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.
Blogroll
This academic life
Academic CoachConfessions of a Community College Dean
Learning Curves
The Little Professor
My Hiding Place
New Kid on the Hallway
One Bright Star
Planned Obsolescence
Tall, Dark, and Mysterious
Math blogs
Ars MathematicaMathForge
MathPuzzle
Think Again
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Vito Prosciutto: Teaching community college math on the road to a PhD.
Friday, October 31, 2003
14:26McDougal Littell Algebra
On the other hand, they defer talking about percentages until they deal with ratios, direct variance and rational expressions, which has some benefits, I think.
Thursday, October 30, 2003
20:23Saturday teaching plan
I will have a quiz on the 15th: It will be a randomly selected subset of questions from the 8th so that the students will have some incentive to make sure that they understand the material on the test that they may have gotten wrong. I'll put up a copy of the test on the class website after it's been administered.
08:02Geometer's Sketchpad, some early notes
 Sketchpad wants to give lengths with units. I don't want lengths with units. I want to tell sketchpad, segment AB has length 1, and have all other lengths given in terms of that. As near as I can tell, this isn't possible.
 Some sketchpad objects don't seem to get written to the HTML/Java pages.
 It doesn't seem willing to give me angle measurements greater than 180 degrees.
 It doesn't have a graphic export. OK, I'll do a screen grab and save a bitmap, but it would be nice to have export as EPS or WMF or something.
Wednesday, October 29, 2003
13:57Teachingthe best route to learning
08:18So that's why the Cubs lost
The World Series is over but not the speculation about which jinxes prompted the dramatic collapses of the Red Sox and Cubs in postseason play. I'm surprised that no one has mentioned the dreaded O.C. Curse.It befell manager Dusty Baker, whose teams blew big leads in the World Series last year and the league playoffs this year.
Baker has had nothing but bad luck ever since he declared on the eve of the 2002 GiantsAngels World Series: "Our focus is 'Beat L.A.' " When it was pointed out that Anaheim isn't in L.A., Baker insisted, "It's Southern L.A." You insult Anaheim that way, you pay for it.
08:11A New Fanaticism, Pure Arrogance, or Sheer Naïveté?
07:17Tuesday night math ed class
Do you see the problem yet?
My group's turn.
What a completely unrealistic experience. What are the odds of group teaching a lesson in my career? Close to zero. And if that group is all math teachers? I'd have to say even closer to zero. I'd say zero without qualification, but I suppose there is some tiny chance that it could happen. In bizarro world.
OK, sure we have 30 students in the class so each person can't have a whole class period, but the way I figure it, if we have each student teach a 40 minute lesson, we can in 10 weeks have each person teach. My organization plan for the class would be to have each person teach for 40 minutes, then we'd take fifteen minutes to discuss and critique that student's lesson plan. Now that would be a valuable learning experience. And it's not like this idea comes out of nowhere: There's a program called Lesson Study that iirc originated in Japan, and provides a means for teachers to engage in a continuous professional development and develop their lesson planning and implementation techniques.
So here's an interesting idea: Teachers trained with this sort of lesson study, and given an opportunity to engage in it as part of their training, might well evangelize for it when they're actually out training. So we'd not only be training teachers, but we'd be producing teachers who would have a goal of improving the overall quality of teaching in their schools and tools that they could use to implement this.
Tuesday, October 28, 2003
20:33Another teacher deemed unqualified by NCLB
09:14Test review strategy tried again
Monday, October 27, 2003
20:47There's a growing community here
I'd still keep a journal of my teaching, even without the internet, but the way that I can let people read my journal, without risking too much of myself, and get their feedback makes this an especially great way to reflect on the process of teaching.
20:44Geometer's Sketchpad
Sunday, October 26, 2003
04:23Yesterday's teaching
Next week is a shortened day which I hadn't been really given sufficient advance warning of. Now I have to decide how much of the class we'll be able to do. The geometry kids I had told that my plan was to not lecture on the material at all, but rather to give them a reading assignment and homework based on that. I also have parent conferences next week so I'll want to get grade reports for all students assembled so that they can see how their students are doing and in what areas they're falling behind.
