Monthly Archives: August 2013

Kashawn Campbell

Predictably, many regard the Kashawn Campbell story as proof of low school standards. But I would argue that the underlying problem is grade fraud, which is a different issue.

I’ve been writing about grade fraud for college admission for a while now. Wait, you say, that’s a link to a KIPP piece. Well, yeah. Charters are among the worst offenders in grade fraud, which is the tacit admissions directive enabled by Top Ten % or eligibility in the local context plans: the kids with the best grades in their schools are guaranteed entrance to the public universities.

The policy rewards compliance more than ability, as I’ve also written; I routinely see bright kids with low GPAs in every type of school. If we are going to lower standards to bring in underrepresented minorities, far better to find the brightest ones—which aren’t necessary the ones with the best grades. And when I complain about this, some folks say some version of “Well, what’s wrong with rewarding hard work?”

Well, what’s wrong with it, eventually, is Kashawn Campbell. The people who value grades like to believe that the difference between an A and a B is nothing more than effort, when in fact, teachers can give whatever grades they like, with only a few restrictions that limit how low we can drop a grade. None limit our ability to give an A.

So the people blame crappy schools, because of course the only thing that prevents Kashawn from learning is a school that wanted the easy way out. And if we’d have Common Core, then we would have known Kashawn didn’t know anything. This line of thinking ignores the fact that California state tests almost certainly showed that Kashawn didn’t know anything—assuming, that is, he took the standard tests (more on that later). And then you have the affirmative action complainers—this group, I generally agree with but I am coming to the point of finding college admissions so revoltingly corrupt that affirmative action for blacks and Hispanics seems almost benign compared to the contortions universities go through to bring them in under alternative means.

But that’s not what interested me.

No, I’m wondering why the reporter, Kurt Streeter, who is African American, hinted at so much. Some details are so instructive that I can’t figure out why he didn’t go further or, more typically, leave them out.

What details? Well, the big one I wonder about: is Kashawn brain damaged? (Or, as a National Review commenter said in summarizing this essay, perhaps he is not neurotypical?)

“When I delivered him, I thought he was dead,” said his mother, Lillie, recalling the umbilical cord tight around his neck. “He was still as stone but eventually he came to. Proved he was a survivor. Ever since, I’ve called him my miracle child.”

Umbilical cord around the neck is pretty common and doesn’t usually lead to brain damage. The “still as stone” bit makes me wonder, though, if he was oxygen starved during birth.

He filled his dorm room with Cal posters, and wore clothes emblazoned with the school’s name. Each morning the gawky, bone-thin teen energetically reminded his dorm mates to “have a Caltastic day!”

“It was clear that Kashawn was someone who didn’t know about, or maybe care about, social norms,” said one of his friends. “A lot of people would laugh at first. They didn’t understand how someone could be that enthusiastic.”

and

They sat together in the front row. One teacher noticed that Kashawn subconsciously seemed to mime his roommate: casually cocking his head and leaning back slightly as he pondered questions, just like Spencer.

Kashawn reveled in the class in a way he hadn’t since high school. He would often be the first one to speak up in discussions, even though his points weren’t always the most sophisticated, said Gabrielle Williams, a doctoral student who helped teach the class.

and

Many of them jaywalked. Not Kashawn. Just as he’d been taught, he only used crosswalks, only stepped onto the street when the coast was clear or a light flashed green.

and

Sometimes in the dorm room, Spencer would look over at Kashawn and see him sitting in front of his computer, body frozen and face expressionless, JVC headphones wrapped over his ears, but no music playing.

He’s weird, in other words, and completely unconscious of it. Nothing wrong with that. Except he was prom king, and most likely to succeed.

His teachers and his classmates at Jefferson High all rooted for the slight and hopeful African American teenager. He was named the prom king, the most likely to succeed, the senior class salutatorian.

That strike you as a tad odd? Since when do high school kids name socially awkward kids prom king? Huh. Something comes to mind. But take a look at this first:

Part of the pressure came from race. ….When Kashawn arrived, 3% of Berkeley undergraduates were African American.

Kashawn’s high school is 91% Hispanic. So Kashawn went from being a 9% minority to a 3% minority. Not entirely sure he’d notice that difference.

A black kid with a goofy affect, limited social skills, geeky, awkward, and attending an all Hispanic school is declared prom king and most likely to succeed?

You know when a slight, geeky, weird guy with awkward social skills is voted most likely to succeed and prom king? When it’s an act of charity, an act that makes a group of tough kids feel good about themselves—that is, when the kid in question is “special”. You see it in all those feel-good articles about a special day student who becomes kind of a mascot for the school, the one everyone loves, who brings all the feuding elements together. Naturally, there might be another explanation. But anyone familiar with high school dynamics has to wonder about the specifics of Kashawn’s popularity.

Which is what I’m wondering, because even within the context of a low income, low ability school, Kashawn’s writing problems and his failure to improve seem significant.

And then, of course, there’s the friend, Spencer:

Spencer was raised in a tough L.A. neighborhood by a single mom who had sometimes worked two jobs to pay the rent. Spencer had gone to struggling public schools, receiving straight A’s at Inglewood High. Spencer didn’t curse, didn’t party, didn’t try to act tough and was shy around girls.

To Spencer, Berkeley was the first place he could feel fully comfortable being intellectual and black, the first place he could openly admit he liked folk music and punk rock.

He was cruising through Cal, finishing the first semester with a 3.8 GPA despite a raft of hard classes. “I can easily see him being a professor one day,” said his political theory instructor, noting that Spencer was one of the sharpest students in a lecture packed with nearly 200 undergraduates.

Why not write an article about Spencer? Wouldn’t it be nice to see a story about an inner city kid who was prepared for college? You could even include his SAT scores–hey, speaking of metrics that are totally absent.

