Monthly Archives: September 2015

Handling Teacher Preps

I was initially horrified at my schedule when I first saw it last June. Having since conceded the possibility–just the possibility, mind you–that I might have overreacted, I thought I’d discuss teacher preps.

Preps is a flexible word. A teacher’s “prep period” describes the free period the teacher gets during the day, ostensibly to “prep”are. “I’ll do that during my prep” or “I go get coffee during “prep”. But if a teacher asks “How many preps do you have?”, the query involves the number of separate courses the teacher is responsible for. So a teacher could say “I have no prep, but I’m only teaching one prep–geometry” or “I’ve got three preps and it’s brutal” without explaining which prep is which.

Non-teachers can’t really understand preps properly without realizing something I’ve mentioned frequently: teachers, particularly high school teachers, develop their own curriculum.

Odd that I’m mentioning Grant Wiggins again, but a little over a year ago, he said that too many teachers are “marching page by page through a textbook”. I’m sure that’s true, but said even teachers who march through a textbook using nothing but publisher generated material, make decisions about which problems to work, which test questions to use, and, unless they are literally walking through the textbook as is, which sections to cover. And those are extreme cases. Most teachers that I would describe as “textbook users” still make considerable decisions about their curriculum, including going “off-book”.

So preps are a proxy for workload. A teacher with four preps has a much greater workload than a teacher with one prep.

I’ve taught at 4 high schools (including my student teaching) and observed how many others operate. So this next description is typical of many schools, but variations on the theme occur.

At both the middle and high school level, math teachers are kind of like the swimmers in Olympic sports—we’ve got the most events.

English has many courses, but more of them are electives (journalism, creative writing) and then there’s the “ELL” split that few teachers cross. Most students take a four year sequence by grade, either honors, AP, or regular. Science and history courses add up because unlike math, each course has an AP version. Science has a 3-year sequence that lower ability students take four years to get through; the rest take an AP course in one of the same subjects, or an elective. History has a four-course sequence over three years, and can’t take an AP course again, which is too bad.

High school math has a six-course sequence that students enter at different points–five course if you count algebra 2/trig as one. From geometry on, each course has an honors version. Calculus is generally offered in both general and AP versions AB and BC. Algebra often has a support course. Then there’s statistics and AP Stats, and usually Business Math. Toss in Discovery Geometry. What is that, 17? And unlike ELL vs. regular English, we math teachers cover it all.

English and history high school teachers rarely have more than two preps, often a primary and secondary. I won’t say never. Science teachers are the most likely to have single preps, or general and honors in the same subject, because they have specialized credentials.

Math teachers often have three preps. Larger high schools may have more specialization. Maybe in big schools you’ll hear someone described as a geometry teacher, or a calculus teacher. But that’s just never been the case in any school I’ve seen.

To the degree math teachers do specialize, it’s a range of the 6 year sequence. The most common is the algebra specialist, a gruesome job that others are welcome to. (It’s only been four years since algebra terrors, my all-algebra-all-the-time year, can you tell? I still get flashbacks.) Some algebra specialists have limited credentials and unlimited patience. Others are genuine idealists, determined to create a strong math program from the bottom up. All of them can go with god, so long as I don’t go with them.

Sometimes you find the high-end experts, the ones that teach AP Calc, honors pre-calc, AP Stats, or some combination of. Sometimes these folk are the prima donnas with the math chops. Other times, they just aren’t very good with kids so they get stuck with the most motivated ones—they also teach the honors algebra 2 and geometry courses sometimes, because they just can’t deal with kids who aren’t as prepared or motivated. (No, I’m not bitter. Why would you think that?) And while we don’t have a name for what I do, it’s not uncommon for a math teacher to focus on “the middles”, the courses from geometry to pre-calc.

But not all schools go the category route. Others require all math teachers to cover a low, mid, and high level course in the sequence to be sure that no one gets cocky.

So now, after that explanation of preps, go back to the beginning, when I mention my hyperventilation over easy, familiar preps that I thought would be boring. Many teachers would agree—quite a few colleagues in all subjects commiserated with my dismay. Other teachers consider it rank abuse of power when admins assign them two preps, much less three.

Why? Because some teachers love the additional workload, love building and developing curriculum, mulling over the best way to introduce a new topic. For teachers like me, that’s an essential element of teaching—and repetition, teaching the same content three or four times a day, is so not essential, but rather Groundhog Day tedious. Others see curriculum as something they want handed to them or will do, reluctantly, once. Or, something they’ve honed after umpty-ump years and it’s perfect so they aren’t changing a thing. To these teachers, curriculum is a distraction from their primary job of teaching, the delivery of that curriculum–the job they actually get paid for. Give them the day of the school year, they know what they’re teaching.