Friday, October 24, 2003
17:37Literacy in math class
The teacher in question talked about how reading science texts is an alien experience for most students (the same thing applies to math), and so she has her students read through passages in the textbook together and she teaches them how to read these dense texts and how to pick out the important information.
Talking about this with classmates today and on Wednesday, the consensus seemed to be that this was a really good idea. In many math classes that we've seen (and experienced) the textbook is little more than a repository for homework problems.
I suspect that the ability to read a math textbook can make the difference between a student being a student who "gets" math and a student who does not.
So if you're that original blogger and you see this, please leave me some comments. I'd love to discuss this some more.
Update: I heard back from Ms Frizzle who was the teacher to whom I was referring.
10:32Second exam
Thursday, October 23, 2003
11:14Oops
State law mandates that beginning teachers get special training and mentoring programs to obtain a standard teaching certificate required after four years on the job. But those programs don't exist.And it's not just that some school districts lack the program. Or that many school programs lack the programs. There are no programs at all.
There's also the question of, what sort of mentoring program makes sense for a teacher who has been teaching for four years. Implementing a onesizefitsall program is a recipe for disaster, as those teachers who have more experience will be doubtless annoyed if they have to go over the same "here's how to write a lesson plan" material that beginning teachers implement.
Once again, one of those situations where a wellmeaning regulation at the state level causes havoc because it's not thought through.
08:57Standards
I've got two minds on standards. On the one hand, I think that it's a very good idea, to come up with a set of topics that should be addressed in a standard high school course (there are too many classes in math, at least, in urban areas which go by highlevel names but offer lowlevel content). But on the other hand, the standards have to be properly written and designed. Illinois' standards have whole sections which don't correspond to the high school curriculum at all, while other portions of the curriculum are underrepresented (Trigonometry) or omitted entirely (Calculus/Analytic Geometry). Even those areas "addressed" are inadequately addressed.
Then there's the question of inadequately addressing the whole matter of how standards should be used. I think a big part of this comes down to the faculty preparing teachers (and a lot of teachers themselves) haven't had to deal with standards, so they tend to viewed as "look through the list to find something that kinda sorta matches what I'm teaching today and list that on my lesson plan" kind of thing. Ideally, the standards, lesson plans and curricular materials should all automatically flow out of each other. I've not looked too closely, but it looks like the California standards do a better job of this (at least in terms of having the standards more closely align with the standard course offerings).
08:51What makes a teacher highly qualified?
I'll go a step farther and say that math teachers need to know not only the subject matter that they teach but at least two years of progress in the subject area beyond what they teach. It's not enough to know what's in the book, you need to know what the book is preparing students to do in their next class.
And this applies to the people writing the books too. I've ranted before (and I'll rant again) about "geometry" problems like:
Angles 1 and 2 are supplementary. If angle 1 has measure 2x+1 and angle 2 has measure x2, what is the measure of angle 1 in degrees.That's not a geometry problem and as far as I know it doesn't correspond to any actual use of geometry. It's an algebra review pretending to be a geometry problem. Maybe if we dumped problems like this we wouldn't have to offer geometrywithoutproofs classes.
So I would argue that we need to have educated people writing the standards and we need to have teachers who know the material inside and out. Frankly, I think that the tests that I've seen are in fact inadequate. The test that I took for certification only verified that I can do high school mathematics. It didn't test any sort of understanding or ability to connect knowledge within different subtopics in the discipline or across disciplines. There's no point, for example, asking Calculus questions unless you also address how calculus and physics are related.
But there is the very real issue of ability to teach, and this is an ability that is gained only in one way: By actually being in front of a classroom and teaching. And I have yet to see any multiplechoice test that can measure that. Apparently, at one point in California, there was an actual simulated classroom test for credentialing, with college students pretending to be the (unruly) high school students a teacher might face. Now there's an idea that's worth resurrecting.
