I am quickly coming to the conclusion that being a good teacher is extremely time intensive. I'm not saying that I wasn't a good teacher previously, but I certainly have not put as much thought into my lessons and what I'm doing in the classroom in the past as I have in the last couple of years. Case in point: Friday I gave my Algebra 2 students their first assessment. It was over solving systems of equations by graphing, substitution, and elimination. They did fairly well on the two algebraic methods but only about half of my students earned 4s or 5s on graphing. In the past, I would have just let it go, chalking it up to that they didn't prepare well. Even though I know they did not do a good job practicing solving systems of equations by graphing, I also am recognizing that they don't have the concept and will need aspects of it for what we are doing next (solving systems of inequalities by graphing). So, I sit here tonight still pondering what to do.
My first inclination Friday after I finished grading their assessments was that I needed to spend Monday going over how to graph a linear equation. I had originally tweeted for some help on this Friday night and, although I didn't tweet real clearly what I needed, I got some suggestions to think about. As I continue to ponder this today (Saturday), I am wondering how to best handle it since about half seem to have a pretty solid handle on how to graph. I had thought about pairing the students up so that one partner had a good idea of what to do and the other did not, but the question still remained in my head - what do I have them practice? When I tweeted my dilemma, there were a couple of tweets that got me really thinking:
@fawnpnguyen Wonder maybe they haven't had enough real-life context of systems.Both of these intrigue me. Fawn's tweet intrigues me because I know they haven't had enough real-life context, period. When I brought in word problems this week, they were already nervous and asked whether I was putting them on the assessment. In my haste to make the assessment, I left them off. However, after a brief discussion with @MSeiler and @4mulafun yesterday about including word problems, I think I really need to incorporate them as much as possible to get them past their discomfort.
@jacehan I had a lot of students who didn't see why we'd solve graphically with equations, so didn't/couldn't, but saw why with inequalities. It can help.
James' tweet really intrigues me. I am really sitting here tonight wondering if it's worth going back to review solving systems by graphing when I am preparing to do graphing a linear inequality, followed by systems of inequalities and linear programming. My students will get a healthy dose of graphing over the next week or so. Maybe that will help with their graphing with systems of equations problems, as James suggested. Maybe I really don't need to spend Monday stepping backward to go forward. Instead, maybe this time I will deliberately push forward to a different, but related concept which will help cement the one they struggled with.
When I taught Geometry, I spent my first year trying to pound proofs into my students' skulls starting with the really annoying proofs (proving that perpendicular lines form 90-degree angles, for example!). And nothing really worked until we started proving triangles congruent. Then they were like, "oh, I didn't know these would be congruent, but look, I found these two angles and these lines that have to be congruent to the corresponding parts in the other one, so now I know the whole triangle has to be congruent!" They saw proofs as puzzles and arguments, not annoying arbitrary nitpicking.
ReplyDeleteSo... the next year I had the idea to still do the angle proofs but to wait for formality and mastery until we got to triangles. Just my stance of being relaxed and letting the concept develop across multiple applications seemed to help the students get it. So it sounds like your stepping forward to step back plan is a great one!
Max