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Teacher and tutor

What It Looks Like In Practice

“Matt, are you getting anything done?”

“I’m Mark. And yes. I’m on problem 13.”

“You’re Mark? No. I thought I had this straight. You’re Matt.”

“Nope. Mark.”

“Well, crap. I was just going through the quizzes and saw a Mark and a Matt and thought ok, there’s Matt who I always want to call Mark. And I was wondering who the Mark was, trying to visualize which Mark I was missing.”

“No, I’m Mark.”

“Huh. Matt must be in block 2, but I don’t think I have a Matt in block 2. But then, I don’t think I have a Mark in block 2. I have a Mark in US History, but that Mark isn’t one of the students I have for both US History and Trig. This is all very confusing.”

Tonee snorts. “Dude’s just messin’ with you. That’s Matt.”

“Oh. Phew. Left to be discovered is who’s Mark. But don’t do that, Matt.” Matt grins, the class gets back, somewhat noisily, to work. I wander round the room one more time, then settle in to my desk to put the quiz grades in.

Casey meanders up to my desk. “I think I can clear up some of your confusion.”

I look at the petite, redhaired senior, delicate features marred (in my view) by two horrible lip piercings. “You can? What confusion?”

“The Mark/Matt thing.”

“Oh! Lord, that was, like 20 minutes ago. I’d forgotten all about it. You know the Mark I’ve somehow completely lost track of?”

“I am Mark.”

I stop typing. Look over at, it turns out, Mark, who I learned for the first time last year was merely biologically female when an ex-student Connie walked by and said “Hey, you have my foster brother Casey in your class. He says you’re great!” and only acknowledged after ten minutes of demands that Casey wasn’t “actually a guy, but you know, wants to be.”

“Sh**.”

“I’m sorry.”

SH*****t.”

“I used my last name! I thought that would be the clue.”

“Case…Mark, I can’t even remember Matt isn’t Mark, and you think I keep track of last names? Sh**.”

“I’m sorry.”

“Don’t be silly. I’m swearing because I made a public deal out of this and I’m feeling bad. It’s not you. Any other sane teacher would have wondered wait, who the hell is Mark on this quiz and resolved it right then, but I’m teaching so many different classes with so many repeating students and doubled up students I just figured I was forgetting someone. And I shouldn’t swear, of course, but you’re a senior. Anyway, I’m sorry for screwing this up.”

“Well, I wouldn’t have used my new name, but you were so cool about it last year…”

“I was so cool last year? I kept on screwing up your pronoun.”

“You were so really nice about it. I appreciated your support.”

“You’re nuts. Anyway, what the hell? I thought Casey was your new name.”

“Yeah, I decided on Mark.”

“OK. Thanks.”

“I’m really so…”

“Shut up. I’m a disorganized teacher. This happens. Get back to work.”

Later on, giving the tests back, I say “Matt, come get your quiz.”

“I’m Mark.”

“No. You’re Matt.” Matt starts to wilt under my glare, but notices who comes up to get Mark’s quiz and doesn’t claim to be Mark again.

Related news: A special ed teacher told me I was selected by two of her senior students as the one they most enjoyed having and asked me to put together a little paragraph as part of a plaque she’s giving to each. One of them, Victor, wears makeup, nail polish, and curly hair in a casual bun. I’ve heard Victor doesn’t like to be called gay.
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I hope Casey and Victor forgive me, should they ever learn that I thought the Obama directive on k-12 schools and transgender bathrooms to be idiotic and enraging. I’m quite worried that the current Supreme Court will decide it makes perfect sense to force to accomodate transgender teens in their quest for bathroom freedom. Given the conservative Justices’ contempt for public school teachers, my original fear was they’d give Gavin bathroom rights to strike one more nail in our coffin. But I wronged them mightily; the four conservatives voted to overturn the Fourth Court, with Justice Breyer the only hope as a swing vote, voting with the conservatives as a “courtesy” to maintain the status quo, the horrible repressive status quo we live in now, the one that allows us to ignore Obama’s directive and require bathrooms match biology.

I believe those who adamantly insist on having gender reaassigment surgery are mentally ill. Kids who want to be the opposite gender are probably going through a phase. Some simply love the attention; others are depressed or troubled. Still others just like being different. I have no problem with respecting phases. I’m appalled by the current trend of honoring these phases to the extent of hormones and gender surgery, and pleased that the Trump administration appears to be undoing the Obama idiocy.

I’m blissfully untroubled by the knowledge of what bathroom Mark who was once Casey uses. Every so often one of our more adamant social justice teachers gets up and demands that our grading and attendance software “reflect our students’ desired gender” and I roll my eyes so hard I get a seizure but beyond that we haven’t had any staff discussions on the subject. Please, god, keep it that way.

I wonder if many people opining on transgender schools understand how schools handle them. Do they know what it looks like in practice? Do they think schools are busy insisting on biological reality? Quite the contrary, and political views aren’t really involved.

I treat transgender kids the same way I’d treat other kids who face difficult social situations. I call them whatever the hell they want. I try to avoid pronouns (as I have in this piece) because they’re much tougher than names. I would ruthlessly step on any teasing or harassment, assuming kids in our world-wise school would ever be so mean. I will leave decisions on their gender treatment to their parents or guardians. My job is to educate them to the best of my and their ability, and to the extent possible, make them feel safe and comfortable as they navigate the crazy teen years.

If Gavin Grimm loses the case, I doubt schools will do anything differently. Most teachers will go much further than I do in supporting students who identify as transgender.

If Gavin wins the case, I expect that charter schools will soon have one more advantage that they’ll never mention directly, but will nonetheless be seen as a clear advantage by otherwise progressive parents. And there will be one more item to add to the meme “Why Trump Won”.


Understanding the 2016 Election, High School Edition

So my new “year” has started with the onset of the new semester. I am, oddly, teaching only 50% math. My school couldn’t find a new English teacher (note, again, the pain point for principals is hiring, not firing). Since I was already teaching a full schedule with no prep, the entire math department schedule had to be revamped to get someone to cover one of my trig classes.  So ELL, Trig, US History, Trig. Busy.

Anyway, I have kicked off my planned US History curriculum and on one day’s experience, it’s going gangbusters. I decided the students would best grasp the significance of the electoral college if we began with the recent election–give them a frame of reference as we then look back.

First, I gave them a copy of Article II, section 1 and the Twelfth Amendment, explaining that the elections we’d be reviewing would use both the original and amended text. But the big takeaway I wanted them to get for the first go-round was:  Each state shall appoint, in such manner as the Legislature thereof may direct, a number of electors, equal to the whole number of Senators and Representatives to which the State may be entitled in the Congress: but no Senator or Representative, or person holding an office of trust or profit under the United States, shall be appointed an elector.

This was new information–well, more accurately, it was relevant information, something they’d clearly been wondering about. When we got to the text about the electors meeting to elect the president, I played that Martin Sheen et al video.

“These actors were trying to change the electors’ minds. As we just read, if no candidate receives more than half the electoral vote, the House of Representatives elects the president. So you can see they didn’t have to change everyone’s minds, just enough to push the vote below the halfway mark.”

“And they’re Democrats?”

“No. The House is controlled by Republicans. I have to say I never quite understood the logic of this effort.”

“Why do they keep repeating everything?” Elian asked.

“They must think we’re stupid.” Bart observed.

“I think they did it for artistic effect. But let’s move on. That’s how the president is actually elected. So now lets see how many electors each state gets. Who knows how many Senators we have?”

The guesses were all over the place until I asked for the names of our senators. Then they all figured out it was two.

