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Vito Prosciutto: Teaching community college math on the road to a PhD.

Saturday, February 28, 2004

15:13
Scholarship applications 

I had decided with the Saturday classes to do a "digression" today from the progress that we were making on factoring based on the question that I ended class with last week: Given the prime factorization of an integer, can we find how many factors that integer has? This lead quite nicely to some basic combinatorics (and it was interesting how many of the students knew their way around some of the features in their calculators). We worked through what the odds were of winning the lottery (and to give them a sense of how big that number was, I proposed that they and 99 of their closest friends would pool their funds to buy every possible lottery ticket. If they bought 1 ticket every 20 seconds, working non-stop 24/7 it would still take them over 5 weeks to buy all the tickets. And they'd win less money than they spent.

From there we worked out the odds of being dealt certain poker hands in five cards, which kept most of the class quite interested in the problem. We got to look at permutations and think about when we needed to multiply our odds by 5, 5! or 5 choose 2, etc. to compensate for the fact that we've been specific about the order of the cards.

And I got a chance to point out to the students that no matter what the game, when it comes to gambling the most important rule to remember is: The house always wins.

But then before I could teach the second class, I was told that all of the students would be working on financial aid applications in the computer lab. Gee, thanks for letting me know this in advance.

It was interesting to see what looking for college scholarships looks like in the 21st century. When I was an undergrad, to be honest, I didn't really look for scholarships. The college I attended had a need-blind admissions policy and a high enough nominal tuition, that I would have had to come up with over $7000 in additional scholarships per year before it would affect my actual cost of attending: Anything less than that would just reduce the grant that the school gave me.

Many of the students were using Monster.com's FastWeb service. A couple of things:

The second point requires some elucidation: To start searching, there's a long application process which includes numerous attempts to get students (or their parents) to agree to receive marketing e-mails, apply to DeVry and Lord only knows what else. The presentation was seldom clear and there were many times as I was watching the students navigate through this that I wasn't sure what was being asked and I have almost 20 years more experience resisting advertising and scams. I wonder if there's something equivalent to FastWeb without all the sales pitches. That would be a good thing.

Friday, February 27, 2004

16:51
The inner lives of students 

I've gotten so far behind on my journaling with my week of being sick (feeling better, by the way, but still not 100%), that I almost forgot some of the more interesting items of the week (and also a good reason for why I write this anonymously: To protect my identity, but also my students' identity).

I have two students in my morning Algebra classes who are apparently going through a fair amount of inner turmoil in their lives. One showed up about 30 minutes late to class yesterday, in tears, asking for a pass to see her counselor. I wrote her one immediately. I wasn't able to understand what she said was the problem, but apparently it was sufficient on her return to class today for me to ask her if things were better for her today. When I see her in the hallways she looks genuinely pleased to see me. Sometimes it only takes a little bit of effort to build trust.

The other student has been absent the whole week. On the attendence report we receive from the main office she came back with an attendence code my mentor had never seen before: It turns out it stood for "runaway". The report is that she's been recovered, but she wasn't back in class today. I would never have guessed that this girl would be in that situation, and I hope that I can do whatever small thing is necessary to build trust with her.

On the flip side, one of my geometry students seems to have decided that I don't like her and has been rather openly resistant to my teaching. I'm not sure how to manage this. I'm pretty careful to make sure that I treat all of my students fairly, but I can see how a student who doesn't bring her homework to class could come to the incorrect conclusion that my exhortations to bring homework would be an indication that I was picking on her. I'm thinking perhaps that next week, I'll try and catch her before she flees the room at the end of the day to talk with her briefly.

14:43
A few miscellaneous tidbits from the rest of the day 

Once a week (roughly), in Advanced Algebra, there's ACT prep. My mentor is keeping control of that part of the class, but since most of my section is seniors, the rest of the class effectively has a study hall. I ended up using this time to do some individual re-teaching of the material for students who had some difficulty being caught up with the homework or understanding some of the concepts. It's kind of relaxing and a nice way to interact with the kids for the period.

Geometry was a bit chaotic. We spent a bit too much time in both classes reviewing homework problems, so I felt a bit rushed getting through the distance formula and analytic proofs. I think that what I might do for Tuesday is give them a handout with the homework worked out and have them come in after school with further questions. I gave them a handout today which consisted of "hints" for the problems on the last test. Students who want to retake the test need to re-do any problems they got wrong correctly. Once they've done that, I'll let them take a new test to improve their grade.

14:35
Oh no, the F-word 

No, that F-word. Fractions.

We started a new chapter with the Algebra kids today and I discovered that most of the students gave me blank looks when I showed them how to solve a proportion like

x/4=3/2

and they had to multiply 3/2 by 4. My mentor teacher's solution was to only have them learn to solve proportions by cross-products. And when I did that in 2nd hour, that seemed to go more slowly, but we still need to make sure that fractions are not a problem. I'm thinking that I really want to do a remedial fraction lesson with these kids. OK, sure, it might be easier for them to get around the fraction issue in this problem by cross-products so we now have 2x=4×3 and x=6, but then they'll be lost when we start doing more complicated rational expressions.

The chapter that we're starting is, I think, a great collection of material because it's the culmination of Algebra I: It takes everything that they've done for the whole of Algebra I and combines it into nice tasty problems. You add, subtract, multiply and factor polynomials. You add, subtract, multiply and divide polynomials. You solve for x. You can even graph the functions. The only thing that we don't really use from the class is solving systems of equations. And the most important concepts of all, are the fraction problems. I think perhaps I'll give a quick quiz on Tuesday (we get a three-day weekend!) to gauge where the kids are with fractions and do the fraction lesson on Wednesday.

