Tag Archives: Common Core

Letter to Betsy (#2): Drop Out.

Hey, Bets.

Well, I did say in my last note that you hadn’t shown  much capacity for original thought, that your primary contribution to ed reform were your contributions. I didn’t expect you to prove it so completely in your first at-bat.

Let’s avert our eyes from the tonedeaf response on guns at schools. I’m agnostic on the issue, but you should know that grizzlies aren’t a reason this is a tier-1 conflict. That bespeaks an ignorance I find…unsettling. I accept that you don’t care much about preschool, but what sort of conservative Republican would you be if  you thought universal pre-K was effective? Accountability, on the other hand, is a word you’ve heard before, so your constant evasions were seen–correctly–as attempts to avoid answering that you don’t think charters should be accountable to the same degree that public schools are. (No. Charters aren’t public schools.)

All of these could be explained away, or at least considered tertiary issues. You could say you hadn’t been properly briefed. And in fairness, you did have a nice moment with Bernie Sanders on college tuition: “free college” is indeed a misnomer.

But on two points, you displayed ignorance so profound that Republicans should vote against you.

First, you had no idea that IDEA and other federal legislation requires that states pay for absurd and often useless interventions for a wide range of disabilities, including many mild learning disabilities for which no meaningful interventions exist.

Less than a week before you went to Congress, the Supreme Court heard arguments as to whether or not a school district should provide an autistic kid with private school if the educational benefit the school could provide was “only trivial”.

Left unmentioned was the fact that on any given day, mainstream kids aren’t given this right.   I don’t often get infuriated at education reporters, many of whom do a pretty good job, but  not a single one has pointed out the absurd unfairness of a law that gives a select group of kids the right to sue for the private education of their choice on the grounds that they aren’t benefiting from the education their school provides.

I know many people will snicker–yeah, if all kids could sue their schools, teachers would hate it! Unlikely. I’d expect a lot of kids suing over disruptive classrooms, which would give schools cover to expel troublemakers. I’d expect others to demand the right to be taught what they don’t yet know.  Right now, my Algebra 2 junior who counts on her fingers can’t demand to be taught at a school that will instruct her in ratios and basic math, just as a sophomore with fifth grade reading skills can’t sue his district demanding the right to attend a school that won’t insist on pretending he can understand Antigone or Romeo & Juliet. Of course, no such school exists because they aren’t allowed to. Few teachers  would oppose safer schools or appropriate curriculum.

Once people figure out that giving all kids the right to sue wouldn’t work out as expected, they’ll look at removing the privilege from that select group. I wrote an entire article promoting the repeal of IDEA. I’m very much in favor of special ed being returned to the states and giving voters a say in what priorities special education receives compared to the wide range of needs that schools and their students have.

Betsy, I would have loved to see you  boldly call for an end to federal intervention in special education, to leave these decisions to the states. But you didn’t even know that the responsibility had to be returned! Of course, if you had known what the law was, you’d have burped  up (ladylike, I’m sure) a bromide, followed by a platitude and everyone would have patted themselves on the back for caring about disabled kids.

That leads to the second of your gross errors, about which I have less passion but is far more revealing.  Growth versus proficiency is something that teachers themselves have been talking about for decades, but education reformers have only really stumbled onto in the past few years, as the need arose when  charters didn’t attain the proficiency numbers they expected.  But you should know that. This is right in the ballpark of the field you fund so generously. And you were clueless. Franken was right to interrupt and dismiss your answer. (He was wrong to meander off into gay rights, a matter of trivial interest in public education. Put that in the “Why Trump Won” category.)

If  fifteen or more years actively supporting charters hasn’t brought you up to speed on the fundamental issues determining their success,  then how can we assume you have the capacity to learn about anything less central to your interests?

Bernie Sanders asked the right question. And you proved the correct answer was “No.”  A better woman would have said “I was almost certainly selected because I’m a billionaire who has given money to causes. But I also have a real interest in making life better for poor children.  That’s why I’m here.” That, at least, would be honest.

Better you should go back to writing checks.

Unlike most of the people opposing you, I accept that the incoming SecEd will be someone I disagree with, someone who openly snorts derisively at my profession, while protesting he does no such thing. I’m fine with that. I’d just like someone…smarter. Someone who really does know the research. Someone who, ideally, has been around the block with education reform. Someone who knows it’s more than the platitudes that typical conservatives spill, that “fixing schools” as they envision it hasn’t yet worked out.

My pick, and I’ve thought about this for a while, is Checker Finn. He’s old enough not to worry about his next job (which is why I eliminated Michael Petrilli and Rick Hess from consideration). He’s cranky and willing to offend. He’s wrong, of course, but then all education reformers are.  But when he’s not shilling the reform spiel, he’s knowledgeable on many different aspects of education. And he’s canny. Apart from yours truly, he’s the only person to observe that Trump voters aren’t exactly the target audience for talk of vouchers and charters. He has also recently observed that the era of education reform is over, and wondered whether Trump should even bother with a SecEd, given the restrictions that ESSA has put on the feds. (yay!). This suggests an appropriate level of humility for a long-term reformer, one who understands that 25 years of getting what he wanted in reform hasn’t fixed the achievement gap, that  reformers’ grand scheme of killing ed schools with the 1998 Higher Education Act failed miserably.  Checker Finn understands full well that Common Core was rejected; he argued in favor of them because he hoped they would result in less federal oversight.

Checker was Never Trump and, as mentioned, pro-Common Core, which is two strikes against him in Trumpland. But Betsy, if you decide to take my advice, I hope you put a word in for Checker with your not-to-be boss.

But since you’ll probably ignore me, see you next letter.


Not Negatives–Subtraction

In summer school, I’m teaching what used to be known as pre-algebra and happily, my colleagues had a whole bunch of worksheets that I got on a data stick. Very nice, and the curriculum was very good, leaving me time to tweak but not spend all my time inventing.

It’s not like the curriculum was a surprise: integer operations and fractions played a big part.

Of course, when we math teachers say “integer operations”, we mean “operations with negative integers” because while we don’t really care all that much if they’ve memorized their plus nines and times sevens (sorry, Tom!), kids that don’t fundamentally understand the process of addition are usually un-included by high school.

But negative numbers are one of those “Christ, they’ll never get it” topics. I don’t reliably have an entire class of kids who answer 9-11 with -2 until pre-calculus. I’m not kidding. They say 2, of course. But not negative 2. And if you give them -3-9, they will decide it’s 12 or -6 or, god forbid, 6. But not -12. They’re actually not terrible at subtracting negatives, provided that it’s subtracted from a positive. So they know 9-(-12) is 21, but have no idea what -9-(-12) is, and wildly guess -21.

I’ve suddenly realized that negative numbers aren’t really the problem. Subtraction causes the disconnect, as a result of the tremendous bait and switch we pull when moving from basic math to the abstractions needed for advanced math.

In elementary school, kids learn addition and subtraction. They are not told that they are learning addition and subtraction of positive integers. Nor are they told that they are only learning subtraction when the subtrahend is less than the minuend and, by the way, we need new terms. Those are horrible. In fact, kids are told that they can’t subtract in these cases.

subtractionuntruths

At no point are kids told that everything they’ve been taught is temporary, and that much of it will become irrelevant if they move into advanced math. Consider the big fuss over Common Core subtraction, which is all about an operation that has next to no meaning in advanced math other than grab your calculator. (No, this isn’t an argument pro or con calculators, put your hackles down.) Or consider the ongoing drama over the aforementioned “math facts memorization” which, frankly, gets turned ass over tincups with negatives and subtraction.

Common Core requires that sixth grade math introduce negatives. Along with ratios, rates, fraction operations, and statistical analysis, all tremendously complicated concepts. In seventh grade, things get serious:

ccseventhgrade

Never mind that most non-mathies would clutch their pearls at the very thought of parsing these demands, or that these comprise one of nearly twenty standards that have to be covered in seventh grade. Leave that aside.

Focus solely on NSA1B and NSA1C which, stripped of the verbiage, define the way we math teachers reveal the bait and switch.

So first, you teach the kids about these negative numbers and how they work. Then you show them that okay, we kind of lied before when we taught you that addition always increases. Actually, the direction depends on whether the added value is positive or negative.

But that’s it! That’s all you have to know! Just this one little thing. So negative numbers allow us to move in both directions on the number line.

And subtraction? Piffle. Because it turns out that (all together now!) Subtraction is addition of the opposite. Repeat it. Embrace it. Know it. Then everything makes sense.

So we teach them these two things. Yeah, we lied about adding because we had to wait to introduce negative numbers. But there’s this one little change. That’s all you have to know! because subtraction is a non-issue. Just turn subtraction into addition and funnel it all through the same eye of the same needle. Dust your hands. Done, baby.

Well, not done. As I said, we all know that negative numbers are brutal. We build worksheets. We support the confusion. We do what we can to strengthen the understanding.

But over the years, as I started teaching more advanced math, I realized that subtraction doesn’t go away. Subtraction is essential. It’s the foundation of distance, for starters.

And what the standards don’t mention is that introducing negative numbers changes subtraction beyond all recognition. The people who “get” it are those who reorder the integer universe spatially. Everyone else just stumbles along.

