Two Weeks / One Post

Yeah, I've been neglecting the blog for a couple of weeks now. I'd feel worse about it if I weren't so busy! Then again, I will now have a difficult time trying to reflect on my initial teaching forays, since I'm doing it after the fact. Most of my writing takes place on the job these days: I try to jot down observations from each class period into a sectioned spiral notebook that I keep at my desk.

I have lead taught several lessons by now, and done so for each class in my schedule. Some of those sessions were planned out in advance, but a few were spur-of-the-moment appointments. On the Thursday before last, Ms. Cranford had to rush home to care for one of her sick children. She called in a sub, of course, but she left three of her classes in my hands that day with naught but her notes as preparation -- and I had never lead taught for any of those students before. As nerve-wracking as it may sound, I actually rather enjoyed that experience. When given time to prepare a lesson I tend to over-analyze my approach, just as I tend to over-analyze many things. (It's a common occupational hazard for mathematicians.) While I do not plan to make a habit of going up cold and improvising, it does generate a healthy surge of stage adrenaline (I got over stage fright long ago) which loosens me up a bit. I don't how smooth my delivery was for my students -- you would have to ask them yourselves -- but I must not have screwed up too badly as Ms Cranford was able to pick up right where I left off when she returned the next day.

Whether I get to plan my lesson in advance or not, I'm learning firsthand about the role schema play for students. I'm often surprised by what they do and do not know coming into a classroom. Just today, when I was grading an assignment about scientific notation, I noticed that several students did not seem to know how many zeroes are found in millions, billions, and trillions. Naturally they had trouble with word problems in which quantities were expressed using those words instead of just numbers. Oh well, teach and learn. Sometime in the future, expect a post from me about the mathematical concepts I think every student needs to know. Some of them may surprise you.

So far in my lessons, I have stuck to the basic format espoused by Ms Cranford: spend 10-15 minutes answering questions about yesterday's topic, demonstrate the concept of the day through lecture and whiteboard, and then leave the students with time to start working on the corresponding assignment. It's very traditional -- some critics may even call it obsolete -- but Ms Cranford carries it off very well. I'm not sure that I want to go down that road myself -- I'm not sure that I can travel that road with any degree of success once I'm teaching solo -- but I haven't yet figured out how I want to break from this model. Maybe our upcoming Methods courses will shed some light on the topic. I've heard about different approaches for running a math class during our summer MAT courses, but I've watched math teachers implement the classic approach for many years now. A certain amount of internalization has taken place, I fear. I get the feeling that any serious experimentation will have to wait until I have secured my own teaching position: Ms Cranford's students seem comfortable with her style of teaching, and there is something to be said for having a student know what to expect in class. I don't want to mess up her system just to satisfy my own curiosity, especially when she's getting such good results from it overall.

No doubt some of you are wondering why I'm not fully comfortable with the review/lecture/assignment routine. I have my reasons, but the exploration of those reasons will have to wait for my next post -- whenever I can take time out for another round of blogging. Sleep beckons.

People-Watching; Connect the Blogs

Ah, Fridays. Many LHS teachers subscribe to the 'Casual Friday' dress code, including Ms. Cranford (my cooperating teacher). And I am taking full advantage of that policy by wearing loose-fitting carpenter jeans, beat-up sneakers, and the most flowery Hawaiian shirt in my wardrobe. After spending the rest of the week wearing 'nice' shirts and Dockers in a futile attempt to appear well-dressed and conventionally respectable, this feels good.

As I've mentioned before, one of my primary tasks in the classroom is to help out students when they get to work on their current assignment in class. Ms. Cranford has a knack for spotting students that are struggling on their own but have not yet worked up the nerve to actively seek help. It's almost uncanny: out of nowhere, I'll see her stroll over to a student's desk and ask if s/he needs help, and nine times out of ten s/he accepts the offer. I've tried to pull this stunt a few times, but my batting average is far, far lower than Ms. Cranford's.

Nonverbal communication has never been my strong suit. I suck at gathering intelligence about people through discreet observation. I hope to improve my skills through practical experience, but I have good reason to doubt that I will ever be as proficient as someone like Ms. Cranford. Of course, she also encourages students to help each other solve problems -- and therein lies my salvation. When I finally land my own teaching gig somewhere, I think I'll have better luck with measures designed to help students help themselves. Any student who meekly waits for me to notice their plight may end up waiting for quite a while.

