Thoughts on my Last Lesson

Today marks my last day at Kent Place School in Summit, New Jersey.  In August, I will be teaching full time at Moravain College, a much shorter commute from my home in Easton, PA. This marks the end of my 26th year of teaching.  You may think that after teaching for that length of time that I had nothing to learn about teaching, about students or about myself.  However, I have continued to grow as a teacher and I have gained insights in each of these areas this year .

Thoughts on My Last Lesson

I'll known for a while now that teaching is more than just understanding a subject.  It is about the students in front of you at that precise moment. Yesterday was the last day of school.  It was a half-day.  No exams, no regular classes.  Just final good-byes and one last chance to have students think and perhaps learn something new. Faculty were asked to design an activity and students would sign up to attend the 30 minute session of their choice.  The one I led was "The Case of the Stolen Jewels".  Seven volunteers were actors in a mini play.  The players were the cook, the chauffeur, the maid, the butler, inspector Euler Toots, Lady Shmendrick and the narrator.  Jewels were stolen from the mansion and the thief dragged his feet through the snow to throw off the authorities.  The testimony did not fit what was on the map.  However, I asked the students if they could tell from the map alone who stole the jewels.  (Can you tell?  Hint: Think Euler path.)

Map for "The Case of the Stolen Jewels"

I did this session three times and each time the student interaction was different.  Not only the interaction of the students with each other, but my questioning of the students.  Usually when I teach a lesson multiple times, my last time is the best.  Reflecting on how the lesson went the previous time(s), I can anticipate student questions and the direction of the lesson better.  However, my first time of leading "The Case of the Stolen Jewels" was the best yesterday and I think it was a result of my questionning.  I believe there are three main questionning techniques that can either open up a lesson or shut it down.

Number 1: Type of question  

Consider the following two questions. "We said you could trace a path if you start and end at the odd vertices.  What other questions might Euler have investigated related to odd and even vertices?" versus "Do you think it is possible to trace if we have three odd vertices?" 

The first questions directs students to focus on the vertices, but doesn't suggest any specific changes to make.  Any answer to this question is open to exploration. This was the question I posed to my first group and we had a lively discussion related to changes they suggested - 3 odd vertices, all even verticies, all odd vertices, etc. They were thinking like mathematicians. 

The second question removes the mathematician agency from the students.  It is a yes/no question and leads students in a very specific direction.  And since it definitely has a right answer - it can be traced or not - students hesitate to answer because there is a chance of being wrong and in the eyes of many students, even on the last day of school, wrong is bad.  This second version of the question was asked to my third group of students and it definitely changed the atmosphere of learning.  I had to follow it up with multiple questions and the discussion overall fell flat.

Number 2: Wait Time

This year I became better at wait time.  When I would ask a question, I would often restate the question - either word for word or slightly revised.  This gave students who hadn't fully heard the question the first time to hear it and it gave some more time for students to think.  Also, I did not go with the first person to raise her hand as I would have in the past.  Doing this often rewards the fastest thinkers and leads other students to think "I don't need to think about this question, because she will call on Susan. Susan knows all the answers."  Instead, I would wait until many hands were raised and often call on students who participate less often.  And, even if those students say something that isn't fully correct, we unpack it as a class.  Early in the year, students learn that mistakes are a valuable part of the learning process. You can learn so much from doing something wrong.  In response to mathematical misunderstandings, you can often hear me say things like, "I hadn't thought of that. Thank you for sharing that idea." or "Let's think about that some more.  There is something we all can learn from what you just said." or "That is an interesting thought.  Let's see what happens when we do that."

Number 3: Share with Others First

Not all students are risk takers. Think back to your days as a student. How many of you would say "I loved to share my thoughts that could be wrong and incomplete in front of 15-20 of my peers for them and the teacher to critique."  Students prefer to participate when they think they are mostly right and will be validated for their correctness.  So, how do we get students willing to take risks and share?  When I ask a question and see that no one wants to take a risk to answer it, I say "share some thoughts about that question with your group for a minute."  Then, I walk around the room and listen in on the conversation.  Sometimes, I will even tell specific students that I'll be calling on them to share their idea.  More students are willing to become risk takers after that minute of sharing with others first.

This summer I will be leading/co-presenting at several different workshops or conferences. Often the pace of the workshops is frantic, but that generally doesn't lead to deep understanding.  Sharing, risk-taking and reflecting will be a large part of my workshops this summer, as it has been in my classroom this year. Be sure to visit my blog in the fall to hear about my reflections in the college classroom and if you are a teacher, be sure to take some time for yourself this summer to relax and reflect.