14:19
Random play 

From Frog Blog via What in Tarnation, this challenge:
Step 1: Open your mp3 player.
Step 2: Put all of your music on random.
Step 3: List the first ten songs it plays, no matter how embarrassing.

My results (courtesy of iTunes)

  1. Kinski (Black Tape for a Blue Girl, The Scavenger Bride)
  2. A Dear John and Marsha Letter (Stan Freberg, The Very Best of Stan Freberg)
  3. In Your Eyes (Jeffery Gaines, internet download)
  4. I'll Never Fall in Love (Burt Bacharach and Elvis Costello, Austin Powers 2 Soundtrack
  5. Quand Tu Danses (Jean-Jacques Goldman, En Passant
  6. The City of the Sun (NDV, internet download)
  7. Pie Jesu (St John's College Choir Cambridge, Maurice Durufle, Requiem)
  8. Biko - Radio Edit (Peter Gabriel and Sinead O'Connor, internet download)
  9. I'm in Love with a Wonderful Guy (Monica Lewis, My Favorite Things)
  10. Algo Termina Mal (Enanitos Verdes, Solo Exitos Con Los Enanitos Verdes)

That was interesting. My iTunes collection is a bit more eclectic than my CD collection (which is pretty eclectic already), largely because it consists mostly of

I was somewhat surprised that even though they comprise a significant portion of my iTunes, no songs recorded by my band or the choir that I sing in made this sample. Although one cover my band recorded ("Step Right Up") just popped up at #11.

Speaking of music, I'm now back to listening to my newest CD, the quite delicious Oscar Levant plays Gershwin which is a great performance of all the "serious" Gershwin works (Rhapsody in Blue, An American in Paris, etc.)

14:04
That's three four 

34 years ago, a band consisting largely of graduates from the school where I'm student teaching had their lone top-ten hit. This year the school is celebrating a major anniversary, so as a consequence I'm hearing this song an awful lot. I'd joked about keeping count. As I went upstairs to the room where I teach geometry, I realized the song that was being played during the passing period was that song again. That's three, I said to my mentor as I came in. We both laughed. Then after school, they played it again. That's four. If I go to the anniversary celebration tomorrow, I'll almost certainly hear it yet again.

Thursday, February 26, 2004

15:53
Well that was relaxing 

Today was a nice day to be sick... Tests first three periods and in the geometry classes, I had the students working in groups on the more involved problems with the Pythagorean theorem. Almost no talking all day. Of course now I have a stack of grading to take care of tonight.

14:44
Wednesday  

I've continued to be sick all week. I've been going in since Tuesday, but it's been miserable. Each day, I go home after school and sleep. This makes planning a bit rough.

Yesterday was a full day of teaching. Algebra was not too demanding: I had the students working in groups of reviewing the chapter's material and I was able to spend a lot of time not talking. Advanced Algebra was quite a bit worse, and as I was teaching the use of dummy variables to convert equations like t2/5-t1/5-2=0 into quadratics I was faced with a lot of blank stares from the students. I suppose I'll see whether they managed to pick up the material from the examples and the homework when I grade today's quiz.

Geometry, on the other hand went rather well, and my mentor commented that this was the best I'd ever taught: With a couple exceptions, my boardwork was fine and I managed to get pretty good responsiveness from the students.

Then for added fun, at the end of the day when I went to the office to pick up my coat, I spotted a fight starting in the hallway and, being the big dumb sort that I am, immediately ran to break it up. One of the other teachers who was in the office at the time told me that I shouldn't have gotten between the fighting students. Oops. Fortunately, I managed to stop things before it moved from shoving to punching and another teacher took care of the hard disciplinary part (she collected IDs and took the students to the dean's office).

Tuesday, February 24, 2004

16:01
Still sick 

But I went in to school today. I felt like I was among the walking dead. I managed to get through my teaching, but I don't think that I did as well as possible. I didn't get a chance to talk with my geometry mentor before class so I discovered too late that I didn't know how she taught yesterday's material.

Monday, February 23, 2004

05:46
Sick day 

I've been fighting off being sick since sometime last week, and today sick won. I'm going to stay home and in bed.

My big challenge of the morning was trying to reach someone to tell them. One mentor teacher had her cell phone apparently turned off, and I seem to have misplaced the other mentor's cell number. Oops. I didn't have the direct-dial number for the math office. And it was before 7:30am so there was no one answering the phone at the district number. Dial-by-name didn't work, and the option that would allegedly reach the school gave me instead "not a valid option". I played voice mail roulette until finally at 7:30 someone answered the phone. It took her 2 tries to get me to someone who could convey news of my absence and today's assignments to my mentors.

So now, I can finally go back to bed. When I wake up later today, I'll write a bit about the weekend.

Friday, February 20, 2004

20:59
Another quick day of comments 

My boardwork is improving considerably. I'm making a point of being more organized about what I do, and I hope it's paying off.

On Fridays the school has been doing the 2nd hour announcements on video. Today's announcements started five minutes late, then ran for half an hour. This called for a bit of adjustment in the lesson plan to say the least. There was one point during the extended video included in the announcements where the narrator said something along the lines of "but we're not finished yet!" which had my mentor and I both visibly rolling our eyes in frustration with this.

