One of the goals of the Algebra 4 All statewide project that I am apart of, is to get students to ask questions about mathematics. The goal is to shift the focus from the teacher as the source of mathematical ideas to the students as the source of mathematical ideas. This is definitely not an easy task. I find that students are so used to being told how to do math problems that when you try to make them think they sometimes shut down. Luckily by this point in the year my students are getting used to the idea of working through problems on their own. By this point in the year they are asking each other for help and sometimes even tell me to "go away" because "I got this".
This week we were working on solving systems of equations by graphing. After completing 7.2 and discussing it in class several of my students were upset that not every students' answer to the problem matched when it came to finding the intersection point from student generated graphs. This led to a great discussion about accuracy and the disadvantages of graphing (which we've been discussing all year). One student even mentioned that he thought there must be a better way to solve the system. Luckily for him we'll start solving systems of equations algebraically this week. Who ever would have thought that students would actually get excited about solving systems of equations because they wanted to be able to find a more accurate answer. I'm convinced that these kinds of student revelations do not happen when using a traditional textbook and lecturing (the way I was taught).