Mathematical collocations
There is a phrase people use when talking about statistics that really bugs me. It's "non-parametric data". I see it all the time in statistical teaching materials and I hate it because I know what they mean, but what they've said is simply wrong. Whoever writes this phrase has a tenuous grasp of what the word non-parametric means. If they really understood what it meant, they would realise that the word non-parametric can only be used to apply to a statistical procedure, not to the data itself; the words "non-parametric" and "data" just can't be put together like that.
Ok, so now I've had my rant, let me tell you about the word collocation. I was looking at what was on the other side of our scrap paper recently (this is always a good way to procrastinate), and I found myself reading drafts of the PhD thesis of Julia – one of the Writing Centre team. The bit I was reading concerned whether people understand certain idioms and how you might include information on what these idioms mean in a dictionary. As is appropriate for a scholarly work, Julia spent quite a bit of time discussing what is meant by an idiom, and here is where collocation comes in.
One of the features of an idiom is the fact that it contains certain words which need to go together in a certain order. For example, the phrase "a piece of cake" has to contain both the word "piece" and "cake" or it just doesn't mean the same thing. This phenomenon is called a collocation – some words just go with other words, and other combinations either just don't happen or have a different meaning.
Julia pointed out that part of learning a new language is learning which words go with which words in order to make a collocation. For example, you need to know in English that "piece" collocates with "cake" in this way, but that you can't say "a slice of cake" and mean the same thing. As another example, you need to know that the word "hand" can be used in collocations such as "hand in", "hand up", "hand over" and "hand out", but not "hand under". And as a final example, you need to know that the word "fro" can't stand on its own as a word but must be used in the specific collocation "to and fro". These are difficult things to learn because most native speakers don't even realise they are doing it; it's just natural to them. And the native speaker can often tell there's something wrong with what a non-native speaker said, but sometimes can't quite figure out why it sounds wrong. So the teachers of language have to point these things out explicitly as new words are learned.
And it occurred to me while reading this that collocations are really important to know about when learning maths too. In geometry we say that a point is "on a line", but we say a line is "in a plane". In set theory we say that an element is "in a set", but a smaller set is "contained in a set". (We even use different symbols for element-in-set, and set-contained-in-set.) In calculus we say that this is the Taylor series "for this function", not "of this function." And in statistics the word "non-parametric" collocates with the words "test" and "statistics", but not the word "data".
Yet somehow we expect our students to pick this up all on their own. I think we need to learn something from our esteemed colleagues teaching language...