Until this summer, I never addressed this issue. I’m pretty sure most math teachers don’t, but I welcome feedback.

How do we change subtraction?

For starters, we violate the rule they’ve been taught since kindergarten. Turns out you can subtract a bigger number from a smaller number. (And, when a kid asks, “Well, in that case, how come we have to borrow in subtraction?” we teachers say…..what, exactly?)

But that’s just for starters. Take a look at the integer operations, broken down by sum and difference. (Much time is spent on teaching students “sum” and “difference”. More on that in a minute.)

addopsunmatched

So first, a row of numbers like this brings home an important fact: the Commutative Property ain’t just for mathbooks. This provides a great opportunity to show students the relevance of seemingly abstract theory to the real world of math.

But notice how much simpler the addition side is. I color-coded the results to show how discombobulated the subtraction pairs are:

addoppsmatched

Middle school math teachers spend much time on words like sum and difference, but I’m not entirely sure it helps.

For example, consider the “difference” between -9 and -5, which is -4. First, -5 is greater than -9, a complicated concept to begin with–and -4 is greater than both. And–even more confusing to kids taught to limit subtraction–none of those relationships matter to the result.

So -9 – (-5) = -4. Which is the same as adding a positive 5 to -9. So the difference of -9 and -5 is the same as the sum of -9 and 5.

Meanwhile, -9 – (-5) is subtraction of a negative, which we have hardwired kids to think of as “adding”–which it is, of course, but adding in negative-land is subtracting. So what we have to do is first get kids to change it to addition, then realize that in this case, the addition is a difference.

It’s not illogical, if you follow the rules and don’t think too much. But “follow the rules and don’t think too much” works for little kid math. As we move into algebra, not so much–we discourage zombies. Math teachers are always asking students, “Does your answer make sense?” and how can a student answer if subtraction makes no sense?

One of the things I’m wondering about is the end result of the operation. Any two numbers have a difference and a sum, all expressed in absolute values. 9 and 5 have a difference of 4 and a sum of 14, and no matter what combination of sign and operation used, the answer is the positive or negative of one of these two. So I ordered them by the end result.

addoppsendresult

Notice that P+P, N+N, P-N, N-P are ultimately collective sums. No matter the relative size, P+P and P-N move to the right, N+N, N-P move to the left, and result in a positive or negative sum of the two terms.

That looks promising, but I’m not sure how to work with it yet, particularly given the confusion of the actual meanings of sum and difference.

Here’s what I’ve got so far, and how I’m teaching it:

  1. What students think of as “normal” subtraction is actually “subtraction of a positive number”, where the subtracted number is smaller. Subtraction of a positive number always involves a move to the left on the numberline.
  2. In subtraction, the starting value does not change the direction of the operation–that is, -9 – 5 and 9 – 5 will both go to the left.
  3. The starting value must not change. This is a big deal. Kids see -9-5 and think oh, this is subtracting a negative so they change the -9 to 9. No. It’s subtracting a positive.
  4. Please, please PLEASE sketch it out on a numberline. Please? Pretty please?

Hey, it’s a start. I also use a handout I built six years ago, during my All Algebra All The Time year (pause for flashback) and has proved surprisingly useful, particularly this part:

I am constantly reminding kids that subtraction is complicated, that the rules changed dramatically. Confusion is normal and expected. Take your time. I am seeing “success”, with “success” defined as more right answers, less random guessing, more consistent mistakes in conception that can be addressed one by one.

I don’t know enough about elementary and middle school math to argue for change, except to observe that much more time is needed than is given. I once took a professional development class in which a math professor covered an abstruse explanation of negatives and finished up by saying “See? Explain it logically and beautifully. They’ll never forget it again.” We laughed! Such a kneeslapper, that guy.

But I’m excited to get a better sense of why kids struggle with this. It’s not the negatives. It’s subtraction.


Education: No Iron Triangle

I came from the corporate world, which invented the project management triangle. (“Fast, Good, Cheap: Pick Two.”)

Education has no triangle.

Money, of course, doesn’t work. Just ask Kansas City. Or Roland Fryer, who learned that kids would read more books for money but couldn’t seem to produce higher test scores for cash. Increased teacher salaries, merit pay, reduced class size are all suggestions that either don’t have any impact or have a limited impact….sometimes. Maybe. But not in any linear, scalable pattern.

“Good”? Don’t make me laugh. We don’t have a consensus on what it means. Most education reformers use the word “quality” exclusively to mean higher test scores. Teachers do not. Nor do parents, as Rahm Emanuel, Cami Anderson, Adrian Fenty and Michelle Rhee have learned. Common Core supporters have had similar moments of revelation.

So until we agree on what “good” is, what a “high quality education” means, we can’t even pretend that quality is a vertex of education’s triangle, even if it existed. We could save a whole lot of wasted dollars if people could just grasp that fact.

Time is an odd one. We never use the word directly, but clearly, politicians, many parents, and education reformers of all stripes believe we can educate “faster”. Until sixty years ago, calculus was an upper level college course. Once the high school movement began, fewer than 3% of students nationwide took trigonometry, between 10-20% took geometry, and the high point for algebra was 57%–over one hundred years ago–then declining to 25%. (Cite.) One of the little noted achievements of the New Math movement was to alter the math curriculum and make high school calculus a possibility. At first, just kids with interest and ability took that path. Then someone noticed that success in algebra I predicted college readiness and everyone got all cargo cult about it. By the turn of the century, if not earlier, more of our kids were taking advanced math in high school than at any point in our history.

And that was before kids started taking algebra in seventh grade. Sophomores take now take honors pre-calculus so they can get a second year of AP calculus in before graduation. Common Core has gone further and pushed algebra 2 down into algebra I.

Yet 17 year old NAEP scores have been basically stagnant for the same amount of time our high school students have been first encouraged, then required, to take three or more years of advanced math.

Not only do we try to educate kids faster, we measure their gain or loss by time. Poor kids of uneducated parents lose two months learning over the summer. CREDO, source of all those charter studies, refers to additional days of learning. Everyone comparing our results to Singapore always mentions the calendar, how much earlier their kids start working with advanced math. These same people also point out that Singapore has a longer school year. Longer school years don’t appear to work reliably either.

Except maybe KIPP, whose success is mostly likely due to extended school hours. KIPP focuses on middle school and has not really been scrutinized at the high school level. Scrutiny would reveal that the program doesn’t turn out stellar candidates, and while more KIPP alumni complete college than the average low income black or Hispanic student, the numbers are reasonable but not extraordinary when compared against motivated students in the same category who attended traditional schools. Particularly given the additional support and instruction hours the KIPP kids get.

So KIPP’s “success” actually adds weight to the NAEP scores as evidence that time–like money and quality–doesn’t respond to the project management constraints.

Kids learn what they have the capacity to learn. Spending more instruction hours will–well, may–help kids learn more of what they are capable of learning in fewer school years. But the NAEP scores and all sorts of other evidence says that learning more early doesn’t lead to increased capacity later. And so, we’ve moved 1979 first grader readiness rules to preschool with considerable success, but that success hasn’t given us any traction in increasing college readiness at the other end of childhood. Quite the contrary.

I probably don’t have much of a point. I was actually thinking about the increasing graduation rates. It’ll be a while until part 2. I’m swamped at work, moving again, writing some longer pieces, and really would like to post some math curriculum rather than detangle my mullings.

But the triangle thing is important. Really.

Take note: under 1000 words. Hey, I have to do it every year or so.


Teaching is Unknowable

While I’m really enjoying teaching this year, the job is taking tremendous mental energy. I’m teaching three classes. One of them isn’t math. I’m thrilled. But it’s taking an enormous amount of work, because I have a very clear vision…not so much of what to teach or how to teach, but how I don’t want to teach the class. Having gone into the experience with my eyes wide open, I haven’t been disillusioned or disappointed by how much more difficult the class is. But I’m way outside my comfort zone—which is amazing in and of itself. I have a comfort zone in teaching math! Who knew?

But then, my math classes are outside my comfort zone, too. I’m teaching trigonometry for the first time and recall, folks, I’m not a mathematician. I know right triangle trig very well, know the graphs well, know the identities. But I’ve never taught it. The last time I taught a new class, pre-calc, I followed the book pretty faithfully the first time through—lots of lecture, lots of book work. I lost a good half the class in the first month, and while most of them were saved, I learned that for whatever reason, I should avoid lectures. The second through fourth times through I slowed it down, designed more activities, did less lecturing, and kept the whole class moving forward each time.

So the first time through trig, I’m trying to avoid straight book work. I’m helped here by more subject matter knowledge, and designed the opening unit to take advantage of this. I had some breathing room until I needed to dig in to the new stuff. The class definitely needed the time. Trig, like geometry, with all its facts and spatial notions, comes as kind of a shock after years spent having algebra processes beat into your head. So the class is going well and is, in fact, the closes thing I have to a comfort zone this year. Just one problem—I spent all that breathing room working on the brand new subject class AND…

…my Algebra 2/Trig class, and to explain what’s up with my A2/Trig class I have to discuss administration a bit, and so I want to be really clear that I’m not criticizing. Not only am I not criticizing, I fully acknowledge that there may be facts on the ground of which I am unaware.