“Right. Two for each state. Each state, no matter how big or small, gets two senators. And since we have 50 states, we have a total of…..” (I always wait. Are they paying attention? I get 100 back pretty quickly.) “House of Representatives works differently. The House, for reasons we’ll discuss later, assigns representatives based on population. But about a century ago, Congress froze the number of seats at 435.”

“Why?”

“Good question. We’ll explore that later. For now, I just want you guys to get an understanding of the rules on the ground.”

“So every state gets two electors, no matter what, right?” asks Pippa. “Because they have two Senators.”

“Yes, good. They actually get three, no matter what. They elected two senators and one representative, so three electoral votes.”

“That sucks,” Eddie observed. “They only get three people to represent the state.”

“Actually, that three is a good deal. Let’s just take two states: Montana, with a population of about a million, and New York, with a population of 20 million. So New York is twenty times bigger than Montana. Montana gets 3 electoral votes. Any guesses as to how many New York gets?”

“Well, if it’s twenty times bigger, they should get sixty.” Anita.

“That can’t be right, though,” observed Priya.  “New York isn’t the biggest state, and if it has 60, then how many does Texas or California have?”

“Very good.” and I passed out the worksheet I’d cobbled up. One side was an image of the country with electoral votes by state,  the other was a table looking something like this.

“Wait. New York only has 29 electoral votes? Holy crap.”

“Yeah. Now you’re starting to see. New York only gets nine times as many electoral votes, despite having twenty times as many people.”

“That’s not fair to the big states!”

“It might feel that way. However, there was a lot of reasoning that went into that decision. We’ll be talking about it later, and you can judge. For now, here’s a simple task. I want you to mark the map with the winners, as many as you remember or want to guess. Then, on the back, put your guess and then the electoral vote total in each column. I don’t expect everyone to know all of them. I just think it will be a good discussion, get you seeing how much you know or remember. Then I’ll help you fill it in.”

I was pleased to see kids filled in a good bit of the map based on their own knowledge. Many knew the South was mostly Republican. They all, without exception, called Florida for Trump. A cheering number was aware that the Rust Belt states had flipped. After ten minutes or so, I brought up the same map on my Promethean and marked it up with their results, correcting for reality as needed. During the conversation, I added in some tidbits–what the polls in each state had showed, what states Hillary never saw coming, demographic voting patterns, DC’s three electoral votes, and so on.

When we finished marking the map up, Kevin mused, “Jesus. Trump won a lot of states.”

“He did indeed.”

On instinct, I went to a browser and brought up the 2016 electoral results map.

It was a good instinct. The class literally gasped.

“Holy sh**! He won all those states?” Eduardo was aghast.

“Huh.” Eddie, as dedicated a Trump hater as ever existed, had bitterly snarked about borders in an inequalities lesson immediately after the election. I’m hoping he’ll  feel less hardly done by in the future.

Here is something I learned: the kids had been told many times that Hillary Clinton won the popular vote. They understood what that meant. But not until this moment had they ever genuinely grasped the visuals of Trump’s win. What Trump’s win looked like. The map was a huge reveal. Minds weren’t changed, but perspectives were.

“Our Constitution gives voice to all citizens, but through the states. It’s a balance. It’s not always perfect. But it exists for a reason. Maybe this map gives you a sense of why.”

I had an extra fifteen minutes, so again on impulse, I brought up the classic youtube compilation of famous and influential people saying, with confidence, that Donald Trump could never win. I pointed out the lesser known ones, but they got the drift and loved it. I will note they were shocked (and not in a good way) at Seth Meyers’ disrespect. Loud applause at the end. I hit pause and got their attention.

“Here’s what I want you to know: not a single person in that compilation lost their jobs. Well. Except Obama, but his term was up. Every person on TV, acting as an expert. Every comedian. Every politician. You just saw pretty much every famous person in America laughing hysterically at the very idea that Trump might win. And none of them were held accountable. None of the media people who confidently predicted Trump had no chance of winning got fired. If you supported Hillary Clinton, you could easily have assumed you could stay home. Why bother voting? Trump couldn’t win. And when Trump won, these same media folk were all aghast. Then they ran all these stories about  devastated people, heartbroken by Trump’s victory. Rarely did you see stories on people who voted for Trump, who were thrilled at his win.”

Silence.

“I want you to go home tonight, turn on cable news–well, except Fox–and you’ll see all those people you just saw and more, talking about the demonstrations against Trump’s new immigration policy. Trump’s naming a new justice, maybe there’ll be more demonstrations. All the people on TV, many of them who are newspaper reporters talking about their own print stories, will talk about how big the demonstrations are, how meaningful they are, how important they are, how the people are speaking.”

“And when they sound certain. When they sound like experts. When they talk to experts who sound certain. I want you to remember that video. Because then it might not come as much of a shock to learn that 49% of Americans polled support Trump’s immigration EO.”

“Yeah. I get it.” Omar nodded. “It’s like the media only shows people who agree with them.”

“It’s like they don’t even realize people don’t agree with them.” said Amy.

” So if all the cool people hating on Trump, maybe no one will want to, you know, be a d*** who likes Trump.”

“But I do hate Trump!” said Eddie.

“Well, I’d like you to think about using a different word than ‘hate’. But sure. LOTS of people disagreed with Trump. More people voted who wanted Clinton, remember? That’s where we started. ”

“It’s like, don’t be fooled. Don’t think that just because all the famous people think the way you do, that everyone does.” Omar again.

” If you surround yourself with people who think just like you do and never associate with people who don’t, you might lose track of what’s normal. It’s called ‘living in a bubble’.”

“You know,” observed Pippa, “I’ve always thought it was kind of cool that Trump won.”

“WHAT???” Eddie, outraged.

“No, I hate him. I mean, I disagree with him. But now that I see that video, I think it’s even cooler. All these famous people were laughing at him.”

“Yeah, mocking him. Nasty stuff.” agreed Lennie.

“And he went out there and ignored them and took his ideas to the people. And won!”

“I swear to you, Pippa, that’s exactly what I love about this election. I said that verbatim to my advisory. I truly believe that only in America, only with our rules, could someone go out and speak to the country and get the votes needed to win the presidency.”

The bell rang.

Good first day.


The People Who Share Their Reading Origin Stories

When I was very young, my grandfather took my book away as we were sitting companionably on the davenport, reading together. “You can’t possibly be reading that fast.”

Confused, I said, “Why not?”

“No one reads that fast. I read 600 word per minute, and you’ve flipped the page three times while I’m still on the first page.”

“But it’s a little kid book. You’re reading a big people book.”

Grandpa  read back over the previous two or three pages of The Bobbsey Twins or The Hardy Boys or whatever I was reading, quizzed me and, as he told the story for the next quarter of a century, I passed with flying colors. From that point on, Gramps was the only one of my relatives who really “got” me, understanding that living overseas left me starved of reading material. Every Christmas and birthday, where others would send me one or two books I’d devour in an hour or so, he’d send me a huge box of books chosen largely at random from the bookstore, adult-level reading books for a pre-teen and early adolescent.  Many of Grandpa’s books  built my eclectic content knowledge over the years, as my reading outpaced my age, then doubled it and beyond.

In the late sixties, increasing reading speed was all the rage (you can read fast, like the hallowed JFK!). We got tested often, in two ways. First, we’d be given a passage to read in time conditions, followed by comprehension questions. On these, I consistently clocked 1000 words per minute, probably the maximum speed on the meter, generally with 100% comprehension. Then, we were tested on tachistoscopes , which flashed a line of words on the screen or in a visor at the speed mentioned.