So bottom line, I agree with Assorted Stuff that the standards for "highly qualified" are insufficient, but I disagree in that I think that demonstration of subject area competence is necessary.
08:21The cards on Thursday...
There allegedly is a better correspondence between the sample test and the midterm tomorrow so I'm cautiously optimistic that this will see higher exam scores on the test this week.
I did have the mystery student who showed up for the test but has missed every quiz this semester appear in class today, so I can't just delete his row in Excel. He is in fact real.
Wednesday, October 22, 2003
14:09How does this relate to my life redux
 ... the question will not be “how does this relate to my life?” but “how do I make my life relate to this?”
14:04Improvement is a twoedged sword
The suggestion that city schools are on the upswing put Chancellor Joel I. Klein, who is overhauling them, in a tricky position. While the chancellor's critics pounced upon the higher scores as evidence that the school system did not need such an overhaul, some of his allies acknowledged that he would now be under even more pressure to show gains next spring.So now Klein is forced to argue that the test scores are not necessarily reliable, which raises the question of whether the whole concept of using test scores to evaluate schools is a good idea to begin with.
Tuesday, October 21, 2003
09:36One strike over, but another looms
Meanwhile, in Chicago, the teacher's union has voted to reject the current contract offer and has entered mediation. A strike may result, but the hope is that the district and union can come to an agreement.
09:33Tuesday teaching thoughts
Monday, October 20, 2003
20:16My plan for tomorrow
13:27Grading despondency
Saturday, October 18, 2003
18:49Third period is a trial and tribulation
18:49When are we going to use this in everyday life?
Perhaps never. At least not with the everyday life that you lead now. But what you should aspire to, is to lead a life that calls on you to use your mind in new ways. To learn not only what we're doing today, but to want to explore beyond what you know now, perhaps because you use it, but perhaps because you enjoy learning and expaning your mind.Or maybe I'm just a hopeless dreamer.
Friday, October 17, 2003
08:39The Mathematical Approach to Life
On a related front, something that I've seen in geometry textbooks which leaves me perplexed are questions along the lines of:
Angles 1 and 2 are supplementary. If angle 1 has measure x and angle 2 has measure 2x + 3, what is the measure of angle 2?Is there any case outside of a contrived problem like this where this will come up? I have a vague notion that I saw questions like this in one of the ACT prep books that I looked at, but this has no relation to how someone actually works with supplementary angles. It's not a geometry problem, it's an algebra problem, and while students should be able to solve this, the contrived nature of the problem is such that its ex nihilo nature outweighs the benefit of the algebra review, I think.
08:25No School Left Unfailing Part III: Your Talking Points
Thursday, October 16, 2003
12:16Homework Solver
Visiting the site, I found:
We know that doing homework isn't a lot of fun, so that's why we'll do it for you!What a horrible idea.Mark T~ "This service is great. I had 10 problems in math and they solved all of them in a few hours. Now I have a shot at an A."
Howard S~ "Tutors are great when I need someone to teach me things about the subject. But when I just want the answers, Homework Solver gives me them fast! PayPal makes it soooo easy!"
Or not.
Personally, I think that it's a good idea to assign homework problems for which the answers are available by some means. Homework should not be an end in itself, but rather a route to learning. If a student does 10 problems incorrectly, they won't learn. If they do the problems and get the answers so they can check whether they have the answers correct, that's a bit better.
But of course, there's the issue of grades and measuring whether students have actually learned. On that front, I'm not entirely convinced that grading homework is a good or useful thing, and services like this Homework Solver group actually will ultimately force teachers to be a bit more thoughtful in how learning through homework is evaluated. My approach is to grade homework on a "was it done?" basis, but then have quizzes that pull from the homework to verify that students managed to learn something from the homework. Ideally, the quizzes would call for students to synthesize ideas from the homework, but that might be asking a bit much at the secondary level. Or perhaps I could ease them into it after a few weeks...