Notice that Spencer and Kashawn take African American studies together. Notice that Kashawn got an A on the essay and a B on the midterm–and an overall A in the class, and that he “copied” Spencer’s every move. And notice that his writing professor basically accused him of cheating:

After reviewing his writing, though, it was clear to her that he had received far too much help from someone else.

It’s never mentioned again, this little cheating episode.

Questions remain:

  1. How did Kashawn pass the Introductory Science class with a D? No information about that class or the teacher is included.
  2. Why did the writing instructor give him an Incomplete twice instead of an F?
  3. What did Kashawn’s African American studies essay look like? Was it a deserved A, or a pity A? If the former, why could Kashawn only write well in this class? Why didn’t Streeter ask to see the A essay?
  4. Why doesn’t Streeter mention what classes Kashawn took in high school? Kashawn was a junior in 2011, which would be the last year he took the California end of state tests. Only 22 juniors at Jefferson High were black that year. Nine of them took geometry, nine took algebra II, two of them took Summative Math (for precalc and beyond). Which of these was Kashawn?
  5. Streeter clearly reviewed the school’s test scores. What were Kashawn’s scores?
  6. Did Streeter know that Kashawn’s school was 91% Hispanic? If so, why imply that Kashawn felt isolated in a non-black environment?

See, Kashawn’s story isn’t unusual—well, if he’s suffering from brain damage or is actually mentally retarded, then it’s a bit unusual. Otherwise, thousands of African American and Hispanic kids enter college every year, woefully unprepared to even begin to succeed. And, as the story clearly illustrates, the ones that work terribly hard or show the slightest bit of effort are often given passing grades out of some combination of pity and paternalism.

I am puzzled, however, that Streeter has left clues. Why mention Kashawn’s unusual affect, his nomination as prom king, his faithful copying of Spencer, to make it fairly clear to a closer reader that there’s something really off about the kid? Why be so uncompromising on the point of Kashawn’s incoherent writing and his failure to improve in any way, unless it’s for the same reason he includes only one quote from his mother which suggests his birth was unusual?

If Streeter wanted to indict the University of California admissions system, he has the stuff: an illiterate, possibly retarded, student is accepted via a standard specifically created to bypass the affirmative action ban. But he could have been more explicit: included SAT scores, state test scores, courses taken, specific examples of Kashawn’s writing.

If he wanted to indict Kashawn’s high school, which is how most readers seem to interpret the story, he could have gone even further and shown exactly how deep the fraud went. What math had Kashawn advanced to? What were his state scores? What books had he read in English class? How badly had his school fooled him? But all of that data is missing in action.

Of course, he might not have included this data because it would have given far too much away.

Or perhaps Streeter just wanted to illustrate the tremendous internal pressures experienced by a clearly wonderful young man who has no ability to complete college level work. Leave aside blame. Leave aside larger policy considerations. Just tell his story. Okay. Then why just hint at the special ed and the cheating?

Reporters often tell me they simply seek to tell the story, that they don’t think of policy issues, which strikes me as just a tad disingenuous. I have no idea what Streeter’s response would be but surely not that. How can any reporter tell a story about an unprepared African American student at the top public university in the country without thinking of the larger social issues he represents? He can’t. And if he can avoid the larger issues, surely his editor wouldn’t?

Then I read the article comments, and interspersed between the jeremiads about public education and complaints about affirmative action, I see:

Keep up the hard work Kashawn, college is not easy and your story is not an isolated one. There are thousands of college students that struggle like you, remember to stay motivated and keep working hard. If college was easy everyone would go (and graduate).
…..
Keep it going Kashawn! Nothing that is worth it comes easy! Everyone is looking for “that chance.” I don’t think it’s wrong to give him one.

Keshawn – do not let anyone take away your stellar record and GPA from Jefferson or your heartbreaking first semester at CAL. You have heart and you will continue to make it. Good luck.

You can do it, Keshawn! I am a Cal grad who had the advantage of tough private school training. Your story makes me realize how lucky I was. You’ve got my full admiration for your integrity and determination. Don’t ever quit!

…and I realize that for some people, Kashawn’s story represents a beautiful struggle and success. And maybe Streeter is just writing for them.

The rest of us should avoid drawing any policy implications, and just pick up on the hints.

*************************
Updated to add: A few commenters have suggested that Kashawn has Asperger’s or autism. I thought of including this originally, but I’m not an expert, even though I sound like I think I’m one in the comments.

Kashawn doesn’t seem anything like the Asperger’s students I’ve worked with, but then, none of them have been low IQ. I’ve only worked with one diagnosed autistic student, and I do see some similarities.

But if Kashawn was autistic, wouldn’t Streeter mention this? UC Berkeley has a huge organization dedicated to helping students with disabilities, including autism, and extensive support for learning disabilities. Yet there’s no mention of that in the story.

I’m not any sort of expert on autism spectrum disorders. It could be that autism, rather than hypoxia at birth, is at the root of Kashawn’s oddness. However, I still don’t see any reason for withholding information about Kashawn’s high school academic record unless it would reveal that Kashawn’s cognitive abilities were profoundly limited.

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The Reverse Drinking Game

Well, school’s about to start and I’m two thirds of a way through a piece that I probably won’t finish for a while, and I’ve decided I need something longer than Twitter but shorter than the usual me to send out when people are being annoying.

So let’s call this the reverse drinking game post. Every time someone doesn’t mention cognitive ability while discussing student outcomes, go grab a beer.

So for example, Michael Petrilli writes about the problem of proficiency:

Proficiency rates are terrible measures of school effectiveness. As any graduate student will tell you, those rates mostly reflect a school’s demographics.