I hated those exercise. Hated. “That’s not how I read!” I still tested at 800 wpm or thereabouts, but it was horrible.  For the same reason, I would laugh at those idiotic Evelyn Woods speed reading commercials, because who on earth reads one word at a time? It’s so…limiting.

I believe the correct term for my early reading is Hyperlexia I–unusually bright child who happened to be an early reader.  A whole ‘nother line of thinking holds that all early readers are either visually spatially or linguistically disordered–although I have often written, of course, of my spectacularly weak spatial abilities, the description doesn’t fit me. I wouldn’t be surprised to find it’s linked, though.

No explanation for the speed, though. All authentically fast readers I’ve ever read or talked to mention some form of gulping, just as I do here in this old discussion at WestHunt.  Reading speed is linked with vocabulary (word identification), where I’ve been blowing past the 99th percentile my entire life.

I am a bit puzzled by the assertion that everyone–even I–subvocalize when reading.

Try this sentence: The bold spoken words could not sway the jury’s decision.

When I first began test prep instruction in the old SAT writing test, I constantly missed these ISE (identifying sentence errors) on adjective/adverb confusion. The question is designed to identify people who can’t hear the difference. Since  I don’t “subvocalize”, I wasn’t hearing the difference. I learned that many grammar errors are much easier to catch aurally than visually, and up until now I’d only reviewed my own writing for errors.  My eyes were fine at catching punctuation and wording mistakes, but I was vulnerable to usage mistakes that were most normally “heard”. I did not train myself to subvocalize. It was easier, for me, to train myself to spot the mistakes visually.  So while I accept the experts’ assurances that I’m subvocalizing, I sure don’t know when it’s happening.

I wasn’t ever terribly enamored of reading aloud to my son, who wasn’t a huge fan of it either. Movies were our bonding activity, from the time he was eighteen months old and beyond. Movies and Star Trek–before he was 2, he was making phaser noises and firing a water wand. His friends to this day marvel at his encyclopedic film knowledge. But while I was reading at three, he showed no interest in reading until the video game “Where in the World Is Carmen Sandiego” came out right after his sixth birthday. I refused to stand over the computer and read to him, so he informed his kindergarten teacher he had to learn how to read. Mission accomplished in a couple weeks. Within a few months, he had reading scores may not have been as high as mine, but were in the same ballpark, and much later scored a perfect 36 on the ACT.  He never read for pleasure save Harry Potter (he was from the original age group).  I’d long since stopped giving him piles of books, having figured this out (I’m not a nagger) but on impulse  I gave him some of my favorites for his 17th Christmas (Sewer, Gas, & Electric, Mark of the Horse Lord, Ender’s Game, Moon is a Harsh Mistress).  The books weren’t touched until we went on a long road trip in the era before smartphones, and he grabbed a few. I’d chosen well, and he became an enthusiastic reader during college, ripping through my extensive library and building his own favorites. Today he tracks his reading on goodreads. He reads quickly for a mere mortal, but nothing approaching my numbers.

I should mention that my dad, mother, aunt, and grandmother enjoy (or enjoyed) reading, mostly bestsellers (romance and spy novels, mostly) with a lexile level of, say, 800L.

**************************************************************

So a working class kid developed mad reading skillz at the age of three and a PhD level vocabulary by middle school, despite working class parents and pulp fiction content, has a son who develops wowza reading comprehension and vocabulary despite never reading much and rarely being read to–and having parents who divorced when he was two.

Tales like mine often lead others to gasp and share their origin stories. “Oh, I loved to be read to. Here are my favorite stories. What were your favorite stories?” They will build lists of books that oh, if only other parents would share with their children, if only teachers would understand the beauty, the transformative power of these books, then the world would be so much different. How can parents be so cruel? And uneducated parents, if only they understood how they are crippling their children, they’d take them to the library.

“Oh, but my mom was a Serbian immigrant who never went past sixth grade and every week she took us to the library! That’s how I was able to do so well. All these parents could do the same thing. The library is free!”

“But no, these parents are working two jobs. That’s why teachers are so important. That’s why curriculum is so important, to help these children catch up and know what their peers know.”

Education reformers sneer at “cultural deficit thinking“. Those failing teachers in failing schools argue that kids in poverty don’t have the same experiences as the middle class norms are simply lowing expectations to make their jobs easier–doing what’s best for them instead of what’s best for their students. Rare is the reformer who accepts that they, too, engage in deficit thinking. They consider children with low reading abilities to have deficits. These students are….not normal. The difference lies in their demands that the deficit be addressed, that with this deficit are otherwise doomed.

But tales like mine should, ideally, lead people to realize how little all  their  shibboleths matter to academic outcomes in face of the brutal thumb on the scale provided by intellect and personality.  Tales like mine should remind all those people with college educated parents and reading enriched childhoods that my abilities likely skunk theirs threefold, and that my kid’s might, too. Tales like mine should make people wonder if all their reading nostrums are a few steps up from homeopathic medicine. Reading chiropractic.

Tales like mine should, ideally, remind all those eager participants of those who aren’t in the conversation.

We do not hear from the millions who don’t fondly recall their favorite childhood books. From the people who didn’t read Playboy for the articles –who didn’t read Playboy at all. From the people who enjoy Readers Digest and TV Guide as a significant portion of their reading activity. From the people who are not tweeting lists of their favorite books, are not rhapsodizing in the comments section about the joys of reading aloud. From the people who are not asked to join in the discussion, because the people who are in the discussion can’t imagine they exist. Not really. Not past a punchline or a parent to be escaped from.

People who tell their reading origin tales could, that is, realize their perception is strangled by an almost unimaginable restriction of range.

No one really thinks of the others because these exercises are, at heart, narcissistic feel-good nonsense,  but if the non-readers of the world were to be considered, their opinions would be rejected as not only uninteresting but actively dangerous. They represent what our education policy seeks to avoid.

And so,  dear readers, spare me your origin tales. Accept, for the moment, that our education policy is not informed by the adults who don’t care to read, who can’t read well, or both.

Ask yourself  who might (just might, and I do mean that) have benefited from realistic, functional, purpose-driven reading instruction. The sort of instruction that the people who tell their reading origin tales never nead.  What education policy will help the other sixty percent or, god forbid, even more of the student population who don’t consider reading the most effective method of gathering information? How do we craft policies that will tease out motivation to build on existing skills, to make reading a useful tool for anyone, regardless of their comprehension level? How do we stop pretending that functional illiteracy is a meaningful term?

Can we craft an education policy that increases content knowledge to the level a student can absorb it, recognizing this limit differs? Can we continue to build student content knowledge gradually throughout school, again at the level they can absorb it? Or are we going to continue to have foolish expectations of assigning “challenging texts” to kids who can’t read at that level, and don’t want to, and make them hate reading even more?

In short, how do we stop from making reading a moral matter?

So if you read this tale, spare me the happy talk of your origin story. Answer those questions instead.

 

 


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.


2016: Five Years On….and then Trump

Having done three posts in a week–no small task for this slow writer–I was going to abandon a retrospective post this year. My traffic is down, and while I’m not concerned, I thought eh, no reason to write about it.

But I’ve written a retrospective every year. I started this blog on January 1, 2012 as a New Year’s Resolution, and when the anniversy went by I instantly felt a nagging sense of guilt and duty–and so, a retrospection. But not really on my blog.

For the first thirty years of my  working life, I played mostly at the edges of occupations. A friend once introduced me as someone who does “obscure technical things” and that was when I worked at a large corporation. For many years, I made a decent living doing things few people cared about, or thought you could make a living at like, say, tutoring. Teaching is a mainstream, non-niche profession if ever there was one, but I was reminded that my opinions are still niche when I tried to write about my career.  Getting any publication interested in my experiences or observations was a total non-starter. I occasionally got nibbles, but the intersection between what I could write about in 750 words and what someone was interested in publishing was almost non-existent–and I gave up trying rather easily.