I have a new student in my geometry class. It's the end of the fifth week of the semester and they're still moving kids around! She looks like she's going to be a good student though, there were many points where she was the only student taking notes.

In the evening I went to a meeting of the local chapter of NCTM. The primary focus was on motivating students to want to do proofs. This is a big problem with so many of the proofs that we do in geometry class: There primary purpose is to give the students something to do with their theorems. I wish I had the time to come up with more project-oriented proofs in each chapter. Next year perhaps. Or maybe next chapter.

13:45
I generally don't link to Joanne Jacobs... 

... but doing an internet search on "The Lizzie Method" turned up this discussion at her site and reminds me of why I ignore her site.

Much like at isomorphisms, the commenters revel in the ignorance of the reporter on the story, but here they reveal their own ignorance.

factoring polynomials - a fairly important operation in college-level math and in the mathematical sciences, but it only works well when there is a whole-number answer.
Actually, not quite. You can factor when there is a rational solution to a quadratic equation. The applications of factoring also go beyond solving quadratics: It's also important for working with rational expressions, a subject covered in Algebra I (which is hardly "college-level" mathematics).
Or it is possible to derive the quadratic formula by trying to apply this method to arbitrary coefficients, through several pages of algebra.
Um, no, it's not possible to derive the quadratic formula using this method (finding factors p and q of ac that sum to b is not possible without specific values for a, b and c). The quadratic formula is derived by completing the square. I did this in Advanced Algebra yesterday. It's short enough that I didn't bother to write the derivation in my class notes, but to get from ax2+bx+c=0 to the quadratic formula takes 6 steps.
why she's getting praised for a method that's so difficult
Difficult? It's by far the simplest and easiest to teach method for factoring ax2+bx+c that I've found. The quadratic formula, incidentally, is of limited use for simplifying rational expressions.
Lizzie seems to me to be FOILing backwards
Um, factoring is taking a product and writing it as a product of two factors (thus the name). So of course it's going to look as if she's FOILing backwards. The problem is figuring out how to get from the product to the factors. It's much harder than it seems.

Thursday, February 19, 2004

20:30
A bit overloaded 

I've got a stack of grading that I'm behind on, lesson plans to write for tomorrow, so writing here is a bit low on the priority list.

A couple quick notes:

Wednesday, February 18, 2004

19:52
Geometry - I like having staggered tests 

I keep getting little days of rest along the way. Today geometry had a test, so I was absolved from standing in front of the class for a couple hours in the day. Tomorrow algebra has a quiz, another couple hour break. It's the small things that count.

19:48
Advanced Algebra - finally teaching 

I'm finally in front of my class for Advanced Algebra. Upper-level math classes are so cool. One of the first things I said as I walked among the students checking on their work was, "wow, you guys are great at this!"

I did make the fatal mistake of not re-reviewing the homework before teaching so I left out some example problems that I really should have covered. We'll see tomorrow how much difficulty this causes the students. That's the big minus with planning out homework assignments a week in advance. I fixed that for tomorrow, I ran through the whole advanced algebra homework assignment for tomorrow already so I know what to include in my lesson plan.

19:40
The Lizzie method redux 

I ended up teaching the Lizzie method two more times today. The first was at the school's math department meeting. The second was for my student teaching seminar. The math teachers were more receptive of the Lizzie method than were the student teachers. I guess the long experience of how hard teaching this sort of factoring by traditional methods leaves them more open to a better way. The student teaching seminar presentation ended up being a lot of a focus on how to teach factoring. An afterthought question that I added on to the original presentation ended up being a bit of a distraction (I had posited the question, "what do students need to know before we teach this factoring?").

19:20
Job interview! 

I got a call today from the first district with whom I applied inviting me for an interview. They gave me the choice of an interview here in April or there whenever I happen to get out there (yes, I'm planning on moving to another state in May). I'm actually a bit surprised since this is the sort of large urban school district that tends to do a poor job of teacher recruitment. But apparently this particular large urban school district doesn't meet that particular stereotype. Or perhaps they're good at the interview phase, but I won't see a job offer until August.

I need to finish up job applications for the other schools on my list soon so I'll have them ready when the job fair takes place next month.

Tuesday, February 17, 2004

19:30
Geometry 

Not a whole lot to say about geometry today. It was a review day. In the first class, my supervisor came and of course the kids were awfully wild (no observerations, kids act fine). We ended up losing a lot of time on reviewing homework and had I the chance to do that class over again, I would have just given them a handout with the homework solutions that they requested so they could use that to study. We ended up only getting to two student presentations in class.

Second period there was no leftover homework review so we spent the whole class on presentations of the review problems. It worked rather well although I had a brain crash and thought that we had ten fewer minutes of class time than we actually did, so the "lightning round" questions were a bit more rushed than necessary.

Now to finish typing up the test for tomorrow.

14:16
Algebra - The Lizzie Method 

Teaching factoring of quadratics in the form ax2+bx+c is always a challenge, so when Vlorbik pointed me to this discussion at the now-defunct isomorphisms, I was intrigued to see what was said.

So here's the short version of what it's all about: A sixteen-year old girl found a "new" way of factoring quadratic equations in the form ax2+bx+c and the local newspaper wrote a breathless article extolling the virtues of what she did.

Most of the commentary at isomorphisms focused on the idea that her process isn't really revolutionary in a mathematical sense. And this is true. But from a pedagogical perspective, what she's done is actually rather useful.