If you’ve never really considered teacher preps before, certain questions might come to mind. Does teacher effectiveness (however measured) vary with the number of preps? Does teacher effectiveness vary by subject? (I’ve wondered before if I’m just better at geometry than algebra, for example.) Could we improve academic outcomes by giving weak teachers one prep in a limited subject, and strong teachers multiple preps (assuming we know what that is)? Do teacher contracts negotiate the maximum number of preps that can be assigned? While Ed’s informed assertions are interesting, surely there’s better data that gives a better idea of how many preps high school academic teachers have, on average? Or middle school teachers?

What terrific questions. They all occurred to me, too. And while I’m a pretty good googler, I began to wonder if I wasn’t using the right terms, because I could find no research on teacher preps, no union contracts restricting preps.

Let’s assume that some research has been done, that some contracts exist but escaped my eagle Google. Teacher preps still are clearly not on the horizon. I can’t remember ever hearing or reading a reformer mention them. When I was in ed school, the subject never came up—how to identify the best combination of preps, what number was optimal, and so on. Given how little control teachers have over preps, ed schools may just count it as one more of the nitty-gritty elements of the job we’ll discover later.

Education reformers simply don’t understand the degree to which teachers develop or influence curriculum and the resources it takes. They don’t understand the tremendous range of curriculum development that takes within a school. Moreover, most reformers don’t even understand that preps exist or have any impact on teacher workload. Few of them ever taught at all. So they don’t really know what a “prep” is, and then assume that most teachers rely largely on a textbook. That doesn’t leave them much room to mull.

Researchers don’t discuss preps much, either. I’m not even sure Larry Cuban, who describes teacher practice better than almost anyone, describing here the multi-layered curriculum which explicitly describes teacher-designed curriculum, has never written about preps. Many researchers also tend to confuse textbooks with curriculum.

I wonder if researchers are prone to ignoring high school preps because they would have to acknowledge how questionable their conclusions are without taking preps into consideration. If a researcher compares two high school teachers using a new curriculum, does it matter if one teacher has one prep and is teaching the same topic all day? This may give that teacher more time to adjust, notice patterns, change instruction. Meanwhile, the busy teacher with three preps who is just teaching one class with the new curriculum may just be doing it as an afterthought. Alternatively, teaching one class all day may also bore the teacher to the point of rote delivery, while the teacher with one class jumps in with enthusiasm.

Once I really started thinking about preps from a policy perspective, I became really flummoxed at the lack of play it gets. I may be missing a whole field of research, that’s how odd it is.

Administrators keep preps firmly in mind; whether contracts require it or not, they rarely give high school teachers more than whatever a commonly agreed amount is (usually three). Ideally, they will limit new teacher preps, although my mentee from last year had three preps each semester. Now that I think on it, I had three preps, too. Never mind—they pile it on newbies, too.

If VAM ever gets taken seriously at the high school level (which I find very unlikely), preps are likely to become a contract issue. Teachers being judged on test scores will probably demand a large sample size, which means fewer preps.

Fewer preps for teachers, of course, means far less flexibility for administrators putting together the dreaded master schedule. Ultimately, it means more teachers on the pay roll or fewer courses offered, because fewer preps and less flexibility must be compensated for somehow.

And hey. I just realized that Integrated Math (bleargh) schools have fewer preps. Maybe this is another foul plot of Common Core.

For myself, I do not want limited preps, even if my feet are forced to the fire on the point that hey, I’m really enjoying this easier year. But honesty compels me to point out that preps should be explored for their impact on teacher satisfaction, teacher productivity and–to the extent possible–academic outcomes.

I have no real ideas here. Only thoughts to offer up and see what others have on tap.

However, there’s another issue never far from my mind that perhaps the above mullings cast some light on: that of teacher intellectual property. Stephen Sawchuk just wrote a great piece on various issues in the related arena of teacher-curriculum sharing, and mentioned IP and copyright. I have huge issues with the absurd notion that districts own teacher-developed curriculum, which I’ll save for another post.

But surely this post makes it obvious that if teacher preps vary, then one of two things must be true. Either teachers in the same subject are getting paid the same salary for doing dramatically different jobs–and I don’t mean quality here, just work expectations.