And so the blog, with this resolution. I could focus on what interested me, not what was fashionable, and build an audience writing on topics as they occurred to me, not on what was timely. I could maybe start getting my audience to look at education as I did, or find like-minded folks, or both. I achieved more success than I ever dreamed in the first year and every year since has been better.

Then this year, this year that so many in the media rather provincially declare a gruesome annus horribilis, because they’re a bunch of narcissistic puppies who demand we share their misery. But I had a simply splendid time and for reasons directly related to the biography above.

I love politics, but as a spectator sport. My life is as niche as my careers are (custodial divorced parent, first generation college graduate, low six figure income, white, English major working in technology OR teaching math–pick three and you still have trouble forming a club,  much less a political action committee. Heads of households who make too much for the Child Tax Credit: not a big interest group.)

So since I never expected politicians to speak to my interests, I became very interested in determining who politicians were talking to, which eventually led me to realize that politicians were weren’t talking to. Broadly, I realized that politicians were flatly ignoring an important interest group: working people making less than, say, mid-six figures. Note I said “interest group”. Many vote ideology, just as I do, despite their income level and best economic interests. Politicians seemed to be taking this for granted. They were running on issues largely ideological terms, both left and right. But they were ignoring areas that clearly affected and interested wide swathes of the electorate.

I came to this realization via immigration and education, two areas that I’ve been watching and reading about for thirty years. I was unaware of the depth of disaster done by China to manufacturing in this country, but it plays to the same failure to speak to the public’s interests.

So even before Sean Trende pointed it out, I was wondering why no one was making a play for white voters. This realization is one of the issues that led me to notice the great Steve Sailer in the early oughts. Like Steve, I’m not a white nationalist–in fact, I believe that implementing the “Sailer Strategy” would ultimately result in more blacks and Hispanics coming to the GOP. But white voters were a large enough group to make zeitgeist defiance a worthwhile risk. From there, it’s a short step to understanding that the GOP was just giving lip service to immigration and cultural issues because, in part, the conservative elites shared the same values as the media and liberal elites and had no plans to change anything.

Like many others, I’ve long believed elites were engaging in an effort to shut down opposition to these key values. The left and right both brought about political or economic doom for those who went against the grain–no donors to run for office,  shaming, job loss,  whatever was needed to achieve an apology or social and economic obliteration. That’s….not how our country is supposed to work. I have a close friend who said, years ago, that the only person who could break through would be a really rich person who didn’t give a damn about winning approval. I went further than that: I was certain that many in the country were deeply disgusted with the media’s enforcement of the canon, whether or not they called it The Cathedral, and were longing to see someone take them on–and that person, yes, would have to be really rich and already famous.

Enter Trump, but this isn’t about the election. It’s All About Me.

Instead of playing my usual role disengaged but passionate political observer, I was watching a neophyte politician with a genius for stagecraft promoting exactly the ideas that I thought were necessary to win disaffected white voters, using exactly the unapologetic, flagrant violation of media expectations I thought it would take. I had skin in this game. I wanted Trump to win the GOP nomination. I hoped he would win the presidency.

Not only was I fully engaged, but I had genuine understanding and insight into the forces driving the greatest and most shocking presidential campaign in our history. No longer niche, baby.

This mattered to no one but me. My Twitter engagement numbers exploded, but as mentioned, my blog traffic was down. Moreover, I’m not a predictor. I didn’t make any Ann Coulter or Scott Adams calls early on, didn’t go out there like Bill Mitchell and confidently call the election. I’m all about if-then. In fact, while I expected Trump, my hope for his victory was an if-then:

What I valued about the experience isn’t increased fame or respect (“strange new” or otherwise). I cherished the opportunity to really participate in an earthshaking event. When you’ve spent your life in niche issues, reading about politics but not caring terribly who wins or loses,  playing on the main stage, even as one member of a huge choir, is exhilarating.

I watched the whole thing happen. Unlike the vast majority of conventional thinkers that populate the airwaves and web, I understood most of the events. I understood Trump’s popularity. I understood why the media’s anger and outrage only helped him. I understood why he didn’t apologize, didn’t back down, struck hard when attacked. I understood why his voters wanted this.

Thanks to Twitter, I got to voice my disdain of the experts (who often answered, if only to block me), as well as my considerable outrage that cable TV, in particular, gave little time to Trump voters, while over-representing Never Trumpers. (My concern was not for equal time, but for the very real probability, early on, that the Never Trump folks would undo the primary results without giving the opposition a fair hearing. Fortunately, polls intervened.)

Best of all, I found kindred spirits, people who were watching the election with very similar insights and hopes. Ed Asante and David Pinsen were , like me, were  “ordinary” people who happened to support Trump (often referred to as “sane Trump Twitter supporters”), and I thoroughly enjoyed agreeing with them throughout the year.  Media folks Mickey Kaus, Michael Goodwin, and Mark Krikorian also viewed the election through the same lens of media skepticism and enthusiasm for the ideas of Trump, if not necessarily the imperfect vessel himself.

I don’t know if I can adequately convey how much sheer fun I had actively participating, being “on point”to others  unless you, too, are an introvert whose concerns, professional and personal, are usually shared by perhaps a dozen people. Maybe a thousand or so nataionwide. And suddenly, the single biggest issue in my interest area was shared by millions.

I even learned something. While I still believe immigration won Trump the primary, I’m leaning towards the notion that trade was essential to putting him over the top. If it’s true that many Obama voters in the Big 4 (Michigan, Pennsylvania, Wisconsin, and Ohio) voted for Trump this time round, then that has to be trade, not immigration that moved them. However, Trump couldn’t (and can’t) back down on immigration, because he can’t let down the GOP base.

The campaign period was not without difficulties, but they were all the struggles of any Trump voter: reading your favorite writers express utter disdain for you, never mind Trump, getting blocked early on by conservative writers who simply couldn’t grasp what was happening to their beloved party, feeling outraged at the media’s utterly unhinged misrepresentations and open bias. Nothing to dim the joy I felt.

I don’t know if I’m going to feel more vested in political events going forward. I’m going to enjoy finding out.

So. That is my retrospective on the year.

Blogwise: traffic was down, but I still had more “big” pieces than 2014, which is still my highest traffic year. I’m down from 2015, when I had 11 pieces over 1500, this year I had only 5. The midlists were off–I had no essays with 2000 pageviews, and a ton of work that usually hit 1000 plus views didn’t make it that far. I’ve been looking at the quality and topic of the pieces, and don’t see a huge difference. Given the disconnect between my twitter growth and my blog page views fall-off, I’m thinking it might be a falloff in my teacher readers. I hope not.

But it might just be that haven’t been promoting my work as vigorously. I’ll try to do better.

I set my sights on 48 essays. Hahahahaha. I did make 37, one more than last year! I shall try again for 4 essays a month.

Essays written this year with over 1500 page views:

Title Date Views
Notes from a Trump Supporter: It’s the Immigration, Stupid! 01/31/2016 5,147
Defining the Alt Right 09/05/2016 3,499
Citizens, Not Americans 06/16/2016 3,264
The Many Failings of Value-Added Modeling 05/20/2016 1,968
The SAT is Corrupt: Reuters Version 03/29/2016 1,903

Pieces I think are quite good:

Happy Teacher Stories–I think you need to be a skeptical cynic to really deliver in this genre, so I’m born for it:

  • Citizens, Not Americans (above), is one of my favorite pieces ever; I was pleased to see it do well. I have a good friend who is a highly-esteemed professor of education, who was devastated by Trump’s win. When we go to lunch, he asks about Dwayne, Chuy, and Omar. And if you want to know how they felt about Trump’s win, check out Celebrating Trump in a Deep Blue Land.
  • Graduating My Geometry Class: I taught roughly 75% of my school’s class of 2016, including a group of freshmen four years ago in the first class of my (and their) first year.
  • A Clarifying Moment: a student comes back to visit. By the way, Hui brought me some insanely amazing baked goods for Christmas.

