*Women are called for aliyot. Men and women sit apart during services, separated, he says, by a seven foot mechitza. The bima is placed directly beside the mechitza; when a woman is called for an aliya she walks through a gate in the mechitza, and is immediately at the bima. Zman Biur makes the case for this practice:
The main source of interest is the baraita in Megilla 23a:Moreover, as my young Israeli friend said, today Orthodox women are seated in Parliament, so, in our day, how can it be considered beneath the dignity of the congregation to honor a woman, or to be addressed by a woman?
Everyone can be counted towards the seven [aliyot on Shabbat], even a child and even a woman, but the sages said a woman should not read the Torah because of the dignity of the congregation (kevod ha-tzibbur).
Kevod ha-tzibbur is conventionally understood as the damage to a community's reputation by the implication that, if a woman is reading the Torah, presumably the men are all illiterate. But when the baraita was formulated, there was no ba'al kri'ah; each oleh read his own aliyah from the Torah. Today, when the oleh only says the blessings, calling up a woman cannot possibly reflect negatively on the literacy of the men.
Furthermore, in modern times, with widespread literacy among both men and women, the very implication that the men are illiterate is unreasonable. Thus, in theory at least, it should be legitimate today to give women at least some of the aliyot, and even to allow them to read.
My one quibble with the Shira Chaadash practice, as it was described by my friend, is that single and married women alike are called for aliyot and even women who are dressed immodestly are welcome to receive aliyot. Married woman, imho, especially married women with children, should not be called; at services, a husband/father represents his entire family. And even if the act of giving a single woman an aliya is not immodest (as the Gemarah seems to say) if she is improperly dressed this, imho, is an affront to the congregation and to the dignity of the synagogue.