Algebra 2/Trig is becoming, in many schools, an advanced class. It combines both algebra 2 and trigonometry in one class. So the kids currently in my trigonometry class took algebra II (also known as intermediate algebra), taking two years to go through what A2/Trig covers in one year. However, as most math teachers will tell you, it’s insane to actually cover second year algebra and trigonometry in one year (particularly in half a year, as our classes are set up). Trig often becomes little more than the unit circle, a brief run through identities, and lots of graphing (amplitude, period, and so on).

Lordy, I just cut two paragraphs of the history of Algebra II/Trig and a rumination on where the hell Pre-Calc started (does anyone know? I’d love a link). Stay focused, Ed.

The point is, I insist on teaching something approximating advanced math in Algebra II/Trig, because if I pass a kid, the next stop is Precalc. But there are only 14 kids in my A2/Trig class right now. And of those 14, only two, maybe four have any business being in A2/Trig. The rest should be in Algebra II, and they wouldn’t be getting an A.

But I couldn’t boot any of them down, because the Algebra II classes are filled to bursting—36 in two, 33 in the other. And I could only boot one of the advanced kids up to Honors A2/Trig (don’t get me started) because that class also has 36 in it.

I emailed all the administrators and saw two personally, pointing out what I thought was the obvious solution: convert my class to an Algebra II class, move some of the overloaded classes into mine. Take the two or three kids ready for A2/Trig and move them into honors, or just switch their schedule around. I pointed out that not only was this a better allocation of teaching resources, but also made a more equitable solution. For various reasons, my Math Support Class For Kids Who Hadn’t Passed the Exit Exam, had been cancelled because of section count. If I was only going to be teaching 14 kids, shouldn’t it be kids who really struggle and can benefit from the direct attention?

And for some of the same and some different various reasons, none of my suggestions were taken. Keep in mind we still don’t have a math teacher and are using a sub (but firing teachers–that’s the big pain point!). One history teacher left mid-September (for good reasons) and they had to hire someone. We were also dealing with the usual beginning of the year craziness, district mandates, and so on. Admins have their own insane workload, which is why I always laugh like a fiend at the idea that they should also be teaching experts.

Then, of course, what I proposed meant altering a lot of students’ schedules. I can’t blame them for saying no. You haven’t been to hell until you’ve done a master schedule, is the AVP motto, and filling that schedule is second.

So I’ve got 12 kids who struggle with most algebra one concepts in a class that, if I pass them, leads straight to pre-calc. I’m planning on putting most of them into trigonometry after this, assuming it’s allowed. The class has other problems on which I won’t elaborate, but planning takes much more time than one would expect for the only class I’ve taught before.

There are about a million and a half high school teachers. I can guarantee you that half or more of them right now have a story about this year similar to one or more of the three I’ve described above: new class in new subject, new class, weird class caused by administrative hassles. Or some other story, maybe like my second year of teaching All Algebra, All the Time. Or just administrative problems—unavoidable, or deliberately inflicted. And for those that are having a smooth start this year (as was true for me last year), we can all come up with another story from another year. Then there’s a whole group saying what, you’re only teaching three classes? Shut up with the whining! and then we can go a few rounds on block vs. traditional.

I’m not writing as much because I’m working my ass off, because even when I’m not working I’m thinking crap, I should be mapping out my next week, making copies, making tests, building some new curriculum, thinking up activities. Even now, I’m writing this because I think I can kick it out in an hour and get “my blog is being neglected” off my list of obsessions so I can go to Starbucks to read up on a topic to plan some lessons. I rarely can’t think of job-related tasks right at the moment. And remember, I’m not a workaholic and definitely not a control freak, two attributes commonly found in Teacherville.

How do teachers react to the demands of the job? It depends on their personalities. I would wager to say that most are like me and work harder when given a new challenge—whether effectively or not, who knows? Some undoubtedly just shut down and get stubborn. Still others meander around incompetently—not because they are incompetent, but because their job has been defined in such a way that it’s now no longer recognizably their job.

At this point, many teachers aggravate me by going the martyr route. See how hard it is to be a teacher? See how hard we work? And all for the kids!

No. I do this for the intellectual challenge. I see nothing incongruous in doing hours more work a week for the same pay, work that will not enhance my resume in any meaningful way, that won’t make it any easier to find a job should this school decide to dump me—and please God, they won’t. (Nor will doing this new work increase or decrease the likelihood that they will keep me, by the way.) I’m an idiot who spends hours a week researching for my blog unpaid, though, so I’m weird.

But can you blame people who do? Say your job for the past decade involved teaching AP Physics 5 times a day, and helping motivated kids learn how the world works, helping them pass a test that gives them college credit, and you were suddenly told great news! You’ll be teaching integrated science to 9th graders who don’t give a damn. So now you’ve got hours more work a week planning activities in an entirely different field for entirely different kids. And, by the way, you are pretty terrible at working with unmotivated kids.

Now if you’re me, the idea of teaching one subject for ten years is grounds for divorce. But not everyone’s me.

I’m not asking for sympathy or understanding. I’m asking for an awareness that no one has a clue what teaching is. Even other teachers can’t be certain what the job means in any universal sense.

The job of teaching is very nearly unknowable to outsiders, because outsiders don’t understand that teaching isn’t one job. Any one teaching position is actually a million interactions between the teacher’s personality, the subject(s) taught, the balance of classroom ability and interest, sculpted by administrative dictates, district and parent socioeconomics, state policy, and school logistics. What I think of as teaching another would consider anarchy. Other teachers hold jobs that I view as little more than sinecures, through little more than luck.

(Edited to add in what I thought was obvious, but comments here and at Joanne’s site (thanks for the link) seem to need explication:)

Obviously, many professions have similar complexity. Lawyering, doctoring, police work, nursing, professional atheletes–all have an enormous range of features from which the individual jobs are sculpted. And should we ever be seeking to describe one huge profession adequately in order to advocate for policy or position changes in the hopes of improving outcomes, saving money, or changing the nature of the people who enter that profession, its unknowability will also be relevant.

**end addition**

Which means please stop surveying 1600 teachers out of a group of 20,000 or so and trumpeting the results as indicative of teacher sentiment on Common Core. Which means stop coming up with plans to create world class teachers because no one agrees on what that is. Which means stop letting teachers testify about tenure and LIFO as if their opinions or experiences are in any way relevant (on either side). Which means, reporters and education writers, please stop saying “teachers” when you mean “elementary school teachers” because this, at least, is a distinction that’s easy to grasp and incredibly relevant.

For good reason, people are reluctant to acknowledge the many aspects of our population that makes teaching so many different jobs, so impossible to easily categorize. But as long as y’all are going to flinch on the big issues, stop pretending you understand teaching.


Reading in the Gulag of Common Core

(if you’re here to see KPM’s bio scrub, scroll down to the bottom)

I have five other pieces going and a serious case of writer’s ADD, but Kathleen Porter Magee just really annoyed me.

Porter Magee works part-time at Fordham Foundation, recently tasked with churning out paeans to or defenses of Common Core, and also at the College Board, where she works for the guy who wrote the Common Core, and I’ve yet to see the media inquire as to whether this might be a conflict.

KPM, as she is often called, has been singing the praises of Teach Like a Champion Doug Lemov for a couple years now, which is inconvenient because Lemov pushes prior knowledge, and her new boss Coleman spits upon it. But anyway, she’s trying to thread both needles here—push Lemov and the Common Core insistence that all students be forced to read “grade level books”.

The money quote bolded:

And the pushback against this particular CCSS directive is growing. For example, self-described “small-town English teacher” Peter Greene likened assigning texts based on grade level “without regard for the student’s reading level” to “educational malpractice.” This pushback is backstopped by an entire industry built up over decades on the premise that students should be kept away from complex texts at all costs.

Really? Are you kidding me? There’s an industry devoted to keeping students away from complex texts? Cite, please? The organization that says “my god, we can’t have kids reading hard words!”

That’s insane, but so is her position that teachers should ignore their students’ actual reading ability and insist on assigning books the polite kids just pretend to understand and the impolite kids just ignore entirely. That opinion is very North Korea, frankly, although NK and the chubby new Leader would be much tougher on the impolite kids.

For the record, there is in fact no industry dedicated to keeping kids from reading Metamorphosis. More immediately relevant, KPM is wrong in insisting that teachers should ignore reading ability when assigning texts.

I was interested to realize that Common Core standards differ by subject in their willingness to acknowledge the below-level student.

So the math standards include some advice on what to do with kids who are behind and , like NCLB, has nothing new to offer: tutoring, algebra support, summer school. Yeah, thanks for the tip. None of them worked last time, either.

But the ELA standards largely refuse to acknowledge the reality of struggling readers—not even, I was a bit stunned to see, much recognition for English Language Learners, flatly rejecting the notion that they might struggle a bit and leaving any support to the states to figure out. Common Core’s refusal to placate the massive ELL lobby is telling, because in that case there’s going to be no recognition of native English speakers who simply aren’t smart enough to read at grade level, so English teachers, you’re screwed. Just kidding, because as we all know, standards throughout history have always called for kids to read at grade level, and teachers have and undoubtedly will continue to pick texts targeted to student ability whenever possible (it isn’t always). They’ve always done that, which begs the question why Fordham Foundation is acting like a wild hair has intruded someplace uncomfortable on the subject.