Grab a beer.

When Checker Finn rebuts Petrilli, saying:

One more point: Mike began his argument with the assumption that many schools have scads of entering pupils who are already far below “proficiency” when they arrive. He had in mind middle and high schools—and there is no doubt that many such schools do indeed face a large remediation challenge with incoming eleven- through fourteen-year-olds who have already been gypped educationally in the early grades.

Crack one open.

When Richard Venning writes:

The inconvenient truth I describe below is that when we benchmark academic growth rates, the best velocity is often not adequate to catch kids up to college and career readiness within a reasonable time.

and

However, far too many schools also have students in poverty making low-growth rates, where they progress more slowly than their advantaged peers and that is not acceptable.

Grab two beers. Three, if you spot: “Among students that score in the bottom performance level in Colorado, the percent making adequate growth is in the single digits. The statewide goal is 100 percent. Schools with top statewide velocity for low-income students are not moving kids to proficiency within three years—and Colorado is not alone.”

When Rick Hess, Rishawn Biddle, Michael Brickman talk about lowered AP scores, the importance of entrance standards vs. the importance of high expectations, go grab a whole sixpack. Or maybe some single malt scotch.

When Jason Bedrick, Michael Petrilli, or Andrew Rotherham sneer at the public schools “failing children”, it’s time to bend an elbow.

When the primary ed school credentialing organization proudly announces that it is raising the bar on “teacher quality”, when everyone goes all atwitter about Jason Richwine‘s work on teacher cognitive ability (before he broke the rules on Hispanic cognitive ability), ask yourself why so many people are willing to discuss the impact of teacher cognitive ability on academic achievement (you mostly have to squint to find any ) but never mention student cognitive ability. But do it before you get a beer, because I find, at least, that I often start banging my head in annoyance and it’s best to do that unarmed.

When people say that income matters more than race to academic achievement, tell them they are lying or misinformed on your way to the fridge.

Tweet or email whenever you spot an opportunity to play.

Hey. Under 500 words! A new record.


My #FF list, or Ed Folks I Read

If you want to know why Mike Petrilli irritates me, look no further than his recent post on top education Twitter feeds. Does Petrilli not know the difference between propagandists advocates, analysts, and hobbyists? What the hell is the point of putting Arne Duncan at the top of the list?

New annoying buzzword: curate. Petrilli should have curated. He’s a major education policy propagandist advocate; what would be interesting is his own personal list of education policy writers and specialists. Not completely out of the question is the possibility that Petrilli picks his twitter feed based on Klout score, so he was giving us his reading list.

I thought I’d show Petrilli what he should have done—assuming he was trying to advise people who actually are looking for education policy writers, as opposed to providing a self-congratulatory fist bump list for the Twitter Titans. And, since many of my readers aren’t solely or even primarily interested in education, I’m writing for a novice audience.

I don’t have a reader. My blogroll is randomly selected to demonstrate range, not totality. I periodically peruse my twitter followers—that is, the ones that I don’t follow—to see what they are up to. If I don’t follow you, it doesn’t mean I don’t read you at all. I go to blogs just as it occurs to me, and I find Twitter, which I’ve used for only a year, to be very helpful in keeping up with education topics. The people on this list have either a blog or a Twitter account, usually both. The names are in no strict order.

Paul Bruno, a middle school science teacher, has his own blog and used to write (still writes? Not sure) at This Week in Education. Bruno is the only blogger/writer who I identify with, whether we agree or not. We need more teachers writing on ed policy from an analytical perspective, rather than advocating for one side or another.

Joanne Jacobs–the best reporter’s education blog out there. Joanne rarely links to one article; she anticipates the objections and finds an effective advocate for the opposition. Everyone should read her.

Stephen Sawchuk, at Teacher Beat, is often stuck writing about topics that should be insanely boring—union conferences, pension reform, teacher preparation standards—and he does a great job making them interesting and understandable. Joanne goes wide, Sawchuk goes deep. He wins extra points for being the only person, other than, say, me, who raises red flags about minority teachers in the current push to “raise teacher quality”. I read him frequently; his stuff often leads me to interesting questions.

While you’re on the site, most of the Ed Week blogs are worth evaluating. While some of them are just advocacy sites, I find Catherine Gewertz’s Curriculum Matters useful, and many of the teacher blogs are worth checking out occasionally.

Tom Loveless–He doesn’t have a blog that I know of (AEI blogposts) and I was only able to include him here because he’s on twitter. But he’s badass. Let me put it this way, and he’s the only one on this list I say this about: if I ever disagreed with him, I’d worry I was wrong. For about 90 seconds. But still.

Larry Cuban‘s blog is excellent and wide-ranging; he never offers easy answers but always interesting questions.

John Fensterwald at Ed Source is a good reporter, particularly for California education news. He’s invaluable on Twitter.

Another valuable twitter resource is USA Today’s Greg Toppo, whose education reporting is also good stuff. No blog. Start one, why don’tcha.

Alexander Russo‘s blog, This Week in Education, is very good, but he, too, plays a major role in my information queue on Twitter, where he’s always got interesting stuff I hadn’t otherwise found.

Andrew Old (pseudonym, I think), who blogs at Teaching Battleground, is a traditionalist advocate, but I follow him because he’s a great source of info on education policy in England (UK? Britain? Great Britain?) and through him I get a lot of insight into what’s going on. I don’t know who that person is in Australia or if there are Scandinavian teachers tweeting in English, but if there are, I would like to know about them. Through Andrew Old, I’ve found bloggers like Harry Webb who I enjoy reading as well.

Mathew DiCarlo is the only guy I read at Shanker Blog. I find his analyses very useful. His resulting policy conclusions, on the rare occasions he mentions them, are often puzzling, since they seem contradicted by his analysis.

