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In lesson 7 it states that the patimokkha is recited on Uposatha days, those being the full moon days and the 14th of each month.

In my local Thai temple I believe they area done on full moon days and quarter moon days.

Curious about this tradition, I checked Access to Insight, where a general statement is made with regard to variances among traditions, without any specifics.

"The calendar of Uposatha days is calculated using a complex traditional formula that is loosely based on the lunar calendar, with the result that the dates do not always coincide with the actual astronomical dates. To further complicate matters, each sect within Theravada Buddhism tends to follow a slightly different calendar."

According to Bhikkhu Nyanatusita, preview of the text available here from Google Books,

"The Buddha allowed bhikkhus to gather together on the fourteenth or the fifteenth, and the eighth day of the half-month to speak Dhamma, but later amended this to a legal act of Uopsatha consisting of the recitation of the Patimokkha; Mv II 2,1/Vin I 102.

The Patimokkha may not be formally recited on any day but only on the Uposatha-day once in a half month (pakkha); Mv II 4,2/Vin I 104

There are two types of Uposatha days; the fourteenth and the fifteenth; Mv II 14,1/Vin I 111. The Uposatha should not be done on a non-Uposatha day unless it is for the sake of unity of the community (sanghasamaggi); Mv II 36.4/Vin I 136 & MV X 5,14/Vin I 357."

Other experiences traditions?
Any suggestions on what the difference is in the "type" of Uposatha day between the 14th and 15th as referenced by Nyanatusita?