"Infants do not take communion, neither do any children in the parish who have not received the appropriate instruction about what they are receiving."
They do in the Eastern Rite Churches in communion with Rome, of course there it isn't lay catechism teachers who decide who does and does not get to receive the sacraments. Frankly, I think what this teacher is doing, apparently with the approval at least of the parish priest and perhaps even of the diocese is at a minimum unfortunate and at a maximum, downright heretical as a denial of the grace of the sacrament. What does intellectual, physical understanding have to do with theosis by the grace of God imparted through the Mystery of the Eucharist, or any other sacrament for that matter?
As for a piece of bread and grape juice at the Methodist Church, well, that simply isn't the Eucharist and so far as I can see, doesn't pretend to be.
"Infants do not take communion, neither do any children in the parish who have not received the appropriate instruction about what they are receiving."
In the western (Roman) Catholic church this is true. It is not true in the bulk of the eastern Catholic churches. In my church, infants are Baptised, Chrismated (confirmed) and given first Eucharist at the same time.
The points of emphasis of the eastern Catholic churches are different than that of the western Catholic church. This is clearly one of those areas where the eastern and western perspectives differ. The eastern point of view sees the Mysteries (Sacraments) more from a gift perspective than as a right that is to be earned.
In my personal opinion, the eastern Catholic churches are correct on this. But then again, you'd probably guess that given that I'm going to an eastern Catholic church :-)
As for a Sunday school teacher being qualiifed to be the arbiter of who should and should not receive first Eucharist. I guess I'll have to add this to the list of innovations that I disagree with my Roman Catholic bretheren about.