The Cato libertarians Jason Bedrick and Neil McCluskey (not much of a fan of the big boss, Andrew Coulson) are both excellent reads. I agree with almost every word of their analyses and then politely skip over their prescriptions. Both have been particularly outstanding on Common Core issues.

As I understand it, Michael Petrilli and Rick Hess don’t work for the same organization, but for some reason they show up on a lot of videos together. For that reason, I suppose, I think of Hess as Wally to Petrilli’s Beave (god, I’m old). I’ve also referred to Petrilli as a “gormless Richie Cunningham” and following his writing for any length of time invariably calls to mind the mutant dogs in Up (“Squirrel!”). And yet, he’s one of the few people on the reform side I consistently read. Go figure.

On his excellent blog, Hess spends so much time criticizing the reform movement that the newcomer might not realize he wants that team to win. He’s mostly wrong about reform, but his criticism of the movement goals is excellent. I thought his article Our Achievement Gap Mania was outstanding, but I haven’t really enjoyed any of his books I’ve read thus far. Where Petrilli looks up Klout scores, Hess comes up with an interesting, original metric to rank education scholars. A number of the AEI staffers (I guess they’re called) are worth reading, too, particularly Michael McShane.

Daniel T. Willingham rarely mentions cognitive ability (geez, I can’t think why) which allows him to post more happy talk than perhaps he should. I read him anyway.

Deborah Meier is another progressive I find to be largely on the money and, like Cuban and unlike most other education advocates, she spent a long time teaching.

Robert Pondiscio used to be the reason I read Core Knowledge’s blog. He’s doing something else with civics now, but he’s still very useful on Twitter.

Pedro Noguera is on twitter, although I don’t follow him, but that qualifies him for my list despite his lack of a blog. I rarely agree with him, but like Meier and Cuban, I find him thoughtfully progressive.

Teacher bloggers—not the same as teachers who happen to write blogs—are mostly a group that doesn’t interest me. I do like Michael Pershan, who’s enthusiastic without the slightest degree of tedium. All math teachers should check out his blogs and if he ever starts writing more about policy, he’d be very good at it. Reformers should like him–he doesn’t have a credential, I think.

If you’re a teacher who wants to become a teacher blogger, Larry Ferlazzo is the go-to guy to find out who’s blogging and what you might like–again, good blog, balanced approach, not my kind of thing.

The Math Twitterverse Blogosphere, or whatever it is called, is very angry at me for my meeeeeeeean Dan Meyer post and then for what they see as my racist writing, but in fact, I’ve checked into Meyer’s blog on and off for three years or so. I thought I posted fairly about his good points, but his comments section is really where the action is. If you’re a math teacher who hasn’t really engaged online, start with his blog and blogroll and you’ll find plenty of food for thought.

Dave, blogging at Math Equality, manages to make teaching seem miserable and joyless, but he’s exceptionally good at documenting just how brutally hard it is to teach unprepared kids at both ends of the spectrum–he teaches both calculus and algebra to kids who aren’t even close to ready for the subject. If you think I’m just making things up, go read Math Equality.

And of course, Eeyore, Gregory Taylor, who should start some sort of comic book with his math serializations.

Teacher advocates also aren’t a group I find appealing, but the best of these are all progressive: Anthony Cody, John Thompson, Gary Rubinstein are all effective, but predictable. Of these three, I think Rubiu8nstein is the only one currently teaching. They all write solid blogs and all have experience working with tough kids: Cody in Oakland, Thompson in Oklahoma, Rubinstein for TFA in Houston (although the last has been teaching smart kids in a selective school for the past decade or so, he approaches his work using his formative experience with tough kids). I read all of them occasionally, but not regularly; they just aren’t what I look for. If there are any genuinely interesting working teacher reform advocates, I’m unaware of them.

People you should probably investigate if you’re looking for education policy reporters/writers/think tankers, even though they aren’t part of my regular reading list: Andrew Rotherham (I’m really not a fan of any of the folks at Bellwether, but everyone else is), Lisa Fleisher, Stuart Buck, Andy Smarick, both Porter Magees, Lisa Hansel, Dana Goldstein, Jay P. Greene, California Teachers Empowerment Network, Rishawn Biddle, Valerie Strauss, Jay Mathews, National Association of Scholars, John Merrow. And of course, branch out from there.

People I actively advise against:

  • Diane Ravitch, not because she’s terrible, but because you’ll drown. And hell, you’ll hear if she wrote anything interesting through the other people you follow, so let them wade through the onslaught. Read her books instead; her early histories are outstanding. While I agree with most of her critics, reporters and reformers both show a tremendous distaste for her that is, I think, based on her cult-like following of teachers. After all, teachers are morons, so anyone they think is awesome can’t be all that.

    Something that’s a bit off topic but I’ve been meaning to write for a while: Ravitch is attacked for what critics see as unhinged assaults; in this particular example she is attacked for being mean. Note to ed policy wonks, and the reporters who cover them: Folks, the bulk of you are mean to teachers Every. Single. Day. When you talk about kids being trapped in failing schools, when you talk about the need for more talented teaching candidates, see neighborhood schools as death traps, when you argue that teachers unions (but not teachers, no!) care only about adults, and when you push Common Core training because teachers don’t know the subject matter—you are insulting teachers. To the bone. Go right ahead, I’m not saying you should stop. But don’t think you’re somehow superior because you don’t call teachers out by name. You’re saying we’re not terribly bright, that we don’t care about kids, that we are failing at our jobs (unless we teach at charters). You insult all of us in ways well beyond the pale as a matter of course. And you look like jackasses when you whine that one of yours is being insulted just because his name is used.