The text that we use for beginning Algebra at the high school where I'm student teaching offers one method for factoring ax2+bx+c: Guess and check. It's possible to use some educated guessing to shorten the process, but it's still a lot of work and students will generally not get far factoring this sort of problem.

What I've found works well (and what my mentor teacher uses) is known by a variety of methods: Factoring by grouping, the split method, the ac method, the British method (the supplementary materials for our textbook include this approach), and who knows what other names are lurking out there.

The "Lizzie" method, on the other hand, eliminates the somewhat difficult final step in the ac method which requires factoring by grouping or a bit of educated guess and check. The process is actually remarkably straightforward, and what I found was that by the third problem, about 90% of the class was successfully factoring polynomials with a leading coefficient (and the remaining 10% were having difficulty because they still had trouble with the simpler process of factoring polynomials in the form x2+bx+c). If you teach math, definitely check out the Lizzie method. So far every teacher that I've shown it to has responded with the following reaction:

  1. Try it on their challenging problem to see if it really works.
  2. Write down the steps so she can use it when she teaches the material.

Friday, February 13, 2004

19:42
Planning next week 

Still waiting to get into that comfy first class seat. I've been looking over my schedule for what remains of the chapter for my Algebra class, and I'm feeling a bit frustrated in some ways by my mentor's efforts to direct how I teach this material. Factoring equations in the form ax2+bx+c is a difficult thing to teach, but I've been through this lesson a number of times (albeit with college students). I've got a pretty good sense of where I want to go with this. I appreciate her ideas, but the more I think about it, the less willing I am to go in precisely the direction that she wants me to go. I fear that I may drive my fiancée nuts a bit this weekend as I think about different ways to get from where I am to where I want to be.

Advanced Algebra, I briefly considered starting the new chapter with the graphing section. I would prefer to do that, because it gives some motivation to what we're trying to do (when I taught an introductory algebra class last year to 7th and 8th graders, I used graphing as a motivator to just about everything we wanted to do in the class. But I'm going to resist the urge to get creative here.

Geometry. It's a little bit cushy, actually. Tuesday is the second day of review, Wednesday is the exam, so that just leaves two days to plan and looking in the book, the material is a bit thin between those two days. I need to look again to make sure about the second section ("an introduction to circles"), but presumably we shouldn't have to spend too much time on either. I'll split the first section's homework into two parts, though, in case going back over the test that we just took takes too much of the class time.

19:17
First Class 

My plane arrived slightly late at the airport where I was to make my connecting flight. Then it sat on the tarmack for half an hour waiting for another plane to leave the gate. I ran from one gate to the next only to discover that my connecting flight left without me. Fortunately, the original offer of being booked tomorrow morning was rescinded in favor of a flight to an airport near my original destination with a first class seat. Groovy.

The last time I flew first class was a rebooking at Christmas time when I was in college. Unfortunately I was also deathly ill and I slept the whole flight. This might not be much better, as the flight's scheduled departure time is not much earlier than my typical bed time these days.

16:48
Homework policy 

I've had a chance to talk a bit more with both of my mentors about homework policy. The two have rather different policies. My algebra mentor's policy is that late homework is accepted (but with a 50% penalty). Students who are missing three or more homework problems are given detention and have to come in to complete the homework. Most students will get themselves caught up to avoid this, but it also provides a chance to get additional assistance.

My geometry mentor on the other hand does not accept late homework, largely justifying this on the basis that students will abuse the policy.

My own feeling is that the point of homework is to reinforce classroom learning. If late homework is not accepted, there is almost no chance that the student will do it. On the other hand, if late homework is accepted, perhaps the student will just copy the answers, but if we give homework with the answers in the back of the book to begin with, then that's not really an issue (plus it allows students to more immediately get feedback on their efforts).

Much of this is discipline-dependent. In math classes, homework is a learning tool. In other disciplines, such as English, the homework is the assessment so in that case it's more important to insist on timely completion of the work.

16:28
Miscellaneous 

Blogging at 15,000 feet as I fly out to see my fiancée for the long weekend. A potpourri of leftover comments at week's end:

Algebra class had a quiz today, and it was kind of relaxing to have the kids working individually and silently for the whole period. I graded one quiz at the airport and the result was a bit disappointing, but this was a student who has not done well so far to begin with.

It also gave me a nice uninterrupted time to deal with individual student issues like missing homework and passing out replacement worksheets for students who had lost theirs.

I think that I'm going to revise my filing system. Right now I have colored folders for each day of the week. Completely useless for me. I'd heard this suggested elsewhere and thought I'd give it a try, but this sort of organization doesn't really gibe with what I do in my files. The files that I use the most are the folders labelled "[Class/period] To Be Graded" and "[Class/period] To Be Returned". What I need are folders of "future worksheets" "past worksheets" "future quizzes/tests" and "past quizzes/tests" and perhaps a "This class" folder.

I'm also going to make a minor change to my system for keeping track of students' work in the index cards I print up for my Algebra II class. For that group, I'm going to include space to track attendence/tardies and also spaces for the quiz and test scores so that the card can be a complete class record in the palm of my hand. One of these days, I'll upload a sample card to a free image hosting site so that my system will be clearer to my readers here.

Geometry saw the beginning of a two-day review period. Today the student worked in groups. Because we hadn't had a chance to go over homework yesterday, I incorporated homework review into the homework. As I checked in homework with each group I instructed them to compare answers so that they could see which problems were difficult for them. I don't think that this aspect of the review worked very well. Towards the end of the class, I read off the answers to problems which had short answers and it seemed as if the students hadn't done the comparison work.

