Jessica Till asks a good question on Twitter:
If math is supposed to be discovery-based, what do my fellow math minds think about posted objectives? Do they take away from the opportunity for students to figure things out? @ddmeyer @gfletchy @robertkaplinsky @joboaler #mathchat #math— Tilli (@JessicaTilli1) September 25, 2018
and Graham's response stood out to me:
Telling students we're going to work on addition and then giving them a problem that requires addition is a license to not think.— Graham Fletcher (@gfletchy) September 25, 2018
Just because we do it in other subjects doesn't mean it must be done in math. If we effectively close a lesson we can talk about what we learned.
Turning this around (also mentioned by Will Dunn later in the thread), what would happen if we taught a lesson or went through an activity without positing the objective and then have students state the learning as an exit ticket or closing discussion. What insight could we glean?
Intentions are important, but implementation is harder.