Sotah, Chapter Five, Mishnah Four
This is the third midrash of Rabbi Akiva. It deals with the Song of the Sea, a passage familiar to those familiar with shacharit, the morning prayer service. We should note also that the sages use their knowledge of prayer practice to interpret how the Song of the Sea was performed when the Israelites crossed the sea.
1) On that day Rabbi Akiva expounded, Then Moses and the children of Israel sang this song unto the Lord and said saying (Exodus 15:1).
a) For the Torah did not need to say saying, so why did the Torah say saying?
b) It teaches that the Israelites responded to every sentence after Moses, in the manner of reading Hallel; that is why it says saying.
2) Rabbi Nehemiah says: as is the reading the Shema and not Hallel.
Section one: The beginning of the Song of the Sea seemingly has an extra word lemorsaying. Rabbi Akiva understands that this word reveals that when the Israelites were crossing the sea, they sang the song in the same way that Hallel (the collection of psalms recited on festivals and other holiday) is sung. The way Hallel was done in Rabbi Akivas time is that the leader would say a series of verses and everyone would repeat the beginning of the first verse after him. In other words, the leader would say Halleluyah and everyone would say Halleluyah. Then the leader would say the next verse and the people would repeat Halleluyah. The other psalms also would be repeated in a similar manner. Hallel is not done this way anymore.
We should note that again Rabbi Akiva finds scriptural support for what was only a custom until his time.
Section two: Rabbi Nehemiah says that the Song of the Sea was recited in the way that people publicly recited the Shema in his day. The leader would say the beginning of the verse, and the congregation would recite the end of the verse. The Shema is not sung in this manner anymore, nor has it been since the time of the Talmud itself.