  • Michelle Rhee or Students First. Hack. For all Ravitch’s many faults, she has at least had original ideas and a coherent vision—which is why her conversion mattered. Michelle Rhee owes her entire existence to felicitous connections; the woman has never had an original thought or accomplishment in her life, and she’s a thug. I really wonder why her marriage to an accused sexual harasser and her role in the cover-up isn’t getting more attention.
  • Any union website, twitter, or representative. I’m not saying they’re wrong, they’re just not very interesting. If Randi Weingarten has had an original thought, she’s kept it well-hidden.
  • National Council on Teacher Quality–I’m not a huge fan of Jay Greene, but his takedown of NCTQ’s ed school ratings was perfect. These guys aren’t just boring and predictable, they’re flat out wrong. They don’t know what they are talking about. They lower the IQ of a website just by showing up.

So there you go. A lot of people I read and enjoy (Charles Murray, Razib Khan, Jonah Goldberg, Kevin Drum, Robert Verbruggen, Steve Sailer, Megan McArdle, Dave Barry) only occasionally or never touch on education. And HBDers looking for ed recommendations, um, there’s a reason I’m the only education writer on the network.


Polynomial Operations as Glue: Second Year Algebra

A couple years ago, I suddenly realized that my students rarely evaluated quadratic expressions. And when I thought about it, I could see why.

Create a table of values for y = x2 -6x – 16. Start with -3

evalbysub

These are kids who aren’t too great at working with negatives, yes? And it’s a whole bunch of work for a relatively small gain. Makes it tough to guess and check, to work velocity problems, and so on. I want something simpler.

Enter the Remainder Theorem: the remainder of the division of a polynomial f(x) by a linear polynomial x-a is equal to f(a).

We usually teach synthetic substitution when introducing with the Fundamental Theorem of Algebra, which is when we give advanced students the bad news—at a certain point, factoring higher-degree polynomials becomes guess and check. Here’s the Holt book, for example: Chapter 5, Quadratics, covers evaluation by substitution (aka, plug it in). Chapter 6, Polynomials (meaning degree greater than 2), covers polynomial division, synthetic substitution/division, remainder theorem, and factor theorem, leading up to the fundamental theorem of algebra. Notice, too, that the book is a tad soulless on two of the more remarkable theorems, as I write about here.

So this is screwed up. First, quadratics are polynomials, thankyouverymuch. Second, synthetic substitution/division solves the problem I started with: it’s brutal to evaluate quadratics if you can’t do it in your head—and most of my students can’t.

Then, there’s the fact that polynomial operations in algebra 2 are like kissing a sister; students don’t really learn the purpose for these operations until math analysis and calculus. Over half my students are in their last high school course and won’t be taking anything more advanced in college, but they will need knowledge of these operations for math placement tests. The other half will be moving on to math analysis, and need the skills.

Over the past two years, I’ve played with different ways of teaching polynomial operations, and different ways of introducing synthetic substitution for quadratics.

My algebra II/intermediate algebra class is comprised of four modeling units: linear equations (and inequalities), quadratic equations, exponential functions, and probability. I intersperse polynomial operations, inverses and logarithms between these four units. Logarithms fit organically with exponential functions; polynomial operations and inverses, not so much in a world where I’m not going on to the more rigorous parts of algebra 2. But inverses work as a good review of multistep equations, so the kids get some good practice in another skillset they need. Leaving polynomial operations as just….out there.

I haven’t been terribly unhappy with this, given the purely functional nature of the lessons, but I want my kids to know synthetic sub/div, dammit, and I want an organic way of introducing it. Right now, I go from linear equations to polynomial operations, ending with multiplication, which takes me into quadratics. That works, but not as smoothly as I want.

A couple days ago, I was pondering how to explain the synthetic substitution/division problem as a blog post, when I suddenly thought of a way to better integrate polynomial operations in and around my first two modeling units. I can use function operations as a method of introducing the transitions. Normally, I just introduce the function notation so they’re familiar with it. (Composites don’t normally show up on the test, and are covered again in pre-calc.)

This is just an outline, but remember that I have all the units done. All I’m describing, broadly (without any curriculum yet) is the transitions, the points at which I introduce and then return to polynomial operations.

After Linear Equations and Inequalities,

FuncAdd

I could start with a question like: “Part 1: Sami needs three more dollars to buy the new hoodie that he wants. Model a relationship between the money Sami has and the money he needs, and plot.”

Then, Part 2: “If Sami skips the hoodie, he needs just one more dollar to buy a ticket to the pizza feed on Friday. Model a relationship between the money he has and the money he needs, and plot.”

Part 3, starting as a discussion: “How much more money does Sami need if he wants both the hoodie and the ticket to the pizza feed?” My guess, although I’m happy to be wrong, is the kids will say that Sami needs four more dollars. And so how can they use the graphs to show otherwise?

So we can show graphically and algebraically that adding the two equations together will give us one equation that we can use to see how much more money Sami needs. At this point, I can introduce polynomial addition and subtraction in its simplest form. This will just be a couple days–one for addition, one for subtraction. But it allows me to reinforce linear graphing one more time, in addition to the new concept.

Then I can move from addition and subtraction to multiplication.

Introduction to Quadratics

I’ve always introduced quadratics with the modeling exercise above, then moved onto binomial multiplication. I really like the possibilities that come up after adding and subtracting linear functions, by asking the question (without the graph, at first):

FuncMult

“Okay, we’ve added two lines. What happens when we multiply two lines?”

In class discussion, I’ll point out the negative values, the positive values and the points at which one graph is positive and one negative. What’s going to happen when these are multiplied? (Hey, it never hurts to remind them about negative integer operations.) I haven’t completely thought through implementation—I definitely want them graphing this. Maybe give them the two lines at first, have them multiply the values.