Thursday, February 12, 2004

20:09
Geometry - working on getting better 

Today, we had my mentor teach the first section of geometry, and I taught the second. I picked up a few good ideas in teaching the material (like pointing out that a theorem with a name is probably important).

After class, we sat down and talked a bit about what was happening and one of her comments was pretty much right on the money: My relationship with the students is tense. I'm not sure how to remedy this, but I can see that this is a big difference between my successful and unsuccessful classes.

One interesting thing was that for whatever reason, working from the same lesson plan, I was more rushed and covered less material in the same time as my mentor. Neither she nor I were able to explain what had happened here.

14:18
Algebra - I've got to admit it's getting better 

I'm beginning to feel a bit more comfortable with the algebra class, and I feel like I did a better job of executing the Making Minutes Count question strategy with the class. One thing that I've started doing is explicitly instructing them on how I'd like the class to run, and that helps a great deal. I didn't get through as much new material as I would have liked to, so I'm going to end up rescheduling things tomorrow. Second period was a bit less comfortable for me than first period, but still not too bad.

Wednesday, February 11, 2004

20:19
Math/English or Math/Psychology 

Subject matter qualification in my state apparently operates on a buy one get one free basis. By virtue of my undergraduate coursework I can be authorized to teach a second subject, but I only get to pick one. I meet the requirements to be authorized to teach English or Psychology. I have to choose by March 17th. Anyone care to weigh in on which one I should pick?

20:06
Good Teachers 

There's a lot in this post at a school yard blog, but it's worth a read.

My comment on it (reacting to someone else's comment, given below in italics):

This list is interesting, Schoolyardblogger, but it's a list for saints, not teachers.

But it gives us something to aspire to, no? I wouldn't consider schoolyardblogger to be an infallible oracle. Some things I'll look at and say "yes, I agree." Those I don't I should look at and see if I can understand the argument and if I can then maybe I'll accept it maybe I won't. But it gives a starting point for the quest.

19:35
Good and bad 

My geometry mentor suggested that we each create lists of what I've been doing well and what I need improvement in. I had a very hard time coming up with the good things.

During seminar, one of our group exercises was to name a favorite student and explain why. This was followed by a suggestion to try and remember something positive about each day. I'm realizing that I have a tendency to dwell on the negative, which is not good for my mental health, especially right now. I'm going to want to make a point of doing this.

Among today's teaching, what I'm most happy with is that I've managed to get everyone to be able to solve a problem using similar triangles related to the homework problems. I've been using the book Every Minute Counts for suggestions and finding it helpful.

I also had what seemed a positive encounter with one of my students outside of class. As a matter of principle, given a choice between my students liking me, or my students learning from me, I'd pick learning from me. But that doesn't mean that I'm indifferent to whether they like me or not. I'm occasionally a bit jealous of how some other teachers interact with students, and it's nice to finally get something positive.

19:18
TeacherInsightTM 

TeacherInsightTM is a product provided by The Gallup Organization (yes the polling people) as a means of HR screening. It's used by the major metropolitan district where I'm applying (and as many other school districts as the Gallup Organization was able to sell the product to). It's about 30 questions or so long and my initial reaction to the product, that I don't like the idea of a website trying to do what a job interview should do, was reinforced when I actually did the questionaire.

Item one: If you have to do this, it's probably a good idea to fill it out when you're feeling good about your teaching. I'm guessing that the selection will be biased towards people who are happy positive teaching-is-a-great-career types. Which is not to say that I'm not that, but this past week has been rough enough on me that I probably ended up coming out a bit more negative than I might otherwise (curse my pathological honesty!).

Item two: Many of the questions in the multiple choice/Likert scale section were the sorts of questions that I would have liked to have given more nuanced answers than were possible in this context.

Item three: It did give me a sense of the sorts of questions that might be asked in a real life job interview.

But I still vote thumbs down to TeacherInsight, and it seems like it's a bit of snake oil being sold to school districts.

19:12
Seminar 

This was in some ways a good week for seminar: One of the people in seminar showed a way of teaching altitude on hypotenuse theorems that I will use when I get to that part of the material in my own teaching. I like what he did for an opener as well, and with some clarifications in the material will be something that I use as well.

But on the other hand, I ended up volunteering to show some material as well. This in itself is not bad, but I have to resist my urge to devolve into my tendency to consider myself an expert. In theory, sure. But in theory I can play any band or orchestra instrument as well (in practice not so much).

On the third hand, to have the opportunity to teach in a non-threatening environment was nice, although on reflection I spotted something which is my tendency to want to resort to abbreviated explanations. With this audience, I can get away with that (to show, for example, why if you create a triangle by using the diameter of a circle to provide one side and then connect the endpoints of the diameter to any point on the circle you have a right triangle).

On the fourth hand, I'm still a bit emotionally fragile, I'm realizing. At points during my presentation, it was all I could do to keep myself from bursting into tears as I attempted to teach. I'm feeling better now, but I suspect that might be entering a depressive phase for a while.

19:00
Algebra with Pizzazz 

Algebra with Pizzazz is a big binder of worksheets for classroom use. I've used a few of them. I'm not all that crazy about them because they use variations of mutliple choice and matching as the sole way of checking answers, and each worksheet is based around some awfully corny joke ("Where did the Tadpoles in the pawnshop come from? A Frog Pawned.") But I did notice that the order of the factoring worksheets follows exactly how I'm covering the material! It's nice that haven been driven from the book's curriculum, I picked an order that matches someone else's (although I think that this is probably based on vague memories of one or the other of the textbooks that we use for the remedial algebra classes at the university).

