Classroom Culture

December 24, 2010 at 1:28 pm (All, Methods, Observations, Reflections, Struggles, Student Teaching)

Something that keep popping into my head as I go through my teaching days is classroom culture.  Now that I’ve been out of the classroom for a week, I think I can finally say something coherent about it.

One of the problems that my CT and I have been running into lately is that our students don’t seem to be making the choices we want them to make.  In particular, they are off-task during class time.  Mostly they are just talking to one another about lots of stuff having nothing to do with math.  Some students are trying to pay attention, but I think it can be difficult for them when so many people are chatting.  Most of the students, even those trying to pay attention, act as if they are bored.

To this I would add something interesting I noticed regading a disconnect between what the students think they know and what we think they need to know.  The day before giving our last group quiz, an overwhelming number of students said they felt ready for the quiz.  As it’s a group quiz one might logically expect that those few that didn’t feel ready would get help during the quiz from their classmates.  But overall scores were very low on the quiz, telling me that the students were not actually ready.

After thinking about this, I think a major problem is that there is a serious disconnect between what we as instructors are expecting our students to do and learn, and what they think they’re expected to do and learn.  I have a feeling that the responsibility for this disconnect lies largely with myself and my CT.    There are a couple of reasons for this.

First, we rarely explain clearly what it is the students are supposed to get from each lesson.  We appear to assume that they’ll just figure it out.  The recent group quiz scores are evidence that this isn’t happening.  Second, I have yet to see anyone in the math department at this school engage in anything like long-range planning.  I am not sure that the instructors know what’s really expected, so it’s no surprise that our students are feeling lost.

What I know right now is that we have covered the exact same material this year that we did last year.  And last year they did not cover some pretty important material.  Continuing to do what we’re doing will result in our again not covering what we need to cover (and yes, I realize that covering material doesn’t mean students are learning it).  As a student teacher, I realize that I have little power to make changes in the way this particular math department operates.  But what I can do is start practicing good habits for when I (hopefully) have my own classroom next year.

Toward this end, I’ve decided that during winter quarter’s student teaching experience, I will be writing my own unit plans and doing long-range planning.  Whether anyone else in the department makes use of this information is immaterial.  What matters to me is that I have a sense of what we’re doing and where we’re going.  That way, I can begin to make small changes to our current classroom climate by providing more of a sense of coming from somewhere and going somewhere else.  I think fostering the idea that there is coherence in mathematics is important.

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Exhaustion

December 10, 2010 at 8:33 am (All, Methods, Reflections, Struggles, Student Teaching)

One of the biggest challenges I am facing right now is overcoming exhaustion.  I was home at 3pm yesterday – had I not had a bunch of work to do to prepare for today, I probably would have gone to bed.

Part of what’s making me tired is the mental effort required in learning for so many hours in a row.  I have a lot of sympathy for my sixth period students, who sometimes seem to have little brain power left so late in the day.  There are so many things to know and do well as a teacher that after a day of practicing, I am usually worn out.  I don’t think it needs to be this way for me, though.

Another factor in my exhaustion is that it’s almost the solstice.  Days are very short.  I always get tired at this time of year.  I sleep a lot in the winter, not so much in the summer.  When the sun’s up, so am I (most of the time).  Now that it’s dark for about 15 hours a day, I am really struggling to have enough energy. My body is pretty clear in telling me that it thinks I ought to be hibernating.

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The Sarah Show

December 8, 2010 at 4:06 pm (Methods, Reflections, Student Teaching)

Until today, I have put most of my energy into getting involved in and then taking the lead in the two algebra 1 classes I have.  This morning, my CT asked me if I would be willing to take the lead in the Algebra 2 honors classes.  She said she knew it was short notice, but in exchange she offered to take both algebra 1 classes.  I said sure, but probably looked a little uncertain.  After all, I haven’t done anything to prepare.  Although I had looked at the task the day before, and felt comfortable with the material (factoring quadratics), I didn’t have any idea what the homework covered.  So first period (one of our algebra 1 classes), I got out the book and did the homework from the night before.  Then I got the task key out and went over that more closely.

