I think the pedal is still needed for the right hand, so that those notes sound nice too. I haven't started that piece yet though π
What I like about following all three method books: they don't cover everything at once. In the first two books they didn't cover much theory at all, because they know we beginners just like to touch the piano ππ½ And our brains are not ready yet for super complicated techniques, we struggle enough just reading the score, finding the notes and making our fingers obey.
But now the third Alfred book is starting to apply the thumbscrews... circle of fifths, more chords, more scales, diminished 7th chords and soon arpeggios. Another buzz word everyone keeps telling us they are so important... but I was patient and waited for Alfred to introduce all those things. That gives me time to also do stuff I like, such as the blues course π
Actually I am really loving this third book though. Towards the end it will allow us to play some actual music, such as original versions of the first movement of Moonlight Sonata and Fur Elise. But I am starting to think that my first love might become lighter music such as blues and easy listening... it's too early to tell still.
Either way, we need to continue to learn - and this forum is really helpful in providing both tips and motivation π