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At the end of my previous post, I briefly floated the idea of linking all the EOU student teaching blogs together. The whole point of blogging, after all, is that it gives us a way to share our observations and reflections with others and learn from their experiences in return. Any measure that facilitates this sharing process works to the benefit of us all.

Sharon Porter has posted links to many (but not all) of our blogs on Blackboard. I propose taking things one step further. If you look to right of these posts, you will find a hyper-linked list of EOU student-teaching blogs. I'm not going to claim that it's a comprehensive list, but it's a start. You too should strongly consider adding such a list to your own blog, or expanding the one you already have. If enough of us do this, we could connect every active MAT blog to every other MAT blog. Any link missed by one list could be archived on another, and eventually shared with the rest of us.

I got the idea after browsing the MAT blogs I had already been following. I stumbled across a link to Word on The Street, Jessie's blog. This was a great find for several reasons: (1) her blog address had not found its way onto Sharon's Blackboard list; (2) Jessie writes well; and (3) she had compiled the longest list of MAT blogs to date, including a few others I had not read. I am now following those blogs.

If anyone needs help setting up their blog list, let me know by posting a comment. I will respond in kind.

First Impressions; Brain-Lock

Today marks the second full day of regular classes at LHS. Ms. Cranford and I have now had a chance to meet all of our students and observe their conduct during a lesson. I think we lucked out with this bunch. Every last one came to our room classbroken. They brought books and writing utensils; they settled down when the tardy bell rang; they listened quietly and took notes when Ms. Cranford explained and demonstrated the day's lesson. (Today we reviewed the graphing of linear equations.) At one point during the lecture, she asked a question and received a response from over half of the class. The noise level increased when the students were turned loose to work on their homework assignment in class, but almost all of the chatter centered on the task at hand. Needless to say, I was impressed. The nature of our schedule may play a role: we aren't teaching any courses below Algebra Plus in the mathematics progression. Ms. Cranford also has a reputation for being a friendly but no-nonsense type of teacher.

I will be teaching my first lesson next Tuesday, after Labor Day. In the meantime, I have been trying to make myself useful where I can. This includes assisting students that get hung up on the assigned exercises. I think I've spent too much time out of tutoring practice this summer -- my initial interventions have not gone as smoothly as usual. One episode in particular deserves a moment of reflection.

A couple of students had trouble evaluating an expression involving fractions. Upon learning of their difficulty, I thought to myself something along the following lines: Aw HELL no. These kids NEED to know how to work with fractions. Time for a crash-course refresher. Within the context of the exercise, I proceeded to demonstrate the methods for multiplying fractions and adding fractions with different denominators. My attempt did not take; the bell rang and they left unsure of their work. I told them we could go over it again later. When I related this episode to Ms. Cranford, she mentioned that she usually recommends multiplying by least common denominators whenever possible, thereby clearing the fractions and sidestepping the fraction gridlock altogether.

This approach would have been far more elegant, in hindsight. I've even used it with tutoring clients before for that very reason. Yes, the underlying discomfort these students have with fractions will have to be resolved eventually, but it will certainly be addressed in detail when they learn about rational expressions in future algebra lessons. Somehow I let myself get fixated on addressing the issue right then and there, to the detriment of solving the problem at hand. That bothers me. I'm not sure why I got hung up like that; none of the post hoc explanations I've run through my head seem to get at the root of the problem. Maybe I'm just overthinking my response to the situation; hindsight is the only 20/20 vision I've enjoyed since childhood. Still, I should strive to approach students' questions with a greater degree of flexibility. I'm sure I'll get a better feel for this kind of thing with practice -- and that's what this year is all about.

Remember what I said about posting new stuff on Fridays? Scrap that. From here on out, I blog whenever I feel the need to debrief myself after something interesting happens. And I find a lot of things interesting, so check back here often. On tomorrow or Friday I'll present an idea about how to link all of the EOU student-teaching blogs together along with a case for the benefits of doing so.