08:24First five minutes feedback
08:12Math teaching methods annoyance
The prof vetos this idea. Suddenly we're teaching a single lesson to a 10th grade class. Everyone else's material can be easily adapted to this change, but mine not so much. I've got five minutes to come up with an alternative.
Which I do.
Instead of that proof, I decide that we can look at countability of infinite sets. The Math Circle in Boston does this with 6th graders so it's certainly within the grasp of 10th graders (although I intentionally move the proof that the cardinality of the set of reals is not equal to the cardinality of rationals into the "if time" section of the lessonI'm not at the level of overlearning with this concept to be as comfortable with it as I'd like).
So I'm pretty happy with how I managed to dodge the bullet, but generally annoyed with how the class as a whole is being run. I'll be so happy to be done with all this education stuff and finally start teaching.
08:12Why there are so few teacher blogs
Tuesday, October 14, 2003
11:50Oh yeah, I love this guy
I agree that the idea behind education should be to challenge the students. It's a matter of really pushing the envelope, making them do things that they think are beyond them. When I told the 10th graders on Saturday that we'd be doing trig, there were (predictable) protests, but I hope that as they work through their assignments, they'll see that they can do it. Frankly, I think that of all the secondary math curriculum, trig is the easiest stuff. All you need to know is the Pythagorean Theorem, some stuff about similar triangles and one simple diagram (which I can't show you because I don't particularly want to pay for hosting), and you're good to go.
11:11Today's No Child Left Behind nightmare
11:08Another reason to remain anonymous...
10:38Tuesday teaching report
During my tutoring hour, I had a student come by with a questions that I could not answer (nor could I see from the chapter how it would be solved): The problem was to find the remainder when x^{10}+x^{8} is divided by x1, without using synthetic or long division. From the chapter, it would seem that it is somehow related to the fact that the polynomial has zeroes of 0, i and i, but I was baffled at how to solve it. I sent her off to find a precalc TA. I think that I might stop by the bookstore and spend $50 on my own copy of the book. The way that precalc is taught is so different now, it would behoove me to relearn it myself.
10:28Yeah, I'm bucking for hits
Monday, October 13, 2003
09:09Grading Behavior
 Was the student on time for class?
 Did the student have all required materials for class?
 Did the student ask a question, answer a question, or otherwise contribute to the class discussion?
 Did the student behave appropriately in class?
08:40Have you voiced your opposition to No Child Left Behind yet?
Sunday, October 12, 2003
12:59First day of Saturday teaching
So after all the lastminute schedule changes and problems (the classroom that I should have had at the university was locked, so I ended up in the room next door), I managed to get things moving. The first class was trig with the 10th graders. I was unable to do demonstrations of how to do the constructions of the diagram on the overhead since none of my markers worked in that context (I really need to get one of those blackboardstyle compasses), and we ended up spending more time constructing the diagram of the six trig functions than I really wanted to. Next time I teach this lesson, I'll just let them draw the lines freehand. I hope I managed to cover everything adequately for them to understand, but I'll need to get the online notes up soon.
Then it was advanced algebra/geometry for two classes of 9th graders. The first class was good, and there were some who actually knew their way around the Boolean algebra that we did already (one asked about the twoway implication, which we'll do more with next week). The second class seemed a bit of a nightmare. They were harder to keep quiet, and harder to keep interested.
I've not had a chance to review the videotape of the lessons. I'm guessing that I'll do that tomorrow afternoon or evening. My general sense, though, is that I lectured far too much and didn't have enough inclass work on the material. I fear that our curriculum is too ambitious for the time that we have.
Friday, October 10, 2003
09:18It's always the math teacher
08:30Schedule change for Saturday
08:23Assigned Seat
The newsbased postings here, by the way, will doubtless subside as my classroom time increases.
