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It may seem to you quite obvious what is countable and what is not. Perhaps you think that some nouns, like apple are countable and others, like cheese, are not. Moreover, you might think this is very easy to explain to students. You might even think that somebody who didn't get the concept must be a little slow.
If you check the LDOCE – and you should check it regularly because it has lots of great information about words – you'll find that apple has both countable and uncountable senses, as does cheese.
Well, here's how the LDOCE defines uncountable: "An uncountable noun has no plural form and refers to something which cannot be counted or regarded as either singular or plural, for example ‘money’ or ‘happiness’."
Unfortunately, the LDOCE has fallen into the precise thinking trap I warned you about. So, let's try looking for counter examples. Can you think of something that DOES have a plural form but which cannot be counted, in other words, a plural noun for which you can't say two X?
So, we see that the definition of uncountable in the LDOCE is wrong, even though the LDOCE is generally a very good resource. Maybe this isn't so easy. But definitions aside, you may think it should be quite obvious what is countable and uncountable. But if that were the case, then we would find the singular nouns always translated as singulars and plural nouns always as plurals (at least, when a language has plurals). If you speak another language, perhaps you can think of counter examples. After you've given it some thought have a look at this:
What makes things even more puzzling is that synonyms in English aren't even consistently countable or uncountable. For example, advice is uncountable, but opinions are countable. Can you think of any other pairs like this?
Each of the following is typically countable, and each has an uncountable synonym.
It's easy to think that ideas that we take for granted, such as whether a word is countable or not, are objective facts. In many cases like this, they are actually intersubjective judgments, each one unpredictable to those outside the community of speakers of a given language or dialect.
Many language-teaching materials treat countability as if it were obvious from mere introspection. Far from it! Consider the following explanation from a textbook, which is perfectly simple if you speak English and almost entirely unhelpful if you don't.
The book assumes that plums are countable because you can count them, and you can count them because they're countable. What could be easier? What about rice and seed? There is no way for a learner of English to guess that you can say two seeds but not usually two rices meaning "two grains of rice". You'd have to be talking about two types of rice).
There is great diversity in the world. Don't be so blind as to believe that your way of categorizing stuff into that which can be counted and that which cannot is in any way natural or objective. And remember that when your students make the Standard English choice, you should respect them for having achieved an insight into our peculiar way of looking at the world.
Surely, something as basic as the distinction between singular and plural nouns would be straightforward. In English, regular plural nouns are marked with an -(e)s (e.g., cats, things, students, studies, etc.). But what is the meaning of plural? Most people take the everyday meaning, "consisting of or containing more than one of something." But is this true of plural English nouns?
What critical thinking strategy should we employ here?