I'm sure that many a schoolboy, BBC reporter, or Mother Superior must have thought long and hard about this most important of questions. 'Is it more efficient to sweep towards yourself, or away?'
My own thinking suggests that to sweep towards you somehow manages to collect more detritus (dust, dog hair, or dead leaves) than if one pushes away. I can offer no scientific evidence to back my claim, just some satisfaction in hoping that I'm right. I do quite a lot of sweeping (especially leaves, etc) so an answer to this question might save me hours.
Of course the quality of the brush or broom makes a great difference to sweeping, but given the right kit there should be an optimum method of sweeping. Maybe some Oxford boffin would like to do research into this subject; that is, if they're not too busy removing photos of H M The Queen from halls.
I have never bought a broom with instructions suggesting an answer to this thorny subject. All brooms SHOULD come with instructions.