Not having experienced 'whole word' or 'phonics' - I am yet suspicious of all such simplistic solutions as imagine that small homo-saps may be homogenized and a Best Technique\ufffd determined by the TLA creators (and textbook Corporations).
My own experience - that which I can recall only via a few 'vivid' snapshots of the classroom and of exchanges - is likely irrelevant to a 4 yr. old's place. I too was read to a lot, and an aunt with whom I stayed for a time, was a grammar school teacher ie. my 'epiphany' occurred prior to 'Methods' and classes. (I would also surmise that kids generally, Could learn a lot more about reading, lots earlier - given that priceless Attention that is in such short supply now.)
Still FWIW - I recall an easel with large posterboard, many leaves/sheets turned over. Word-length from 4- to ~12? The sheets were progressive.. more for length I think - certainly no hypertext relevance to the sheet or succeeding ones. These were useful to my grokking the system, too - even though I was 'advanced' vs the rest. "Their/there" and such - became perfectly clear.
Repetition of common words - their sound and what they looked like, was interspersed with what I now suppose was some attention to varying sounds of similar letter groups. Then reading aloud, with corrections - but not obsessively. That is, sometimes the teacher would 'praise', go on and illustrate any corrections in her own speech, but later on. (A subtlety I noted - and it may be an important detail.) But these were classes with perhaps a dozen - 20 students and Lots of teacher attention. No knives, guns, beepers or dissing, etc.
Prolly like many here, I spent my 'reading' period either reading the stories at the end or in another book - unmolested by a teacher intent upon regimentation. I guess that isn't the norm now.
Good luck - you may be able to divine 'how' your charges are angled to learn by trying several approaches, even intermixing the dogmas of the Pop methods. If they are interested enough to ask (any kind!) questions: you're on to something.
You might even want to pick up a copy of Summerhill from library: an English school which pretty much threw out the books on 'what school might be for', and how can that be tailored for very different individuals? It's old but then - so are people.
Hell.. if we Knew! how to create marvellous teachers...
Cheers,
Ashton