invasion of the required mcblogs: #'s 2 (late), 3 (late), and 4 (early?)

#2: inductive vs. deductive

in a more patient world, i would be able to:

(a) develop an equal parts competent/mocking/insightful dialogue between the Platonic (in a very cheap way) characters of Inductive and Deductive
(b) infuse thier voices with a glaring and pastiche cold war subtext (does not democracy deduce? does not a single, unfallible cry boil in the hearts of every worker? )
(c) draft a faux screenplay in which the voices are played by out-of-context superheroes, and in which their megaphone/thesaurus battle is passed off as a 2nd tier batman vs. superman crossover ("once again... a greater evil... universes collide... a difficult partnership... the medicine or the disease... will america never learn?").
(d) produce, direct, and star in the film - as both characters.
(e) write the trade paperback adaptation of the film - complete with a median insert of movie stills.
(f) turn in (e) as my blog entry.

instead:

i'll talk about how inductive teaching methods have always made more sense to me as meaningful forums for learning. in fact, the inductive moment is exactly the moment of meaning itself - when a student, as a learner-creator, fixes the indellible value of progeny upon an item of knowledge. it is their moment, and something derived of their language - whatever that is. on the other hand, deduction seems - at it's hastily reflected-upon core - to be a look into the consequences of a set of "meanings," and in this respect a sure enough avenues for second-tier meanings: curious stitches that in turn depend on the certainty of a loop. ask cantor, or godel, or anyone else i'm fumbling to reference. uh... it's like communism and capitalism... and how neither can exist in isolation... yet neither in harmony... this is nothing like cantor... but both make excellent halloween costumes...

of course, teaching inductively - which consists of priming an environment for individual response - takes more time. and there's the whole leading a horse to water stuff (because maybe this a horse that doesn't drink water - it depends on a substance necessary for its methane-based chemical structure [which is a concievable alternative to our carbon-based whatever], which may act as a poison for us. or a nonsequitor. like a melody. sing to the methane horse. sing!) and the whole gathering each of this somewhat personal discoveries into a communicable whole.

but, there are many more "a-ha's!" which is nice. so i try and have a small inductive exercise to each new lesson - sometimes it turns into its own lesson (time), sometimes it flops (methane horse/language), sometimes it does OK ("a-ha!"). like for solving linear systems by graphing:

in the event that students can graph lines (sometimes they can't, even if they're in algebra ii, and even if they're 12th graders), you can say: "here are two lines. graph both of them on the same coordinate plane. what do you notice? what else could have happened? what information can you tell me about what happened? why don't you have your binder out? why are you touching him? who are you?" and so forth.


#3: success story

i have two that i want to talk about

(3.1) hand turkeys, et al.

i am very generous with extra-credit, especially when it's couched in absurdity or creativity. a constant venue: a bonus section at the end of my tests, which essentially allows a student to make up for a missed problem as long he or she is willing to laugh at himself/herself/me. so far i have assigned the following (which i am more than willing to accept from any of you - for which you will recieve 5 pts):

1. Our class mascot – the large yellow spider named Hennessey – seems to have passed on to better windows and bigger dreams. Please write a short poem in his honor. Use at least one mathematical word or phrase.

2. Draw a flattering picture of Mr. Molina.

3. Write a poetic/freestyle/whatever-you-call-it tribute to the “teepee” method of adding fractions.

4. Draw a humorous comic strip about your adventures in Mr. Molina’s math class. Possible characters: you, your classmates, your cellphone, your homework, Mr. Molina, Hennessey the Spider, the Teepee Method, Alice, Reebok Classic sneakers, the Not Math Box, a peanut-butter and jelly sandwich, etc.

5. Last night, Mr. Molina fell asleep reading the Algebra II text book. What did he dream about? You may draw a picture, make a comic strip, or write a paragraph.

needless to say, (1) i'm an unrepentant egomanaic who masqeurades as a cultural theory enthusiast, (2) i've gotten some amazing bonus responses.

however, my most "successful" of these silly things were my hand turkeys (you all know what a hand turkey is...), which i assigned the thursday and friday before thanksgiving break as a spur of the moment 5pt extra credit opportunity. i had originally intended this to be something completed during break (with construction paper, glitter, and dry macaroni), but at some point a student offered to put a hand turkey on my front board as a submission, which i allowed - thereupon beginning an avalanche of brilliance upon my walls. this happened on the friday before break, and - as fridays are my test days - students would go up to the board (without directions to do so, mind you) and add his or her hand to the mix - with different colors sometimes; and scenery; and commentary (endless "eat me!"s and "don't eat me's!" and the well-crafted "run and run as fast as you can/you can't catch me, i'm the turkey hand!"); and/or intentional sloppiness (one awkward turkey amazingly labeled as "my little pony").

pure bliss. creative. absurd. 5 pts.

