So my student reads the sentences, and first looking disconcerted and then exasperated, says “Why is the word 'up' there? I hate that word!”
I was taken aback, this student not usually given to such paroxisms. Seeing my perplexity, he explained himself: “Why is the word 'up' in the sentences? Can't you just say, 'I'm heating the beans' and 'I'm eating the beans'? Now I understood. To him it looked like 'up' was a useless, unnecessary word someone had stuck into the sentence. What was it doing there!?
By the way, I actually relish these moments of being taken by surprise and maybe even being thrown slightly off balance. After you've been teaching for eons you need this sort of thing to keep you on your toes.
Anyway, my first response was probably quite typical: blame someone else! In this case, the authors of the coursebook. In their endeavor to come up with these minimal pair sentences, they've written, what for me at least, is a pretty unlikely sentence: 'I'm eating up the beans'. Although you never know, maybe it's more common in the UK (I'm from the States): I'll have to ask my colleagues.
In any case, my student's forgotten all about the pronunciation: he wants to know: which is it? 'I'm eating the beans' or 'I'm eating up the beans'? I basically said the above (it's the authors' fault), and that 'I'm eating the beans' is much more likely, though the other sentence is possible with little change in meaning. Well, perhaps it suggests you're eating all the beans. And likewise, 'I'm heating up the beans' is more likely.
So, being the ever-inquisitive teacher that I am, I asked my erstwhile positive student if there were other words he detested, and why. Basically he said he hated words you often see and with lots of different meanings, because they can be hard to figure out. Other examples he gave were 'get, set, go, make, come'.
By the way, all this reminds me of a sort of gimicky way I once saw to sell English courses, which was something like, '1,000 words to English fluency'. They claimed studies had revealed that native speakers use just 1,000 words for 80% of their communication, so all you had to do was learn those 1,000 words and viola! you were 80% fluent (I suppose). The implication was that this was a shortcut to language competency. I really believe there are no shortcuts per se. I mean, the best way to learn English is to get a good teacher and work your tail off.
In any case, the above 'methodolody' ignores the existence of chunks of language, such as collocations and various types of fixed expressions. For example, returning to 'up', some expressions are 'It's up to you', 'I'm up for it', and 'up to now'. These really need to be learned as single language items: knowing the meaning of the isolated word 'up' doesn't help much. So the 1,000 'words' are probably more like ten or twenty thousand language items.
By the way, the Lexical Approach calls the words my student dislikes 'delexicalized words', which means common words with lots of meanings, so alone they have very little meaning, thus context and co-text are very important to know what's going on. For example, the word 'get' alone doesn't say much, does it mean 'obtain' (I got the ticket), or does it mean you stopped lying in your bed (I got up early)? We could contrast this with low frequency words with few meanings, for example 'identify' and 'verify', where the meaning is fairly clear from the word alone.
One thing we can do to help our students is to explain the above to them, let them know the nature of the beast, so to speak. Furthermore, I sometimes find it helpful to share my own trials and tribulations when I was learning the basics of Spanish. For example, Spanish has delexicalized words too, like the word 'picar', which can mean to snack, to itch, to sting, to chop, to be spicy; and more. Of course 'poner' and 'ponerse' are great; 'ponerse' can mean anything from 'put on clothes' to 'lay an egg'!, so words like this need context and co-text to clarify meaning.
In any case, getting back to my student, I would love to be able to wave a magic wand and have him learn all the meanings of 'up' and 'get' (except that I might be out of a job). Unfortunately you can't download knowledge and skills into your brain like they do in the film Matrix. The main 'shortcuts' are a good teacher, good study skills, and hard work. A lexical notebook is useful, for example, students could have a section or page just for expressions with 'up'. Whenever they run up against a new one, they add it to the section, until they fill it up!
Another issue is keeping things positive. I think when students really come to grips with what they're up against, they can feel discouraged, after all, learning English is quite daunting. Who knows?, they may even start hating words. But it's vital for them to feel they're progressing. OK, I'm not going to lie, it's a long road to language competence, but if at least they're getting a rich diet of English language and are progressing, they'll be motivated. Before long they'll be able to heat up their own beans.