CM would say that a child the age of 9 on up who can do his/her own readings should do them independently.

We've always used that guideline with our own kiddos for history and science. Depending on which guide you are in, for example if you are in Bigger Hearts, then you could start having an 8 year old read his own science if desired. This is because the science readings in Bigger are quite short. Just make sure the retention is there.
I also started guiding my kiddos to read directly from the guide in science first in Bigger to start training them for the "I" boxes coming in Preparing Hearts. This was just me, because my kiddos could read well and were ready for more independence, and I was busy, busy, busy. So, it benefitted us both!

When they turned 9, I had them take over the history readings in Bigger too.
Blessings,
Carrie