18:51
Assembly 

So I got to attend my first assembly since I was in high school myself today. The band has improved quite a bit from where they were when I saw them when I was doing observations in September, although their intonation was still a bit off at times.

Tuesday, February 10, 2004

15:00
Geometry 

The quiz that I gave today seemed to help a bit, if only because it was relatively easy. I decided to extend the homework deadline to Thursday (there's an assembly tomorrow, so only one section will be meeting, and it made the most sense to push off the homework for both classes), and instead used the remaining portion of the class time to go over more examples relating to the homework. Unfortunately, one of my examples, turned out to have an error in it. I cannot afford to underplan. As a consequence, I've decided to skip my Tuesday evening class to make sure that I've got everything put together for tomorrow and Thursday.

I've had some students re-take the chapter exam, and among those who have so far I have 3 who have demonstrated mastery of the material and 1 who has not. There are a few more to grade.

14:11
Algebra  

I'm feeling reasonably comfortable with the teaching in Algebra, but I'm also getting hit with a lot of the administrative aspects of teaching at the same time. It's a bit hard to keep up with all of this. Attendence, tardy slips, referrals, this all takes a lot of time away from my teaching. Time, ok, but attention, there's a problem. I've not been keeping up with students who are missing homework assignments, so I'm going to make up some slips tonight or tomorrow to give to students missing homework. The grade distribution is still pretty good, and it appears that students are learning.

I've done a decent job of implementing my question goals in Algebra, although there's still a lot to be done. Some of it is a matter of getting the kids to adjust to a new way of providing answers.

03:52
My objective for today 

is to ask better questions and to have less lecture and more question and answer to generate the knowledge for the question. In Algebra, we're looking at the zero product rule and how it lets us use factoring to solve equations. I'll see how well I can put this into place for that class. Geometry, I'm not entirely sure how I'll manage this...

Monday, February 09, 2004

17:30
Dressing like a teacher - the big challenge of the kind-of-tall guy 

I stand about 6'2" tall and have a 36" inseam. This is worth noting because I have a rotation in my work clothes of 2 suits plus a sportcoat that I wear with slacks. I discovered over the weekend that both of my pairs of slacks had reached the point of no return for school use, so I went shopping for new slacks at the local Sears. In the main men's section of the store, every single pair of slacks had a 34" inseam or shorter. In the big and tall section of the store, every single pair of slacks had a 38" inseam or longer.

I'll be wearing cuffs on my trousers.

17:28
Geometry - hmm, that's interesting 

The last period geometry class was much easier to deal with today than the first geometry class I have. I think some of it was a result of having gone over the material once already when the last period kids came in, but I also think that my mentor had said something to the kids before I got in the room, because there was a palpable difference in behavior of the kids themselves.

17:23
Algebra - mostly about absenteeism 

Little by little I'm getting a handle on teaching the algebra class. The overall quiz results were a bit disappointing, but I think that the kids are beginning to get how to do this. I still regret deviating from the book for the material that I'm teaching, and I should have stuck with my original plan. Oh well, hindsight is 20/20. I did check some of the most poorly performing students and saw that they were poorly performing before I took over the class, which while it's encouraging for me personally, is still not something that I like to see.

One challenge that I have with the algebra class (and to a lesser extent with the geometry) is absenteeism. I have one student who's going to be gone from tomorrow through next Tuesday (presumably a family vacation). Then there are students who have been suspended or are just plain absent. Most of these students, if I could get them in the classroom every day could be doing much better.

Saturday, February 07, 2004

12:07
Job search tips 

Our dear Ms. Frizzle has offered some specific suggestions on resumes. Definitely welcome for me. I've got my first job fair coming up on March 20th. My resume is actually in good shape, although I've not updated it in a while so I need to go back over it and make sure that it reflects changes in my Saturday teaching job. Then there's the big question: Do I include my student teaching experience on the resume?

11:58
Saturday teaching - signs of life 

I had very different experiences with the first and second classes today. The early kids followed the lesson pretty well (we went from reviewing the laws of exponents to seeing how these translate into rules for working with logarithms and ultimately how to find, e.g., log45 using your calculator which has no logx button. I think that I may have to start writing two lesssons. But not yet. Next week is a three day weekend so I'm going to visit my fiancée. I'm leaving behind a computer exercise where the kids will do some function graphing using Microsoft Excel. The week after that is another day that I may not be present depending on what the schedule will be for testing (I know I'm taking my last certification test that day, but not whether I have a morning or afternoon time slot). So it won't be until the 28th that I have the kids again. We'll see how much they remember then and for March I may start writing dual lesson plans. I'm hoping at that point that I'll have a better handle on time management with the student teaching so adding one more lesson plan a week won't be that hard.

Oh, one last note: The kids seemed very curious about where I teach. After one class, one girl told me that I should try to teach at her high school next year. It's nice to get that occasional bit of praise, especially after this week.

Friday, February 06, 2004

18:09
Advanced Algebra 

Watching the Advanced Algebra class today I was working on being very conscious of the flow of time. My mentor spent 10 minutes on the homework check-in at the beginning of class, then answering questions about the problems took another 10 minutes or so (while I was working on it, I wasn't necessarily succeeding at the work!), followed by a homework quiz on the material and then finally she got to the new material, with just 15 minutes of class time remaining. This was clearly less time than she had planned. I have my schedule for the Advanced Algebra, so that helps a bit. I'm going to try to get the first week of that class planned over the weekend. I'd like to have at least one class that I can look back at and say, I did very well with that.