I mentioned earlier that I’ve been looking for a better method of modeling quadratics. While this approach doesn’t involve situation modeling, it does organically introduce the shape of a parabola. It will also help them spot zeros.

And this leads in perfectly to my binomial multiplication unit, which I already extend to include higher degree polynomials. With the strongest kids, I can even give them three lines and have them determine what a cubic function looks like.

Factoring, Division, Remainder, Synthetic Sub/Div

funcDiv1

Then, when I’m moving from binomial multiplication to factoring, I can show a graph like the one at right and ask:

“So we multiplied the linear equation by another linear equation to get the parabola. What are the equations you see, and what’s the missing linear equation?”

which, of course, brings up function division, and allows me to introduce factoring as a variant of division–and, a month or so after we’ve done linear equations, they get to review the concepts. As I write this, I’m trying to think if it makes more sense to introduce long division and synthetic substitution at this point, or to work on factoring for a while and then bring up division. TBD.

If you’re not familiar with synthetic sub/div, take a look at long division and synthetic division side by side:

Evalbylongevalbysyn

Synthetic sub/div is far easier than substitution, even in quadratics. It’s also noticeably easier when evaluating fraction values for velocity problems.

After I’ve finished all of linear and all of quadratics, I can do a few days on polynomial operations and function notation, just to wrap up.

Again, this is very skeletal. I just had the idea because of the writing challenge. Thanks, blog! But I know it will work; I can feel it. I just have to be careful and think through the transitions thoroughly, make sure I’ve given the kids plenty of support. For example, I don’t want to overemphasize the function operations of this. I just want the kids to be comfortable with the notion of addition, subtraction, multiplication and division of equations. That will give me the entrance to teach them synthetic div/sub, as well as the reason for practicing polynomial ooperations.

Those of you who are thinking, “Hey. This is really algebra one.” well, welcome to my world. My kids learn a whole bunch of first year algebra in my algebra II and geometry classes. But I cover about 60% of the algebra II standards to kids with very weak skills, and the class is pretty conceptually interesting, I think. It’s definitely not just a rehash of algebra one.

I’ve also been thinking a lot about this post on curriculum mapping, which I found very interesting. I hope it’s okay that I borrow his image:

I was talking with Kelly Renier (@krenier), director at Viking New Tech, and we began discussing the concept of “power standards” or “enduring understandings” or “What are the Five Things you want your students to know when they leave your class?” then build out from there. However, we didn’t discuss building those Five (or whatever number) Things out into linearly progressing units, but rather concentric circles.

So this is absolutely how I teach, as regular readers may know. Teaching Algebra, or Banging Your Head with a Whiteboard covers, literally, the Five Big Ideas of algebra I. I also have them for geometry and algebra II (for my students, anyway). I thought the advantages of this approach were interesting in that I didn’t realize how many teachers don’t do this already. Again, quoting:

  1. Students get to revisit a general topic every few weeks, rather than a one-and-done shot at learning a concept.
  2. Students have time to “forget” algorithms and processes and when they see a scenario they have to fight their way through it accessing prior or inventing new knowledge, rather than relying on teacher led examples. Yes, I consider this a benefit.
  3. Teachers may formatively assess more adeptly.
  4. Students may see math as a more connected experience, rather than a bunch of arbitrary recipes to follow.
  5. It probably better reflects the learning process, which happens in fits and starts, and frankly, cannot be counted upon to be contained within a specified time frame.

This is a really good explanation of what I see as the advantages to my approach. I have never taught in anything approaching a linear fashion, probably because I used CPM, which spirals as a matter of course, in my first two years and was nonetheless shocked at how much kids forgot. So once their forgetting is shoved in your face, it’s hard to go back to the linear curriculum design.

I don’t obsess with getting every single connection made from the first time I teach the class. Sometimes I’ll just acknowledge, as I’ve done with polynomial operations up to now, “Hey, this is kind of an odds and ends thing you just need to know.” There’s nothing wrong with making clean breaks between some units—it doesn’t automatically turn the curriculum linear. For example, I make a very clean break between quadratics and exponentials, because the kids have never seen exponentials before. I show the connections between linear and exponential functions, but I also don’t just lead in. NEON SIGN: NEW EQUATION is a helpful way for kids to realize they’re getting something new. (Common Core says they’ll be learning this in Algebra I. Jesus. These people are friggin’ delusional.)

Going back to who I am as a teacher, I start with explanations. Not necessarily verbal explanations every time, but making sense of a concept before doing it is an essential element of my teaching.

That doesn’t mean I start with a lecture, which I rarely do, or an explanation. I often begin a unit or a concept with an activity. But if I’m asking my students to engage in an activity with no concept or prior understanding, then they can be sure it’s going to be simple, straightforward, and illustrative.


Dan Meyer and the Gatekeepers

I have at least one more post on reform math, but I got distracted while looking for examples of Dan Meyer’s teaching (as an example of his math in action) then realizing that many of my regular readers wouldn’t know Dan Meyer, and so started to construct a brief bio. In doing so, I got distracted again in considering Meyer’s quick-yeast rise and what it says about the gatekeepers in the education racket and access to microphones.

This may seem like insider baseball, but I hope to illustrate that Dan Meyer is an unobjectionable guy with a good idea, whose unhesitating adoption by the elites represents a real problem with educational discourse in this country. I will probably overstate and paint a picture that suggests plan and intent by those causing the trouble, when in fact it’s fuzzy and reactive with only big picture general directions, but probably not to the extent that Diane Ravitch (or, indeed, Dan Meyer) commit that particular sin.

