I did partially use this approach today that John Scammell blogged about last week. I think the next time I use it, I will follow the approach as it was blogged about - when I was thinking about it this morning on my way into work, all I could remember was showing which points made the inequality true. In my first class, I had students choose any point on our grid (both x and y values go from -6 to 6 on it) and they all chose points with two positive coordinates. None of those points worked, so I had them choose a coordinate that had at least one negative coordinate and we got some points that worked. Also with the first class, I didn't have them graph the points we came up with. We just graphed the shaded area that did work. For my second and third classes, I had them plot the points we found that worked on their grid before we graphed the inequality on the grid. They then graphed the line and we talked about testing a point to determine which half of the plane to shade. Below is the pdf of my SMARTNotebook file from my last class.
In that last class, one of my students who has struggled with math spoke out as we were working through the problem. We had graphed the individual points that we found that worked and had just finished graphing the boundary line and right as we finished drawing it in, he said "I get it now!" I hadn't even gotten to the point where we talk about testing a point in one of the half-planes - he already saw where the answer would be and "got" why that was going to be the answer. That was worth it. #win
Getting back to the opening... I know I have done things differently this year. Yes, things are mostly the same. However, due to the twitter-blogosphere and reading and conversing with other math teachers, I have incorporated some different approaches to instructing my students and I think that has made me a better teacher. However, as I look at my classes, I am frustrated because they are so dependent. It's almost as if they don't know how to think.
In my Advanced Algebra 2 class, where we're working on solving systems of inequalities by graphing, we had this discussion about the test point today. It started first by clarifying how to determine which half to shade based on testing (0,0), which is the point I use unless it's on the line. Then the conversation shifted - can I test (1,1)? What about (2,2)? After answering the same question but with a different point for the third time, I got a bit frustrated with them. It was as if they couldn't take the concept of checking a point to represent the region and shift it to a different point. And these are supposed to be my "better" and/or "brighter" students. Granted, I didn't use the same start as I did with my Algebra 2 classes today, and that may have made a difference, but it was very frustrating to me that they couldn't transfer the idea to different points. As I said earlier, it's almost as if they don't know how to think.
Last night I was trying to get caught up on my Google Reader, this post by crstn85 caught my attention about studying for math. Since I was at 130 or so when I started trying to clear it out, I really only skimmed the post and starred it to go back and read later. However, as I continue to reflect, I think I may go back and read it much more thoroughly to see if I can use what she did with my classes. Maybe it will be helpful to them.
So here I am at the beginning of the