Tosfos cites a Yerushalmi which notes that Ben Azzai does not follow the exposition of Rabbi Elozar ben Azaryah. For it is written regarding the mitzvah of Hakhel that men, women and children should assemble. The men come to learn, the women come to listen and the children come so that those who brought the children can earn reward. According to Ben Azzai, the reason why the women come is to learn, just like the men. However, according to Rabbi Elozar ben Azaryah, who holds that one should not teach his daughter Torah, the women are not coming to learn; but rather, they are listening to the words of Torah in order for them to know how to fulfill the mitzvos that they are commanded to perform.
The Rambam rules that a woman who studies Torah receives reward, but not in the same capacity as a man. However, the Chachamim commanded a father not to teach Torah to his daughter, for women, in general, are not capable of understanding the intricacies and the fine details of the Torah, and it will lead them to incorrect halachic conclusions. This admonition is only applicable to the Oral Law; however with respect of the Written Law, one should not teach it to her, but if he does, it is not regarded as if he taught her lewdness.
The Maharatz Chiyos asks: According to the Rambam, Rabbi Elozar ben Azaryah could also expound the verse by Hakhel to be saying that the women are coming to learn Torah, for there, the king was teaching the Written Law, and there is no prohibition whatsoever to teach that to her!?
He writes that after careful scrutiny of the Rambam’s language, it is clear that there is a prohibition to teach one’s daughter the Written Law; however, it is not with the same degree as the prohibition regarding the Oral law.
The Tur (Y”D 246:6) seemed to have a different version of the Rambam, for he writes that the Rambam holds that the concept of lewdness only applies by the Written Law, but with respect of the Oral Law, there is no lewdness; however, one should not teach it to her, but if he does, it is not regarded as if he taught her lewdness.
The Beis Yosef writes that it must be a printer’s mistake in the Tur, for the Rambam says the exact opposite.
The Rama rules that the laws pertaining to a woman, she is obligated to learn. The Bach writes that it is for this reason that a woman recites a birchas HaTorah in the morning.
The Aruch Hashulchan comments that it was never the custom for women to learn from a sefer. They were taught orally all the halachos that were relevant to them.
The Chafetz Chaim in Likutei Halachos writes that these halachos only applied in earlier times when the children lived in the same place as their parents and the tradition was strong. Then, it was forbidden to teach the women Torah, and the women followed the examples of the previous generations. However, in today’s times, when children live far away from their parents and the tradition has been weakened, and especially because the woman are studying the language and writings of the secular world, it is an important obligation to teach the girls Chumash, Prophets, the Writings, Pirkei Avos and the ethical teachings of our sages in order to strengthen their faith. For if not, they are liable to stray from the correct path of Hashem. The Steipler Gaon writes that in today’s times, it is more dangerous not to teach them Torah than to teach them. He even rules that one is allowed to teach Mishna to girls. However, Reb Moshe Feinstein (Y”D III, 87) rules that Mishna is part of the Oral Law, and the original prohibition is still intact, and therefore, girls should not be taught Mishna in school.