In this post I am going to argue that the meaning of the word ἀνάμνησιν in 1 Corinthians 11:24-25 does not provide evidence one way or the other as to whether children may participate in the Supper, since the whole question depends on a prior question of whether infants participated in the Passover.
First of all, I reject the interpretation of the word that makes it into something that God remembers.
The reason for that is very simple. The folks who have argued for this position have been using the wrong Old Testament precedents for arguing as its meaning. John Barach, for instance (and I think Leithart also goes this direction), looks to the Noahic covenant and the rainbow as a precedent for understanding the term in this way. The problem here is that there is a much more direct precedent for understanding the term, and that is in the institution and instructions for Passover itself. Even Leonard Coppes agrees that the Passover is part of the background for the Lord’s Supper (Coppes would argue that most of the other Old Testament feasts participate in the type as well). Deuteronomy 16:3 says this:
לֹא־תֹאכַל עָלָיו חָמֵץ שִׁבְעַת יָמִים תֹּאכַל־עָלָיו מַצּוֹת לֶחֶם עֹנִי כִּי
בְחִפָּזוֹן יָצָאתָ מֵאֶרֶץ מִצְרַיִם לְמַעַן תִּזְכֹּר אֶת־יוֹם צֵאתְךָ מֵאֶרֶץ
מִצְרַיִם כֹּל יְמֵי חַיֶּיךָ׃
In Greek: οὐ φαγῇ ἐπ᾿ αὐτοῦ ζύμην· ἑπτὰ ἡμέρας φαγῇ ἐπ᾿ αὐτοῦ ἄζυμα, ἄρτον κακώσεως, ὅτι ἐν σπουδῇ ἐξήλθετε ἐξ Αἰγύπτου· ἵνα μνησθῆτε τὴν ἡμέραν τῆς ἐξοδίας ὑμῶν ἐκ γῆς Αἰγύπτου πάσας τὰς ἡμέρας τῆς ζωῆς ὑμῶν.
In English: You shall eat no leavened bread with it. Seven days you shall eat it with unleavened bread, the bread of affliction—for you came out of the land of Egypt in haste—that all the days of your life you may remember the day when you came out of the land of Egypt.
The point here is that “remembering” is clearly second person in both Greek and Hebrew: “You will remember.” The verse has a summarizing feel to it such that this is the purpose for the Passover, so that the people will remember.
Exodus 12 does nothing to shake this conclusion, since the whole emphasis is on the people remembering. They do all the necessary preparations so that they will remember everything the Lord wants them to remember. There is no indication in Exodus 12 that the Lord is doing the remembering. Of course, Tim Gallant argues (pg. 86 of Feed My Lambs) that it is both God remembering and the people remembering. He argues that ἀνάμνησιν means both, and that it is the purpose of the Sacrament, not a prerequisite (pg. 85). I am personally leaning towards the people being the ones who remember on this one, as I see no indication of Passover meaning anything else. There is no proof that the word means anything other than the people’s remembrance. Even if there were, it would not prove that the word meant that in 1 Corinthians 11. If the Passover is the main antecedent in the Old Testament (which I agree that it is), then the Passover’s theology of remembrance should carry over into the Lord’s Supper. The reason why this argument cannot be used in favor of credo-communion is that it is debated as to whether children partook of the Passover. If they partook of the Passover, and yet they can still be said to be doing the remembering by their very partaking, then the argument is not proved one way or the other. The whole question will then turn on whether children partook of Passover or not.