(3.2) haywood

jeremy haywood's test grades look like this: 50, 29, 44, 109.

after receiving his last test grade, jeremy went to the front of the class and thanked them - tearfully clutching the rolled up 109 with oscar speech overstatement - for being quiet sometimes and letting him learn. of course - they booed him back to his seat.

i had a soft spot for jeremy from the first week of school - caught by his flair for the well-judged goof-off moment, and, well, the fact that he's generally adorable. however, it became clear early on that - charm aside - haywood wasn't performing well in the class. conversations with him revealed a general lack of confidence in math (comments a la "i do well in my other classes... i just get into math class and my brain stops working" and "i think i understand it when i'm in your class, but then i get to the test and... nothing"), and a love for the game of baseball - which jeremy was afraid he would not be able to play this year if his grades in my class did not approve. conversations with his mother were of the same effect. i encouraged jeremy to come to my tutoring sessions (at the time, every wednesday after school), and he - like many others - promised to show up but never did.

eventually, however, he wandered in on a wednesday and we had some time to focus on the objectives in class that never seemed to stick. somewhere in this mix, something began to click in jeremy's head - and solutions seemed to come for the first time, and then continued, seeming easier and easier. from a testing perspective, it seemed that all he needed was the initial spark of confidence; haywood came into the next test confident and energetic, and gave the aforementioned oscar-winning performance.

now it's a matter of keeping haywood's confidence up, and getting him to do all of his homework. there's also a strangely tragic subtext that always seems to be pulling at him (nothing new for adolesence, i imagine) - comments about wanting to just leave mississippi and go to a place where he doesn't know anyone and can start everything over, voiced awkwardness about thanksgiving vacation spent in alabama with the family of his mother's boyfriend, and pastoral fantasies about having nothing to do but play baseball all day. again - nothing new.

#4: reflections on summer blogs

a list of things that have stayed the same (when so much else has changed):

1. my voice is still (and will always be) nasal
2. i should write more haikus
3. i'm still (and will mostly likely always be) a rambly mess, still stuck in meta-bullshit and standup theory
4. i always have a strange dialogue going on with myself
5. the line "where can i find this chief trees" is still endlessly funny
6. i still shake my fist at the sky
7. the sense of being "modeled a situation of little/no accountability, and ... [developing] a teaching routine in a sink-or-swim environment of little beyond peer support" was indeed an early taste of my teacher reality, as is the awkward stampede of high-pressure assessment that just sort of waltzes in from time to time (the most recent being the IB programme's audit of jim hill occurring on friday)
8. i've never really learned how to write on the board and monitor the class at the same time
9. i still think that my summer training could have been vastly more helpful/relevant

voicing concern ii

I. scenario:

sat, oct 29, 2005. class at ole miss. the day's topic is assesment - considering its traditional and non-traditional faces, respective pros and cons, etc. the beginning is spent being lectured to (though i don't remember if the lecture was actually about assessment, i think it was another tough love life-coaching session by our own dr. germaine), complete with "checking for understanding" traps: a veiled rhetorical question is presented to a group of people (e.g. [approximations] "about this time of the year, first year teachers generally start to gain control of the classroom. how many of you feel like things are under control?"; "most people use at least some non-traditional assessment. how many of you use non-traditional assessment in your classrooms?") , for which some of us mechanically raise a hand in the affirmative (others shrug), thereafter understanding being checked for.

after this mess, a longish activity involving group discussions about various assessment methods (traditional, peer assessment, self assessment, rubric, etc.). teacher corps members were placed in groups, and posters describing each method were rotated around to each group. upon arrival of a poster, we were instructed to - i think - discuss the worth of the assessment strategy, and its use in our class rooms.

[key school-of-ed words in the above paragraph: "groups,"and "worth." the former satisfies the educational fixation on "cooperative learning," the latter on the high-end of ye ole Bloom scale: evaluation.]