Or teachers are paid to teach, in which case the actual delivery is the same no matter how many preps we have. Teachers then have the choice–the choice–to use the book and supplied materials extensively, or develop their own, to do the job as they determine it should be done. This seems to me to be the obviously correct interpretation of teacher expectations and the “work” they are “hired” for.

And in my world view, teachers are not paid to develop the curriculum, and therefore the district can keep its damn paws off my lessons.

Hrmph.

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The Test that Made Them Go Hmmmm

So school has begun and despite my palpitations about the boredom of only two familiar preps, I’m pleasantly busy. Last year was a hell of a lot of work, and given the nosedive that my writing time took, I should maybe not be so eager for a less…familiar schedule. So instead of demanding new classes, I accepted the first semester, threw a minor temper tantrum when no one listened about second semester and all is well. Algebra 2 in particular is proving a delightful challenge, given my new emphasis on functions.

In no small part because of this planning breathing room (is anyone noticing I’m saying my panic was a total overreaction?), the senior Water Park Day registered in my awareness ahead of time. In prior years, I didn’t heed the warnings that half my class would disappear, and so would be forced to dump my lesson plan on the Day itself, when the smaller classes would just have a day to practice. But thanks to this old, familiar schedule that gives me more time, I anticipated the impact.

So for the first time, I was able to give serious thought to having a day to pursue math without regard to subject matter or schedule. I could have a “math day”! Then I remembered Grant Wiggins’ challenge to math teachers everywhere in the form of a conceptual knowledge quiz.

hmmquiz

Grant proposed this as an actual test: I will make a friendly wager: I predict that no student will get all the questions correct. Prove me wrong and I’ll give the teacher and student(s) a big shout-out.

What math teachers think their kids would know the answers? I certainly didn’t. In some cases, they probably were taught, but in others, I doubt an elementary school teacher would ever think to bring them up. But even if all the concepts were taught by fifth grade, how many kids of that age could really appreciate the questions?

Most of the questions tease at the paradox….wrong word? tension? between the functional day-to-day applications of arithmetic, and the amazing truths that underlie them. John Derbyshire wrote, in Prime Obsession, that “arithmetic has the peculiar characteristic that it easy to state problems in it that are ferociously difficult to solve.” (I was rereading Prime Obsession last night; there’s tons of useful thought material for math teachers. I need to go get his book on algebra.)

Arithmetic looks easy. (And certainly in the last twenty years, the rush to shove everyone into calculus has led to a certain contempt for “basic arithmetic” classes.) But even if elementary school age children are capable of understanding its ideas fully (and most of them aren’t), they haven’t experienced several years’ utility of arithmetic. They haven’t had time to get bored of the routine rules that they are expected to remember (mind you, many don’t, but leave that for another day.) Yeah, yeah, invert and multiply. Yeah, yeah, you can’t divide by zero. Wait, what the hell do you mean multiplication isn’t repeated addition?

To really enjoy this test, to be fascinated by the underlying truths–or misconceptions–behind certain everyday math tools, requires familiarity with “the rules”. Time spent in the trenches of doing math just because.

That’s when a teacher can spend an enjoyable hour taking the kids back through a re-examination of the basics and what they really know. I’d much rather discuss these concepts with adolescents who have survived two or three years of high school math than try to force sixth graders to “demonstrate conceptual understanding” of dividing by zero.

I had no real expectations—no, that’s wrong. I had hopes. My sense was the students would be interested in the exploration, if I didn’t take on too much or dive in to the wrong end of the pool. But which end was the wrong end?

So for each of my four classes–two Algebra 2, two Trigonometry–I gave them the test and 20 plus minutes to write down their thoughts. I was alert to the possibility that kids would use five minutes to doodle and fifteen to giggle, but in each class the bulk of students asked for and got an additional five minutes to finish up. I collected their answers and will share some of them in later posts; they were often detailed and thoughtful.

After the writing time, the students had a few minutes to “share out” in their groups, so they could learn what questions puzzled their classmates—and also as reassurance that they weren’t alone in their befuddlement. Again, this seems different from Grant’s intent; he considered it a real test that the students would either answer correctly or leave blank in confusion. I listened in on many conversations; they were rich with exchange as the students realized they weren’t alone in their uncertainty.

But certain questions also sparked genuine debate and interest. More than a few students offered up multiplying negatives as an example of multiplication being something other than repeated addition. In every case I witnessed, their group members, who had written something to the effect of “isn’t it always repeated addition?” instantly recognized the roadblock that negative numbers posed to their definition. I came across more than one group arguing whether multiplying by zero counted as repeated addition (“yes, it does. If I have zero groups of five, I have zero!”). Interestingly, no one came up with the roadblock I was interested in, and I’d never once considered negative numbers until my students brought it up.

