The Gaon of Vilna (Biur HaGra) gives us a reason why Shir Hama’alot are recited in the winter and Pirkei Avot in the summer. As the winter days are shorter and Mincha is closer to nightfall, this leaves little time for Torah study without pausing for the Seuda Shelishit. In the summer months, however, when the days are longer, Pirkei Avot replaces the study of Aggada.
The Mishna Berura in his Sha’ar HaTziyyun commentary (ad loc.) explains it otherwise. As we note from the text of the Rema, the study of Pirkei Avot differs from in-depth study – which we avoid even in the summer months at that time because it may interfere with the Seuda Shelishit – as it is rather just an utterance, amira.
However, in his Mishna Berura commentary (ad loc.) the Chafetz Chaim notes that since many people come to shul on Shabbat afternoon and engage in sicha beteila, idle conversation, it is better to listen to words of mussar (words of reproof) which will cause them to refrain from such idle conversations.
[Obviously, when we refer to summer and winter in this discussion, we refer to the times when the applicable prayers for these seasons are begun. The "summer" begins on Pesach, when we start saying Veten beracha and Morid haTal (for Nusach Sefarad and all nusachim in Eretz Yisrael), which are our summer prayers for dew; that is also the time when the days are longer. The "winter" begins at the conclusion of Sukkot, when we start the prayers for rain - Mashiv HaRuach and subsequently Tal u'matar li'veracha.]
Since there are six Sabbaths between Pesach and Shavuot and there are six chapters in this tractate, we devote an entire Sabbath to the study of each chapter. After Shavuot, specifically in Elul, there are weeks when we “double up” and learn two chapters on one Sabbath. We always read the last chapter on the Sabbath before Shavuot, as you note.
Furthermore, this last chapter, which is referred to as Kinyan HaTorah (lit. the method of acquiring Torah), as you indicate in your question, is not part of the original Mishnayot compiled by R. Yehuda Hanasi, but is rather a compilation of Tannaitic Beraitot that were added subsequently and appear in the Vilna Shas as a sixth chapter of the tractate. The term Kinyan HaTorah is based on two Mishnayot (6:5-6). [In most siddurim, the list of the 48 qualities through which one acquires Torah knowledge is included in Mishna 6:6; however, in the Vilna Shas it is split into Mishnayot 6:5 and 6:6.]
The newly published Matnot Chayyim, authored by HaRav Matisyahu Salomon, shelita, Mashgiach Ruchani of Beth Medrash Govoha in Lakewood, New Jersey, and formerly of Yeshiva Beth Yosef in Gateshead, England, contains a compilation of essays about Kinyan HaTorah, as specified in this Mishna. [The book is available through Israel Book Shop, Inc., Lakewood, NJ, (732) 901-3009, or in England at Lehmann's, 191-430-0333.]
In his preface, the author explains why this tractate is studied during the weeks prior to Shavuot, and we shall see that our Sages deliberately set this course of study at that specific time of the year.
R. Salomon explains that the preparations for Mattan Torah, receiving the Torah at Mt. Sinai on Shavuot, are accomplished through the 48 methods of acquisition listed in the last chapter of Avot, which is thus referred to as Kinyan HaTorah. Although there are numerous reasons given for the study of Avot, it is proper to bring the words of the Hasid Ya’vez, as found in Midrash Shemuel: “The Torah can only dwell in one whose being is devoid of negative traits, and who is full of important [and admirable] traits.” This is what Hashem meant when He states in Parashat Yitro (Exodus 19:15), “… Heyu nechonim li’sheloshet yamim, al tigshu el isha – Be ready after a three-day period, come not near a woman.” [Rashi ad loc. explains that this refers specifically to the purification of the women of Bnei Yisrael so that they would be ritually pure at the time of the giving of the Torah. It is understood that the men would be ritually pure as well.]
He adds that similarly, the cleansing of one’s clothes (ibid. 19:10) suggests that one must purify oneself from the ritual impurities and uncleanliness which restrain the soul from reaching its highest level of attainment, and all the chapters preceding this last one are replete with
important matters that enable the soul to come closer to its Creator and thus awaken a person to service to Hashem.
However, he points out, this last chapter of Avot is completely focused on the attainment of Torah, and, as such, Kinyan HaTorah is the appropriate chapter for us to study before Shavuot.
(To be continued)