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

Saturday, January 31, 2004

Saturday teaching 

Curiously, while I had more time this week for teaching than last, I felt like I had less. We just barely touched on logarithims which was what I was building towards in this lesson. We'll do more next week.

Friday, January 30, 2004


We had the first test today. The earlier class got a little talk-y as the students who finished early had to wait out the class period. I ended up giving three detentions. I've only graded a few of the exams, but have at least two students who didn't make the 70% line that I'm demanding of everyone, and I'll have to do after- and before-school reteaching to bring them up to par (so yes, I did get approval for my no failures policy). The first assignment for those getting retaught will be to copy all the theorems from the chapter into their notebooks along with an illustration for each, and to find a problem from the chapter that uses that theorem along with its answer. I'm hoping that this exercise in itself will be a good learning experience for the students.

I had one student appear who has been absent from class for most of the last two weeks. Apparently he was suspended. I never saw the point of an out-of-school suspension when I was a student and as a teacher, I still find the practice pointless. The business of students is learning. Taking them out of the classroom doesn't help that at all, and as a behavioral remedy it seems counterproductive since the student will be behind academically and will have an even harder time in the classroom and will likely behave even worse.


So I officially start Algebra next week. My plan had been that I was going to, as an act of humility, follow the publisher's materials as closely as possible instead of reinventing the wheel as I am too often wont to do: I very frequently will needlessly create my own quizzes, tests, worksheets, etc.

So after school, my Algebra mentor came by to talk with me and her opinion was that the remainder of the chapter that I will be teaching is poorly organized and that I should do this material completely differently. So much for the week's worth of lessons I had planned based on the book. I do see her point, though, and the book that we're using, McDougal Littell Algebra is one that I've complained about before. I do, however like, the supplementary materials.

Half geek, half human 

Blame Citizen Scientist for this one:
You are 53% geek
You are a geek. Good for you! Considering the endless complexity of the universe, as well as whatever discipline you happen to be most interested in, you'll never be bored as long as you have a good book store, a net connection, and thousands of dollars worth of expensive equipment. Assuming you're a technical geek, you'll be able to afford it, too. If you're not a technical geek, you're geek enough to mate with a technical geek and thereby get the needed dough. Dating tip: Don't date a geek of the same persuasion as you. You'll constantly try to out-geek the other.

Take the Polygeek Quiz at Thudfactor.com

Math competition question 

There's a big math competition coming up next week and two of the Algebra II questions had my mentor teachers stumped. One was a problem that I've already seen: x+y=35, xy=7, what is 1/x+1/y? It's actually a kind of standard brain-teaser question (hint: you don't need to find the value of x or y. If you follow the link to the older diary entry, you'll find the answer.

The second is similar in spirit, but a bit harder. We're given two quadratic equations with integer coefficients: ax2+bx+c=0 has its largest root 2, and ax2+cx+b=0 has its largest root 3. The greatest common denominator of a, b and c is 1. What is b+c? I've not yet worked this one out. My instinct is that we would solve this as a linear diophantine equation, but that seems a bit much to expect of Algebra II students. More in the comments to spare those who want to try working it out on their own.

Thursday, January 29, 2004

It's girl scout cookie time 

It seems a bit early this year, but at least this time around it's not during Lent. I got my order in today and I'll apparently have my thin mints tomorrow. Mmmm, thin mints...


We did the second day of geometry today. The game show format seemed to go over pretty well, although it seemed that the first class got more out of it than the second. I wonder if not having the initial questions written on the board might have had something to do with the later class's ansiness during the review. The early class was a bit chaotic, but when the students talked, it was because they were talking about geometry.


I had better responsiveness from the students today when I taught the Algebra. I think part of it may have been from my pointing out at the beginning of class that I would be officially taking over on Monday and the prospect that I would become their teacher soon made it seem a bit like having a sub for them. We went over the second half of special products of polynomials and I used a grid method for multiplying polynomials to help them see how some of the rules work.

Here's a sample grid to show how it works for (x+3)2:

This was a nice segue from showing how to multiply using algebra tiles and has the advantage that it scales well to multiplying trinomials and longer polynomials.

I also think that for understanding why we lose the middle term in the product of a sum and a difference and for seeing why the middle term of a square is 2ab, this helps make the material clearer.

One last thing was that many of the students were still having difficulty with yesterday's material, so I may end up having to do some re-teaching next week as we get into factoring.

Wednesday, January 28, 2004

I am a limerick 

I'm the limerick, mired in muck.
I refuse to be bored or get stuck.
   I like to offend,
   But not, in the end,
As much as to thwart expectations.
What Poetry Form Are You?

