Learning to Teach

I had a bit of an aha… hahahaha moment today while grading tests.  The last part of a multi-part question asked, “How can you be sure the rule you found for the pattern is correct?”  One student’s response:

Because it is math… Math is solid.  I know what I’m doing as well.

That’s right, folks.  Math is solid.  It’s not one of those squishy subjects like English.  When you know a thing in math, you can be sure of yourself.  Although I am pretty sure this particular student didn’t lack confidence to begin with.  He knows what he’s doing, after all.

Aside from the chuckle I got grading this test, this incident stands out as an example of just how much personality each of my students has.  There are so many fascinating students in this school… it’s amazing.  I wish I had the time to really get to know every single one of them.  We have football-playing violinists.  A young man with the most perfect penmanship I’ve ever seen.  A young woman, quiet as a mouse, whose whole personality seems to be trying to escape through her hand, rendering her handwriting illegible.  A cancer survivor.  Another who mourns the recent death of her friend.  Yet another who, as a junior, is finally realizing that this graduating thing is really important, and has finally decided to pass algebra.  These people are really awesome.  I hope they stay that way.

Every Tuesday I have a Long Day.  I arrive at school around 6am.  Classes end around 2pm.  I have a planning meeting from 2pm to 3 or so, and then go to my other school (UWB) for a class from 4pm to 7pm.  Some weeks, by the time I get to my night class my brain has slowed down so much from trying to process the day that just paying attention to three hours of discussion seems like a real accomplishment.

I am not complaining, though.  Not really.  I feel like I am always exposed to something in those classes that’s of real value to me.  I just wish that 1) I had more time to really process what I’m experiencing, and 2) I had more opportunity to do that processing in the company of others.  It would be really fantastic if our seminar, for example, contained a debriefing session each time we met, so that we had a chance to compare notes and get support on issues we might be struggling with, and that our cooperating teachers may also not know how to solve (yes, this happens; teachers are not omniscient).  Nothing’s ever perfect, though, so I am doing the best I can with what I’ve got.

Today I assigned myself the grand task of aligning the textbook we use for both of our classes to the state standards.  The district has provided a document that explains which standards each section of each book align to, but they failed to list those standards that are not met by the texts.  I took the task on in part because I thought it would be a good planning tool, and in part because I thought it would be a good excuse to spend a lot of time getting to know the standards. Thankfully I am student teaching, so I can take some time out of my day to work on this, instead of having to do later in the day when I should be sleeping, like a “real” teacher would probably have to do.

As I mentioned in yesterday’s post, I noticed an interesting pattern when I looked closely at which standards were and were not being met by the textbooks.  After finishing an analysis of both the algebra and and advanced algebra textbooks, I found that for the most part, all of the state standards were covered.  But there was one major exception.  In both cases, neither text met the eighth standard: Reasoning, problem solving, and communication.  This is the standard that has a lot of do with making sure that students really understand the mathematics.  For example, one of the sub-standards refers to students being able to, “Synthesize information to draw conclusions, and evaluate the arguments and conclusions of others.”

Maybe I am being overly cynical, but it is hard for me to see this pattern and not wonder what motivates this choice.  Is it possible that authors just don’t know how to write a textbook that would be considered traditional, but still includes questions that make students have to think critically?  Does this mean that the traditional approach itself is flawed in some way?  Is there some kind of “neo-liberal” conspiracy to reinvigorate factory-style schooling in order to keep future generations from questioning their control?  Was is just an oversight?  That our state standards include reasoning skills is an indication that their importance is pretty well accepted.  Why, then, would a major textbook manufacturer ignore this set of skills?

Perhaps it’s that our edition is not written specifically for the state of Washington, and thus they left reasoning out of the textbooks in order to accomodate states that do not have these as a standard.  But given that the NCTM stadards have included communication for years, and the coming Common Core standards also include reasoning and critical thinking requirements, it would stand to reason that these would be better to include even if they aren’t always needed, rather than ignore.

I do not understand this choice.

Today we had what is called a “building day.”  What this means, apparently, is that students get the day off so everyone in the building can work on teachery things.  The first part of the morning was dedicated to a building-wide meeting.  The staff has decided to focus this year on formative assessment, and so they are participating in a series of professional development seminars/meetings to learn more about ways to increase their use of formative assessment.  I sat at a table with several other interns and math teachers.  One of them, M, showed considerable resistance to the training.  He chose to grade tests rather than participate in the planned activities, and kept saying that he preferred direct instruction to group work.  As we are using complex instruction in the mathematics department, this is an unfortunate preference for him.

During the late morning the math department met as a whole to discuss some issues.  I was unclear as to what our objectives were, but it seemed that it had a lot to do with discussing the upcoming visit and meeting with the district superintendent and other high-level administrators planned for Monday. The administration had asked the staff to prepare a list of requests and recommendations for things they could be doing to help mathematics teachers have more success raising test scores.  The requests seemed very reasonable, and I had trouble understanding why they weren’t already being done.  I find I have this reaction pretty regularly when I spend time in public schools.  Yes, they do lots of good things.  But sometimes decisions are made (usually by the administration) that makes me wonder if they know that they’re administering a school, where people are meant to learn things.  They seem to behave sometimes as if they are administering a workplace set up for their own amusement and comfort.  I try not to have a bad attitude about this, but some days it’s very difficult.

The morning meeting was pretty productive, but I think would have been better if my group members had all been interested in participating.  The afternoon was the most productive, when we were free to work however we wanted.  I spent time working with another teacher candidate on planning the lessons for our next chapter in algebra, a class we’re both helping to teach.  I am excited about this collaborative process, as I am already learning a lot about planning, and I have yet to write a single lesson!

Today was “quiz day” in every class.  Quiz day, like other days, means group work.  As far as I can tell, the only activity that students complete on their own are the chapter tests.  Otherwise, they are not only allowed but encouraged to use the other members of their group as a resource.  Depending on the class, they are also allowed to use the book and their notes.  Calculators are always acceptable, even on chapter tests.

Watching so many sections of group quizzes was very interesting.  Although students are generally on task pretty well, today they were all focused.  Not only that, but they seemed much more willing to work with one another.  Sometimes group work devolves into individual work.  This isn’t necessarily bad, but it does indicate that the problems are probably too easy.  Group quizzes are different, though.  Because it is expected that students work with one another, the questions posed tend to be more challenging.  And because students get a group grade for their quiz, they are motivated to make sure that everyone in the group has the correct answer (although they are not necessarily motivated to make sure they all understand).  There were some really great mathematical conversations going on, for the most part.

One group had never managed to find a way to work together during classwork.  Because of this, they struggled to work together during the quiz, and wasted some of their limited time arguing.  When I graded their quiz later, they missed several questions that I thought they should have been able to answer, given their individual performance over the last week.  After class, one of the students asked to be switched to another group.  He had not yet seen his grade, but he seemed to have reached the peak of frustration.  What I thought was really interesting about this request is that this same student had been disciplined earlier in the week twice for reading a book instead of doing his classwork.  He seems to be willing to put a lot of energy into not being part of the group.  I am curious to see how he does in a couple of weeks, when the group assignments are changed (they’re randomly reassigned every two weeks).