Their discussion time was about ten minutes. My goal wasn’t to have them determine the answers; rather, I wanted them all to have a shared experience before we discussed them as a class, and I gave them the “answers” (to the extent I knew them). That way, there’d be more of a sense of “we”–yeah, we thought of zero, too! yeah, we all have 3F=Y–that’s not the answer? yeah, we think dividing by zero gives you zero–it doesn’t?

So then we went through the answers as a group.

I had taken a subset of Grant’s list, ignoring the last three items. Doing it again, I would have swapped out question 2 for question 11 “appropriately precise”), because while question #2 is good, it really requires its own day. The rest of them are easily covered and discussed in at most 15-20 minutes each.

The questions I really wanted to spend time on, to explain in at least introductory depth, were 1, 3, and 5. From a practical standpoint, I wanted to be sure everyone understood why they got questions 4, 6, and 8 wrong, assuming most missed at least one of them. I was genuinely interested to see what they had to say about 7 and 9 but was going to take most of my lead from them. Question 10, I wanted to know if the trig students knew it; obviously, my algebra 2 students learn about imaginary numbers for the first time.

My trig classes are quite different in nature. Both are small, just 25 in each. Both are doing quite well; I have no kids who simply shouldn’t be there, as I did last year. My first block class is stronger, on average, but has more surly kids who mouth off. It’s very irritating, frankly, since the five or six kids giving me quite nasty sass are seniors who are doing relatively well (Bs and Cs), and who openly acknowledge that they think I’m a hell of a teacher. Two of the surlies had me last year for algebra 2, when they were much less trouble, and had been switched into my class because they were failing with another teacher. But these other teachers, who they didn’t like (and often failed, forcing them to retake a fake summer school course if they couldn’t switch to my class), didn’t get nearly the lip. I’m a tad flummoxed. My second block class has more kids who are amiable and interested but not taking the class as seriously as they should, so several more low scores on the first test. First block has a stupendous top tier, but it’s just three or four kids. Second block has a top tier of close to eight, but they aren’t quite as strong.

Anyway, I was expecting more interesting conversation from second block, and I had it backwards. First block was on point, even the cranky ones. They loved the test, wrote detailed responses, discussed it thoroughly in group, and were wildly participatory in the open discussion. Easily 90% of them came up with the correct response to imaginary numbers (and the ones from my algebra 2 class identified multiplying by i as 90 degree rotations in the complex plane, which was quite gratifying, thanks so much). Second block, the amiable, mildly uninterested ones pulled things down slightly, goofing around and making jokes while the stronger kids would have preferred more time to explore things. The conversation was still great, the students learned a lot and enjoyed the discussion, but I had the enthusiasm levels backwards.

My algebra 2 classes, I nailed in terms of expectations. Block three is a fairly typical profile, except I have a lot more sophomores than usual (which is due to our school successfully pushing more kids through geometry as freshmen). But still a good number of seniors who barely understood algebra I, a lot of whom are just hoping to mark time til graduation without ending up in summer school. (One of my specialty demographics.) And in between, juniors and seniors who are often thrilled to find themselves actually understanding math and succeeding beyond anything they’d ever hoped (another specialty of mine). Typically, many of the seniors were in class, as they lacked the the behavior or grade profile (and sadly, in some cases, the money) to go to the water park. So I expected conversation here to be a bit lower level, with less interest. Happily, everyone engaged to the best of their ability and many told me later how much they loved just “talking about math”. I spent much more time on questions 4, 6, and 8, and could see them all really registering why they’d made the mistakes they did. But they still were enthralled by questions 1, 3, and 5, which is great because it’s going to give them some memories when we review percentages in preparation for exponential functions.

Last up was block 4 algebra 2, a ridiculously strong class; only five students are of the usual caliber I expect. The seniors are all well above average ability level. Two of the kids are so skilled that I’ve already introduced three dimensional planes and the matrix, while still forcing them and the other really strong kids to deal with complex linear word problems (mixture questions! I usually skip them, so it’s a trip). They stomped all over the test, writing at great length, discussing it with their teams and then shouting out to other groups to see what they’d answered for multiplication. The class discussion took so long that I actually allowed it to continue for 20 minutes into the next day, when I invited one of my mentees to watch. He came away determined to try the test in his honors geometry class.