Dan Meyer, 31, is in the process of becoming a celebrity math teacher (hey, it’s a small group). Much of his rapid trajectory upward can be explained by his message, which involves a digital curriculum that will (he says) instantly engage and perplex kids and thus resolve all classroom management issues (more on this later), a message tailor-made to appeal to both techies, since it implicitly attacks all teachers, and progressive educators, since it is inherently constructivist.

Most of the rest of his said trajectory can be explained by his excellent luck in his early audience—not only were they progressives and techies, but they were influential progressives and techies–Chris Lehmann, O’Reilly Publishing folk like Kathy Sierra, Nat Torkington and Tim O’Reilly himself, Brian Fitzpatrik of Google, and Maggie Johnson of Google and Stanford.

A teeny-tiny bit–ok, maybe more–of that trajectory can be explained by the Great White Hope factor. As I’ve written many times, every corner of education is desperate for young teachers, particularly young male teachers, most especially young white male teachers. Smart young white male pushes technology-based teaching, implicitly or explicitly declaring that all those old teachers (mostly white female grandmas) are doing it wrong. Hard to resist. So attractive message, demographic felicity, and luck. Not bad.

I’m going to summarize what I see as the relevant points of Meyer’s career thus far, but go straight to the source: Meyer describes his teaching career in this excellent video, which I recommend watching to instantly “get” his appeal. Go watch. I’ll wait.

He taught his first year at a Title I school in Sacramento, CA and, as he says above, was both miserable and ineffective, which he blames on his failure to create a “classroom ethos”. The improvement in classroom ethos began during his second year at San Lorenzo Valley High. It apparently never occurred to him to wonder whether the “classroom ethos” improvement at his second school, was helped along by a student demographic that was 87% white. Meyer actually noted the novelty of a non-English speaking Hispanic student which is the only time he ever mentions a minority student on his blog, best I can see.

While he made numerous videos that ended with the tagline, “I like to teach”, he in fact wasn’t all that attached to teaching. At the beginning of his third year, he was already predicting he’d be in school for either an administrative credential or doctorate by the end of the next year (he was off by two), because “I’m just keenly aware how much of my strength as a teacher derives from my ability to relate to student culture, to talk like they talk and dress like they dress” and his awareness that he feels “obliged to entertain”. He often implied that he’d mastered the technical aspects My personal favorite::

I am at a place, for example, where classroom management no longer challenges me. Not that every day is all smiles and hard work, just that I have identified the mix of engaging instruction, mutual respect, and tough love that eluded me for years.

Four ENTIRE years, this eluded him! This meme runs throughout his blog and is, in fact, the seed of his image-based curriculum. Meyer states time and again that he worked hours on end to keep from boring his students, thinks student approval as essential to improved learning outcomes and thus presents his curriculum as a better way to entertain kids, to perplex them in a way they will value, and once entertained and perplexed, they will learn.

Then, at the end of five years, he declared he was quitting teaching because he’d been transformed from “miserable to happy, incompetent to competent” (astonishing, really, how few of the commenters openly laughed at his hubris). He originally planned to attend UC Santa Cruz’s PhD program but his aforementioned contacts got him a year as curriculum fellow at Google, and he taught part-time for one more year. While at Google, he made his first TV appearance on Good Morning America (probably via Google) to discuss his theory as to whether regular or express grocery lanes were faster.

At some point after that, he pulled a TEDx invitation—very nice work if you can get it—which got him onto CNN and good lord, how could Stanford let him get his doctorate at Santa Cruz, after all that publicity? So now he’s at Stanford in year 3 of his doctoral program.

A star was born.

Like most teachers, Meyer’s a good talker; unlike many teachers, he’s good with any audience. He’s a bright guy and his videos are genuinely entertaining (go to the end to catch his early work), and I say that as someone who disagrees with very close to all of his primary assertions. As a young white male teacher he could demand nearly anything, and he nonetheless stayed in algebra and geometry, rather than push for advanced classes that his principal, eager to keep him, would easily grant. I suspect that some of his willingness to stay in low status classes was caused by his short-timer’s attitude, while another part of it was caused by his 70-hour work week. Anyone working that hard and long on classes he’s been teaching for years is unlikely to embrace new subjects. But those stated priorities nonetheless reveal a guy who is well beyond committed and flat out obsessed with doing a good job.

He’s hard to pin down ideologically not because he’s an original thinker but because he was, and is, profoundly uninterested in education policy. So no coherent philosophy, but Me Like, Me No Like. He would disavow the charge that he is on the “reform” side of the math wars, although less vehemently than a few years ago—Jo Boaler, High Priestess of Reform Math, is his adviser, after all. But even now, a few years after starting a Stanford PhD program, he’s very foggy about the specifics of major debates in math education. So he’s been trying to consolidate his positions, but he’s not always sure what the right ones are. In his earlier iterations, for example, before he became well-known, he often adopted strong education (not math) reform positions—he had an “educrush” on Michelle Rhee. In the early years of the blog, he dripped contempt on most teachers, particularly older ones, including coworkers. Early on he harped often on the need for professionalism, and asserting we’d be better off without teachers that do it just for love. But once Stanford put him on the doctoral payroll, he’s become more typically math reform, which means he’s disavowing education reform positions and doing his best to walk all that talk back. Well, not all of it–here he is on a forum last year talking about the need to train teachers on Common Core:

I think if you’ve taught for thirty years under a particular style of teaching, it has to distort what your perception is of math and how it should be taught. It’s unavoidable, to be steeped in that for so long. So to realign yourself, I imagine, is a very difficult thing. So PD that involves problem solving, involves reasoning, argumentation, that’ll be essential going forward.

So the nastiness to older teachers, still there. I don’t blame anyone who wonders if promoters consider that a bug or a feature.