I was really grateful that I did the homework, instead of trying to wing it, for a couple of reasons.  For one, during our homework checks our students tend to ask a lot of questions.  Often, it is not enough for them to be shown that something works.  They want to know why.  Having the math worked out ahead of time at least insured that I could demonstrate how to do the factoring without making any errors, which let me focus on thinking about why things worked the way they did.  Second, during task work I actually wound up carrying the worked out homework around with me, and used it to demonstrate some principles to the students.  I even got compliments on how nice my work looked.

Leading the class actually turned out to be easier than I thought.  I sometimes struggle with knowing the right pace with my algebra 1 students, but I feel like my natural pace is just about right for the alg 2 honors kids.  And because most of these students actually like math and want to learn, I wind up getting in to a lot of great mathematical conversations.  I also worry less that challenging them to think will cause them to stop, rather than work harder (my intended response).

Late in the morning, my CT explained why she wanted me to take the lead in Algebra 2 Honors.  She thought she might need to miss work two days next week, and wanted to make sure I got a chance to get up in front of all of the classes before that happened.  So although we’ll have a sub who, in theory, can lead the class, I’ll be teaching all day Monday and Friday.  And yes, that’s Friday, the last day before the break.  But I am excited – I feel like I have a good rapport with all of my students.  I know what to do in every class individually… this will be a chance to see what it’s like to have a whole day.

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Success (or at least a small glimmer of hope)

December 6, 2010 at 9:39 pm (All, Methods, Reflections, Struggles, Student Teaching)

My program requires that I tutor two students.  I don’t actually have students that I am “tutoring, ” because I think of that as academic help.  Since I feel like I’m helping all of my students academically (and because I already have ten years’ experience as a tutor and don’t really need this experience), I have chosen to help two students that need help with other things.  One of them seems to struggle with the whole “getting to school” thing.  I don’t know why it’s an issue for him, but he’s missed something like 49 days this year (I think some are partial days, but still).  Once he gets to school, he hits another obstacle, something called “learning.”

Last week on Thursday I asked him if he was going to start coming to school more often.  He said he just didn’t know, because it was really hard for him (something about buses being full).  I don’t remember exactly how I responded, but I did tel him that it would be really good for him to come more often, because I was starting to see some real progress in his mathematical learning, and the more often he came to class the more he’d learn – and of course then the easier it would all get.

Today, completely unprompted, he got my attention as I was walking past my desk.  He told me that he’d made it his goal to come to class every day this week.  This, I think, is amazing.  He set a goal!  It’s reasonable!  He’s likely to have success!  I was so excited about this that I was almost gushing to my CT.

Now I have no idea if my attention toward him has been part of his decision to put more effort into coming to school.  I suppose I could ask him, but it’s really not that important.  What matters to me is that two weeks ago, this same student would not do any math, because he felt completely lost.  He told me lots of people had tried to help him and it never seemed to do any good.  Friday, he did four math problems (400% improvement from the zero problems he used to do!) and today, he’s got a goal.  That tells me he’s found a reason to be hopeful.  He’s shifted from “I can’t learn math,” to “I might be able to learn math.”  Maybe I’m being a little overdramatic, but to me this kind of change is really earth shattering.  With this change in attitude, a whole universe of possibility just opened up for this guy.  My job now is to do the best I can to make sure he sees himself as having success and making progress, so he sticks with it.

Moments like this are why I teach.

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Failure

December 6, 2010 at 12:29 pm (All, Methods, Reflections, Student Teaching)

This weekend I spent several hours grading chapter tests.  I’ve graded chapter tests in the past, and they did not take this long.  What really held me up on these is that so many students did so poorly.  I spent a lot of time trying to make sense of their math so I could give them as much partial credit as possible.

In the end, an average of about 30% of my students did not pass this test.  This is much lower than on previous tests and quizzes, and it got me thinking.  At first, I was surprised.  Th chapter covered solving single-variable equations and working with ratios and proportions.  I know students have actually been doing this since middle school, so this isn’t really new material.  The problems we’re working with are more sophisticated, perhaps, but the same rules still apply.  I had noticed that some students seemed to need to think about things more than I thought they should, but the test results made me feel like there were a lot of students who were completely lost.  I wondered how I could have missed that (and I am still not sure).