Catholic Schools Week 

I'd been meaning to comment on this since Sunday when I got a church bulletin which announced that this was Catholic Schools Week. One of the activities is teacher swap day, when at lunch, the teachers at the parish's elementary school will draw names from a hat and change classrooms. I keep wondering how such a thing would work. I can see how it could be interesting for the students, but I would worry about the educational value of such a thing at the same time. How can the teachers teach anything meaningful in such a context?

Another bonus day of Algebra 

My Algebra mentor won't be in tomorrow, so she phoned me up with a set of last-minute lesson plans for tomorrow so that her classes will be covered. Her Algebra II class gets a real sub plan (such as it is), and the Algebra that I'll be teaching will have mostly review as we finish out special products for the quiz on Friday.

Review in Geometry 

The review for the test went surprisingly well. There are still some basics that some kids lack and not all students have all the formulas that they need down, so I'm modifying tomorrow's review slightly. Today I had them work on end-of-chapter review questions in groups and the plan for tomorrow was for randomly selected students to put the answers to these questions on the board. The class would end with "lightning round" questions. Short-answer questions such as what equiangular polygon has angle measure 108o? I've modified this to include a lightning round at the beginning of class where we will come up with answers to questions whose answers are essentially the theorems from this chapter. This way we can have some hope of getting this information into everybody's notebooks, at least.

Cliff's Test Prep ACT 

So I pop over to Border's to take a look at some ACT test prep books to pick up some ACT-style questions for Friday's test. Some of the books, like Kaplan's didn't have any appropriate questions, but the Cliff's did. And they were all much harder than my students are prepared for. Now I'm wondering whether the real ACT geometry questions are at this level, and if they are, whether we're short-changing the students in our teaching of them. I think that buying a copy of the Cliff's book might be well worthwhile to incorporate this sort of material into future lessons.

Tuesday, January 27, 2004

My no failures policy 

I'm thinking of announcing tomorrow (as we approach the first geometry exam), the following policy on failures:
I intend to assign no failing grades in this class. What this means is that if, after, any exam, you are failing in this class, you will be required to come in before or after school for additional review until you are able to take a test on this material and score a B or better.
My inspiration on this was a comment from the teacher institute a couple weeks ago where the consultant talked about schools where students who didn't fulfill the performance objectives for a section of the course were required to redo that material until they did. This is one of those things that seems like common sense upon hearing it, and yet is completely absent from most practice (although one of my fellow grad students said that she saw this at the charter school where she observed in the fall).

I was going to talk to my mentor teacher about this today, but she had a doctor's appointment (same sub as yesterday) so she wasn't present.

Teaching as Organizing 

I've been meaning to link to this Pedablogue post for a while and since it's shown up on a few other teacher blogs, it's about time to add my own comments to the discussion. In some ways the post title, "Teaching as Organizing" kind of says it all. In some cases, with good curricular materals, a lot of the organizing, at least at the global scale, is taken care of for us. To me, an ideal text book would be written so that we would be able to cover the entire text, spending one day on each section, for a whole school year. Whether I ever have such a textbook, remains to be seen.

But there's also the question of dealing with the organizing within the lesson. And this is where things become more art than science. As a teacher I need to be aware of what will help the students learn best, and will also let me remedy any deficiencies that the students may have, both in the learning that should have taken place in my class, and also in the classes leading up to my class.

Planning ahead 

I sat down this evening and I mapped out the whole semester of geometry (including the 4 weeks after I leave at the end of the university semester). I didn't finish Algebra because I spent some time talking with my mentor teacher and my first two chapters' material was, if anything, a bit too compressed(!). Planning the extra schedule actually helps because it gives me a global perspective on the semester. This will definitely be something that I carry with me to my full-time teaching assignment in the fall.

He doesn't explain very well 

I graded today's homework quiz and was surprised to see that Juan, the kid who always had his hand up yesterday and always had the answer scored a 0. On his quiz, he wrote, "I don't understand this, he doesn't explain very well." I did, however, feel pretty good about how I taught the rest of my class and it was worth noting that most of the class did pretty well on this short quiz with the median score at 75% compared to 50% on the previous homework quiz. Surprisingly, the problem which was biggest for the students was a simple distributive law problem along the lines of 3x(x2-3x+6) where too many students tried to split up the 3x like they would 3+x.

Teaching induction 

If I ever teach induction to high school students again, I think that I need to plan more than one class period for it. It's just a bit too esoteric for them otherwise.

Monday, January 26, 2004

A taste of what teaching full-time would be like... 