18:03
Geometry - in the computer lab 

Today's geometry class was time spent in the computer lab. The kids may not have felt like they accomplished much in some cases, but looking back on it and ahead to next week's lessons, I think that this reinforced (and in sometimes established) some key concepts in the kids' minds. There are some good questions that were raised in the exercise that we'll bring up on Monday, in particular, the idea of identifying the corresponding segments for similar polygons. We'll also use one of the activities to consider some aspects of proportionality that we hadn't really looked at previously.

Aside from a typo on one of the steps, my handouts worked really well. I credit my periodic stints as a technical writer for that.

17:58
Algebra - The rich get richer 

I'm feeling a bit better about my algebra teaching again. I've graded about half the quizzes and there are still a lot of students struggling with the material, but it is rough material, so that's not entirely unexpected. My mentor has me doing a lot of the administrative work that needs to be done as a teacher, which is really pushing things a bit for me. I'm ok with attendence, but tardies are difficult for me to keep track of (I think that I'm going to start closing the classroom door so that I'm more conscious of late arrivals), and I've failed on the assigning detentions on later tardies. Dealing with students who miss a great deal of class marks another challenge. There's a part of me, as awful as it is to admit, that looks at the 10-absences-and-you-re-dropped rule with a bit of anticipation in some cases.

One interesting thing that happened was that the two classes moved through a classroom exercise with algebra tiles at very different rates. As a consequence, the first class got only a cursory overview of how to factor trinomials with a minus sign, while the second class got a very good overview. It will make for an interesting class on Monday to see whether the kids read through the section as instructed before attempting the homework. Worse still, when I looked at the homework, I saw that not one assigned question was in the form ax2+bx+c! They all had at least one subtraction in them, and most had the third term negative, which was the form that the first period kids got the least exposure to! (And I keep writing with exclamation marks!)

I did get some sense of what sort of questions will be raised on Monday, though, since I had one student come in after school to take a quiz and she asked me about some of the homework questions she had done and why her numbers didn't match the back of the book.

16:15
An interesting account of math ed reform 

A schoolyard blog has a good account of "Ted", a teacher who was fired from his math teaching job after implementing the NCTM standards. Shortly after the firing, he was named Colorado High School Mathematics Teacher of the year. It's a very long post, but one thing stood out for me about giving students verification that their work was correct:
I stopped certifying student responses as correct. I insisted that the students verify the validity of their responses. Nobody told Newton or Euler when they were “right or wrong”. They were their own highest authority. Why should I expect less from my students? Having Mr. D say, “Yes, that is correct.” Is warm and fuzzy. It also ultimately destroys the critical thinking edge of my students.

There is a story of the new recruit at an engineering company, fresh out of college, who was given a circuit to analyze on his first day on the job. He worked on it for most of the day and then brought his solution to the manager who had assigned the task that morning. The recruit placed his solution on the desk and waited eagerly for a response. The manager looked at the paper and then filed it. The recruit lingered for awhile and then said, “Well was I right?”

The manager was shocked. He asked, “Why would I pay you to find answers that I already know?”

Thursday, February 05, 2004

18:23
Geometry 

The kids in geometry are getting better at telling me how to teach to them. One thing that they told me was that they were being confused by my explaining a concept to them different ways at different times. I think that explaining things differently is valuable, but what I should try to do is preface a change in explanation by something along the lines of, "here's a different way of doing this."

I did have one minor problem where I accidentally wrote down the page number for today's homework assignment wrong in my notes so the first geometry class was assigned the wrong problem for homework. At least there was a problem 11 on page 300.

17:00
Advanced Algebra 

Today was largely a review. One thing that I noticed was the amount of time that was spent reviewing the homework. I'm not sure how typical that is, but I tend not to spend a lot of time on this, and perhaps I should work on evening out the balance. It's difficult for me to see how to balance the homework review with the new material. With the algebra class which I'm teaching, we spend two days on each lesson (the course stretches algebra I into a two year sequence), so perhaps I can try covering everything in the first lesson, and I can spend most or all of the second day reviewing the homework and preparing them for a second set of homework.

14:25
Algebra 

Something seems to have started to click for the kids with the factoring. Almost all of the students did the homework on the second attempt and based on the quizzes that I've graded so far today they understand the lesson pretty well. There are still a few who are having trouble with addition and subtraction, so we'll need to try to reinforce the correct way to handle that. My plan for tomorrow will be to use algebra tiles to model factoring x2+bx+c.

Wednesday, February 04, 2004

21:08
A bit of much needed levity before some downer posts 

Since most readers read these backwards, a chance for something light before stuff gets heavy. I'd actually made the map previously, but for some reason had resisted the urge to include it here. Not much chance of guessing where I live based on this map, is there?
create your own visited states map or write about it on the open travel guide

19:31
Geometry 

It seemed as I was checking in the homework that I had a pretty good completion rate among the students. I'll see what things look like with the quiz tomorrow. I'm avoiding being creative with the quiz questions and instead I'm picking questions that are very much like the problems that we saw in the homework and perhaps that will help. It's a bit frustrating for me to see the students frustrated (and for my mentor teacher as well). She wasn't really able to offer any specific suggestions on what to do to improve my teaching, saying that she didn't see anything different about how I taught compared to her.

