When Do We Say Enough?

I find myself struggling with a dilemma.  Over the past several weeks I have been furiously working with and encouraging struggling students to seek out extra help beyond what I can give them within the classroom.  My Algebra 2 students just finished a unit on Systems of Linear Equations and Inequalities and I found that many of them are unable to consistently graph linear equations.  We spent many extra minutes each and every day working on graphing in Slope-Intercept and Standard Form.  Each passing day I was stealing minutes from the daily lessons and interactions with students to remediate graphing.  At what point does a teacher need to put an end to it and move on?  Is it appropriate to allow those struggling students to use a graphing calculator to do their graphing?

The past several days I have had a few breakthroughs with some students who have taken the initiative to come in after school for some extra help.  In a class of 33 students it is tough to be able to understand and assess what each and every student really knows.  Spend a few quality minutes with them one-on-one and they open up.  Not only do voices open up but so do their minds.  The thinking is obvious.  One young man stated as he left my room the other evening, "if I knew it was this easy to think about math I would have done it a long time ago!"  For many students "doing" math is a difficult task, but even if the task it self is difficult all students can spend time "thinking" about math and "talking" about math.

I have been reading numerous other blogs from some seemingly great teachers.  They talk about many of the same struggles that I am experiencing in my 16th year of teaching.  Just as the pressures of state testing and meeting AYP are mounting I am finding myself searching for a better or smarter way to teach.  I am drawn to the idea of teaching math from a true problem solving perspective and am excited to try new things.  I have expressed interest in this with some of my colleagues in the math department but no one seems to be sharing the vision.

I am currently working on a unit for Quadratic Equations and Functions that will include a problem solving activity to kick things off.  The activity is based on some clothespin catapults that other teachers have used and posted on their blogs.