Classroom Action

Pedagogy

Teaching Issues–you know, these are all interesting aspects of teaching that most people don’t think about and got little traffic, so pass them on.

Education Policy:

Finally, one piece that may become more viewed in the Trump era: Arizona’s Experience and the Tale It Tells, about the Wall Street Journal’s report on Arizona’s illegal immigration law.

Thanks, as always, for reading.


Letter to Betsy (#1): Dance with the Ones Who Brung Him

Hey, Bets.

Before I start: My parents loved Amway products and I still think SA8, LOC, Pursue, and Trizyme are the awesome. Please give my best to your father-in-law. Now, to business.

Congrats on being a relatively uncontroversial Trump cabinet pick. You have been subjected to all sorts of advice, I know. But I have some qualifications that are not often found in combination.  I am the only college graduate in my family. I teach three subjects at a Title I high school.  I voted for Trump. You’re 0 for 3 thus far.

Plus, while I have no money, fame, or influence, I’m an original thinker.  You…aren’t. I’ve reviewed a number of interviews you’ve given before your nomination. I’ve read your quotes on education. Every comment you’ve made was said by others first. You’re not unintelligent. It’s just that up to now, your primary task hasn’t involved thinking, but rather signing. The education policy field is comprised of the occasional thinker, ideologically-driven funders, and far too many hacks grovelling for  whatever notion gets them the check. You’re the one in the middle.

So your contribution to education has been, literally, contributions, the checks you’ve written to further your conservative values through education reform, and therein lies a potential problem. Education reform was born out of the conservative movement, and education reform, traditional conservatives and the neo-liberals, went all in on Never Trump.  I mean, y’all didn’t even try to be nice. But then Trump won, and wow, talk about a lucky break: education is one of the areas that Trump doesn’t care about, so is happy to give out jobs to conservatives like kibble to puppies.

But precisely because Trump doesn’t care much about education, because he picked someone without giving much thought to policy, you could get into trouble. Remember that feeling all you traditional conservatives had during the primaries? The horrible, stomach-turning realization that most of the GOP didn’t give a damn about all your dearest principles? The realization that GOP voters had shrugged and voted for your candidates because they didn’t have any other choice? Except now they did?

Bets, you need to remember that feeling and hold onto it for dear life. You live in that traditional conservative bubble, the one that sees black kids getting shot by white cops and blames bad (white female) teachers.  Technically, education reform focuses on improving education, but the reason they get funding is conservative belief that decimating union clout in traditionally blue states, thus disrupting a faithful, powerful Democrat lobby, will make the world a better place.

What, you think I’m cynical? In the metric ton of writing Rick Hess does every year the words “West Virginia” rarely, if ever, appear. (I thought I’d found an example but  it turned out to be a guest blogger.) Michael Petrilli is equally uncaring about the Mountain State, and mentions Detroit often, Michigan rarely or never. Go through the list of education reform organizations and see how often they worry about those isolated Wyoming schools, or whether or not the children of those Syrian refugees Hamdi  Ulukaya brings into Idaho because apparently no native workers want employment in his Chobani yogurt factories.

Reformers might be conservative, but they target blue states and blue voters. Take a look at the school district with the greatest charter penetration  as of 2015:

charterschoolenrollment

Hey, that map looks familiar. Oh, yeah, it looks like this county by county election map for 2016:

Except it’s a weird mismatch, isn’t it? Conservative reformers have had their greatest strengths in  Democrat strongholds. Even the ones found in Trump territory are in majority-blue areas.

Here’s what the reformers never tell you while asking for funds: Charter support requires unhappy parents. But most parents are quite pleased with their schools, and most parents understand, despite years of attempts to convince them otherwise, that native ability and peers matter more than teachers and curriculum. Changing innate ability levels is tough, so selling charters means finding parents who are unhappy with their childrens’ peer groups. Put another way, all parents want their kids away from Those Kids. Charters are attractive to parents who can’t use geography to achieve that aim.

Practically, this means selling charters primarily to two groups of parents: 1) highly motivated but poor black and Hispanic parents in schools overwhelmed with low ability, low motivated kids (the KIPP sell) 2) white suburban professional parents in schools that are either too brown or too competitive for their students, but who aren’t rich enough for private school or a house in a less diverse district (the Summit sell, or the progressive suburban charter). These are very blue groups.

Understanding the charter constituency explains the discrepancies between the charter and election map, and why the discrepancies go mostly in one direction–that is, why are there blue spots on the map that don’t have significant charter penetration?

In overwhelmingly white districts, parents aren’t buying. Vermont, an all-white state, doesn’t even have a charter law, last I checked, despite being so progressive that networks called the state the minute the polls closed. The California Bay Area doesn’t have the battalion of charters you see in Los Angeles–and many of the ones that do exist are in Oakland, the only place in the Bay Area with enough blacks to support urban charters. The Bay Area and other wealthy suburbs with lots of Hispanics do get some limited support for progressive charters like Summit, in part because Hispanics aren’t easily districted out in the suburbs without inviting lawsuits and in part because suburban comprehensive high schools can be very competitive and some parents would prefer a softer environment for their snowflakes.

In dominant red states,  charters aren’t selling. Not a lot of charters in rural Mississippi and Alabama, despite the pockets of black voters, because teachers unions are historically weak in the South. Nothing of interest to conservatives. (See? Told you it wasn’t about making education better.)

Chinese, Korean, and Indian immigrants tend to build ethnic cocoons which create Asian majorities in public schools. Increased Asian presence in schools drive out whites, who find their approach to education….unattractive, giving a whole new meaning to the term white flight.  Asian immigrants are much better than whites at crafting race-segregated environments, and they aren’t terribly tolerant of blacks or Hispanics. Hence, not much need for charters. We’ll see how this all plays out when we get to third or fourth generation Asian American in significant numbers. When they don’t have enough numbers to create an enclave, Asian charter selection most closely mirrors whites–they like progressive charters or better yet, competitive ones.

None of this should be news. Michael Petrilli has been desperately trying to convince the suburbs that charters matter to them because their schools suck. Such a compelling message.

So charters, the only real success of the reform effort, have seen  their efforts pay off with quasi-private schools for people who aren’t going to be voting Republican any time soon.   GOP voters, those faithless bastards who voted in Trump, aren’t terribly interested in reform. Education Next surveys the public on those values traditional conservatives hold dear. You can see all the 10-year trends at this link, but I thought I’d pick out GOP and general public trends on a few select–and somewhat damning–questions:

First up: support for charters, unions and merit pay. GOP responses first, general public second. You can click to see the enlarged version, but  you can clearly see that two of them have flatlined and one of them is increasing slightly.

 

gop10yrtrendschartersunions

gp10yrtrendscharterunions

The increasing trendline? Union support. Yes, Bets, GOP belief that teacher unions are a net positive for schools is on  the rise. Charters and merit pay? Decreasing slightly, but look at them over time. No movement. Needle’s stopped. Public opinion, same.

I grant you, of course, that GOP voters still like unions less than Democrat ones. But I think you can agree these trendlines are all resistant to happy talk.