Look, the whole day was teacher crack. Take a day. Try the test. I’ll be discussing individual questions and my explanations in future posts, but this introduction is offered up as invitation. High school teachers working in algebra 2 or higher would be a good starting point. Honors classes in algebra and geometry would also benefit. Every math teacher can find links from this test to their math class—but then, that’s not the point.

As for me, I started out the day with hope, but also a determination to see it through as part of a way to honor Grant Wiggins, who felt very strongly that students needed to do more than just march through curriculum. I promised myself I wouldn’t abandon the effort even if it went wrong. It didn’t go wrong. Quite the contrary, the test sparked delighted interest and intellectual curiosity among students who are often hard to push into exploring mathematics in depth. So hey, Grant, thanks for the idea–and the inspiration.


Education Proposals: Final Thoughts

I’m trying to remember what got me into this foray into presidential politics last July.

It’s the age of Trump. Many people I greatly admire or enjoy reading, from Jonah Goldberg to Charles Krauthammer to Charles Murray, are dismayed by Trump. Not I. What delights me about him–and make no mistake, I’m ecstatic–has nothing do to with his views on education policy, where I’m certain he will eventually offend. I cherish his willingness to say the unspeakable, to delight in unsettling the elites. I thought Megyn Kelly was badass for telling her colleagues not to protect her. I also think she’s tough enough to deal with an insult or three from The Donald, and I imagine she agrees. What’s essential is that the ensuing outrage wasn’t even a blip on the Trump juggernaut.

Why, given Trump’s popularity, haven’t other Republican candidates jumped on the restrictionist bandwagon? Why did John Kasich, who I quite like, go the other way and support amnesty?

To me, and many others, the reason is not that the views aren’t popular, but because some vague, nebulous top tier won’t have it that way. The rabble are to be ignored.

This isn’t bravery. Politicians aren’t standing on their principles, looking the people in the eye firmly, willing to lose an election based on their desire to do right. Ideas with regular purchase out in the real world are simply unmentionable and consequently can’t become voting issues. Americans on both sides, left and right, feel that they have no voice in the process. I could go on at length as to why, but I always sound like a conspiracy nut when I do. The media, big business, a vanilla elite that emerged from the same social class regardless of their political leanings…whatever.

And along comes Trump, who decides it’d be fun to run for President and stick everyone’s nose in the unsayable.

I understand that conservatives who oppose Trump are more than a bit miffed that suddenly they’re the ones on the wrong side of the Political Correctness spectrum, given their routine excoriation by the media and the left for unacceptable views. Better political minds than mine will undoubtedly analyze the Republican/conservative schism in the months and years to come.

I don’t know how long it will last or what he will do. I just hope it goes on for longer, and that Trump keeps violating the unwritten laws that dominate our discourse. The longer he stays that course, the harder it will be to instill the old norms. That’s my prayer, anyway.

Anyway. Back in July, someone complained that education never mattered in presidential politics and expressed the hope that maybe Common Core or choice would get a mention. Maybe a candidate might express support for the Vergara decision!

Every election cycle we go through this charade, yet everyone should know why education policy doesn’t matter at the presidential level. No presidential candidate has ever taken on the actual issues the public cares about, but rather genuflects at the altar of educational shibboleths while the Right People nod approvingly, and moves on.

So I decided to demonstrate how completely out of touch the political discourse is with the Reality Primer, a book the public knows well, by identifying five education policy issues that would not only garner considerable popular support, but are well within the purview of the federal government. (They would cut education spending and reduce the teaching population, too, if that matters.)

I support all five proposals in the main, particularly the first two. But my agenda here is not to persuade everyone as to their worthiness, but rather illustrate how weak educational discourse is in this country. All proposals are debatable. Negotiable. We could find middle ground. The problem is, no one can talk about them because the proposals are all unspeakable.

No doubt, the Donald will eventually come around to attacking teachers or come up with an education policy that irritates me. I’m braced for that eventuality. It won’t change my opinion. Would he be a good president? I don’t know. We’ve had bad presidents before. Very recently. Like, say, now.

But if he’s looking for some popular notions and wants to continue his run, he might give these a try. Here they are again:

  1. Ban College-Level Remediation
  2. Stop Kneecapping High Schools
  3. Repeal IDEA
  4. Make K-12 Education Citizen Only
  5. End ELL Mandates

In the meantime, at least let the series serve as an answer to education policy wonks and reporters who wonder why no one gives a damn about education in politics.

As for me, I got this done just an hour before the Starbucks closed. I will go back to writing about education proper, I promise.