"All in All, a Pleasant and Educationally Sound Experience for the Children."

do you remember the first math lesson you taught in your career? what did you teach? what did you learn? what would you tell your rookie self now? #mtbos #iteachmath

— chase orton (@mathgeek76) October 16, 2018

OK, not the first math lesson I taught, but pretty darn close:

December 17, 1986

     At the time this lesson took place, I had been teaching for about 3 1/2 months.  The administrator conducting the observation was Dr. Frank Gardella, the district's math supervisor.  (Frank, who would soon leave East Brunswick, is now a professor at Hunter College in New York City.  Years later we would reconnect during some summer PD at Middlesex County College.)
     Even after reading the write-up, I'm not exactly sure what happened during this lesson.  Did it come out of a teacher's manual?  If not, where did it come from?  Did I make it up?  Clearly it was aimed at developing the relationship between addition and subtraction.   Unifix cubes were handed out.  I tried to connect my students' ideas of what related meant in their lives (family relations) to what it might mean for addition and subtraction equations.  Best I can tell I led the students through some direct modeling with addition facts with sums of 14, matching them to subtraction facts with a minuend of 14, and then did the same with addition facts with sums of 13.  The unifix cubes were used.  I modeled what I wanted on a piece of chart paper and the kids followed my lead at their seats on paper of their own.  It appears that this took 22 minutes.  Then we played a game of "practice races" for 10 minutes.  Finally I collected the unifix cubes and gave a homework sheet.
   
Here are Frank's comments:

A kind, humane administrator is a blessing for any teacher, first year or otherwise.

         What might I tell my "rookie self"?  What might I do differently?

• The lesson was very teacher directed.  Now, as an intro, I might throw up some related facts on the board and ask: What do you notice?  What are you wondering?  Allow the kids to do more of the mathematizing.
• I liked that I used unifix cubes.  But now I would let them explore on their own, in pairs or groups of three.  Maybe something like: Take 13 unifix cubes.  How many different addition and subtraction equations can you make? Then I might walk around and monitor their work, and find some related equations that I could use as examples.  (How did we do that in 1986?)  After consolidating some of the learning, I would give them a choice of using any number up to 20.  
• I'm not sure what "practice races" are, but I feel confident I wouldn't be doing those.
• I need a better closure.  Collecting cubes and giving a homework sheet doesn't cut it.  Maybe: Tell me everything you can about: 6 + 5 = 11  and 11 - 5 = 6

     Some other thoughts:

• As a first year teacher, I was fortunate to have, in addition to Frank Gardella, some very supportive administrators.  For example my principal, Mike LaRaus.  I'll never forget what he told me back on my first first day of school, that September of 1986.  I showed up at like 6:00 AM, after a sleepless night, nervous as anything.  He found me, near paralyzed in my classroom.  He told me it was normal to feel that way, that I would always get that feeling on the first day of school.  Then he said, "Just relax and do your thing.  No one's going to bother you.  I'm not even going to set foot in your classroom for the first two weeks of school, and neither will any other administrator.  Get your footing and then we'll talk."  I can't tell you how relieved that made me feel.  Thanks, Mike!
• Are you surprised I have a copy of the evaluation? I have them all.  Every single one I received during my 31 years of teaching.  What strikes me is how bare bones it is.  Three pages.  The two narrative paragraphs above, the first on page 1 and the second on page 3, with a checklist of performance practices, from Exceeds Expectations through Not Observed, on page 2.  The last formal observation I received was on January 31, 2017, and it came to me via e-mail.  I printed it out.  It's 14 pages long.  No wonder Frank left.
• It's interesting to think back to the 25 year-old, first year teacher that I was.  Yes I was nervous at first, but I was also a little cocky.  I thought I knew a lot more than I really did.  (Now I know I don't know all that much.)  Also, I was a bit stand-offish.  (If you don't believe me, ask my wife.)  In time I learned how to be a good colleague; a supportive and sharing grade-level teammate and a helpful and contributing member of the staff and the wider school community.  That is to say, I grew up.
•  I'm spending a lot of time this year coaching first year teachers.  They're brand new, right out of college.  Many of them have wanted to be teachers since they were kids, when they'd spend hours in their rooms "playing school".  Now their dreams have become realities.  They're nervous and excited, overwhelmed and overworked, and stressed out.  I love them.  I want so much to help them, to make their lives a little less stressful.  To let them know that they're doing a good job.  They're not much older than my own kids, and when I sit with them and talk to them I think about how I'd want someone in a position of authority to treat my son and daughter when they are just starting out in their first jobs.  Frank could've torn the lesson apart, but he didn't.  (Maybe he did think it was a "good lesson!"  Maybe he saved his real criticism for our post-observation meeting.  I don't recall.)  But I didn't yell at anyone, didn't make anyone feel stupid; I wasn't sarcastic or intolerant.  He recognized that.  My issues were with pedagogy and instruction, and those things can be improved with time, patience, and a desire to work at getting better at the craft.  I'm still trying to get better.

My first class.