Observations on Learning

In considering the one on one aspect of my student teaching my cooperating teacher considered a non native English speaker, U. as a candidate for me.  He felt that U. was struggling and that it was due to language issues.  After reviewing some of her homework I realized she was struggling in the class.  I choose her as one of my subjects to observe.  To contrast my observations of U. I also choose to observe a native English speaker, M, who through her homework was showing success in the class.  My assumption was that both girls were similarly capable of math but that language had created a barrier for U. that didnot exist for M.  I think if the roles were reversed M. would be struggling in class.  This is a vast oversimplification of both girls but it did focus my attention during my observations of both.  I was always thinking about language as I observed both girls.
M.’s attention during class was almost exclusively on the screen at the front of the class where work was being explained. Or it was on her own work and notes or the work of others tablemates during group work.  I would say this represented 90% of where her gaze laid, with another 8% on the teacher and a last 2% on other things, like other students, the windows, or the clock and these were usually in the form of quick glances.  Her gaze was steady, as she maintained a rhythm of raising and lowering her eyes from her notes to the screen.  When she looked at her notes it was almost exclusively to write more, she almost never just looked at them.  As the teacher moved through the figures on a table I could almost see her eyes movements mirroring the movement of his pencil on the screen.
As the teacher conducted a lesson or reviewed problems he would address the class with questions.  Typically about half the class answers questions.  M. would almost always answer.  There were two forms the delivery of her answers could take.  She might state her answer with and interrogatory tone, posing her answer as a question, in a voice just loud enough for the teacher to hear but few else.  Another possibility was her clearly stating her answer, with slightly more volume than her interrogative style of response.  The two responses seemed to indicate two different comfort levels with the answers she was offering.  When stating an answer with the interrogatory style a sense of doubt about the response’s correctness seemed to be intoned.
Occasionally M. would ask a question.  When she would ask a question she would look into the teacher’s eyes when stating it and then look at either the screen or her notes as he explained it.  Clarifications of the question and the response might or might not follow but she would end the exchange when asked if the explanation satisfied her by making eye contact with the teacher and saying “OK” while nodding her head in assent.  M. used English in her moment to moment participation in the class, she answered questions out loud, and she posed questions as well.  Language was simply not an issue for her in class.
U. had a different style in the classroom.  During lessons she would maintain attention to the screen and to her notes but when looking at her notes she was not always writing.  Sometimes she would be studying her notes without writing anything, with her gaze going back and forth from her notes to the screen and back.  She probably took as many notes as M.  but spent a lot more time looking at her notes.  Her gaze was mostly upon the screen or her notes or the work the work of others tablemates during group work.  She spent very little time with her gaze anywhere else.
U. did not speak in class.  When the teacher asked the class a question she never vocalized an answer, she also never asked questions.  Yet she was not afraid to talk or timid in one on one conversation as evidenced daily when she would speak in her native tongue to another student of her nationality.  She was also willing to ask questions one on one, as I observed one day after school when she came in to ask for some clarification of some homework problems.  Her questions related to word problems which my cooperating teacher had suspected might be a source of difficulty for her.  She would give the problem number and he would walk through it step by step with her acknowledging each step as he asked if she understood.  When he would complete the problem and ask if she understood she would say “Thank you.”
What I really want to do is start a conversation with her over her next homework and try to get a sense of how fluent she is in English.  I think that could lead me to some strategies for her approaching problems, especially word problems, that might help her in class.

Observations on Learning

Today marks five days in the classroom with students.  We have three sections of Algebra 2 and two sections of AP Statistics.  My activities in the class have involved posting descriptions of the day’s class, and uploading files, to “The Source”, the Seattle school district’s site which allows students and parents to check on what is happening in class.  I also have been learning all the classroom related computer programs involving taking attendance, recording grades, and the smart board.  While I regularly help students one on one, most often with calculators, I have gotten my toes wet in two related areas: checking and reviewing homework.  This has been confined to the Algebra classes. The way we check homework is to go around the class while the students are working on a warm up problem and look over the assigned problems.  We are not really checking the work in detail but we are looking for a few correct answers and certainly an indication that the problems were tried.  My cooperating teacher (CT) and I have been handing this task off to each other and I really enjoy it.  The most valuable part of it is that it forces me to learn names as I say every name directly to the student to try to cement it in my head.  It is slowly teaching me all the names.  My CT will go over the warm up problem while I check homework. 

In considering what observations tell me whether students are learning, checking the homework ranks high for me so far.  After checking several student homework’s I can see what the students have learned and what they have not learned.  This can be really helpful if I get up and review some of the homework which is what we do after the warm up problem has been explained.  One day I reviewed a problem without having checked a single homework.  I was at a loss as to whether the students had learned anything from the homework or my explanation.  I was in front of a sea of faces I could not read as hard as I tried.  When I asked if they got it or not I got no response.  My CT made the point that specific questions to specific students would give me a better sense of what they understood.  With the benefit of having seen some of the homeworks I can address specific problems I saw directly to the students.  This seems to get conversation flowing and I get a better sense of what they have learned and what they need more help with.

The biggest concept of the last few days in Algebra has concerned the role of u_(n-1) in recursive formulas.  With the introduction of u_(n-1)  there was some bewilderment as to what it was all about but as the days have progressed I have observed students using u_(n-1) in their speech in a way that indicates fluency; they are equating it with the prior term.  This has been the strongest evidence I have that new concepts, which did not immediately make sense, are being learned.  Tomorrow is our first investigation: modeling the height of a bouncing ball with a sequence.