I then remembered that last year they had the same problem.  I’ve been looking over what was done for chapter four last year, and saw that they had taken three days out to reteach some of the content in chapter three.  I don’t think the kind of mistakes that were made would require three whole days.  And it might even be possible to weave the reteaching in with the new chapter (solving working with linear equations).  That’s promising… apparently we’ve done better than last year.

For a while I was angry at myself.  Was I really not paying enough attention to notice that a third of my students have been lost for weeks?  Then I realized that the test was given on the Tuesday after Thanksgiving break – a break made longer by two snow days.  So our students had a single day to review after being out of math for almost an entire week.  Maybe they just didn’t remember.

When I made a list of the most common mistakes I was seeing, I noticed that much of the time students missed points because they did not follow directions, or were a bit lazy in their math and made simple errors like dropping negative signs or adding incorrectly, and especially not checking their work.  I even had several students who checked their work, saw that they had gotten the wrong answer, and then just left the problem as is.  After thinking about it, I decided that the students seemed to understand the procedure generally, but they made a lot of thoughtless mistakes in the application process.  This makes me wonder a bit.  I believe that it’s important to learn to do mathematics with accuracy and precision.  It’s important to work neatly and communicate results clearly.  Most of my students do not display these traits.  I think it’s time to start upping the expectations and making this an explicit part of the instruction.

In the end I decided that it was really alright that a third of my students didn’t pass the test.  A great many of the students who didn’t pass haven’t really been taking their learning seriously.  They’re often absent, never make up missed work, and rarely do their homework.  Is it reasonable for me to expect that they pass the test?  Perhaps not.  Even with such a poor score, most students are still getting a C or better.  For those that aren’t, my CT and I have agreed that tomorrow I will pull them out, one by one, and talk with them about developing a plan to get them caught up and passing.  There is still time for most of them.  And even for those that probably cannot pass, I think it’s still important for them to make an effort and continue to learn – if they work hard they still have a chance to pass the end of course exam, even if they don’t get that first semester math credit.  We’ll see how it goes.

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Writing Tasks

December 1, 2010 at 4:06 pm (Methods, Reflections, Student Teaching)

As I’m sure I’ve mentioned before, I am student teaching in a department that uses complex instruction as it’s content-delivery model.  I know very little about the actual system, aside from what I have learned “on the job.”  What I understand is that the majority of learning takes place via group work, and that group work should be directed toward “tasks.”  Tasks are basically sets of problems that the students should be able to solve given their current understanding, and relying on their group members and the instructor as resources.

I think I have a kind of talent for writing tasks.  I have always thought of myself as a very practical mathematical person.  The math I know best is that which I use in daily life.  And if there’s anything in my daily life that can be enhanced with a little mathematics, chances are I’ve tried it.  It turns out that this is a pretty good background to have for writing tasks, because it makes it easy to write problems that are set in an authentic context.

One of the difficulties I see with the situation I am teaching in is that while this department uses complex instruction, the other secondary schools do not.  In addition, the district recently adopted a very traditional textbook, and expects all schools to use it (including ours).  Trying to develop tasks that don’t diverse too much from the textbook (so that we can assign homework problems from it) is an interesting challenge.  What I also find interesting is how poor the word problems are, in general.  They are written in such a way that only a minimum of mental effort is really required.  This assessment seems to be shared by the district, who, although they purchased the textbook, made it clear in their document aligning it with the state standards that it dos nothing to meet any of the critical thinking and problem solving state requirements.

That makes me wonder why they chose it.  Were the other options so much worse?  I can think of at least one curriculum that would have met all of the standards… why were these not options?  What factors really are involved in choosing textbooks, anyway?  Although it’s too late here now, I think that as a new teacher I might have to get involved in whatever committee makes these sorts of decisions.  I have the sense that politics and economics, rather than the interests of student learning, rule decision-making in many cases.

But I could be wrong.

And I’m off topic.  That happens with me, sometimes.

On the subject of tasks, I would just like to add that this process, while sometimes time consuming, is incredibly rewarding and, I’m finding, a very creative process.  I am keeping everything, too.  I may not find a way to use all the material next year (or any of it), but I will try.  Or maybe I’ll rewrite everything again.  That sounds like more fun, anyway.

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Direct Instruction Revisited

December 1, 2010 at 3:51 pm (All, Methods, Observations, Reflections, Struggles, Student Teaching)

I had a major Aha moment on Monday.

