Saturday, September 10, 2022

Learning from my students

This week, I saw an algebra student try to find the factors of 15 by repeatedly multiplying numbers by 2 to see if the result might be 15.  I saw an advanced algebra student not remember how to simplify an expression using the order of operations.  And I saw the lesson of two very experienced teachers fail miserably.  (Full disclosure: the two teachers were me and my coteacher.)

But I also saw that algebra student excited to learn how to factor trinomials and differences of squares and know when she whether she was correct or not.  I saw that advanced algebra student smile when he realized he could understand function notation and its relationship with a graph when he used his calculator to do the arithmetic. And I saw two experienced teachers put their heads together to create a lesson that engaged their students, and uncovered some of the reasons why the previous one failed.

Teaching is full of large and small disappointments as well as tiny joys and enormous wonder.  And just like my students, sometimes I fail.  And when a lesson designed for an 85 minute block fails, that's a long 85 minutes.  Especially when you realize it's going off the rails in the first 15 minutes, and you keep scrambling to try to pull it together for the remainder of the block, but you keep failing for more than an hour.  Wednesday was rough.

At the same time, Wednesday had many moments of joy, like the two students who learned how to factor and use function notation.  It also included a group in one class becoming gleeful that they solved a problem unexpectedly by thinking about a different question.  And another class all gathered in one corner of the classroom to learn the definitions of sine and cosine.  (And I had forgotten about these last two moments until I was writing this post; it's not always easy to remember the good stuff when I'm trying to figure out where I went wrong.)

A two by three grid with A in the lower left corner, and B in the upper right. The puzzle was to find how many ways to get from A to B, following lines only upward or to the right.

Anyway, my coteacher and I decided to revamp our thinking for Friday's lesson to figure out what went wrong on Wednesday.  We started the lesson with a non-curricular puzzle at the white boards (NPVS's for those of you following along).  The puzzle engaged the students, most groups came up with an answer they were happy with after a few trials, and four groups explained their solving process, two of them inventing notation to keep track of their work*.  Clearly, the students have the ability to think, communicate with each other, and problem solve.

The class then moved the desks out of the way, and put the chairs in a large circle.  We stood in a circle to acknowledge the power of seeing and hearing each other, which took a few minutes, as the kids were feeling a bit squirrelly, probably uncomfortable with the process.  (Who wants to be seen and heard in a math class?!)  After we sat down, my coteacher invited comments about how everyone thought the class was going.  We had asked questions three weeks ago in this format about what everyone hoped for and what success would look like for them in class.  This time, it was quiet for a moment, until one student asked if we really wanted to hear stuff, and could they be honest?  We answered yes, and another student quickly started the conversation with "I don't feel like I'm learning anything in this class."  And that opened the gates.  We talked about all kinds of issues:

  • We don't like the random groups every day.
  • We do like the groups we sit with (which were self-chosen).
  • We don't like working at the white boards.
  • After we work at the white boards, we don't have enough time to practice.
  • We don't know everyone's name.
  • We spend too much time on get-to-know you activities.
  • There's too much homework.
  • We need a break during class.
And so on.  There was one moment that stood out for me:  One of the students said that he didn't think the homework was too much, but he doesn't like doing it, so he just copies the solutions.  A few other kids jumped on him for his opinion about the length of the homework, and he started to retract the statement.  I interrupted to tell him that how he was feeling was perfectly valid, that he clearly spoke only for himself, and that I would not stand for other students ganging up because they shared a different opinion.  As the conversation continued, other students were making general statements about the class, and I continued to push them to speak only for themselves.  More students started using statements that started with "I feel ..." rather than "The class ...".

The circle discussion took longer than I had expected, and we did not get to any math content.  However, the students did agree that sticking with the same random group for the white board work for one week would be okay and that spending less time on the white boards each day and more time consolidating the ideas and then practicing them would be helpful.  The points about taking a break and homework length got tabled for a future discussion.  Everyone helped put the desks back into the pods formation, and we had a few minutes to hang out before the bell rang.  While students were having individual conversations, I checked in with a few students who had not spoken during the circle conversation.  A couple agreed with what was being said, and offered me their viewpoints.  Two students said that they liked the class the way it was, but didn't want to say anything in front of everyone else.  I also thanked the student who commented about his experience with homework for speaking his truth.

After the students left, my coteacher and I agreed that the conversation had been a good one.  While a few students checked their phones during the discussion, the engagement level was much higher that it had been on Wednesday, and the time on phones was significantly smaller.  We discussed the pros and cons of doing a white board problem on Monday, with the shorter class periods, and decided to go for it.  We believe the time at the white boards is some of the most important time we spend, and neither of us is willing to sacrifice that.  Given the length of the conversation with the students, we'll have to reschedule a couple things to account for the missed content time, but overall, we believe the trade-off will be worth it.

We'll see what Monday brings.

*One group used a series of shapes to track their work, another used series of arrows.

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