My conclusion: the big focus on “grade appropriate texts” and emphasis on teachers’ refusal to use the Common Core “exemplars” is just strategy. Common Core’s going to fail, so why not build the terrain for the inevitable blame game that’s coming by arguing that even now, at the beginning, teachers are ignoring Common Core by assigning texts their kids can understand, instead of grade-level texts. KPM’s broadside insult to teachers or an unspecified “industry” desperately working to keep kids away from “sedulous” and “balkanization”—and remind me why, again, she’d go work for the guy who’s planning to scrub the SAT of these words?—is, in my view, part of an effort to position the foundation for the standards’ inevitable failure.

And so, their demand that teachers pretend that all kids from kindergarten on have equivalent reading abilities. Yes, some kids don’t read as well, but that’s because they go to the low income schools that have bad teachers who assign some students Dr. Seuss in second grade instead of Robert Frost’s “Stopping by Woods on a Snowy Evening”. In this way, the seven year olds are denied the ability to debate whether the speaker was referring to his eventual death or his desired but delayed suicide, thus preventing them from being excellent readers on their way to college readiness.

I haven’t opined on the totality of the ELA standards yet, but on this one point I have been consistently shocked ever since Fordham released the study in which it declared, with a straight face, their horror that English teachers were using their students’ reading abilities to assign texts. Usually reformers insist on behavior that at least logically makes sense if you don’t have a clue about the reality of education. But the stance on this is absurd. Why would anyone insist on forcing kids to read books they can’t understand?

I taught humanities for one year in public school, to freshman with reading abilities ranging from sixth grade to college level, and I can state with confidence that the low ability kids did not benefit in any way from being forced to pretend to read Twelfth Night. They liked the movie, though. As I describe in that post, I gave up SSR with my students because they simply stared at books they didn’t want to read. When I took away their choice and gave the weaker students enrichment activities designed for bright fifth graders, they engaged and acquired content knowledge. Why would anyone seriously argue against that?

For the past eight plus years, I’ve taught reading enrichment to a mostly Asian crowd of freshmen, with abilities ranging from FOB to reasonably competent (rarely do I have a stupendous reader and writer, but it does happen). Here, too, I have not seen them benefit from reading texts they don’t understand because, despite their outstanding test scores, the kids I teach have mediocre reading abilities thanks to dismal active vocabularies and weak content knowledge. Much of my teaching time is spent, again, assigning them reading they can understand and demonstrating the importance of remembering content knowledge.

So while I haven’t taught a lot of English in public school, my experience with early high school readers is extensive, and Fordham’s position is flatly ludicrous.

On a slightly different note, I’m getting a bit tired of KPM pushing her teaching experience. Her Linked In profile shows clearly that not only has she avoided anything approaching students for over a decade, but that she was only at the Washington Archdiocese, a prominent mention in all her bios, for ten months. She didn’t leave an impression. Likewise at Achievement First, her title may have been impressive but she still worked part-time, according to her husband, and the only document I can find with her name on it suggests she was basically HR. Achievement First is known primarily for its questionable application of “No Excuses” discipline, not its great curriculum.

She was probably a teacher for some period of time from 1997 through 2000, the three years after she graduated from Holy Cross with a degree in French and Political Science before she started her master’s degree. Maybe she just doesn’t list her credential education. More plausibly, she taught for a year or so at a Catholic school, maybe language, maybe French.

Back when she married Marc Magee, teaching was such an important part of her bio that she never mentioned it, only listing her work at Progressive Policy Institute, Hoover, and Fordham. Her footprint at every place but Fordham is non-existent.

I have mentioned before that very few education policy people on either side have any extensive teaching experience, but better to just plead out than pretend.

Maybe she’s got more experience than I can find, or slipped in some teaching while working at Fordham part time. Maybe a reporter will ask her to be specific, produce documents of her curriculum work and her lesson plans. Hahahahaha!

Anyway. If it comes down to a choice between an reticent Kathleen Porter Magee and me, an anonymous teacher blogger….wait. Never mind.

Look, I’m not expecting you to take my word for anything. But if you still accept policy hack bios at face value, think again.

As for the Common Core Reading Gulag, where everyone must read at or above grade level because the Great Leader says so, I’ll leave you with a simple application of logic.

On one side, you have an education reform organization, dependent on the will of its funders, insisting that English teachers everywhere are failing their students by assigning them texts that will be more likely to engage them and thus increase content knowledge, rather than texts randomly declared “grade level” by wishful thinkers. On the other side, you have the majority of English teachers, insisting through their actions that students are best served by reading words they can understand.

Michael Petrilli has tacitly admitted (and said so explicitly on the Gadfly show, as I recall) that he never believed in the NCLB goals of getting all students to proficiency, but he had a boss, and that was the party line. Now, he’s pushing the Common Core party line.

You can believe that Petrilli and KPM are pushing a party line because they get paid to, or you can believe that teachers are part of a gigantic industry dedicated to ensuring that students are never exposed to complex text.

It’s up to you.

PS–I just liked the title; don’t take it too seriously.

**********************************
Addendum, June 12

I am delighted to see that KPM’s bio at Fordham has been thoroughly scrubbed.

Here’s how it appeared when I wrote this piece, on May 17th. It was in place through May 30th, at least, as you can see by the dates of the articles.

kpmbefore

And here’s what it looks like now. A lot shorter. All the company names gone, no mention of her teaching, just “working directly in schools”. Still a bit squiffy, but hey, they had to save face.

kpmnow

Think it was me? I hope it was me. It’d be fun if it was me. It probably was me.


Multiple Answer Math Tests

As previously explicated in considerable detail, I’m deeply disgusted with the Common Core math standards—they are too hard, shovel way too much math into middle school. If I see one more reporter obediently, mindlessly repeat that [s]tudents will learn less content, but more in-depth, coherent and demanding content my head will explode.

Reporters, take heed: you can’t remove math standards. The next time some CC drone tells you that the standards are fewer, but deeper, ask for specifics. What specific math standard has been removed? Do students no longer have to know the quadratic formula? Will they not need to know conics? No, not colonics. That’s what you all should be forced to endure, for your sins. In all likelihood, the drone has no more idea than you reporters do about high school math, so go ask Jason Zimba, who reiterates several times in this interview that the standards are fewer, but go deeper. (He also confirms what I said about algebra, that much of it is moved to middle school). Ask him. Please. What’s left off?

Pause, and deep breath. Where was I?

Oh. Tests.

So the new CC tests are not multiple choice, a form that gets a bad rap. I give my kids in algebra one, geometry, and algebra two lots of multiple choice tests—not because I prefer them, and they aren’t easier (building tests is hard, and I make my own), but because my top students aren’t precise enough and they need the practice. They fall for too many traps because they’re used to teachers (like me) giving them partial or most of the credit if all they did is lose a negative sign. Remember, these are the top kids in the mid-level or lower math classes, not the top kids at the school. These are the kids who often can get an A in the easier class, and aren’t terribly motivated. My multiple choice tests attempt to smack them upside the head and take tests more seriously. It works, generally. I have to watch the lower ability kids to be sure they don’t cheat.

We’ve been in a fair amount of PD (pretty good PD, at that) on Common Core; last fall, we spent time as a department looking at the online tests. The instructors made much of the fact that the students couldn’t just “pick C”, although that gave us a chuckle. Kids who don’t care about their results will find the CC equivalent of picking C. Trust them. And of course, the technology is whizbang, and enables test questions that have more than one correct answer.

But I started thinking about preparing my students for Common Core assessments and suddenly realized I didn’t need technology to create tests questions that have more than one answer. And that struck me as both interesting and irritating, because if it worked I’d have to give the CC credit for my innovation.

On the first test, I didn’t do a full cutover, but converted or added new questions. Page 1 had 2 or 3 multiple answer questions and 3 was free-response, but on that first test, the second page was almost all multiple response:

cca2at2

I had been telling the kids about the test format change for a week or two beforehand, and on the day of the test I told them to circle the questions that were multiple answer.

It went so well that the second test was all multiple answer and free response. I was using a “short” 70-minute class for the test, so I experimented with the free-response. I drew in the lines, they had to identify the inequalities.

CCa2test1

cca2test2

I like it so much I’m not going back. Note that the questions themselves aren’t always “common core” like, nor is the format anything like Common Core. But this format will familiarize the kids with multiple answer tests, as well as serve my own purposes.

Pros:

  • Best of all, from my perspective, is that I am protected from my typos. I am notorious, particularly in algebra, for test typos. For example, there are FIVE equations on that inequality word problem, not four. See the five lines? Why did I put four? Because I’m an idiot. But in the multiple answer questions, a typo is just a wrong answer. Bliss, baby.
  • I can test multiple skills and concepts on one question. It saves a huge amount of space and allows the kids to consider multiple issues while all the information is in RAM, without having to go back to the hard drive.
  • I can approach a single issue from multiple conceptual angles, forcing them to think outside one approach.
  • It takes my goal of “making kids pay attention to detail” and doubles down.
  • Easier, even, than multiple choice tests to make multiple versions manually.
  • Cheating is difficult, even with one version.