08:16Antiunion biases all around
But the NPR story said that garbagemen make $1221/hour. Well, that makes a lot more sense all of a sudden. At the top of your career as a garbageman you might make more than a beginning teacher, but the teacher who's been working as long as you have will doubtless still be making more.
The other disturbing part of the story was the mention that the mayor of Chicago was considering sueing the union for the costs that were incurred because of the strike. But shouldn't the private garbage collection firms also share part of the blame for this? This really bugs me because it's happening in other spheres as well. Eric Gjovaag reports in his blog about a plan by parents in his district to sue the striking teachers, ignoring the culpability of the district in that strike.
Thursday, October 09, 2003
09:27I've moved comments to Haloscan
09:02The second part of Assorted Stuff's commentary on math curricula
I would also (as I noted below), like to see more statistics in the high school curriculum. I think that it's not really necessary for most students to be able to manually calculate the slope and intercept of a regression line, but they really should be able to understand what it means and do it in Excel. Actually, a good course in math for spreadsheets would be an excellent addition to almost any school curriculum K12 and undergrad.
08:20Saturday Schedule
08:17Another day of teaching, another quiz
Wednesday, October 08, 2003
21:08The First Five Minutes
 Respect
 Responsibility
But I was on tonight. It was like I was channeling Edward James Olmos or something. I had great classroom presence. I hope I can do it again on Saturday morning when the room will be filled with high school students.
There were some good uses of powerpoint (for the introduction of a foreign language class), and some ultimately empty (for a geometry class). My favorite intro had the (freshman English) teacher confessing to a reading addiction and playing the Moxy Fruvous song, "My Baby Loves a Bunch of Authors."
21:08One of these things is not like the others
20:17The problem with testing
The Times article is a bit sparse on the details, but it seems to me that the problem here is similar to what I'm seeing with statistics here: The curriculum and the standards are still not adequately aligned. I fear that what might be happening in New York is that they've decided to adjust the standards to match the curriculum rather than looking at both and adjusting the curriculum if necessary.
20:04Attrition
Tuesday, October 07, 2003
21:02A case of misusing calculators in the classroom
And to which, I say, wrong. This isn't a good use of calculators. Instead, we should use substitution to get from phi=1+1/phi to phi=1+1/(1+1/phi) (and of course extending into infinity).
Especially, since we then went into the series of continued fractions:
1+1/(1+1/1)=3/2
1+(1+1/(1+1/1))=5/3
1+(1+(1+1/(1+1/1)))=8/5
etc.
Anyway, this sequence will eventually converge on phi, and the limit proof is easier to get to if you use substitution (as is the proof that each successive continued fraction simplifies to a ratio of adjacent Fibonacci numbers).
10:03Union organizing
And to forestall any antiunion folks who will doubtless comment (assuming I get the critical mass of readers to make that happen), why am I prounion? Because I believe that unions have played a critical role in allowing working people to live in dignity. It's worth noting that the decline of union membership since the 70s directly parallels the decline in real wages and employerprovided benefits as well as the increase in the length of the work week.
Like not working 80 hours a week? Thank unions for that. Like having insurance? Unions. Safe working conditions? Unions.
Working America, by the way, is a worthwhile organization to join for those of you who are ineligible to join unions but care about these sorts of issues. Current lobbying efforts include preserving overtime pay and preventing the gutting of medicare.
Monday, October 06, 2003
21:31The Excellent Teacher's Handbook
The choices given were:
 to make a living
 to retire with a good pension
 to touch the lives of many children
 to feel good about the work being done
Of course, in a job interview situation, it would be wise to phrase this more diplomatically.
13:29Out of curiosity
For that matter, how do the NCLB supporters rationalize the widespread opposition to NCLB by those in education? Do you simply assume that all educators are more concerned with protecting the status quo than improving education? That those on the front lines have less understanding of the issues facing schools than do politicians in Washington?
There are schools desparately in need of reform. Only a fool would argue otherwise. The question really is how best to accomplish this reform, and I've not seen any indication that NCLB is anything close to the way to do it.
