Vito Prosciutto: Teaching community college math on the road to a PhD.
Tuesday, April 20, 2004
21:35
Observations
Not a whole lot to report. I sat in on a teacher's classes who I'd not seen before and got my first glimpse of the precalc class. They were doing infinite series which is a topic that I'm always interested to observe being taught because I managed to more or less miss it in my own formal math education (I took an AB Calc class, but the BC test so I managed to miss that whole portion of Calculus where it's traditionally taught). I ended up catching a slight error in the teacher's instruction where she claimed that
n^{n}/(n+1)^{n}
would approach 1 as n approached infinity. My instinct was that it would have to decrease since we were taking progressively larger exponents of the fraction n/(n+1) which would be less than 1. My first guess was that it might tend towards 0, but I later realized that it would actually tend towards 1/e. I thought of a better argument that it was in fact 1/e then the calculator appeal I was able to use in class when I thought about inverting the fraction and with a bit of algebra I got
(1+1/n)^{n} whose limit as n approaches infinity is in fact e (the advanced algebra text we use, in fact defines e that way).
It felt a bit like being raked over the coals today with the final evaluation. I still have a lot to learn about teaching. My algebra mentor I think really pegged it with me as to where my two biggest shortcomings were: First, I went in thinking that I was going to do great. Second, I was trying to do to much other stuff. I have many of the pieces in place, but I've not managed to get everything in place all at once.
I think that one thing that I may do is to prepare forms to use for my lesson plans that will help remind me of some of the key things that I still don't do with enough consistently, like checking for understanding, etc.
A couple outside school math encounters. First was while stopping at the photographer to make some final arrangements for my upcoming wedding... when the woman at the office learned that I was a math teacher, she proceeded to proudly proclaim her ignorance of math. I would hope that English teachers don't have people proudly proclaiming their illiteracy.
The other was talking to an old friend and discovering that he was using some of the resources on my non-anonymous website to teach his daughter who's currently in pre-algebra how to factor quadratics. She enjoyed it enough that she factored a couple hundred polynomials in an afternoon! I think that I may give that worksheet to my own students next year as an extra credit assignment.
Observing some other classes today, I saw a neat manipulative used in one class: "Algebra dominoes". This consisted of 30 paper rectangles along the lines of
17
If x=17
Then 2x+3=?
It provides a somewhat fun way of reinforcing some of the math concepts that the students will be using. I didn't look closely, but I would hope that there would be a mix of "easy" problems like 2x+3 and "hard" problems like 4+3x.
Then, a well-designed set would be set up to alternate these problems in such a way that a basic mistake like 2+3(4)=20 would quickly lead back to the card to give quick feedback to the student that they had made a mistake. This shows promise as a review activity, or even teaching tool.
As I head into my final week of student teaching and one last unit (one prep, one class this week), I've set a goal for myself of getting the students to do much better on this unit than they have in the past. It's getting a bit depressing with this class that so many of them seem willing to just sit back and get an F. But we're doing stats this week and most of this material is pretty easy and straightforward, so I'm hoping that I can make sure that we've got everything down. I'll see what happens when I check in homework tomorrow. I think that most of them got the basics of the counting principle and permutations, but I'm not 100% sure yet.
After waiting about half an hour in the waiting area, I was finally brough back to the interviewer's desk. The usual sorts of questions: "What's your discipline plan?" "How will you deal with English Language Learners/Special Ed students?" "How do you use standards in your teaching?" No real opportunity for me to ask questions at all. It seems that with this large metropolitan district the final decisions are made by the principals, so at this point I've mostly made it to the qualification stage to be looked at by principals. I was told that if I were open to teaching junior high I could get a guaranteed offer of employment now, but based on my previous experiences with teaching that age group, I don't think that it would be a very good fit. I did discover that the district is divided into sub-districts which makes evaluating schools a bit easier now that I understand how that part of the system works.
Nothing but tests and grading today. I'd never really timed my grading before, and it's grim. One class's tests take me about 2 hours to grade. My goal of finishing all the grading before I left for the day was a miserable failure.
Saw Eternal Sunshine of the Spotless Mind after Holy Thursday Mass. What an amazing film.
My geometry mentor is, I think, rather uncomfortable with someone else in the classroom while she's teaching, and has been trying to push me out of the room since I've wrapped up my teaching. I more or less stopped resisting today and spent my afternoon watching one of the first-year math teachers. I didn't see too much classroom activity because it was mostly a review day for her, but I did manage to see some of what happens with her classroom management. There wasn't anything in particular that I could identify that set her apart from the more experienced teachers that I observed. I think some of it comes down to just body language and classroom presence, and I would guess that this only comes with experience and time.
I did pick up an interesting way of motivating group work: The group work is counted as a quiz. Every student turns in his or her work, but only one student's work from the group is graded. Other rules: Only three questions per group will be answered. Group quizzes cannot be turned in before the end of the class period.
My algebra mentor commented to me today that I tend to show more detailed work with the advanced algebra students (who don't necessarily need to see it) than to the beginning algebra students (who do). I'm not sure what to make of that.
It's a bit late to be trying new things but what the heck. I'm trying something that my algebra mentor mentioned to me as a way of trying to cut down on the amount of the period that we spend on the homework check and review. I pass out handouts at the beginning of the class on colored paper with the homework problems worked out. The students then can use this to compare their work with mine. This also provides a model for how to show work for class. I check in homework as usual, while they're comparing answers and then I can answer additional questions. The students are still adapting to the new approach, and I find myself writing on the board, exactly what's on the sheet, which does appear to answer their questions. When I do this starting in the fall, I'll work a bit better on training the students on how to ask questions. Perhaps numbering steps in the worked out material could help so that they could say things like, "why did you multiply by (x-1) in step 3?" In Geometry this could be especially helpful. This also provides me with a way of providing some homework feedback to students who are absent. I like it, but it's still a work in progress. The teacher who I'm stealing the idea from copies the handouts onto colored paper and collects the handouts back from the students. I've been doing that, but I'm not sure that there's any particular benefit to doing this, especially with my singleton Advanced Algebra class...
So last Friday I get up to the geometry classroom and one of the students is standing at the door with a goofy smile when I get to the room. "Howya doin' Mr Prosciutto" she says and playfully punches me in the arm. "Fine," I say, "what's with the goofy smile?" "What goofy smile? This is just how I look?" "OK," I reply, "but it's still goofy."
Then I get in the room and notice that my mentor's desk has been cleared off and there's a few bottles of soda and a big cake on the desk. Whoa, it's a surprise party. A little early, perhaps, since I'll still be around until the end of April, but it's still pretty cool. I got cards from both geometry classes and got to spend a bit of time just chatting with the students while they did some group work and ate cake and drank soda. I didn't get to spend as much time with the last period geometry class though because I was meeting with my algebra mentor for that time.
This Orange County Register article details a program I wasn't familiar with which provides scholarship funds (up to $5000) for Latino high school seniors who are the first in their family to go to college. There are also similar programs by Sallie Mae (who runs this one) for African-American students and low-income students. The deadline is April 15th, so if you have students who might benefit, it's worth getting the information to them quickly.
Despite the date, this was essentially a prank-free day.
I've got major problems with students not doing homework. I'm thinking that for the last few assignments with the algebra class that I may replace homework check-in with homework quizzes.