Cons:

Really, only one: I struggle with grading them. How much should I weight answers? Should I weight them equally, or give more points for the obvious answer (the basic understanding) and then give fewer points for the rest? What about omitting right answers or selecting wrong ones?

Here’s one of my stronger students with a pretty good performance:

A2cctestsw1
A2cctestsw2

You can see that I’m tracking “right, wrong, and omit”, like the SAT. I’m not planning on grading it that way, I just want to collect some data and see how it’s working.

There were 20 correct selections on nine questions. I haven’t quite finished grading them, but I’ve graded two of the three strongest students and one got 15, the other 14. That is about right for the second time through a test format. Since I began the test format two thirds of the way through the year, I haven’t begun to “norm” them to check scrupulously for every possible answer. Nor have I completely identified all the misunderstandings. For example, on question 5, almost all the students said that the “slope” of the two functions’ product would be 2—even the ones who correctly picked the vertex answer, which shows they knew it was a parabola. They’re probably confusing “slope” with “stretch”, when I was trying to ascertain if they understood the product would be a parabola. Back to the drawing board on that.

Added on March 7: I’ve figured out how to grade them! Each answer is an individual True/False question. That works really well. So if you have a six-option question, you can get 6/6, 5/6, 4/6 etc. Then you assign point totals for each option.

I’ll get better at these tests as I move forward, but here, at least, is one thing Common Core has done: given me the impetus and idea for a more flexible test format that allows me to more thoroughly assess students without extending the length of the test. Yes, it’s irritating. But I’ll endure and soldier on. If anyone’s interested, I’m happy to send on the word doc.

Note: Just noticed that the student said y>= -2/3x + 10, instead of y<=. It didn't cost her anything in points (free response I'm looking for the big picture, not little errors), but I went back and updated her test to show the error.


Core Meltdown Coming

I’ve stayed out of the Common Core nonsense. The objections involve much fuss about federal control, teacher training, curriculum mandates, and the constructivist nature of the standards. Yes, mostly. But so what?

Here’s the only important thing you need to know about Common Core standards: they’re ridiculously, impossibly difficult.

I will focus here on math, but I’m an English teacher too, and could write an equivalent screed for that topic.

I’m going to make assertions that, I believe, would be supported by any high school math teacher who works with students outside the top 30%, give or take.

Two to three years is required just to properly understand and apply proportional thinking–ratios and percentages. That’s leaving off the good chunk of the population that probably can’t ever truly understand it in non-concrete situations. Proportional thinking is a monster. That’s after two to three years spent genuinely understanding fraction operations. Then, maybe, they could get around to understanding the first semester of first year algebra–linear equations (slopes, more proportional thinking), isolating variables, systems, exponent laws, radicals—in a year or so.

In other words, we could use K-5 to give kids a good understanding in two things: fractions and integer operations. Put measurement and other nonsense into science (or skip it entirely, but then remember the one subject I don’t teach). Middle school should be devoted to proportional thinking, which will introduce them to variables and simple isolation procedures. Then expand what is currently first semester algebra over a year.

Remember, I’m talking about students outside the top 30% or so (who could actually benefit from more proportions and ratios work as well, but leave that for another post). We might quibble about the time frames and whether we could add a little bit more early algebra to the mix. But if a math teacher tells you this outline is nonsense, that if most kids were just taught properly, they could learn all this material in half the time, ask some questions about the demographic he works with.

Right now middle school math, which should ideally focus almost entirely on proportions, is burdened with introductions to exponents, a little geometry, some simple single variable equations. Algebra I has a whole second semester in which students who can’t tell a positive from negative slope are expected to master quadratics in all their glory and all sorts of word problems.

But Common Core standards add exponential functions to the algebra one course load and compensate by moving systems of equations and exponent laws to eighth grade while much of isolating variables is booted all the way down to sixth grade. Seventh grade alone bears the weight of proportions and ratios, and it’s one of several curricular objectives. So in the three years when, ideally, our teachers should be doing their level best to beat proportional thinking into students’ heads, Common Core expects our students to learn half of what used to be called algebra I, with a slight nod to proportional thinking (and more, as it turns out. But I’m getting ahead of myself).

But you don’t understand, say Common Core devotees. That’s exactly why we have these higher, more demanding standards! We’ve pushed back the timeline, to give kids more time to grasp these concepts. That’s why we’re moving introduction to fractions to third grade, and it’s why we are using the number line to teach fraction numeracy, and it’s why we are teaching kids that whole numbers are fractions, too! See, we’ve anticipated these problems. Don’t worry. It’s all going to be fine.

See, right there, you know that they aren’t listening. I just said that three to four YEARS is needed for all but the top kids to genuinely understand proportional thinking and first semester algebra, with nothing else on the agenda. It’s officially verboten to acknowledge ability in a public debate on education, so what Common Core advocates should have said, if they were genuinely interested in engaging in a debate is Oh, bullpuckey. You’re out of your mind. Four years to properly understand proportional thinking and first semester algebra? But just for some kids who aren’t “smart”? Racist.

And then we could have an argument that matters.

But Common Core advocates aren’t interested in having that debate. No one is. Anytime I point out the problem, I get “don’t be silly. Poor kids can learn.” I point out that I never mentioned income, that I’m talking about cognitive ability, and I get the twitter version of a blank stare somewhere over my shoulder. That’s the good reaction, the one that doesn’t involve calling me a racist—even though I never mentioned race, either.

Besides, CC advocates are in sell mode right now and don’t want to attack me as a soft bigot with low expectations. So bring up the difficulty factor and all they see is an opportunity to talk past the objection and reassure the larger audience: elementary kids are wasting their time on simple math and missing out on valuable instruction because their teachers are afraid of math. By increasing the difficulty of elementary school math, we will forcibly improve elementary school teacher knowledge, and so our kids will be able to learn the math they need by middle school to master the complex, real-world mathematical tasks we’re going to hand them in high school. Utterly absent from this argument is any acknowledgement that very few of the students are up to the challenge.

The timeline isn’t pushed back for algebra alone. Take a look at Geometry.

Geometry instruction has been under attack for quite some time, because teachers are de-emphasizing proofs and constructions. I’ve written about this extensively (see the above link, here, and here). Geometry teachers quickly learn that, with extensive, patient, instruction over two-thirds of their classes will still be completely incapable of managing a three step proof. Easy call: punt on proofs, which are hard to test with multiple choice questions. Skip or skate over constructions. Minimize logic, ignore most three dimensional figures (save surface area and volume formulas for rectangular prisms and maybe cylinders). Focus on the fundamentals: angle and polygon facts (used in combination with algebra), application of pythagorean theorem, special rights, right triangle trig, angle relationships, parallel lines, coordinate geometry. And algebra, because the train they’re on stops next at algebra II.

Lowering the course requirements is not only a rational act, but a sound curriculum decision: educate the kids in what they need to know in order to succeed pass survive have some chance of going through the motions in their next math class.

But according to everyone who has never worked with kids outside that 30%, these geometry teachers are lazy, poorly educated yutzes who don’t really understand geometry because they didn’t major in math or are in the bottom third of college graduates. Or, if they’re being charitable—and remember, Common Core folks are in sell mode, so charity it is—geometry teachers are just dealing with the results of low expectations and math illiterate elementary school teachers.

And so, the Common Core strategy: push half of geometry down to middle school.

Here’s what the Common Core declares: seventh graders will learn complementary and supplementary angles and area facts, and eighth graders will cover transversals, congruence, and similarity.

But wait. Didn’t Common Core standards already shove half of algebra down to middle school? Aren’t these students already learning about isolating variables, systems of equations, power laws, and proportions and ratios? Why yes, they are.

So by virtue of stuffing half of algebra and geometry content into middle school, high school geometry, as conceived by Common Core, is a stripped-down chassis of higher-order conceptual essentials: proofs, construction, modeling, measurement (3 dimensions only, of course), congruence and similarity, and right triangles.

Teachers won’t be able to teach to the lowest common denominator of the standards, not least because their students will now know the meaning of the lowest common denominator, thanks to Common Core’s early introduction of this important concept, but more importantly because the students will already know the basic facts of geometry, thanks to middle school. The geometry teachers will have no choice but to teach constructions, proofs, logic, and all the higher-order skills using those facts, the part of geometry that kids will need, intellectually, in order to be ready for college.

Don’t you see the beauty of this approach? ask the Common Core advocates. Right now, we try to cover all the geometry facts in a year. This way, we’re covering it in three years. Deeper understanding is the key!

High school math teachers treat Common Core much like people who ignored Obamacare until their policy got cancelled. We don’t much care about standards normally: math is math. When the teachers who work with the lower half of the ability spectrum really understand that the new, dramatically reduced algebra and geometry standards are based on the premise that kids will cover a good half of the math now supposedly covered in high school in middle school, that simply by the act of moving this material to middle school, the kids will understand this material deeply and thoroughly, allowing them, the high school teachers, to explore more important topics, they will go out and get drunk. I did that last year when I realized that my state actually was going to spend billions on these tests. I was so sure we’d blink at the money. But no, we’re all in.