Next up: support for vouchers, both low income and universal.

Whoa, serious tanking there. Isn’t that your primary issue, Betsy? I’m assuming Trump hasn’t seen these numbers, or he’d wonder why he’s hiring a fool who’s gotten nothing for her money all these years. How the hell can education reformers demand merit pay when they’ve failed so miserably at their own assignments?

Reformers haven’t changed public opinion about the overall suckiness of teachers and unions or the fabulosity of vouchers.  Yeah, you’ve got more charters but not dramatically more public support for them–and the people who want and get charters aren’t grateful GOP voters. At least charters provide dramatically better academic outcomes. Oh, wait.

Where was I?

Oh. Yeah. Look. You didn’t get Trump here. The epic wave that gave Trump the win didn’t start or end with education reform. You gotta dance with the people who did get him the job. Your policies aren’t popular. Try to remember that. Try to act like that. Try to care about actually making education better, not enacting reforms that have already failed and don’t have popular support.

That doesn’t mean ignoring black and Hispanic kids.

It means coming up with education “reforms” that speak to all schools, all students. I’ll have some suggestions. I promise they won’t involve spending more money.  You won’t have to write a single check!

And remember: education reform has not traditionally been a friendly place for women in charge. Voters and parents have found them wanting. And the bosses haven’t shown much sympathy. Just ask Michelle Rhee and Cami Anderson. You don’t want Trump to suddenly start caring about education for the wrong reasons, y’know?

Happy New Year.


The Sum of a Parabola and a Line

For the past two years, my algebra students have determined that the product of two lines is a parabola, which instantly provides a visual of the solutions and the line of symmetry.  For the past year, they’ve determined that squaring a line is likewise a parabola, and can be moved up and down the line of symmetry, which is instantly visible as the line’s x-intercept. In this way, I have been able to build understanding from lines to quadratics without just saying hey, presto! here’s a parabola. I introduce them to adding and subtracting functions, and from there, it’s a reasonable step to multiplying functions.

Typically, I’ve moved from this to binomial multiplication, introducing the third form of the quadratic we deal with in early high-level math, the standard form. (The otherwise estimable Stewart refers to the vertex form as standard form, to which I say sir! you must reconsider, except, well, he’s dead.)

At some point in teaching this, you come to the “- b over 2a” (-b2a) issue. That is, teachers who like to build on existing knowledge towards each new step are a bit stuck when it comes to finding the vertex in a standard form equation.

(For non-mathies, the standard form of an equation is ax2+bx+c and the vertex form is a(x-h)2+k.  The parameters “a” “b”, and “c” are often just referred to by letter. Vertex form, we’re more likely to talk about the x and y values of the vertex, just like  when we talk about lines in the form y=mx+b, we don’t say “m” and “b” but rather “slope” and “y-intercept”. But teachers, at least, often talk about teaching different aspects of standard form operations by parameters: a>1, a<0, to say nothing of the quadratic formula.  So the way to find the vertex of a parabola in standard form is to take the “a” and “b” term and use the algorithm -b2a to find the line of symmetry,  which is the x-value of the vertex. Then”plug it in”, or evaluate, the x-value in the quadratic equation to find the y-value for the vertex.)

The only way I’ve found until now of building on existing knowledge to establish it is setting standard form equal to vertex form to establish that the “h” of vertex form is equal to the -b2a of standard form, something only the top kids really understand and don’t often enjoy. (they’re much more interested by pre-calc.)

Last year, I was putting together a worksheet on adding and subtracting lines, and on impulse I added a few that involved adding a simple parabola with its vertex at the origin with a line, mainly to add a bit of challenge for the top kids. I could see that adding a line and a parabola doesn’t provide the instant visual “hook” that multiplying or squaring lines does.

sumparabolaline

It’s obvious that the y-intercept of the sum will be the same as the y-intercept of the line. One can logically ascertain that in this particular case, the right side of the y-axis will only increase—adding two positives. The left side, therefore, as x approaches negative infinity is where the action is. But not too much action, since the parabola’s y is galloping towards positive infinity at a faster clip than the line’s is trotting towards negative infinity. So for a brief interval, the negative of the line will offset a bit of the positive of the parabola, but eventually the parabola’s growth will drown out the line’s decline.

All logically there to construe, but far less obvious at a glance.

This year, I decided to explore the relationship further, because deciphering standard form is where my weakest kids tend to check out. They’ve held on through binomial multiplication, to hang on, at least temporarily, to the linear term so that (x+3)2 doesn’t become x2 + 9. They’ve mastered factoring quadratics, to their shock. They understand how to graph parabolas in two forms. And suddenly this bizarre algorithm that has to be remembered, then calculated, then more calculations to find “y”, whatever that is. Can you say “cognitive load“, boys and girls? Before you know it, they’re using the quadratic formula for linear equations and other bad, bad things that happen when it’s all kerfluzzled in their noggins. That’s when you realize that paralysis isn’t the worst thing that can happen.

Could I break the process down into discrete steps that told a story?  Build on this notion of modifying the parent function ax2 with a line to shift it left or right? Find Raylene a new kidney now that her third husband discovered her affair with the yoga instructor and will no longer give her one of his?

My  first thought was to wonder if the slope of the line had any relationship to the graph’s location. My second thought was yes, you dweeb, “b” is the slope of the added line and b’s fingerprints are all over the line of symmetry. No, no, the other half of my brain, the English major, protested. I know that. But is there some way I can get the kids to think of “b” as a slope, or to link slope to the process in a meaningful way?

(This next part is probably incredibly obvious to actual mathematicians, but in my own defense I ran it by three teachers who actually studied advanced math, and they were like hey, wow. I didn’t know that.)

What information does standard form give? The y-intercept, or “c”. What information do we want that it doesn’t readily provide? The vertex. Factors would be nice, but they aren’t guaranteed. I always want the vertex. So if I graph the resulting parabola of the sum of, say,  x2 and 6x + 5, how might the slope be relevant?

The obvious relationship to wonder about first is the slope between the y-intercept, which I have, and the vertex, which I want. Start by finding the slope between these two points. And right at that point I realize hey,  by golly, that’s the rate of change(!).

sumparabolalineslope

The slope–that is, by golly, the rate of change(!)–is 3. The line of symmetry is -3. The vertex is exactly 9 units below the y-intercept, or the product of the rate of change and the line of symmetry. Heavens. That’s interesting. Does it always happen? Let’s assume for now a=1.

Sum Slope from y-int
to vertex
Line of
Symmetry
units from y-int to
y-value of vertex
Vertex
x2 – 4x – 12 -2 x=2 -4 (2,-16)
x2 – 10x + 9 -5 x=5 -25 (5,-16)
x2 – 2x – 3 -1 x=1 -1 (-1,-4)
x2 +6x + 8 3 x=-3 -9 (-3,-1)

Hmm. So according to this, if I were trying to get the vertex for x2 +12x + 15, then I should assume that the slope–that is, by golly, the rate of change(!)– from the vertex to the y-intercept is 6. That would make the line of symmetry is x=-6. The y-value of the vertex should be 36 units down from 15, or -21. So the vertex should be at (-6,-21). And indeed it is. How about that?

So what happens if a is some other value than 1? I know the line of symmetry will change, of course, but what about the slope–that is, by golly, the rate of change(!). Is it affected by changes in a?