My first time trying to do an entire class period of direct instruction did not go well.  Based on that single experience, I decided that I was just not cut out for doing direct instruction.  Then Monday I got to step back from teaching and observe my coteacher again.  She did 50 minutes of direct instruction, reviewing the topics from the chapter in preparation for Tuesday’s test.

I realized quite suddenly, about five minutes into her talk, that I had not done anything the “right” way.  This is funny to me, because when I was actually doing it, and for the first few days afterward, I felt certain that I had followed her model well, but that I just wasn’t good at delivering it.

I am still not quite sure what I did, but it was nothing like what my coteacher does.

We have two sections of algebra, and today we worked out a plan where she would deliver instruction in the first class, and I would watch.  Then I would do it the second time around. Boy, what a difference.  This saved me for a couple of reasons.  First, I could take notes on the strategies she was using, so I knew what to focus on and what not to worry so much about.  Second, because we use the doc cam to write out the notes, I could use her hand-written notes to work from during my own delivery.  This worked fantastically.

Not that I don’t still need to improve.  I do.  Sometimes I am good at thinking on my feet.  Other times I really suck at it.  Today was one of those days.  We were talking about literal equations, and I could sense that the students were not happy and in some cases possibly even hostile to the content I was covering.  I had no idea what to do about it, though.  Zero.  And then I forgot that class ends at 12:55, not 12:50, so I found myself with about 8 minutes to spare at the end of class.  Thankfully, my brain kicked into gear right about then, and I spend the time talking with the students about what it was they felt was so different about the literal equations.  I don’t know how much it helped, but at least it gave the students a chance to voice their frustrations.  I think that’s important.

My coteacher agreed that I did a much better job today.  We have agreed that rather than have me take over completely for any long period of time, it’s better, at least for the time being, for us to really coteach.  I’ll teach and while, and then she can teach a while.  That will both give me a break, and a chance to process my experiences and then observe her teaching more in the light of this new learning.  I am really excited about next quarter… I can’t wait!

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Direct Instruction

November 18, 2010 at 3:00 pm (Methods, Reflections, Student Teaching)

Direct instruction is not my thing.  I discovered that this morning when trying to work through a set of notes to a class of near-comatose students yesterday morning during first period.  It’s very clear to me now that without feedback from the students, I feel lost.

Which might be how they’re feeling, too, but no one is brave enough to say anything.  But see, I don’t know, because no one wanted to talk with me.

As I think about how things went, I think it might have been interesting to stop for a minute and actually share this feeling of being lost with the students, and explain to them that if they don’t tell me whether they are understanding or have questions, I just have to guess.  And since that’s pretty random, I’d rather not.  So maybe next time I’ll give that a try.

Fifth period was a different story, however.  They’re definitely much more talkative than first period, so I got lots of feedback.  The trouble was that all that extra information wound up misleading me.  I didn’t realize this until I had time to reflect, but because so many students were volunteering answers, they made it difficult for me to remember that there were likely several students who were struggling.  As a result, I wound up going through the material more quickly than I needed to.  Fortunately, we’re covering this material over the course of four days, so the second day’s task will give me a chance to make sure everyone gets a second chance at the material.

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Not enough time

November 17, 2010 at 3:00 pm (All, Methods, Struggles, Student Teaching)

I know teachers say that all the time, but I had my first real experience of that this week.

Monday during fifth period I ran into my first serious dilemma.  There are 3-4 students in that class who rarely attend class.  When they do, they’re unlikely to do any work.  Lately, though, they’ve started to change.  On Monday we did a task, and two of these students were both present and making a genuine effort at understanding the math.  The trouble is that they are so behind from years of poor attendance and effort that they seemed to require my full attention.  That would mean, though, that the rest of the class had to be effectively ignored.  That wasn’t really an option, either.  I finally settled for spending more time with these two students than anyone else, but I found that when I was not there to help them, they would not do any math.  This didn’t seem to be an attitude issue, but because they were just that lost.

What makes this such a dilemma for me is that I feel like the majority of the rest of the class could stand to work on their own for a day, maybe even two or three days.  For the most part, they’re getting the math and don’t really need my help.  The questions they want to ask me have more to do with easing their uncertainty by checking answers and methodology than in understanding what needs to be done.  These two students, on the other hand, are still struggling with basic arithmetic.