Because remember, the low proficiency levels we currently have are not only based on less demanding standards, but they don’t include the kids who don’t get to second year algebra by their junior year. That is, of the juniors taking Algebra II or higher, on a much harder test, we can anticipate horribly low proficiency rates. But what about the kids who didn’t get that far?

In California (I’ll miss their reports), about 216,000 sophomores and juniors were taking either algebra I or geometry in 2012-2013. California doesn’t test its seniors, but to figure out how many seniors weren’t on track, we can approximate by checking 2011-12 scores, and see that about 128,000 juniors were taking either algebra I or geometry, which means they would not have been on track to take an Algebra II test as juniors. That is, in this era of low standards, the standards that Common Core will make even more rigorous, California alone has half a million students right now who wouldn’t have covered all the material by their junior year. So in addition to the many students who are at least on paper on track to take a test that’s going to be far too difficult for–at a conservative guess–half of them, we’ve got the many students who aren’t even able to get to that level of math. (Consider that each state will have to spend money testing juniors who aren’t taking algebra II, who we already know won’t be able to score proficient. Whoo and hoo.)

Is it Common Core supporter’s position that these students who aren’t in algebra II by junior year are by definition not ready for college or career? In addition to the other half million (416,000 or so) California students who are technically on track for Common Core but scored below basic or far below basic on their current tests? We don’t currently tell students who aren’t on track to take algebra II as juniors that they aren’t ready for college. I mean, they aren’t. No question. But we don’t tell them.

According to Arne Duncan, that’s a big problem that Common Core will fix:

We are no longer lying to kids about whether they are ready. Finally, we are telling them the truth, telling their parents the truth, and telling their future employers the truth. Finally, we are holding ourselves accountable to giving our children a true college and career-ready education.

If all we needed to do was tell them, we could do that now. No need for new standards and expensive tests. We could just say to any kid who can’t score 500 on the SAT math section or 23 on the ACT: Hey, sorry. You aren’t ready for college. Probably won’t ever be. Time to go get a job.

If we don’t have the gumption to do that now, what about Common Core will give us the necessary stones? Can I remind everyone again that these kids will be disproportionately black and Hispanic?

I can tell you one thing that Common Core math was designed to do—push us all towards integrated math. It’s very clear that the standards were developed for integrated math, and only the huge pushback forced Common Core standards to provide a traditional curriculum–which is in the appendix. The standards themselves are written in the integrated approach.

So one way to avoid having to acknowledge a group of kids who are by definition not ready for career and college would be to require schools to teach integrated math, as North Carolina has done. That way, we could mask it—just make sure all students are in something called Integrated Math 3 or 4 by junior year. If so, there’s a big problem with that strategy: American math teachers and parents both despise integrated math. I know of at least one school district (not mine) where math coaches spent an entire summer of professional development trying to convince the teachers to adopt an integrated curriculum. The teachers refused and the district reluctantly backed down. Few people have mentioned how similar the CC standards are to the integrated curriculum that Americans have consistently refused. But I do wonder if that was the appeal of an integrated curriculum in the Common Core push—it wouldn’t increase proficiency, but would make it less obvious to everyone how many students aren’t ready. (Of course, that would be lying. Hmm.)

At around this point, Common Core supporters would argue that of course it’s more than just not lying to the kids! It’s the standards themselves! They’re better! Than the lower ones! That more than half our kids are failing!

And we’ll only have to wait eight years to see the results!!!

Eight years?

Yeah, didn’t anyone mention this? That’s when the first year of third graders will become juniors, the first year in which Common Core magic will have run its full reign, and then we’ll see how great these higher standards really are! These problems—they just won’t be problems any more. These are problems caused by our lower standards.

Right.

Or: As we start to get nearer to that eight year mark, we’ll notice that the predictions of full bore Common Core proficiency isn’t signaling. With any luck, elementary school test scores will increase. But as we get nearer and nearer to high school, we’ll see the dreaded fadeout. Faced with results that declare a huge majority of our black and Hispanic students and a solid chunk of white and Asian students are unready for career and college, what will we do?

Naw. That’s eight years out! By that time, reformers will need a next New Thing to keep their donors excited, and politicians will have figured out the racial disproportionality of the whole college and career ready thing. We barely lasted ten years with No Child Left Behind, before we got waivers and the next New Thing. So what New New Thing will everyone be talking about five to six years out, what fingers will they be pointing, in which direction, to explain this failure? I don’t know. But it’s a good bet we’ll get another waiver.

Is it at all possible that the National Governors Association thought up the Common Core as a diversion, an escape route from the NCLB 100% proficiency trap? It’s not like Congress was ever going to get in gear.

But it’s an awfully expensive trap door, if so. Much cheaper to just devise some sort of Truth In Education Act that mandates accurate notification of college readiness, and avoid spending billions on tests and new materials.

Notice how none of this is a public conversation. At the public debate level, the only math-based Common Core opposition argues that the math standards are too easy.

At which point, I suddenly realize I need more beer.


Two Math Teachers Talk

Hand to god, I will finish my post about the reform math fuss I twittered in mid-week, but I am blocked and trying to chop back what I discuss and I want to talk about something fun.

So I will discuss Dale, a fellow math teacher who was a colleague at my last job. Dale is half my age and three days younger than my son. Yes. I have coworkers my son’s age. Shoot me now.

He and I are very different, in that he is an incredibly hot commodity as a math teacher, whose principal would offer him hookers if he’d agree to stay, and gets the AP classes because he’s a real mathematician who majored in math and everything. He turns down the hookers because he’s highly committed to his girlfriend, who is an actual working engineer who uses math every day. I am not a hot commodity, not offered hookers, and not a real mathematician. I also don’t have a girlfriend who is an actual working engineer using math every day, but there’s a lot of qualifiers in that last independent clause so don’t jump to too many conclusions.

He and I are similar in that we both were instantly comfortable with teaching and the broad requirements of working with tough low income kids who don’t want to be in school, and extremely realistic about cognitive ability. We also don’t judge our students for not liking math, or get all moral about kids these days. (Of course, he is a kid).

We are also similar in that we like beer and burgers (he has a lamentable fondness for hops, but no one’s perfect), and still meet once or twice a month at an appropriate locale to talk math. I tell him my new curricular ideas, which he is kind enough to admire although his approach is far more traditional, and ask him math questions, particularly when I was teaching precalc; he tells me that most of the department wants him to be head, despite his youth and relative inexperience. We also talk policy in general. It’s fun.

“I have some news for you,” I told him, “but you will laugh, so you should put down your beer.”

He obligingly takes a pull on his schooner of Lagunitas IPA and sets it down.

“A new study came out,” I said, “and apparently, many high school algebra and geometry courses have titles that don’t actually match the course delivered.”

Dale, who clearly thought I was going in a different direction, did a double take. “Wait. What?”

“The word used was ‘rigor’. Like, some Algebra I courses don’t actually cover algebra I. Same with geometry.”

He looks at me. Takes another pull. “Like, not all algebra teachers actually cover the work formula?”

“Like, not all algebra teachers cover integer operations and fractions for two months. Like not all algebra teachers spend two weeks explaining that 2-5 is not the same as 5-2.”

“Uh huh. Um. They did a study on this?”

“They did.”

“They could have just asked me.”

“They can’t do that. They think math teachers are morons. But there’s more.”

“Of course there is.”

“Apparently, the more blacks and Hispanics and/or low income students are in a class, the less likely the course’s rigor will match the course description.”

He sighs. “I need more beer. Ulysses!” (that’s actually the bartender’s name.) “I’m assuming that nowhere in this study did they even mention the possibility that the students didn’t know the material, that the course content depended on incoming student ability?”

“Well, not in that study. But you know what happens when we point that out.”

“Oh, yeah. ‘It’s all that crap they teach in elementary schools!’ Like that teacher in that meeting you all had the year before I got here. ‘Integer operations and fractions! Damn. Why didn’t I think of that?‘”

“Yes. Actually, the researchers blamed the textbooks, which was a pleasant change from the platitude–and-money-rich reformers who argue our standards are too low.”

“Did anyone ever tell them if it were that simple, whether textbook or teacher, then we could cover the missing material in a few weeks and it’d all be over? Wait, don’t tell me. Of course they told them. That’s the whole premise behind….”

Algebra Support!” we chorused.

“But then there’s that hapless AP calculus teacher stuck teaching algebra support. He spent, what, a month on subtraction?”

“And the happy news was that at the end of the semester, the freshmen went from getting 40% right on a sixth grade math test to 55%.”

“The bad news being at the end of the year, they forgot it all. Net improvement, what–2 points?”

“Hell, I spend the entire Algebra II course teaching mostly Algebra I, and while they learn a lot, at the end of the course they’re still shaky on graphing lines and binomial multiplication. And I don’t even bother trying to teach negative numbers, although I do try to show them why the inequality sign flips in inequalities.”

“But it’s our fault, right?”

“Of course. But that’s not the best part.”

“There’s a best part?”