Sum Slope from y-int
to vertex
Line of
Symmetry
units from y-int to
y-value of vertex
Vertex
2x2 – 8x – 5 -4 x=2 (-4/2) -8 (2,-3)
-x2 +2x + 4 1 x=1 (-1/-1) 1 (1,5)
-2x2 +14x +7 7 x=3.5 (-7/-2) 24.5 (49/2) (3.5,31.5)
4x2 +8x -15 4 x=-1 (-4/4) -4 (-1,-19)

Here’s a Desmos application that I created to demonstrate it.  The slope–that is, by golly, the rate of change(!)–from the vertex to the y-intercept is always half of the slope of the line added to the parabola–that is, half of “b”. The rate of change is not affected by the stretch factor, or a. The line of symmetry, however, is affected by the stretch, which makes sense once you realize that what we’re really calculating is the horizontal distance (the run) from the vertex to the y-axis. The stretch would affect how quickly the vertex is reached. So the vertex y-value is always going to be the rise for the number of iterations the run went through to get from the y-axis to the line of symmetry, or the rate of change multiplied by the line of symmetry x-value.

sumparabolathenut

Mathematically, these are the exact steps used to complete the square but considerably less abstract. You’re finding the “run” to the line of symmetry and the “rise” up or down to the vertex.

Up to now, I’ve been describing my own discovery? How to explain this to the kids? As is always the case in a new lesson, I keep it pretty flexible and don’t overplan. I created a quick activity sheet.sumparabolalinehandout

The goal here was just to get things started. Notice the last question on the back: “Do you notice any patterns?” I was fully prepared for the answer to be “No”, which is good, because it was. We then developed the table similar to the first one above, and they quickly caught on to the pattern when a=1.

I was a bit worried about moving to other a values. However,  the class eventually grasped the basic relationship. The slope from the vertex to the y-intercept was always related to the slope of the line added  to the parabola. But the line of symmetry, the distance from the y-axis, would be influenced by the stretch. This made intuitive sense to most of the kids. They certainly screwed up negatives now and again, but who doesn’t.

Good math thinking throughout. I heard a lot of discussions, saw graphs where kids were clearly thinking through the spatial relationship. Many kids realized that when a=1, a negative b means the slope of the line from the y-intercept to the vertex is also negative, which means the vertex must be to the right of the y-intercept. A positive “b” means the slope is positive which means the vertex is to the left. Then they realize that the sign of “a” will flip that relationship around. he students start to see the “b” value as an indicator. That is, by making bx+c its own unit, they realize how important the slope of the added line is, and how essential it is to the end result.

All that and, you might have noticed, they get an early peek at rate of change concepts.

Definitely no worse than my usual -b2a  lesson and the weak kids did much, much better. This was just the first run; the next time I teach algebra 2 I’ll get more ambitious.

So I can now build on students’ existing knowledge to decipher and graph a standard form equation rather than just provide an algorithm or go through the algebra. On the other hand, the last tether holding my quadratics unit to the earth of typical algebra 2 practice has been severed; it’s now wandering around in the stratosphere.

I don’t mean the basics aren’t covered. I teach binomial multiplication, factoring, projectile motion, the quadratic formula, complex numbers, and so on. But the framework differs considerably from my colleagues’.

But if anyone is thinking that I’m dumbing this down, recall that my students are learning that functions can be combined, added, subtracted, multiplied. They’re learning that rate of change is linked directly to the slope of the line added to  the parabola, and that the original parabola’s stretch doesn’t influence the rate of change–but does impact the line of symmetry. And the weaker kids aren’t getting lost in algorithms that have no meaning.

I could argue about this, but maybe another day. For now, I’m interested in what to call this method, and who else is using it.


Teaching US History in the Trump Era

So the first semester is coming to an end, with its three different preps and an ELL class. Up next: three trig classes. Normally, I kvetch at the idea of teaching three classes in a row. By time three, I’m improvising just to relieve the sense of deja vu (which isn’t as bad as it sounds, since it usually leads to insights into the next day). But I’m unlikely to complain anyway, since this semester I came perilously close to burning out. I managed my Thanksgiving break effectively, getting in sleep, grading, gardening, and holidaying in equal measure. I welcomed Christmas in the normal fashion, without the sense of needing it as I did going into Thanksgiving. So apart from the tedium of grading a hundred plus tests at a time (as opposed to 35 each time now), there’ll be no complaints from this quarter.

And! I’m teaching US History again. Whoo and hoo. I never thought I’d see another year when I’d use all my credentials.

When I last taught it, the big challenge was balancing content. I like teaching history in a semi-linear fashion, but there’s always something interesting in the past to bring up, and I forget all about the time. (Ha, ha.) I forgave my failings because we don’t have state tests and all evidence shows kids never remember the details anyway. You know how all the curriculum folk like E.D. Hirsch, Robert Pondiscio, Dan Willingham all say “Teachers today don’t teach knowledge?” They’re goofy. We do. Trust me. We do. But they tend not to remember. That’s another story.

Anyway. I wanted to get past World War II while still teaching my favorite topics of the past, and have been mulling possibilities in my copious spare time without much progress until The Election Happened. That, coupled with some breathing room over Thanksgiving, gave me a framework.

Five Questions:

  1. Wait–the Candidate With the Most Votes Didn’t Win?
  2. Why Black Lives Matter?
  3. What does “American” Mean?
  4. How Will You Contribute to the US Economy–aka, How Will You Pay Your Bills?
  5. What do Fidel and Putin Have to Do With Us?

I’ll continue to wordsmith the questions, but I do want them to be instantly relevant to a high school junior.

Question One

Main Idea: The Electoral College plays an important role in balancing regional tensions, a role that’s remained constant even as we’ve dramatically expanded the voting pool.
I.   History of colonial development
II. Brief (I said BRIEF, Ed!) history of Revolutionary Era
III.Constitutional Convention
IV. Rise of sectionalism and the role the electoral college played in balancing power (Hartford Convention, Missouri Compromise, Nullification Crisis, Compromise of 1850).
V. Expansion of franchise: all property holders, all men (technically, all women (technically), all citizens (really).
VI. Popular Vote/EC Splits a) Jefferson-Adams (Jefferson only won EV because of slave headcount) b) The Corrupt Bargain; c) Compromise of 1876; d) Cleveland-Harrison e) Gore-Bush f) Trump-Clinton, which I’ll probably defer until later.

Question Two:
Main Idea: “Black Lives” matter because the US violated its fundamental values to achieve and maintain unity, and our African American citizens paid the price.

I.   Development of slavery (I go way back to Portugal and kidnapping, the Papal Bull and so on)
II.  The evitable roots of American slavery and its development: Jamestown, South Carolina, Bacon’s Rebellion.
II.  The rise of Cotton
III. Deeper look at sectionalism from slavery standpoint: rise of abolition, range of reasons for opposition, free black role in movement, etc.
IV.  Civil War, Reconstruction
V.    Rise of black intellectual debate (Booker T, WEB, Garvey, MLK,).
VI.  Post-Civil Rights era–I see history past the Voting Rights as rather gloomy. Maybe examine riots in 60s/70s and compare to today?

Question Three:

Main Idea: From the first Beringian wanderers to the desperate migrants hoping for a miracle in Turbo, everyone wants to find a home here. At some point, the United States imposed its will on the process. What does that mean to the world? What does the expanding definition of “American” mean to its citizens?

I.    Early Americans and Corn Cultivation (one of my favorite topics!)
II.  Age of Exploration (again, brief, Ed!)
III.  Immigration Waves and Westward Expansion
IV.   Restriction: 1888, 1924
V.   Expansion: 1965
VI.  I’m still figuring out how to organize this.

Question Four
Main Idea: The United States’ economy has changed in many ways over the years. Many people think Trump’s victory was due in part to regional dissatisfaction with those changes. How do the transformations in the past help us understand the future–or do they?