13:25Teaching Math: No Simple Formula
Sunday, October 05, 2003
21:24Getting middle of the pack students to go to college
This is exactly the sort of thing that I have as a goal as a teacher: I want to move kids who don't realize that college is an option into the college track. My big concern on this front is that the hyperinflation of college tuition combined with poor state support for public higher education will make college an impossible dream for these students regardless of what they can do. Students who can make it into toptier schools will be able to access generous financial aid (that was my secret to success for my undergrad), but for those who can't get into Harvard, University of Chicago or the Claremont Colleges, what are their options?
15:43Prepping for Saturday teaching
But at this point, I'm thinking that algebra/geometry will be a lot of fun. I've made a conscious decision that the students will do proofs, even though this can't be justified within the ACTcentric framework of the program. I just think that the ability to do proofs is far too important to neglect. In fact, in general, I think that proofwriting is an essential aspect of geometry and schools which teach a proofless geometry are clearly shortchanging their students. It would be far better to spend two years on the material (or better yet two periods over one year), than to leave out the proofs.
The other thing that I've done to revise the class from the original outline is to move much of the algebra out of the lecture and into the homework. Part of each homework assignment will be a daily assignment in which the students will do an ACTstyle word problem which employs their abilities to do algebra. I'll make these a big part of the inclass quizzes and exams to make sure that they don't just skip those problems.
The trig class will still be fun. The homework assignments will be big on discovery and will have them learn some important formulas and rules by working out in a scaffolded matter the bases behind those formulas and rules. For example, finding the formula sin a+b= sin a cos b+cos a sin b can be done using some basic rules of right triangle trig that the students will have worked with in the first week and some fairly simple geometry.
07:20Not actually about teaching ...
Instead, I noticed that there's a requirement for "winning" a new blog showcase that I've entered that I link to three other entries. Fair enough. I do, after all already have some links of my own.
So who to link to? Here goes (in no particular order):
 Quigley's Online Dating Blog To me, the most interesting blogs are those that recount personal experiences and it doesn't get more personal than this. Way back in the days before blogs when people would update the pages by hand, I remember reading a college student's diary of his account trying to find a girlfriend and thought that it was especially interesting. The entries I've read here also seemed interesting.
 Owensoft Another personal experience blog, the entry here is about watching the closing credits of movies, something I generally make a point of doing, being a bigtime movie freak (although grad school looks like it has me trimmed back to only about 30 movies a year).
 Djangowire And just because the topranked blog at the moment has as its tagline, "a nice place to dream about no more liberals", and the post referred to (scroll down to September 28th, his permalinks seem broken) is a nice antidote to that attitude.
Thursday, October 02, 2003
14:22The review technique on a second try
Wednesday, October 01, 2003
19:34No School Left Unfailing Part II: Know Your NCLB
The big problem I see is that taking money away from a failing school can't possibly improve it. There's no mechanism given to improve failing schools, just threats of punishment. Giving more money to a school won't necessarily make it better, but taking money away from a school will almost certainly make it worse.
And one more thing: "to sanction" means to give approval to. "a sanction" is a punishment. The NCLB documents from bush get it wrong, and they speak about failing schools being sanctioned.
19:28Some reflections on discipline
I have, at this point in my high school observations, had a chance to see nine teachers in action. It's interesting to note that teachers tend to attribute student's behavior in the classrooms primarily to the students, but what I've found watching the teachers is that student behavior levels are pretty consistent across classes for a given teacher, but do vary for different teachers. I haven't seen enough to know why, for example, teacher A has consistent talking in class while teacher B does not. I imagine a big part of it comes from the tone set at the beginning of the year by the teacher. My own experience has been that when I had classes start with a relatively social activity (like a nonacademic ice breaker), it resulted in excessive social talking for the whole class. I wonder if that had something to do with how things went?
Any teachers out there reading this, I'd love to have your comments on this.