“If you like black comedy.”

“The Bill Cosby sort, or the Richard Pryor catching himself on fire sort?”

“Someone doesn’t know his literary genres.”

“Hey, we can’t all be English majors. What’s the best part?”

“The best part is that Common Core is supposed to fix all this.”

“Common Core? How?”

“By telling us teachers what we’re supposed to teach.”

I’d forgotten to warn Dale, who was mid-gulp. “WHAT???”

I handed him a napkin. “You’ve got beer coming out your nose. Yes. Checker Finn and Mike Petrilli always use this example of the shifty, devious schools that, when faced with a 3-year math requirement, just spread two years of instruction over three!”

“Wow. That’s painful.”

“Well, they don’t much care for unions, either, so I guess they think that when faced with a mandate that’s essentially a jobs program for math teachers, we teachers use it as an opportunity to kick back. But that’s when they are feeling uncharitable. Sometimes, when they’re trying to puff teachers up, they worry that teachers will need professional development in order to know the new material.”

“How to teach it?”

“No. The new material.”

“They think we don’t know the new material?

“Remember, they think math teachers are morons. On the plus side, they think we’re the smartest of teachers. (Which we are, but that’s another subject.) There’s still other folks who complain because ed schools don’t teach teachers the material they’re supposed to be teaching.”

“But we know that material. That’s what credential tests are for. You can’t even get into a program without passing the credential test.”

“Do not get me started.”

“So when the test scores tank, they’ll say it’s because teachers don’t know the material?”

“Well, they’ve got the backup teachers don’t have the proper material to teach the standards, in case someone points out the logical flaws in the ‘teacher don’t know the material’ argument.”

“Sure. If it ain’t in the textbook, we don’t know it’s supposed to be taught!”

“Don’t depress me. Yes, either we don’t know what’s supposed to be taught or we don’t know how to teach it without textbooks telling us to.”

Dale starts to laugh in serious. “I’m sorry, Governor. I would have taught vectors in geometry, but since it wasn’t on the standards, I taught another week of the midpoint formula.”

“I’m sorry, parents, I would have dropped linear equations entirely from my algebra two class, but I didn’t know they were supposed to learn it in algebra one!”

“Damn. A whole three weeks spent teaching fraction operations in algebra when it’s fifth grade math. I could have spent that time showing them how to find a quadratic equation from points!”

“I didn’t know proofs were a geometry standard. Why didn’t someone tell me? Here I had so much free time I taught my kids multi-step equations because my only other option was showing an Adam Sandler movie!”

“Stop, you’re killing me.”

“No, there’s too many more. Who the hell went and added conics to the standards and why wasn’t I informed? Here I spent all this time teaching my algebra II kids that a system of equations is solved by finding the points of intersection? Apparently, my kids didn’t bother to tell me that they’d mastered that material in algebra I.”

“I can’t believe it! Four weeks killed teaching kids the difference between a positive and a negative slope! Little bastards could have told me they knew it but no, they just let me explain it again. No wonder they acted out–they were bored!”

My turn to snarf my beer.

“Jesus, Ed, I’ve wondered why we’re pulling this Common Core crap, but not in my deepest, most cynical moments did I think it because they thought we teachers just might not know what to teach the kids.”

“That’s not the most depressing, cynical thought. Really cynical is that everyone knows it won’t work but the feds need to push the can—the acknowledgement that achievement gaps are largely cognitive—down the road a few more years, and everyone else sees this as a way to scam government dollars.”

“New texbooks! New PD. A pretense that technology can help!”

“Exactly. I’d think maybe it was another effort to blame unions, but no.”

“Yeah, Republicans mostly oppose the standards.”

“Well, except the ‘far-seeing Republicans’ who just want what’s best for the country. Who also are in favor of ‘immigration reform’.”

“Jeb Bush.”

“Bingo. You’ll be happy to know that libertarians hate Common Core.”

“Rock on, my people!”

“Yeah, but they want also want open borders and privatized education.”

“Eh, nobody’s perfect.”

“But all that depressing cynicism is no fun, so let me just say that I would have taught sigma notation except I thought that letter was epsilon!”

“Hey, wait. You do get sigma and epsilon confused!”

“No, I don’t, or I wouldn’t call the pointy E stuff sigma notation, dammit. I just see either E shape out of context and think epsilon. Why the hell did Greeks have two Es, and why couldn’t they give them names that start with E? Besides, the only two greek letters I have to deal with are pi and theta, and really, in right triangle trig there’s no difference between theta and x.”

“Well, you’re going to have to stop making that mistake because thanks to Common Core, you’ll know that you’re supposed to teach sequences and series.”

“Damn. So I won’t be able to teach them binomial multiplication and factoring and let them kick back and mock me with their knowledge, which they have because they learned it all in algebra I.”

“Here’s to Common Core and math research. Without them, America wouldn’t be able to kid itself.”

We clinked glasses just as Maya, Dale’s girlfriend walked in, a woman who actually uses centroids, orthocenters, and piece-wise equations in her daily employment. The rest of the evening was spent discussing my search for more real-life models of quadratics that don’t involve knowing the quadratic formula first. She offered road construction and fruit ripening, which are very promising, but I still need something organic (haha), if possible, to derive the base equation. So far area and perimeter problems are my best bet, which gives me a good chance to review formulas, because until Common Core comes out I won’t know that they learned this in geometry. I wondered if velocity problems could be used to derive it. Dale warned me that it involved derivations. Maya was confused by my describing velocity problems as “-16 problems”, since gravity is either gravity is either 32 ft/sec/sec or 9.8 m/s/s. Dale interpreted. I’m like Jeez, there are people who know what gravity is off the top of their heads? This is why I don’t teach science. (edit: I KNEW I should have checked the numbers. I don’t do physics or real math, dammit. Fixed. )

But all that’s for another, happier, post.


Algebra 1 Growth in Geometry and Algebra II, Spring 2013

This is part of an ongoing series on my Algebra II and Geometry classes. By definition, students in these classes should have some level of competence in Algebra I. I’ve been tracking their progress on an algebra I pre-assessment test. The test assesses student ability to evaluate and substitute, use PEMDAS, solve simple equations, operate with negative integers, combine like terms. It tiptoes into first semester algebra—linear equations, simple systems, basic quadratic factoring—but the bulk of the 50 questions involve pre-algebra. While I used the test at my last school, I only thought of tracking student progress this year. My school is on a full-block schedule, which means we teach a year’s content in a semester, then repeat the whole cycle with another group of students. A usual teacher schedule is three daily 90-minute classes, with a fourth period prep. I taught one algebra II and one geometry class first semester (the third class prepared low ability students for a math graduation test), their results are here.

So in round two, I taught two Algebra 2 courses and one Geometry 10-12 (as well as a precalc class not part of this analysis). My first geometry class was freshmen only. In my last school, only freshmen who scored advanced or proficient on their 8th grade algebra test were put into geometry, while the rest take another year of algebra. In this school, all a kid has to do is pass algebra to be put into geometry, but we offer both honors and regular geometry. So my first semester class, Geometry 9, was filled with well-behaved kids with extremely poor algebra skills, as well as a quarter or so kids who had stronger skills but weren’t interested in taking honors.

I was originally expecting my Geometry 10-12 class to be extremely low ability and so wasn’t surprised to see they had a lower average incoming score. However, the class contained 6 kids who had taken Honors Geometry as freshmen—and failed. Why? They didn’t do their homework. “Plus, proofs. Hated proofs. Boring,” said one. These kids knew the entire geometry fact base, whether or not they grokked proofs, which they will never use again. I can’t figure out how to look up their state test scores yet, but I’m betting they got basic or higher in geometry last year. But because they were put into Honors, they have to take geometry twice. Couldn’t they have been given a C in regular geometry and moved on?

But I digress. Remember that I focus on number wrong, not number right, so a decrease is good.

Alg2GeomAlg1Progress

Again, I offer up as evidence that my students may or may not have learned geometry and second year algebra, but they know a whole lot more basic algebra than they did when they entered my class. Fortunately, my test scores weren’t obliterated this semester, so I have individual student progress to offer.

I wasn’t sure the best way to do this, so I did a scatter plot with data labels to easily show student before/after scores. The data labels aren’t reliably above or below the point, but you shouldn’t have to guess which label belongs to which point.

So in case you’re like me and have a horrible time reading these graphs, scores far over to the right on the x-axis are those who did poorly the first time. Scores low on the y-axis are those who did well the second time. So high right corner are the weak students at both beginning and end. The low left corner are the strong students who did well on both.

Geometry first. Thirty one students took both tests.

Spring2013GeomIndImprovement

Four students saw no improvement, another four actually got more wrong, although just 1 or 2 more. Another 3 students saw just one point improvement. But notice that through the middle range, almost all the students saw enormous improvement: twelve students, over a third, got from five to sixteen more correct answers, that is, improved from 10% to over 30%.

Now Algebra 2. Forty eight students took both tests; I had more testers at the end than the beginning; about ten students started a few days late.

Spring2013A2IndImprovement

Seven got exactly the same score both times, but only three declined (one of them a surprising 5 points—she was a good student. Must not have been feeling well). Eighteen (also a third) saw improvements of 5 to 16 points.

