The phrase ‘without them knowing’ seems widely used despite the debate about its grammatical correctness. Those who object to this form argue that ‘knowing’ is a kind of gerund, which should not follow an object pronoun like ‘them’, but a possessive pronoun like ‘their’. Those who support this phrase maintain that ‘knowing’ here is a form of present participle, similar to a gerund, so that it is fine to use it to modify the pronoun ‘them’. There are many other cases following a similar pattern – combining object pronoun with a verb in -ing form. Above are some examples.