One of my mentor teachers was out today and I told her that I'd take care of her algebra classes for the day. She has one more than I'd been observing, so I took advantage of the fact that I don't have a 3rd hour class yet to use that as my prep period, such as it was. As an added bonus, because I forgot to give a handout to one of my geometry classes, I had that class doing tomorrow's lesson today (and they'll do today's lesson tomorrow). So I had five classes and three preps for the day. I hadn't realized how much I was using the fact that I was only teaching two hours a day before this.

It's quite different being at the front of the algebra class. I have one student, Juan, who's quite vocal. It takes some effort to keep him from answering all the questions that I asked of the class. We'll see tomorrow how well they did on the homework assignment, which was perhaps a little bit long.

I made a good use of Algebra tiles, I think, in introducing the concept of polynomial multiplication. I hope that pointing out the interesting correspondence between the algebraic notation on polynomial multiplication and the algebra tiles notation. Perhaps later this week I'll put up some pictures of how the algebra tile lesson worked.

I've also finished printing up the cards that I use for my homework check-in and attendence. Each card has the student's name and seat location printed on it, along with a grid that I can use to indicate when students are absent and when they brought in homework.

Homework check-in is a bit of a challenge still. I spend more time on it than I really want to. I think that tomorrow when I'm watching the Algebra class, I'll time how long my mentor spends looking at each student's work and what she does at each student's desk.

Sunday, January 25, 2004

Even the Republicans don't like No Child Left Behind 

In Virginia, the Republican-controlled House of Delegates recently voted to ask Congress to exempt Virginia from the NCLB regulations. Telling quote from the article: Republican House Caucus Chairman R. Steven Landes: "This could cost us more money than the money coming in from the federal government."

Also mentioned in the article was a study commissioned by Ohio Republicans which found that NCLB had been severely underfunded. So much for claims from Joanne Jacobs and her followers that the claims of added costs from NCLB beign prohibitive to local school districts is just liberal whining.

Here's a link with some suggestions on taking action about this issue

Saturday, January 24, 2004

First real teaching with Saturday program 

A bit less well-planned than I'd originally hoped. I started out by giving them a copy of the David Rhodes make money fast chain letter and had them read over it. "Does this really work?" some of them asked. "Well, we're going to do the math and find out," I replied. So we worked through a few scenarios, found that the claimed return on the letter was actually less than what would be expected given their claimed response rate (15 out of 200). Then we kept the math going to find out that it didn't take long before we ran out of US residents, and then people on earth. (I gave the students, as a homework assignment, the task of looking up the populations of our city, state, the US and the world... this in itself is an interesting assignment).

From there we were able to look at some basics of functions, exponential notation, and we finished by seeing that we could solve xn=c by taking c1/n. I had hoped to get to logarithims in this lesson, but there wasn't time so we'll do that next week (we'll vary the model we use to go to six degrees of separation).

Friday, January 23, 2004

Learning names 

One thing that we were required to do as part of our orientation exercise for student teaching was to get a large set of names, including the name of the principal's secretary, the janitor responsible for our room and a worker from the faculty cafe.

It's a great thing to do.

By introducing myself to these people and asking their names, they have all gotten a favorable first impression of me. And as anyone who's ever seen the movie Election knows, it's important to keep a positive relationship with your janitor.

I need to be better organized 

Organization has been causing some minor difficulties for me that are beginning to get worse. I forgot my ID on Wednesday. A minor inconvenience, but not bad. But today I forgot to bring in a pile of papers that I needed... then in class, I forgot one part of the lesson in each class. In one class, I neglected to go over the homework. In the other, I forgot to pass out a handout with their reading. None of this is good.

I also need to be careful about the level of my teaching. My mentor was telling me that I was occasionally going over the students' heads with my teaching.

Thursday, January 22, 2004

An interesting grading exercise 

The algebra class had a short "homework" quiz. Three questions from the book while homework was checked in. I offered to grade these so I'd have some exposure to their abilities (as well as having a chance to develop my knowledge of the students' names).

So I decided when grading the quizzes to go one beyond my usual question-by-question tally of points (which is useful in itself) and I kept a tally of why students lost points.

The tallies themselves weren't terribly interesting, but the experience was very helpful as it made me think a bit more about what was going wrong and what to do about it. What I found as significant problems:

Not always perfect 

Today's teaching was a bit rocky. In the first geometry class I forgot to go over the homework problems so we did just part of the homework before the class period was over. What's worse, when I did one of the problems at home on my own, I accidentally did the problem incorrectly, and noticing that while at the front of the class, I became uncharacteristically rattled and had a hard time working out the necessary steps for the proof. I managed to fix those problems in the second geometry class, but I wasn't able to finish all the new material before the period was over.

