Yes - Look and Say is what USED to be taught, as Phonics, in its current formal sense, hadn't been adopted. When I started as a TA in 1993, we even used 'blends' of letters such as 'tr' and I spent hours teaching 'tr = train, track, truck, trip' etc.
More recently, when Phonics had arrived, I sometimes had pupils who did exactly as you described - the LAST sound they heard was the one they used, and for some reason, they seemed unable to focus on the INITIAL sound.
If you possibly can you DO need to gradually steer her towards using Phonics, and patient, sympathetic support should get her there before too long. I did voluntary help in a Reception class, where children knew books off by heart, and would 'read' accurately, but without even having the book open on the correct page! So that is not 'reading' at all!
I will give you a few helpful items:
ONE - When I worked with less able Yr2 children, who were finding learning to read particularly difficult, we often used a SoundWorks kit, which consisted of a set of wooden letter blocks, which the child used to build simple words.? The theory was that, for some children, it is easier to SPELL words than READ them, which is a later stage.
It started with three-letter words, with a vowel in the middle - "a" glued onto a board.
The child then looked at the individual letter blocks, and was asked to make the word "c a t". Then he was asked, how do we change "c a t" into "h a t", which letter do we need to change? Then change "hat" into "ham" (with an emphasis on the "mmmm" sound).
Work slowly, and pronounce the sounds accurately and clearly. This approach was used with our Yr2 children who had been unable to make progress with more conventional methods of learning to read. It is rather time-consuming, and ideally needs resources to be made, but it does work very well.
So, if you can find or make suitable letters, and make a card with "a" glued in the middle, your child may enjoy building the words. Use letters that are occurring in words in the books he is bringing home, and then go on to make cards for the other vowels if it seems to work with "a".
TWO - An inexpensive and easy to use book, that can encourage children with reading, spelling and writing, and really help them to understand Phonics, is reviewed in the MN Book Reviews section. Just search ‘Phonics’.
THREE - ?When reading harder books with a child, get him to point to words as he goes along. If he knows the word, or can sound it out, he can say it. If he doesn't know the word, he can hover his finger over it, and YOU say the word for him. Don't stop to analyse or discuss the word at this stage, but try and keep the 'flow' of reading going. Review difficulties at the end, if you wish to.
This way, he has the satisfaction of reading more difficult books, without the fear of getting 'stuck' on words.
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I hope these ideas might go some way towards helping you both. I'll look back sometime, and see how she is progressing.