The goal seemed so simple: task the class with creating three hypotheses related to the diagonals of a square. Problem #1: Students ignored that bit about diagonals and just regurgitated previously known facts like the sides are congruent. Problem #2: Students don't make any distinction between an obvious observation and a hypothesis that will require investigation.
The idea was that with each student having their own unique square, any hypothesis they created could immediately be checked, albeit informally, with other squares for validation. The three conclusions I was looking for were: pairs of diagonals are always the same length; the point of intersection cuts the diagonals into equal pieces (haven't defined the word midpoint yet); and that the diagonals are perpendicular.
The first two are fairly easy for students to "discover" if they're willing to put forth the effort to measure the segments. The last one is often thought up, but students have no idea how to prove it. I tried to lead students to the connection between "90 degrees" and "perpendicular" and hope they make the connection back to Unit 1 and see slope as a method (these squares are on graphs for a reason).
For each class I made the brief point about why we spent these 3 days the way we did - I could have simply told everyone those formulas and conclusions on Day 1, but in the long run they wouldn't have a deep understanding of what they were actually doing. Some kids bought my explanation, but others (generally the regular Geo class) would just complain "this is stupid" and "just tell us the answers already."
I don't know how to reach kids that have such a combative attitude toward learning. All the literature I've read claims that if students can take ownership of their education, they'll change their attitude, but I have NEVER seen that work in practice. I still think this is a better way to teach, but I'm stymied about how to handle students who actively fight against the class methods.