I did get tomorrow's quiz written, typed and copied. I had planned on giving the kids an excerpt from The Art of the Infinite on proof by induction, but reading over it last night, I realized that it didn't stand on its own very well, so I retyped it, adding some introductory material from earlier in the book and some marginal comments to help expand on some of the points covered.

Wednesday, January 21, 2004

Day 2, plus seminar 

Second day went well again. This time, there was the homework check-in. I'm not sure if the opening exercise that I selected was too hard for the kids or not. It helped to walk through it for them, though, and I think that it shed some additional light on the homework that was due. I had been worried that I wasn't going to have time for everything that I wanted to cover in class, but my fears turned out to be unfounded, in fact I finished a couple minutes early, so I gave them some time for in-class work, but that seemed to be greeted with indifference. I think the next time that this happens, I'll put a problem on the board and have them work at it individually at their desks.

Which reminds me that I've been doing a bit more direct instruction than I'd prefer with the class and really no guided practice.

I also need to be careful about being sure to give wait time when I ask a question. I waited what seemed an eternity (but was probably about 3 seconds) and was rewarded by one of the students volunteering the answer that I sought.

The student teaching seminar looks like it'll be much less demanding than it had seemed at first. The opening exercise really wasn't a harbinger of things to do, and there isn't any reading due until February, and that is relatively light. I can worry a bit less about all of that.

Tuesday, January 20, 2004

First day student teaching 

It started relatively light. My trig class is up in the air right now so I get an extra prep period mid-day for now, and in algebra I'm just observing, so all I have to do right now is plan and teach geometry. My mentor for the geometry class was very impressed with my teaching. Some of the things that she liked, like my walking over to the student who's asking a question are partly a self-defense measure. I have difficulty hearing speech freqencies a lot of the time, so I need to walk closer to the student to understand them. The modifying my teaching from one class to the next is kind of instinctual for me. I used to teach computer seminars and I'd learn from each class what was confusing for the last group and modify the instruction for the next one. Of course back then, I also controlled the curriculum and instructional materials so I could also edit the text and add new exercises to reinforce difficult material.

I'm not as far ahead in my planning as I'd like to be though. I call it the curse of the 3-day weekend. I figure that I've got lots of extra time to get stuff done so I put things off and end up not getting anything done in the end.

Interesting visitors... 

I noticed that I had visitors recently from the major metropolitan daily in the area where I'll be living next year as well as the department of education. If you're one of those people coming back again and reading this, feel free to drop me a line.

Saturday, January 17, 2004

I like seniors 

So I had my first "real" class with the seniors today, although it was mostly taken up with a pre-test. I gave them the sample test for the university's math placement exam so they can get a sense of what the test is like. It'll be interesting to look at the results and see how to plan the semester based on that.

I also get to do a vocabulary lesson with the kids. I'm given a short passage with a few words highlighted which are the words to be learned. I'm not too crazy about the tracking groups because I think that the students in this case would benefit from a more mixed ability group, especially with the smaller class size. I'm thinking that there's a different between tracking and placement that tends to get lost in the discussion about tracking.

Friday, January 16, 2004

Most inspirational "inspirational" cinematic teacher? 

IMDB's Daily Poll (so if you're going to vote, vote today), is a vote on your most inspirational cinematic teacher. Currently Robin Williams' character from Dead Poets Society has the lead, by a huge margin (over a thousand votes beyond his closest competition, Richard Dreyfuss in Mr Holland's Opus). My pic, Edward James Olmos in Stand and Deliver comes in third, but is only 19 votes out of second. So if you happen to catch this today, pop over to IMDB and help give the math teachers a boost in this poll.

Teacher Institute 

I went to my first teacher institute today and found it surprisingly interesting. Meetings in the "working world" were always deadly dull, but here, we had a daylong presentation from the High Schools that Work people which was rather interesting. Some of it was reinforcing ideas of my own: For example, I've long felt that a 2-year algebra 1 sequence was a bad idea. It appears that the HSTW people had research to back it up. Their suggestion to how to do this was partly also mine: Having students take a "double dose" of math, with one class being the regular Algebra 1 course, and the second being a supplementary course to build and reinforce basic math skills. Other options they mentioned included using a summer bridge program (which seems like it would be very helpful with borderline students).

During discussions about school reform, I found myself thinking about how the best way to make reforms survive changes in faculty and administration would be to build the provisions into the teachers' union contract. I wasn't the only person to have this thought, apparently, as it rapidly developed into a consensus in the room independently.

Another intriguing idea was to re-group students on a 9-week basis rather than each semester. In classes like math and foreign language, I can see this being especially important as a failure to keep up in the first quarter can lead to almost certain failure in the following quarter(s).