The average improvement was larger for the Algebra 2 classes than the Geometry classes, but not by much. Odd, considering that I’m actually teaching algebra, directly covering some of the topics in the test. In another sense, not so surprising, given that I am actually tasked to teach an entirely different topic in both cases. I ain’t teaching to this test. Still, I am puzzled that my algebra II students consistently show similar progress to my geometry students, even though they are soaked in the subject and my geometry students aren’t (although they are taught far more algebra than is usual for a geometry class).

I have two possible answers. Algebra 2 is insanely complex compared to geometry, particularly given I teach a very slimmed-down version of geometry. The kids have more to keep track of. This may lead to greater confusion and difficulty retaining what they’ve learned.

The other possibility is one I am reminded of by a beer-drinking buddy, a serious mathematician who is also teaches math: namely, that I’m a kickass geometry teacher. He bases this assertion on a few short observations of my classes and extensive discussions, fueled by many tankards of ale, of my methods and conceptual approaches (eg: Real-life coordinate Geometry, Geometry: Starting Off, Teaching Geometry,Teaching Congruence or Are You Happy, Professor Wu?, Kicking Off Triangles, Teaching Trig).

This possibility is a tad painful to contemplate. Fully half the classes I’ve taught in my four years of teaching—twelve out of twenty four—have been some form of Algebra, either actual Algebra I or Algebra I pretending to be Algebra II. I spend hours thinking about teaching algebra, about making it more understandable, and I believe I’ve had some success (see my various posts on modeling).

Six of those 24 classes have been geometry. Now, I spend time thinking about geometry, too, but not nearly as much, and here’s the terrible truth: when I come up with a new method to teach geometry, whether it be an explanation or a model, it works for a whole lot longer than my methods in algebra.

For example, I have used all the old standbys for identifying slope direction, as well as devising a few of my own, and the kids are STILL doing the mental equivalent of tossing a coin to determine if it’s positive or negative. But when I teach my kids how to find the opposite and adjacent legs of an angle (see “teaching Trig” above), the kids are still remembering it months later.

It is to weep.

I comfort myself with a few thoughts. First, it’s kind of cool being a kickass geometry teacher, if that is my fate. It’s a fun class that I can sculpt to my own design, unlike algebra, which has a billion moving parts everyone needs again.

Second, my algebra II kids say without exception that they understand more algebra than they ever did in the past, that they are willing to try when before they just gave up. Even the top kids who should be in a different class tell me they’ve learned more concepts than before, when they tended to just plug and play. My algebra 2 kids are often taking math placement tests as they go off to college, and I track their results. Few of them are ending up in more than one class out of the hunt, which would be my goal for them, and the best are placing out of remediation altogether. So I am doing something right.

And suddenly, I am reminded of my year teaching all algebra, all the time, and the results. My results look mediocre, yet the school has a stunningly successful year based on algebra growth in Hispanic and ELL students—and I taught the most algebra students and the most of those particular categories.

Maybe what I get is what growth looks like for the bottom 75% of the ability/incentive curve.

Eh. I’ll keep mulling that one. And, as always, spend countless hours trying to think up conceptual and procedural explanations that sticks.

I almost titled this post “Why Merit Pay and Value Added Assessment Won’t Work, Part IA” because if you are paying attention, that conclusion is obvious. But after starting a rant, I decided to leave it for another post.

Also glaringly on display to anyone not ignorant, willfully obtuse, or deliberately lying: Common Core standards are irrelevant. I’d be cynically neutral on them because hell, I’m not going to change what I do, except the tests will cost a fortune, so go forth ye Tea Partiers, ye anti-test progressives, and kill them standards daid.


On Graduation Rates and “Standards”

Stephanie Simon has a piece out on the increasing graduation rate (while I’m at it, mad props to Simon for the charter school piece, which probably did a lot to alert the general audience to charter selections), and various tweets are hailing the good news but—and this is the funny part—expressing concern that this increase rate might be due to schools lowering standards. Checker Finn has also written disapprovingly of credit recovery.

hahahahahaha. This is me, laughing.

Imagine you have forty 18 year olds, who all read and calculate at the 6th grade level, and another group of forty who all read and calculate at the 10th grade level. They are all high school seniors in a state that requires graduation competency tests. Of this overall collection of eighty, the following distribution is entirely unexceptional (and of course, not the only one possible):

  1. Fifteen screwed around from the moment they entered high school, have a GPA in the tenths, and are currently in alternative high school filling out worksheets. No reason to worry about high school graduation tests, though, because they passed them first time out.
  2. Fifteen are, on paper, identical to the previous group, except they haven’t passed any of their graduation tests and so some of their high school time is spent in test prep instead of worksheet completion.
  3. Fifteen are far behind because they went to a charter school that prided itself on making kids repeat grades, and after two years of failure they went back to public school. They’ve passed the high school graduation tests, and have been doing well since they left the charter, GPAs of 2.0 or so. But they’re far behind, so are taking two hours every day to do online credit recovery.
  4. Fifteen are at a charter school, where they have a 4.0 GPA with a bunch of AP courses on their transcripts, (thanks, Jay Mathews and your horrorshow of a Challenge Index) but haven’t passed the high school graduation tests.
  5. Ten recovered from an early bad start, have a solid 2.5 GPA, but haven’t passed their state graduation tests. Half of them have IEPs and official learning disabilities (which means, of course, they aren’t in charters), and so they’ll just waive the requirement. The others will keep plugging away.
  6. Ten have a solid 2.5 GPA after an early bad start and have passed their state graduation tests.

(Note: In case it’s not clear, the kids who can pass the state grad tests are the ones with tenth grade abilities, the ones who can’t are the ones with sixth grade abilities).

Any diverse high school district in the country, surveying its population in comprehensive, alternatives, online campuses, and charters, could assemble those eighty kids without breaking a sweat.

On the lower half of the ability spectrum, grades and credits are utterly pointless differentiators. Once you accept that we graduate thousands of kids who can’t read, write, or add, there’s no reason to cavil at the method we use to boot them out of the schoolhouse.

No, don’t yammer at me about persistence or compliance or god spare me “grit” of illiterates plugging away at school and therefore being more deserving of the diploma than the lazy but somewhat smarter kid. The concern about the increase was not about persistence or compliance or grit, but academic ability.

And so, rest easy, people. We are already graduating illiterates. The increased graduation rate is not achieved by teaching more kids more effectively, nor is it achieved by shovelling through the bottom feeders and thus devaluing high school diplomas. We are simply taking kids, whether near-illiterate or low but functional ability, who fell off the path that our other near-illiterate or low but functional ability kids stayed on, and putting them on a different conveyor belt.

How? As Simon’s article makes clear, by spending lots and lots of money:

* Launching new schools designed to train kids for booming career fields, so they can see a direct connection between math class and future earnings

* Offering flexible academic schedules and well-supervised online courses so students with jobs or babies can earn credits as their time permits

* Hiring counselors to review every student’s transcript, identify missing credits and get as many as possible back on track

* Improving reading instruction and requiring kids who struggle with comprehension to give up some electives for intensive tutoring

* Sending emissaries door-to-door to hound chronic truants into returning to class

Notice that only one of the techniques used actually involved teaching the kids more—not that I’m in favor of forcing kids to give up electives for intensive tutoring (I still have nightmares). But most of the money spent involved forcing or coaxing the kids back to school—and while the kids are mostly low ability, they are no less and often considerably more intellectually able than kids who just happened to jump through the right hoops.

How does this happen, you ask? As I’ve said many times: grades are a fraud.

Or you could put it another way: the increased graduation rate is a triumph of administrators over teachers. Teachers, except those in majority minority urban schools, are flunking kids with little regard to ability and a whole bunch of regard to compliance, with no regard to administrative or societal cost. Administrators are spending money to work around teacher grades.

In this context, bleats about academic standards do seem a bit….well, silly, don’t they?

And now someone is going to say, “You’re absolutely right. We should be failing kids who don’t or can’t do the work, put teeth into the Fs. That’s the only way to raise academic standards.”

Sorry, that fool’s wrong, too. Higher standards are impossible. No, really. Common Core advocates, much like Mark Wahlberg at the end of Boogie Nights, are parading their favorite toy in front of a mirror in the desperate hope they’ll convince themselves, if no one else. (What, too much? Yeah, it’s late. I’m feeling bleak.) I very much doubt Common Core will ever be implemented (no test, no curriculum, baby), but if it is, nothing will change.

People assume that kids in the bottom half of the ability barrel are there because they suffered a deficit in environment, in parental attention and expectations, in teacher quality. Would that this were so.

Given all the money we’re spending on truancy officers, online credit recovery, counsellors to spot missing transcripts just to push kids through to a diploma, we might just want to consider teaching low ability kids less at a slower pace and stop pretending that they have a “deficit” that can be addressed by college level work and high expectations. We could create a hell of a curriculum for high school kids using nothing more than 8th grade math and vocabulary.

But we won’t do that for the same reason we won’t track, and for the same reason that adminstrators are spending a fortune coaxing kids back to school: namely, the racial distribution would make everyone wince.