II. and then:

i spent the majority of the activity time thinking about how i probably feel disengaged with these classes in the same ways that my students feel disengaged from mine. i drifted into conversations with colleagues about the irony, occassionally reprimanded by an overseer for not re-learning or re-hashing what a rubric is. of course, one substantive difference between our disengagment and that of our students is that it seems like my colleagues and i choose to re-engage in the topic at a level that we value, in this case by reflecting on the implications of our own inadequacies given our very response to a pedagogical front that seems equally inadequate (of course, we could just need a little institutional discipline - spare the rod, spoil the grad student. go rebels.). on the other hand of the meta-irony, our students - upon disengagement - just seem to start talking about humping each other, which is of course a level that they value - though it's not true that i don't; i spend plenty of time thinking about humping, even humping some of the people in my program. the point is, our students don't respond to a weak lesson on linear systems by meditating on the indeterminacy of the fifth postulate, which is tragic (both the indeterminacy and the not thinking about not-humping). furthermore, the sorts of conversations we were developing in our groups were exactly at the level of evaluatory analysis ostensibly promoted by the activity's structure, though undervalued as such in deference to the need to move on to the next aribitrary conversation piece (re: minor controversies at jake's table).

III. possible reasons why i didn't engage in the lesson (with the corollary reflection about why my students may not engage in my lesson, provided that the structural analogy is solvent - and i think it is)

(III.a) preface: i've been spewing forth the buzz-work "value systems" since i've gotten into this mess. it seems quite apparant that if a person does not attribute value to a system or object, he or she will not choose to engage in that system or object - at least not in any way that would expend effort for which the foreseeable return is valueless, and at least not in the same way that someone who does attribute value would engage. this seems to - in a reductive way, sure - allow some illustration for the fact that students who - from an education-institutional sense - drastically lack proficienty, and show few signs of interest in the classroom are nevertheless more than willing to be trained to perform a systems of tasks (of compareable difficulty to most traditional academic objectives) for - lets' say - minumum wage. clearly, something about this performance discrepancy may be the fact that they've chosen to value the immediacy of money, and the culture that preceeds it. and this is of course an understandable choice.

back to (III) possible reasons why i didn't engage in the lesson...

1. lack of fluency

the whole conversation about assessment was rather contingent on my assumed adequacy/comfortability with transmitting content to be asssessed. at the comparative level, this prompt for disengagment is somewhat related to the dilemma facing a student who knows what a linear system is, but can't graph lines in order to show this knowledge. so - in the same sense that the student starts to disengage from the objective by realizing that he or she lacks the basic skills that are prerequisites for performing the objective once learned - i'm reluctant to be concerned at all about being good (or at least being better) at assessing things in the event that i'm not confident that i'm teaching well in the first place. and - sure - part of teaching well is assessing well, and - sure - i'm supposed to believe that good teaching comes with experience, so i should just keep stuffing my toolbox with fancy things i'm afraid to use, and - sure- proficiency will grow on all fronts as long as i stick to it. but, the fact remains that i have no idea what it means to be a math teacher, that i'm struggling to pull things together and make things up as i go along, and that there's an ever-hovering "that's just how it is" myth coming from the gods above, along with the occasional rain of flying cars, cold fusion, and peer assessment- when all i want is a rigorous perspective on how to actually prepare myself to teach algebra ii to my students - not just a spin-cycle of talking about teaching while divorced from its practice, and practicing teaching without having really thought about it, even though i'm in a perfect position to synthesize my own practice of teaching with my own thoughts about it. (response: "the first year of teaching... trial by fire... experience... rewarding... here's a candy bar.") nevertheless, linear systems remain at the theoretical level, as does diverse assessement. of course i know what assessment is, and can rattle off on its flavors, but if i'm still struggling to instruct on a daily basis, and i'm struggling to find time to focus on refining my instruction, discussions about possible assessment strategies are going to be drastically less useful than time to actually reflect upon and develop my instruction, which could easily (gasp) be scoped within the framework of developming my assessment arsenal.

2. "low-level" objective (the Bloom trap)

i mentioned above the veil of "evaluation" that came along with our group-and-poster activity: "we were instructed to - i think - discuss the worth of the assessment strategy, and its use in our class rooms." this evaluatory analysis was called upon despite the directed experience of any of these assessment tools - which is fine, but which keeps discussion at a highly theoretical level. strangely, this is a nice microcosm of the teacher corps approach, which hits the learner [read the bold text in the following]

