"Any time we can ask kids to make something instead of consuming something, we should jump on it."
My point was that merely asking students "what do you notice?" is not likely to yield the desired insight, because what students notice is constrained by what they already know and understand. This is a good thing for students who are not accustomed to applying what they know and understand, but as a strategy, it is limited.
That post triggered this response from Mark Lawton:
Making something rarely requires hints. When was that last time a kid playing with legos needed a hint?Actually, that was not my point at all. Even in the example I gave (Make These Designs, using an electronic grapher) some students do need hints, such as pointing out none of their lines go into the 2nd quadrant. Building with Legos doesn't require hints, because the intended result is wide open, but if I were to build a piece of furniture, say, I would definitely appreciate hints from a carpenter or cabinetmaker, as they would save me much non-productive struggle and wasted time.
In fact, one point of hints is help students avoid non-productive struggle. It's hard to learn something significant without struggling, but not all struggle is equally useful. An experienced teacher can help steer the student towards productive struggle and away from frustrating dead ends.
Mark goes on:
I also think that hints often reflect a situation where there is only one solution to the problem (or the teacher only values one approach).It certainly would lead to more flexibility in hintage, as a teacher with an in-depth knowledge of a topic has a wider range of hint options, and thus can tailor an intervention to the specifics of the situation. It would not have any implication on the desirability of hints, which depends not on the teacher, but on the specifics of the students and their relationship to the problem at hand.
I’ve noticed in my tutoring recently, for example, that when I am helping a kid on a harder problem from calculus my hints become more dogmatic and emphatic. This reflects the fact that I only see one solution at that particular moment.
I wonder if teachers should always teach a few levels below their own edge of content expertise. This might lead to less dogma.
On the other hand, when I tutor, I do feel like it is helpful that the student senses we are both struggling hard to get through a problem. <- any thoughts on that?There's certainly a place for this as well. It is quite helpful for students to see a patient and perseverant attitude towards a problem, as well as the various strategies we use in those situations.
Meanwhile, you must read Michael Pershan's fantastic "Dissent of the Day". In that post, he discusses the concrete experience of a well-chosen hint that repeatedly failed to be useful to his students. I loved that post, because it came from a non-ideological and humble place: what doesn't work? what can be done about it? In the end, that is the main way we grow as teachers.
Michael concludes from this experience that the best time to give a hint is not during an exploration, but after it, and he explains this by his observation that his students were just not capable of listening to him when they were in the depths of working on a problem their own way.
What I love about this is that it directly contradicts the points I made above. The students' struggle was not productive, but it was not within the teacher's power to redirect them in a more profitable direction. In this particular case, they needed to struggle unproductively, and Michael should be proud to have created a classroom environment where the students do not give up, and where they are able to absorb his input the next day.
Do I take back what I said above? Not at all. Context is everything. Nothing works for all teachers, all classes, all students. Like Michael, let go of preconceived ideas, pay attention to the dynamics, listen to the students, and your intuition will grow. You will know when to hint, and when to refrain from hinting.
PS: you may want to read my first post about hints.