Projects
days until the end of spring semester.days until Snakes on a Plane.
Boxes unpacked
Math article project
Finished mathematical core of article. Next: Write analytical core of article.
Dummit and Foote, Abstract Algebra
Finished section 1.6 (86 to go)
Silverman and Tate, Rational Points on Elliptic Curves
FInished 2.5 (31 to go)
Conway, Functions of One Complex Variable I
Finished section 7.5 (27 to go)
Munkres, Topology
Finished section 21 (60 to go)
Royden, Real Analysis
Finished section 2.4 (97 to go)
Nonfiction book project
Todo list uptodate
Fiction book project
1443 out of 100,000 projected words written.
Top 100 novels of all time
Reading Ulysses
IMDB top 250 films
Tengoku to jigoku next in queue.
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Vito Prosciutto: Teaching community college math on the road to a PhD.
Saturday, February 28, 2004
15:13Scholarship applications
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 needblind 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:
 monster.com???
 My God, this is evil.
Friday, February 27, 2004
16:51The inner lives of students
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.
14:43A few miscellaneous tidbits from the rest of the day
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 redo any problems they got wrong correctly. Once they've done that, I'll let them take a new test to improve their grade.
14:35Oh no, the Fword
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
and they had to multiply 3/2 by 4. My mentor teacher's solution was to only have them learn to solve proportions by crossproducts. 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 crossproducts 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 threeday weekend!) to gauge where the kids are with fractions and do the fraction lesson on Wednesday.
14:19Random play
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)
 Kinski (Black Tape for a Blue Girl, The Scavenger Bride)
 A Dear John and Marsha Letter (Stan Freberg, The Very Best of Stan Freberg)
 In Your Eyes (Jeffery Gaines, internet download)
 I'll Never Fall in Love (Burt Bacharach and Elvis Costello, Austin Powers 2 Soundtrack
 Quand Tu Danses (JeanJacques Goldman, En Passant
 The City of the Sun (NDV, internet download)
 Pie Jesu (St John's College Choir Cambridge, Maurice Durufle, Requiem)
 Biko  Radio Edit (Peter Gabriel and Sinead O'Connor, internet download)
 I'm in Love with a Wonderful Guy (Monica Lewis, My Favorite Things)
 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
 Interesting songs that I've pulled off of CDs to put on mix CDs for friends
 Rarities that I've pulled off the internet because I can't find them (easily) on CD.
 Stuff I've recorded myself (solo and band projects)
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.)
14:04That's three four
Thursday, February 26, 2004
15:53Well that was relaxing
14:44Wednesday
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 t^{2/5}t^{1/5}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
16:01Still sick
Monday, February 23, 2004
05:46Sick day
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 directdial number for the math office. And it was before 7:30am so there was no one answering the phone at the district number. Dialbyname 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
20:59Another quick day of comments
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 projectoriented proofs in each chapter. Next year perhaps. Or maybe next chapter.
13:45I generally don't link to Joanne Jacobs...
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 collegelevel math and in the mathematical sciences, but it only works well when there is a wholenumber 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 "collegelevel" 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 ax^{2}+bx+c=0 to the quadratic formula takes 6 steps.
why she's getting praised for a method that's so difficultDifficult? It's by far the simplest and easiest to teach method for factoring ax^{2}+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 backwardsUm, 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
20:30A bit overloaded
A couple quick notes:
 I'm getting a little better at my board work, but I need to keep at it.
 I have one student who's one absence away from getting dropped and a second who's two absences away from getting dropped.
 I somehow misplaced half of my second hour cards for homework checkin. I had them at the beginning of class and by halfway through class, they were gone! I may have to reprint the cards tomorrow morning.
Wednesday, February 18, 2004
19:52Geometry  I like having staggered tests
19:48Advanced Algebra  finally teaching
I did make the fatal mistake of not rereviewing 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.
19:40The Lizzie method redux
19:20Job interview!
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
19:30Geometry
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.
14:16Algebra  The Lizzie Method
So here's the short version of what it's all about: A sixteenyear old girl found a "new" way of factoring quadratic equations in the form ax^{2}+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 ax^{2}+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 x^{2}+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:
 Try it on their challenging problem to see if it really works.
 Write down the steps so she can use it when she teaches the material.
Friday, February 13, 2004
19:42Planning next week
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.
19:17First Class
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.
16:48Homework policy
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 disciplinedependent. 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.
16:28Miscellaneous
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 twoday 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
20:09Geometry  working on getting better
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.
14:18Algebra  I've got to admit it's getting better
Wednesday, February 11, 2004
20:19Math/English or Math/Psychology
20:06Good Teachers
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.
19:35Good and bad
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.
19:18TeacherInsight^{TM}
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 teachingisagreatcareer 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.
19:12Seminar
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 nonthreatening 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.
19:00Algebra with Pizzazz
18:51Assembly
Tuesday, February 10, 2004
15:00Geometry
I've had some students retake 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.
14:11Algebra
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.
03:52My objective for today
Monday, February 09, 2004
17:30Dressing like a teacher  the big challenge of the kindoftall guy
I'll be wearing cuffs on my trousers.
17:28Geometry  hmm, that's interesting
17:23Algebra  mostly about absenteeism
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
12:07Job search tips
11:58Saturday teaching  signs of life
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
18:09Advanced Algebra
18:03Geometry  in the computer lab
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.
17:58Algebra  The rich get richer
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 ax^{2}+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.
16:15An interesting account of math ed reform
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
18:23Geometry
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.
17:00Advanced Algebra
14:25Algebra
Wednesday, February 04, 2004
21:08A bit of much needed levity before some downer posts
create your own visited states map or write about it on the open travel guide
19:31Geometry
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 reuse as class openers next week.
19:24Algebra
18:56I hope this is the bottom
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
20:41Advanced Algebra
20:26Geometry
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.
19:43Algebra
 I need a better transition to the lesson start.
 I have a tendency to ignore the right side of the room when I talk. The suggestion was to change the way that I stand at the board as I turn and talk.
 Write down the question
 Talk as I write.
Monday, February 02, 2004
18:49Georgia Board of Education shenanigans
15:33Geometry
15:12Algebra
We began with factoring monomials out of polynomials (e.g., 3x^{2}+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.