Again, the prevailing mindset is that if something looks new/different, that must mean that they (the students) are not capable of completing the problem. They absolutely refuse to even attempt to forge connections from notes & previous examples in order to tackle a new challenge. And of course, they then become very upset with me that I won't simply show them how to do it.
Couple of things I noticed from student questions:
- Some students are confusing area with distance. When given a picture of a triangle drawn on a grid and asked to determine the length of a side, they'll count half-boxes at the edges. Don't think I've ever seen that one before (but I've never relied so heavily on examples from Geometer's Sketchpad either). I might need to pay better attention to vocab in the future ('spacings' instead of 'boxes').
- The idea of a model is so foreign to most students that they're unsure of how to transfer it to new situations. We created the model for diagonals & side length of squares in Unit 3 for the express purpose of applying said model in this unit with isosceles right triangles. Students have the model written down in their notes and remember using it, but are unsure of how to apply it to a situation that isn't 100% exactly the same (since these are triangles, not squares).
- I really hate how much calculators are foisted upon students these days. They have very little of what I call "number sense" because the magic little doohickey always solves the problem for them. Case in point: the square root of 2. It's almost as though students see the radical sign as some sort of variable that MUST be dealt with. I've been trying to hammer home the idea of precise vs. approximate (as a result of rounding) and why it's totally OK (and even preferred) to leave answers in radical form. My non-honors class literally lost their stuff when I tried to explain the difference.
I'm guessing Unit 4 will take up most of my time leading up the holiday break, but I don't want to start a new unit before 2 weeks off. We only have 9 school days after the break before the end of the semester, so I'll need to work out if/how much of unit 5 we'll get to before the final exam.