In the second geometry class, I somehow ran out of time much faster than I expected, and after I finished reviewing the homework (which I would have guessed was going faster than it had in the first class), I noticed that I only had 10 minutes left. I think that my plan for the last two days of this week is going to be revised. The golden ratio lesson for tomorrow will be scrapped in favor of homework review and some reinforcement of ratio and proportion from the first section. Then the golden ratio computer activity will be revised to be instead a similar polygons lesson. This seems like it will have better pedagogical value. It's a pity that we'll be dropping some of this out, but I think that some of the material, I can re-use as class openers next week.

19:24
Algebra 

I was discouraged as I checked in homework today to see that almost every student didn't even try the portion of the homework that used the special product rules that I spent the whole class yesterday working through with students. I ended up scrapping the original lesson plan for today, and making today a re-teach lesson. I'll try to see if I can cover the extra material that I'd hoped to cover today in the short time after the quiz tomorrow. Perhaps the order that I decided to cover factoring wasn't so wise after all...

18:56
I hope this is the bottom 

I've been feeling pretty awful about my teaching yesterday and today. I keep feeling like I'm not reaching any of the kids. I heard from one of my mentors today that one of my students was asking about transferring out of the class, which I think was the final straw which left me in a pretty serious depression. I'm feeling better now (thanks to my fiancée), but I'm still feeling like I'm in the Slough of Despond. I'm reminded of the following illustration from Assorted Stuff:
It's a little scary that the section labelled disillusionment is so long and flat (and low). I'm hoping that maybe I'll show some signs of improvement with the quizzes tomorrow, but I'm not counting on it.

My plan now, is to go with a view that I know nothing, and do my best to relearn everything from scratch. It's very hard to swallow my pride in this way, but I think that it's almost essential. At seminar, I made a point of being certain to ask questions whenever I didn't know the answer. There's no point in presenting a false front. I need to relearn how to do everything.

Tuesday, February 03, 2004

20:41
Advanced Algebra 

I finally got my third prep assignment. I'll be teaching an advanced algebra class. This will be with my current algebra mentor. I need to see if I can track down a teacher's edition of the text and any supplementary materials. I am looking forward to getting in some more observation time so I can watch teaching with the experiences and critiques that I've had thusfar.

20:26
Geometry 

Geometry went much better today (the benefits of planning). I did underplan one theorem, however, and that came back to bite me during a period when I had one of the student teaching supervisors watching my class. One thing that I felt went very well was the demonstration that I used to similarity. I drew a polygon on an overhead transparency, then used the classroom similarity generator (aka overhead projector) to project the polygon onto the board. I carefully traced the projected image and then was able to demonstrate that I could take the transparency up to the board and show that corresponding angles are congruent by overlaying the angles on the transparency on the blackboard.

Critiques of my teaching from the supervisor focused on my boardwork. Again, one of my key issues is to get more written on the board and improve the organization of what I write.

There was one odd moment near the beginning of the last period class where I had a widespread bout of coughing among the students. They claimed it was some bad odor, but I smelled nothing and suspected it was just typical student misbehavior. Certainly this was the sort of thing that I and my classmates would have done at that age.

19:43
Algebra 

Checking in homework for Algebra, almost everyone had correctly completed the worksheets on GCF factoring. That was a good sign. I had some good tips on trying to organize the board between the first and second periods, although I still wanted more board space than I had available. Some other notes: One other big problem is that I have some hearing deficiencies and I have difficulty hearing whispering. I was aware that I couldn't easily understand when some one whispers to me, but apparently I also don't hear whispering at all from a distance. I need to be more aware of visual cues from this.

Monday, February 02, 2004

18:49
Georgia Board of Education shenanigans 

WHATEVER has a good round-up of the Georgia Board of Education silliness which includes among other things, trying to eliminate the word "evolution" from the biology curriculum and skipping the years 1800-1876 in American History (thus avoiding any significant mention of slavery and the civil war). He provides good material in rebuttal to the Georgia apologists as well. If you haven't heard about this, check it out.

15:33
Geometry 

I was quite underprepared today. I had assumed that the material would be fairly straightforward, but I failed to really read the section so I was caught by surprise in the first geometry class. I'll probably need to re-teach this material tomorrow when we go over the homework. The second geometry class was a bit better, but I think part of that was that they were subdued by the just-returned tests. Results were not good, unfortunately. Median score in the first geometry class was 63.3%, and 53.1% in the second. My no failures policy is going to generate a significant amount of work for me. I have a total of 34 students who will go back over the material to re-take the test. Yikes.

15:12
Algebra 

So today I began my Algebra teaching assignment. Now it's two preps for real every day. It's interesting to note the difference in how my two mentors work with me. My geometry mentor is very hands-off. She'll give me some quick pointers at the end of the period, and check in with me before school, but after the first week or so was over, she really has let me sink or swim on my own. My Algebra mentor is a bit more hands-on, at least right now. Perhaps it's just the contrast and my Geometry mentor was like this two weeks ago, it's hard to say.

We began with factoring monomials out of polynomials (e.g., 3x2+6x=3x(x+2)), with a worksheet to be completed in class and a second to be completed as homework. I feel like I made more progress with the students one on one as they worked on the worksheets than I did in the lecture section. One comment my mentor made (and that was also made in the geometry classes) was that I should write more on the board. I made that change in second period and more students seemed to get it, but 2nd period is also a faster group of kids in general, so I'm not sure I can take full credit for that.

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