Mr. K’s thoughts here. In sum, posting the standard being taught gives away the punchline at the beginning.
Makes me think of a comment by Grant Wiggins (I forget where I read it, somewhere on his blog most likely), where he noted that one red flag for low-quality teaching is when he asks students what they are learning about and they struggle to articulate it.
I think Mr. K makes a good point–but with the assumption that the lesson is an exploration where students get to experience the punchline. Different folks, different strokes.
While posting “SWBAT identify that when multiplying exponents with like bases, the exponents add and the base stays the same” absolutely gives away the punchline in a lesson that is easy to structure as an investigation. But thinking of Grant’s point, students should absolutely be able to say “we’re exploring the properties of exponents” or “we’re trying to figure out what happens when exponents are multiplied”. Many students in classrooms with objectives posted may have trouble articulating that, and I think that is my goal when I think about how students interpret our purpose in math class.