On the other hand, I know that even if I spent an entire week’s worth of classes helping these two students, they would still be way behind.  To really be successful, they would need to commit to come in for help before or after school or during advisory.  So far, this seems unlikely.  Just getting them to attend class probably counts as a success.  If they do work at all, that’s a major achievement.  Or am I setting the bar too low?

I just don’t know.

What I do know is that at least one of the students is willing to talk with me.  I spent a little time at the end of class talking with him about some of the choices he was making in terms of this class, and his responses, although hesitant at times, were very thoughtful.  He showed genuine concern for the success of his classmates.  Part of what prompted me to speak with him is that yesterday he chose to throw out his entire group quiz, rather than submit it with the rest of the group and risk hurting their score because of his lack of ability.  He would rather get a 0.  Through the course of our conversation he decided to give me his quiz so that I could look at the work he did get done, and spend some time thinking about how we could get him some credit for that.  Because he struggles so much with math, I feel that it’s especially important that the work he is able to do gets recognition.  Not in front of the class maybe (I think it’s a bit early for that), but between he and I.

Today I am hoping both students will be in class again.  We’re doing notes (direct instruction), rather than a class.  This can be less interesting for many students, but I think it would be a good opportunity for these two to strengthen the learning they’ve ben struggling to do over the last two weeks.

This is the kind of work I was hoping to find.  It’s something that I didn’t see much opportunity for in my previous school, and is part of what prompted me to request a transfer.  I just hope that the small success I’ve had leads to something more for these students.  It really saddens me to see people who are so young be so lost.

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First day

November 15, 2010 at 3:00 pm (All, Methods, Reflections, Student Teaching)

I have not written much over the last two weeks because most of my spare time was spent planning my unit.  Because my school does group planning, all the algebra teachers will be teaching from my lesson plans.  This made the planning process more stressful than it probably needed to be, because I have so many sets of eyes judging me.  Today is the first day my unit is being taught.  It also coincides with the beginning of my two-week stint as lead teacher in algebra (yes, I did that on purpose).

During the last two weeks I’ve been helping to teach from lessons written by another student teacher.  I felt like I learned a lot from this process, in that I got to see what kind of mistakes she made and (hopefully) not repeat them myself.  The downside is that because I am not already intimately familiar with the material and how it’s being presented, I sometimes had to think extra quickly to help students with their questions.

Now I am teaching on my own.  Although my co-teacher is still in the classroom, she has said that unless I ask for help, she will not step in.  She wants to give me a chance to make my own mistakes and learn to recover from them.  I am very grateful for this.  I know as a teacher I am going to make a lot of mistakes, and I think the sooner I can get comfortable with that, the better.

We have algebra first and fifth periods.  The lesson (a group task) went pretty well first period.  I figured out pretty quickly sometimes my wording is confusing to students.  I wanted them to think about their strategy before actually solving the first problem in the task.  Instead of saying, “take a moment to think about what kind of strategy you might use to solve this,” I said, “decide with side you want to collect the variable terms on and which you want to more the constant terms to.”  I almost gave the strategy to them, but because I used terms that are still new (variable and especially constant), the students really got stuck.  In the future, I will need to really think about what it is I want the students to do, and then ask them to do that.  Hinting doesn’t seem to be a good first strategy.

During fifth period things went differently.  I decided to tell the students not to worry about strategy or the chart I’d provided for organizing their work.  This removed the block the first period students had, and most of the students came very close to completing the entire task.  I am not sure how I feel about this choice, however.  I think it’s important for students to begin to consider how they are solving problems now, when they are still relatively straightforward.  In the end, I decided to skip this thinking in this particular task in order to help students get further in the task, where they encountered equations with no solutions and infinite solutions.  This is the first time most students have seen this, and it’s an important understanding for students as they move into more sophisticated mathematics.

I will be teaching all of the algebra lessons between November 15th and November 30th.  It is very exciting to see how my own lessons play out in a class, especially since I get to teach them myself.  The mathematics we’re covering represents the first material that students really struggle with.  It feels like an honor to be trusted to plan how we will approach it.

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