1) The Tosfos in Gemara Menochos 35a, says in the name of the Shimushoh Rabboh that the three-headed shin corresponds to the normal writing we find in a Torah. The four-headed shin corresponds to the way the shin looked in the luchos of the Ten Commandments. Since the script of the luchos was actually a lack of stone, as the letters were etched out, the physical part of each letter was its background. A circle drawn around a three-headed shin would loosely produce an inverted four-headed shin.
2) The Likutei Hagohos on the Tikun Tefillin #9 quotes a Gemara (which we do not find) which says that Moshe asked Hashem the details of creating tefillin. Hashem said that the shel rosh requires a shin. Moshe asked how it appears, and Hashem (kav'yochol) showed Moshe four fingers. Moshe didn't know if the intention was a four-headed shin like the four fingers he was shown, or a three headed shin like the spaces between the four fingers, so he made both.
3) The Zohar interprets the words "shivasayim" (Tehillim 12:7) as seven times seven. He says that this refers to tefillin shel rosh. He explains that the shin is a composite of three zayins that are joined at their base. With a four-headed shin on one side and a three-headed shin on the other side, we have a total of seven zayins. Since the numeric value of zayin is seven, we have the fulfillment of "shivasayim," seven times seven.
4) The Baal Tikun Tefillin, Rabbi Avrohom of Zuns'heim, a Rishon, says that the configuration of the tefillin shel rosh corresponds to the encampment of Bnei Yisroel in the desert. There are a total of 12 stitches closing the tefillin, 3 on each side of the central cube. This corresponds to the 12 tribes encamped in the desert, 3 on each side of the central area of macha'neh L'viyoh and machaneh Sh'chinoh. In the centre, we have the cube that houses the script, parshios, of the tefillin. The cube corresponds to the ark and the script to the luchos which were inside. The ark had on its lid (kaporres) the two cherubs whose wings were spread aloft. The cherubs with their wings spread aloft loosely had a configuration similar to the letter shin. The luchos upon which the Ten Commandments were etched had as their first word, "onochi." Here again we have a striking similarity. The cube of the tefillin (k'tzitzoh) which houses the script of four paragraphs of the Torah has two letters shin on the outside, similar to the ark and the two cherubs. Rabbi Avrohom adds that these last two similarities are alluded to in the verse in T'hilim 119:162,"Sos anochi." "Sos" is spelled with the letters sin, sin. These are the two cherubs and also the two shins on the tefillin housing. The letters sin and sin, symbolizing the two cherubs are over the Ten Commandments which begin with "Anochi."
5) Rabbi Shimshon "Boruch She'omar" says that the two shinin are alluded to in Shir Hashirim 4:1,2. "L'tzamosheich" equals tefillin. The next verse begins with the word "Shin'ei'yich." We can interpret shin'ei'yich to mean "your two letters shin."
6) He also says that two shins in "mispar koton" (a gematria that only deals with single integers and drops all tens, hundreds, etc.) equal six, to indicate the six days of the week that we don tefillin.
7) He also says that the three-headed shin corresponds to our three Patriarchs and the four-headed one to our Matriarchs. Possibly, the three-headed shin is three zayins, as mentioned above from the Holy Zohar, equaling 21, the same value as the first letters of our Ovos, א-י-י. Rebbi Y.T.L. Michelhoizen (a Rishon) says that the acronym of the four Imos ש-ר-ר-ל equals 730. Shin-yud-nun twice equals 720, plus add 10 for the extra yud stroke in the four headed shin (to which the Matriachs correspond) and we also have 730.
8) He also says that the three-headed shin corresponds to the three days a week that we read the Torah, and the four headed one to the four days we don't. Incidentally the word tefillin is plural, referring to the rosh and the yad. The singular form is "tefillah." The word “tefillin” has a gematria equaling "l'rosh u'l'yad" (head and arm).
