去 and 来

[somethingfunny]

Hmm, I checked some of my textbooks and they do indeed not include the 节.  Maybe I'm wrong.  I just can't imagine a teacher saying it without the 节.

[Shelley]

eddyf's suggestion that it is for actual classes/lessons rather than lessons in a book is confirmed by Pleco - 两莭課 - two periods; two classes.

 

For lessons in a book 第一課 stands.

 

 

[Angelina]

It might be a word association thing. You associate 课 with 节, even though a) it is not the only 量词 used with 课；b) it is better not to use one in 今天我们来学习第一课 .

[somethingfunny]

No.  I just can't imagine anyone actually saying “第一课”.

[eddyf]

Yeah, there are definitely tons of examples of "第一课" online. So I can only imagine that people say it all the time.