Shammai said, make your Torah study fixed, say little and do much, and receive everyone with a cheerful countenance."
So much has been said about this Mishna that one despairs of saying something new. However, when one utilizes a novel methodology one perforce produces new insights and so is the case here.
I start by conisering what "fixed" means. The word that the mishna uses is "kva". What did this word mean in the time of Tannaim?
There are two references to" Kva" in the Mishna in Brochos. The fits mishna of the fourth chapter says that the Maariv prayer is NOT "kva". The Gemara explains that this follows the view of Rav that the evening prayer in not obligatory. More instructive is the statement of R. Eliezer, the Shammaite (Niddah 7b, see Tos) in the fourth mishna of fourth chapter: "He who makes his prayer "kva", his prayer is not supplication". Yerushalmi explains:
R. Abbahu in the name of R.Elazar says that it means that one should not read it as if reading from a letter.R. Acha in the name of R. Yosi says: One must put something new into it every day....R.Zeira said: I always did so and made mistakes....R. Eliezer said a new prayer every day.R. Abbahu said a new blessing every day". In summary, a prayer which is "kva' has a fixed text. Prayer should not have a fixed text but should vary form time to time. Torah must have a fixed text. Thus, when Shammai says that "you shall make your Tora "kva", he means that the your Torah should have a fixed text.
We know from Iggeres R. Sherira Gaon (Ch.2) that in the years prior to writing down of the Mishna, each Tanna taught and organized the material that he had received in his own way. There ws no fixed and approved formulation of halachos. At the time of the Mishna there came to exist various formulation of the same material, each phrased and expressed in a somewhat different language. "Some taught general rule; others added detail; and others expanded and offered many examples and analogies." Presumably, this itself may have led to different understandings and interpretations of the same original traditions. Rebbi elected to follow the formulations of R. Akiva and his students while relegating other collections to "external" status; this explain preponderance of certain names in the Mishna and its focus on citing later Sages.
When did this process of fixing the exact formulation and wording begin? There is evidence that it started in the times of Hillel and Shammai. "Eiduyos 1.3 states: "Hillel says that a full hin of drawn water makes a mikveh unfit; except that a person must use the style of expression employed his teacher; and Shammai says 9 kabs." Rambam in his commentary on the Mishnah wrote: Shemaiah and Avtalion were the teachers of Shammai and Hillel, as is made clear in Tractate Avot. Being proselytes, their speech retained some pronunciations used in their former gentile language, and they would say 'in instead of hin. That is what the Sages meant when they said "a person must use the style of expression employed by his teacher." Similarly. R. Elezer, a student of Shammai, never said something that he did not hear from his teachers (Sukkah 28a). Many ask how is it possible that he NEVER said anything new; did we not learn that .R. Eliezer could expound things that were "more than what said to Moshe at Sinai"(PRD"Rabbi Eliezer, Ch.2)? What it might mean, however, is that he never said something that was not exactly in the wording and formula that he received from his teachers.
This is what Shammai also taught. "Make you Torah fixed", means that on every topic and for every legal principle you should have the one fixed, canonical and exact phrasing and expression, and not, as it was in the past, a general presentation of a topic, relying solely upon the students' understanding of principles to guide him in his future explication of the Law.
Furthermore, Shammai taught that one should "say little" and do much. This means that a teacher should transmit a concise and limited text and explain it well and at length, so that the student has the both fixed text and ample explanations to be productive in future explanations and explication of halacha. WIth time this approach became known as Gemara or Talmud. The word "Aseh" (do) can be used in the sense of "to produce", meaning to produce in the future (See the commentary of Netsiv and Beis Haleivy to Genesis 2:3).

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