Knowledge <--- here
Comprehension
Application
Analysis
Synthesis
Evaluation <----- and here

on Bloom's taxonomy of learning stuff - the holy eucharist of educational instruction. the "Knowledge.... Evaluation" trap basically goes like this: "here's stuff.... how do you feel about it?" (and, the ellipses may represent days, weeks, or months) any development in the middle is left to chance and/or whim - which may allow someone to try and back out of the trap, saying that we're responsible somethings or other, and it's assumed that we do this on our own. this is a silly assumption - not about us being responsible, but about us being so capable that we're going to just adapt immediately to the maelstrom of teaching, and on top of that think to apply all of the things we were told once or twice during the summer.

back to the activity. the information (re: knowledge) isn't too difficult to pick up, and i'm not impressed by getting it again in novel situations (re: posters). [i'm tired, so my tenses are changing, which is frustrating]. neither am i concerned about how i "feel" about assessment (re: evaluation), especially given any credence you may ascribe to the above argument about fluency. that is, i'm not worried about what this information is (again, for the most part, it's not new), i'm worried about how i'm actually going to use it in my actual class (re: the skipped over part of the bloom's list, and my own inadequacies as a teacher). again: not if can use it (re: knowledge), and not if i want to use it (re: evaluation), but how the hell am i going to do this (re: "here's a candy bar...").

IV. class ended....

i. instructor A threatened our professional future.

he had picked up on the first-degree irony, a la [an approximation]: "you guys complain alot about how your students don't pay attention/follow directions/engage(!) during your classroom, but you all seem to act the same way in mine..." however, this comparison is (a) structurally thin, given the content of our disengagment and our voiced desire to engage in productive rigour (in the face of its near absence), and (b) perhaps applied more appropriately (or at least dually) as an illustration of the failed teacher, rather than the failed student; it is as much of an indictment of a situation that fails us in much the way that we construct situations that often fail our students (you know, because we're first-year teachers, and we're pretty much making it up as we go along).

nevertheless, we were thereafter reminded that sometime in our lives we would be moving on to a world where letters of recommendation would be critical currency, and that perhaps we should take into account perhaps needing letters of recommendation from our teacher corps instructors, etc. a tragically laughable position, yes. i'm usualy wary of the term "proffessionalism," but it seems nevertheless applicable in contrast.

ii. instructor B suggested hope

class concluded with the line: "hopefully you can actually use something you picked up today."

the Bloom-gap of the ellipses. "here's stuff. you're on your own to integrate it into your daily practice, but let it be known that down the line you'll be ask to reflect on its worth." i'm not interested in hope. neither am i interested in worth divorced from application, at least in the case where i need to survive as a teacher next week and all i'm asked to engage in today is a head-nod excercise about rubrics being pretty. sure, i'll raise my hand when you check for prettiness, but i'm still going to be scrambling next week to - you know - teach. and i'll create an activity that uses a rubric when i've got things under control, and i can breathe creatively for a second or two. but it'll take time to get there because i'm still figuring out what it means to teach math, and you're asking me to solve a linear system when i don't know how to graph lines. so the assessment mess gathers on the pile of "helpful tips," "how to's," "do's and don'ts," and "in a nutshells" - and i return to sunday with more stuff that "hopefully i can actually use," and no clue where to start, or how to start, or why to start.

iii. classmate C prevails

amidst this all, i notice a teacher corps member sitting beside me, writing a lesson plan. she's crouching down in her seat, curling away from all awkward power posturings and balloons of hope, and actually creating something for her classroom. a handout on one of the assessment strategies is on the desk, and she's got her eyes darting between this an a legal pad, all the while shrinking away from notice - as if her actions are somehow criminal. she's writing a lesson plan. it is beautiful: a moment where someone is actually making a value judgement on the information presented, and applying it - trying it out. there are scratched out ideas all over the paper - because it takes quite some time to develop all of these things - but pieces are being brought together, another fragile day is slowly being fitted with a structure. i watch her, and it's clear that this is the sort of time that should be spent by and with all of these brilliant people, amidst all of these powerful resources, and it's highly upsetting that it has to happen in a fugitive moment. it is as if we have to go out of our way to engage productively in actually applying the things that we're only presented with the hope of actually using. futhermore, these aren't difficult things to learn; it's not too much of a trouble to figure out what "peer assessment" means. but they are difficult things to apply and integrate into one's practice. yet, this is the very thing that we are left to do on our own - lest we risk the wrath of instuctor A, and crouch down amidst his fuming to try and actually develop as a teacher.

[i have no more conclusory sweeps. i'm very tired, and this is a very long post. thank you for reading, if you have. i will try and reflect more on my jim hill classroom soon; it all seems like a teacher corps drama, i'm sure.]