The other thing brought up which really struck me was the idea of having students re-do work that isn't up to the standard. It's one area where I imagine many teachers, myself included, forget that what we're about is making sure that students learn the objectives and let the grade suddenly become the objective in itself. This almost makes me rethink the whole idea of how to grade. I think that grades really should flow out of the course objectives and the students' demonstration of having achieved those objectives.

Thursday, January 15, 2004

Plan plan plan 

I met with my other cooperating teacher this morning to get an outline of what we'll be doing with the geometry students. We're starting with some polygon stuff that's actually kind of fun and interesting. One of my questions, which she didn't really have a good answer for was how much homework would be an appropriate amount. I need to have Tuesday's lesson plan finished for tomorrow morning.

Wednesday, January 14, 2004


I found another math song: I Have CPCTC. He doesn't say, but it seems like this should be song to the tune of "Fire and Rain" by James Taylor.

Books, ID and some minimal planning 

First stop this morning was to get my ID. The woman who handles IDs had left her office an hour earlier than the schedule claimed she would and seemed rather annoyed at having to go back. Apparently the hours for the ID office have changed, so it was actually nice of her to let me get my ID today rather than having to wait for tomorrow. I actually had a bit of a wait after that as it was the brief homeroom period of finals week and my mentor teacher with whom I was meeting had to be in the room with the kids.

After that, it was her prep period and she showed me the scantron readers and how they were being used although she did mess up so she didn't get the item analysis she wanted, then we ran about to arrange for keys and parking (both of which had to wait until noon).

I picked up my textbooks (I just got student copies, I actually kind of prefer to have the exact same book that the students do), and we spent some time going over how she does end-of-semester grading. GradeQuick actually looks like a very useful piece of software. I think that I may go ahead and spend the $60ish that it costs so I can have my own copy running on my Mac (the price--literally!--that I pay for swimming against the current).

Tuesday, January 13, 2004

Back at the high school 

Got back to the high school today and met briefly with the department chair and vice principal. Mostly I was sent on my way. I had to fill out a job application and get over to the district office to fill out paperwork. Tomorrow I'll go back, meet with one of my mentor teachers and get my ID.

Monday, January 12, 2004

Student teaching organizational meeting 

We spent three hours today for the student teaching organizational meeting. The only part that felt particularly worthwhile was the breakout session for the math people where we got some more particulars. This week will not be particularly interesting since it's finals week at the high school. I'm supposed to go in, but what, exactly, I will be doing, well, who knows? I guess the key agenda items will be getting my ID, parking permit and textbooks. I've decided to put off until tomorrow the trip to Office Despot to get the supplies that I'll need for getting organized (my plan is to use colored folders for each day of the week to have everything planned in advance, as well as expanding my index card system to use color-coding for each class.

One amusing moment was when one of my classmates asked about how much time he should spend planning for class. The prof responded, well, you should sleep 8 hours each night, and I'll be generous and give you 2 hours for eating, then subtract 5 times 50 minutes for your class, and you do the math.

I would think that he'd have some idea of the time involved from the fall Ed class. I typically have found that I need about 1-2 hours per class prep most of the time. I'm hoping that it will be lower by the time that I have to do the full 3 prep course load mid-semester.

Sunday, January 11, 2004

Saturday teaching 

I got a call Thursday while I was out of town visiting my fiancée letting me know that yesterday was not going to be a teaching day. Nice of them to give me advance notice. I would have liked to have spent another couple days with her.

I arrived back in town early Saturday morning and courtesy of a comedy of errors just made it to the Saturday session (they still asked me to show up and I wanted to get a parking pass for the spring anyway). I introduced myself to the students and was asked to explain the meaning of the work in a freshman calc class. I think I may have oversold the amount of work.

One student asked if we would do any discrete math. Oh joy! My favorite subject. I told her that this would be very possible. I've come up with an organization plan where I'll do one hour in-class lessons and I'll give them a make-sure-you-know-this sheet before each class to make sure that they're up to speed for the class. Next class I'll do a pre-test based on the university's math placement test and give them a roadmap of university math classes (this latter inspired by some of the questions I heard yesterday).

Monday, January 05, 2004

NCLB rant 

Just a quick link to a NCLB rant to welcome everyone back from Christmas break.

Thursday, January 01, 2004


But before I begin, dig this: I'm writing this using WiFi from a truck stop in Oklahoma. How cool is that?

So my resolutions for the year (or, I suppose, more accurately goals):

Looking at my list of goals for 2003 I went 1 for 6 (although I made partial progress on the other 5). I'm hoping to do better this year.

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