Mondays

Even though it is a short week I found today to be extraordinarily long.  I was excited to teach my Algebra 2 classes as we are starting our Quadratics Unit and I find it fun teaching.  My goal this year is to really create an atmosphere of problem solving and application.  I want my students to not just do the math but to experience it.  I know I can't do this each and every day but I want to make it a habit to start each unit with something fun, relevant and thought provoking.

Today was a weak attempt I must admit.  I drew a picture on the board of a stick person pushing a huge ball off of a ledge.  At the bottom of the ledge was another stick man with a cart he was pushing.  He was about 4 meters from the bottom of the ledge.  The ledge had a height of 5.14 meters.  That's it.  No question, no equation, no formula.  I just let the students absorb it.  Finally one student stated "I wonder if he can catch the ball before it hits the ground?"  That's all I needed.  After a short discussion and some talk about vertical motion models we actually went out in the hall way where I just happen to have a ledge overlooking a stairway that is exactly 5.14 meters high.  We proceeded to see if a few students could "catch" the ball in time.

Next up is graphing.  Letting the students discover the changes to the graphs of a quadratic function.

The Problem Solving Problem

How do we get students to full heartedly engage in problem solving at its fullest?  I am working with my Algebra 2 students to move beyond the complacency of solving equations and the procedural repetitions that we tend to get too focused on.  I would have to say that we have probably spent a good 80% or more of our class time working on the mechanics of graphing/solving linear systems and inequalities.  Even the word problems that we have tackled in class seem very mechanical and my students (those who are doing their work) seem to be able to knock them off fairly efficiently.  Is this all in good faith because we have to prepare them for the MCAII test in April?  I find myself struggling at the moment with what direction I want to take my students.  Many of them would be ok if we simply "did" some math and solved a few problems along the way.  I want to give meaning to the math that we are doing and allow my students to see beyond the equations, to see the bigger picture.

The staff morale in my school (and entire district for that matter) has taken a lot of shots lately as our community has once again voted down an operating levy.  We are facing huge cuts in budget and staff again for next year.  Our class sizes are already growing beyond their means and will no doubt get larger next year.  We are also in a negotiations cycle and have not settled our contract with the school board for this year (and next).  The status of the talks is not good and will probably go on for a long time.  We have been offered "a hard freeze" for the next two years.  This is essentially a fairly big pay cut with the expected increases in insurance.

With that said I can usually find solace in my classroom.  When I close the door and have my students there with me I can let all of those other worries go for the next 50 minutes.  I want this short amount of time to be as meaningful and productive as it can be. Even on those days when my 11th graders are acting as though they have not left the middle school I still feel comfortable within the confines of my room.

Well, enough for now.  As I venture on to the depths of Problem Solving I will continue to keep you posted on my thoughts.

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.

NCTM Minneapolis

Spending two days out of the classroom may be a welcome "vacation" for some teachers but I was really worried about it.  I am glad that NCTM Minneapolis offered some really good workshops.  I managed to sit in on 10 different sessions, 9 of which were worth while.  I really enjoyed the Mathematical Lense session as I have always liked the column in the magazine and, as many of you may know, I also enjoy photography.  The sessions that were centered around problem solving and reasoning were great and the information/discussion sessions about the new publication "reasoning and sense making in high school mathematics" was really enlightening.

I will be out of the classroom one more day on Monday for another workshop (this one local) so I won't see my students until Tuesday.  I am excited to try some new ideas and get my students working on with while problem solving and reasoning.