At the risk of making everyone hate me, I think this suggests it's quite a good question! ETA with a high ceiling (fully understanding all the methods and their pros and cons) and low floor (gaining a basic understanding of what an equilateral triangle is), as the educationalists say - the only pitfall really is kids being too scared to have a go. ETAagain infinitely better as guided exploration in class than as homework, though!
I agree, and the biggest pitfall for poorly implemented exploration type math seems to be when the teacher expects each student to list exactly 4 specific methods of achieving the result. Undermines the whole thing.
I wonder if they circle back on the question in the next class and list the different approaches and the thoughts behind those approaches.
