon as those things are given the name "cation" and "anion", WHOA all the understanding just goes out the window.
Unless students already understand the concept before they are given the names, it becomes an extremely difficult struggle to learn
anything once the names are given. This is a pretty common theme.
Same thing is usually true in real life. Consider things that you put into your body. A contrast:
* When people think about medicines, they don't normally try to classify the medicines. (Jim takes Prozac for depression; he doesn't think about the fact that it's called a "SSRI". He takes Advil for pain, without thinking that it's called a "NSAID".)
As a result, they have a pretty good idea of which drugs do what things to them. They may not understand all the biochemistry, but they'll have a pretty detailed
practical understanding.
* When people think about nutrition, though, they have the term "carbohydrate", which applies to a huge and diverse set of different types of foods -- everything from potatoes to high-fructose corn syrup.
Because the label "carbohydrates" exists, the vast majority of people simply never formulate any understanding of the functions of, or the differences between, the foods that receive that label. So you get people who think that eating brown rice and eating sugar are basically the same. They don't understand the differences at all; some of them don't even know that there
are differences.
It's all the label's fault.
If the label "carbohydrate" didn't exist, people would
think more about how these foods actually affect them, and about the differences that exist between them.
Just keep these examples in mind. And make up more of them. (Imagine if you tried to make a five-year-old memorize the term "jerk" before the child understood what manners are! That would be a disaster.)
Never stick labels on things until you
already understand how they work. Once that understanding is VERY solid,
then go ahead and slap all the labels you want on things.