Serious question here from someone who did A-level Latin back in the dark ages and has a pretty 'traditional' knowledge of English grammar. Do 'connectives' correspond at all to any traditional parts of speech (conjunctions, prepositions etc.) or are they just any random small words that sew bits of English sentence together? 
I realise I'm probably overthinking this and it's probably only the if's, but's, when's and wherever's that the teacher gives as an example (this is primary school literacy, after all) but can anyone with a relevant background (or chalkface knowledge) clear this up? I didn't think 'new grammar' could be as confusing as 'new maths'!