Meyer’s writings never describe his “classroom action” in detail relative to other math bloggers (e.g., Fawn Nguyen, Sam Shah, Michael Pershan, Kate Nowak and, okay, me). He rarely describes the success or failure of a particular lesson, or gives any kind of walkthrough. He never describes a lesson in full detail, down to the worksheets and responses. He often went to the data collection well, and just as often failed, as in his two-month long “Feltron” project in which half the class dropped out early during data collection and had to be given other tasks, or this similar project

Meyer and metrics aren’t a natural fit. A few years ago, he was, comically, shocked by news of California’s Hispanic achievement gap. Dude, didn’t you get the memo? He never blogs about it, never discusses it, then out of the blue: Damn! We’ve got an achievement gap! And then he rarely mentions it again, save for this recap of Uri Treisman’s speech. He almost never discusses his student’s test scores and when he does, they are usually not great, although he mentions once in passing that his algebra students beat the department (no data, though). He cheerfully talked about standards-based grading for a year or two and blew off the commenters who wondered if the students were retaining the skills they’d “mastered” twice in a week. When he did finally get around to looking for that data, the answer was no, and it’s quite clear that he’d never before wondered about this essential element of success. So while I suspect that Meyer was a popular teacher who convinced a lot of kids–mostly white boys–to work hard at math, there’s little evidence of that in his written history of his years teaching.

I can find little evidence of intellectual achievement in education once he left teaching, either. At Google, he and three other curriculum fellows worked for a year on computational thinking projects. When his project shipped he wrote, somewhat obscurely, “Near as I can tell, of the sixty-or-so modules listed, only one of them ….is mine. I always admired Google’s lack of sentiment in deciding when to invest itself and when to divest itself. Still it’s strange to see a year of work reduced to a single entry in a long list.” (emphasis mine)

At Stanford, his qualifying paper was not hailed as an instant masterpiece:

The criticism I remember most vividly: a) my weak review of the literature, b) the sense that I wasn’t really taking myself anywhere new with the study, and c) a claim about equity that had me reaching beyond my data.

In short, he didn’t set the curriculum world on fire at Google, and the critiques of his qualifying paper suggest an analytical lightweight—which is pretty typical for salesfolk. So thus far Meyer has established himself as a stupendous salesman, but not much of an intellectual—at least, not of the sort that Google and Stanford like to pretend they invest in. He was even wrong in the GMA segment. Unsurprisingly, he was unflustered.

Realize that I know all of this because of Dan Meyer’s blog, so he’s not hiding anything. Hell, he doesn’t need to.

But he was brought to Google and then to Stanford and then Apple gets involved, and now we’re talking three of the most elite institutions in the country are pushing him not because they have any evidence of his ability to close the achievement gap, or even whether his digital curriculum works, but simply because he’s Dale Carnegie, and boy oh boy, is that a depressing insight into their motivations, just as his success is indicative of the desires of the larger educational world. It’s not “go develop your ideas and expand and prove them” but “here’s a bunch of elite credentials that will make your sales job easier”. So they dub Dan an “expert” and give him a microphone—which makes it a whole lot easier for a largely ignorant general media to hear him.

No, I’m not jealous. My karmic destiny demands that I enter new communities with neither warning nor fanfare and utterly polarize them within a month, usually without any intention of causing trouble. Lather, rinse, repeat. I gave up fighting that fate fifteen years ago. I have attended two elite institutions in recent memory; one of them ignored me desperately, the other did its best to hork me up like a furball. I don’t want to go back. Academia isn’t for me. And if a corporation handed me money to sell my message, they’d be facing a boycott. My blog has fifty times the readership and influence that I ever imagined, and I love teaching. I am content.

Previous paragraph notwithstanding, this essay will be interpreted by some as an attack on Dan Meyer, who is largely unfamiliar with anything short of worshipful plaudits from eager acolytes (he occasionally heeds polite dissenters, but only occasionally) since he began his blog. But while he’s a dilettante as a teacher, I think his simplistic curriculum ideas have interesting potential in teaching certain demographics, and I wish him all success in developing a coherent educational philosophy. Oh crap, that was snarky. I wish him all success in his academic and business career.

Dan Meyer’s rapid rise isn’t the problem. Dan Meyer himself isn’t the problem. The problem lies with the Gatekeepers: with Stanford, who knows that Dan’s not the solution, with Google, Apple, and publishing companies like Shell Centre (well, they’re in England) and Pearson. That intersection between academia and business, the group that picks the educational platitudes and pushes them hard, while ignoring or banishing dissent. They’re the ones granting Meyer the credentials that cloak him in the illusion of expertise. And I believe that, at least in part, they grant those credentials with a clear eye to the attributes that are diametrically opposed to the attributes they pretend to focus on. It’s no coincidence that Dan Meyer is a young white male. It’s the point. It’s not a fluke that he primarily taught white kids, many of whom were obviously sent to him with strong skills by teachers who valued homework above ability. It’s the only way he could have come up with his curriculum. Yet his message is adopted and embraced by elites who castigate education, particularly teachers, for failing black and Hispanic kids. I don’t know if they do this consciously or if they genuinely believe that all teachers are just meanspirited morons who don’t know math and deliberately deprive certain kids of meaningful math experiences. Ultimately, it doesn’t matter.

I suspect Meyer and others will ignore this essay (Meyer snarked obscurely at my reform piece, assuming this tweet means what I think it does), but whether that’s because he doesn’t like dissent or, more probably, because he subscribes to the Voldemort View, I couldn’t tell you. But maybe this piece will make reporters and educational wonks a bit more wary about the backgrounds of the “experts” they quote, and the gatekeepers who create them.