This is a big section and I’ll have to chop it down. But it’s my favorite, so I’m listing everything to see if I can find any synergies to improve coverage.

I.    Colonial Mercantilism
II.   Hamilton vs. Jefferson (again, a favorite of mine)
III.  Rise of Industry (Eli Whitney! McCormack! Industrial espionage! and so on)
IV.  The “Worker” as opposed to the farmer or merchant (Jackson Kills the Bank will make an appearance)
V.    The Rise of Mechanization and the Industrial Era (immigration will show up again here)
VII. America as Industry Giant (Ford, impact of WWI/WWII on our dominance, the automated cotton picker & Great Migration, etc), including the rise of unions (thanks to Wagner Act)
VIII. Early Computing through the WWW and Information Age
IX.   Globalization and Automation, coupled with the fall of unions.
X.   Growing–and reducing–the work force

Question Five

Main Idea: How has the United States interacted with its neighbors near and far?

As I’ve written before, I’m a big fan of Walter Russell Mead’s Special Providence, and will use that as a sort of syllabus to outline key events in American foreign policy: neutrality, acquisitions, native American screwovers, world wars, and cold wars. I don’t have this one fleshed out, but the topic will definitely include the important international alliances that occurred before and during the Revolution, Founding Fathers, John Quincy Adams (you can get a hint of my thoughts here ). Then I’ll pick key events of interest in the 19th century, limiting my scope. Again, some talk of America’s position post-WWI/WWII, but bulk of time will be spent on Cold War and beyond, is my hope.

So.

I have a lot of these lessons done already. I didn’t like to lecture the last time I did the class because it was too tempting to just lecture the entire time. But with this structure, I think I’ll be able to give lectures as well as do a lot of readings and analysis. That’s the hope, anyway.

 

 


In Which Ed Explains Induction

So I’m at a Starbucks with my mentee, Bart. Bart looks like  Jared Leto playing Jesus. Many piercings, tattoos, big puppy dog eyes, long brown hair. We have been friends since his first day as a teacher, when I showed up in a (successful) effort to offer assistance, and I’m now mentoring him in his second year of induction (third year as a teacher.)

Some context: it is 6:15 pm. We both began our day at 7:15 am for a mandatory  75-minute staff development meeting, and not the sort where you’re surreptitiously grading papers while listening to required procedural instructions you’ve heard eight years in a row. No, this is intense department negotiations on curriculum and pacing. Interesting, but high intensity, and no checking out. Then our normal day.  Then we supervised our twice weekly, 90-minute sessions with about twenty kids working on science projects. Now we are at Starbucks, working on Bart’s induction project.  I don’t normally do the “teachers work long days” whine, but it had, in fact, been a long day.

Bart’s a great teacher, much adored by his students. He has his own idealistic values, like he still assigns homework because he wants kids to want to do it. I smile indulgently at such foolish romanticism. The guy spends hours working on lesson plans, writing extensive notes, building meaningful lessons and assessments. Not too much time–he’s not silly about this stuff–but he is a thoughtful person developing his practice, and he is in fact a really good teacher.

Induction is designed to engage and encourage new teachers to think productively about their practice. Bart and I had, up to this time, spent many hours in fruitful conversation, valuable to both of us, designing a year-long induction plan that interested him and would deepen his teaching experience.  He turned in his plan early, asking for feedback. I was pretty confident he’d be praised–my last mentee had done far less work under a different system and had done very well.

But alas, it was not to be. The induction administrator returned Bart’s plan politely, saying it showed real promise, but required a bunch of nitpicky changes.  In many cases, her changes expected Bart to be very detailed about the results of analytical or exploratory work that hadn’t yet happened.

I was very concerned. Bart thought the whole thing was absurd. So we were spending a few hours retooling his plan so that the wording pretended to comply with her demands. My years in corporate America have given me a thorough grounding in this task as well as an acute fear of failure; Bart has no such protection.

“What is the point of rewording all this?”

“Satisfying a bureaucrat without, you know, sex or money or drugs involved.”

“But why? I mean, why do we even have this induction nonsense?”

“Well, it all started with the achievement gap.”

“Induction will fix the achievement gap?”

“Of course not. Nothing will fix the achievement gap. So while there were some early successes, things mostly stalled out about twenty-thirty years ago.  Meanwhile, we started spending far more on education–bilingual education, increased academic requirements, special ed. Increased teachers–while our pay is about the same, we’ve had way more growth in teachers than in students. Many people noticed we had nothing to show for it, but no one seemed to notice that we are making far more demands on our students.”

“Completely unrealistic demands!”

“Of course. ” (Note: my original history here: The Fallacy at the Heart of All Reform on this topic is still one of my favorites.)

“But what does this have to do with this crappy makework?”

“Well, back in the 80s, when the Nation At Risk declared that we were destroying our country and Russia would win…”

“A Nation at Risk?”

I sighed. “That’s right, you went to one of those online ed schools. It was this huge report written by conservative Repulicans arguing, basically, that American high schools are destroying the country by making school too easy. So that began a wholesale upgrade of required high school courses–except, of course, many kids weren’t capable of learning advanced material. Schools tried tracking, but they were sued out of it in diverse districts, leading us to try things like differentiation and group work and resulting in the wide range of abilities you see in your classroom today.”

“Anyway, back in the 90s, it finally began to occur to folks that not all kids were ready for this material, but rather than change the requirements, they started a big push for “readiness” at the middle school and elementary school level. This is where charters had a lot of success; it’s how KIPP made its bones. Turns out  that if you cream highly motivated kids of average ability and push testing, you can bump test scores, and back in the 90s, everyone screamed that oh, my lord, this is proof that our public schools are disasters and teachers are morons.”

“Did they have success in high school?”

“No, but of course higher test scores in elementary scores would lead to  better high school performance.”

 

“That’s idiotic. High school is much more difficult. So is that when credential tests began?”

“Well, high school teachers have had difficult credential tests going back to the 70s, a fact conveniently ignored by reformers. High school teachers are well-qualified, so we already knew that boosting teacher cognitive ability doesn’t lead to higher student test scores. But what means these pesky facts in face of enthusiasm and certainty? It’s when credential tests for elementary and middle school teachers began, though. (You can read all about it here.)”

“But induction isn’t a credential test.”

“Yeah, I’m getting there. Because, as you’ve no doubt anticipated, a wholesale increase in teacher cognitive abilities didn’t have the desired result–although it did result in a huge decrease in black and Hispanic teachers, once the fraud ring was discovered and broken up.”

“Fraud ring? Like taking tests for teachers?”

“Yep. Long story. Never mind that, while the evidence for smarter teachers getting better results is fuzzy,research shows a much stronger link for achievement if teacher and student race match…”

“Teacher and student race? You’re kidding.”

“Nope. Particularly low achieving blacks. Sucks, huh.”

“Jesus.”

“Where was I? Oh, yeah. Anyway, at some point in there progressives and conservatives found something they could agree on. It was ridiculous to assume that teachers could just….teach. They sit in ed school, which is widely agreed to be a waste of time…”

“Mine was.”

“…and do a few weeks of student teaching, and suddenly, shazam. They’re teachers! Once all the professionals sat and thought about that, they decided it was stupid. After all, these professionals had insanely great test scores and got into terrific schools, but teachers, who have our nation’s kids’ future in their hands!–go to crap schools, have low SAT scores, and then we just put them in a class. This has to change. Some of them are terrible. Some quit. Let’s  invest in their success!  Give new teachers more support. Improve student achievement.Blah blah.”

“Ah. Here’s how induction comes into it. But hasn’t it always been that way? I mean, we’ve always just put teachers into a classroom. Were they smarter? I’ve heard that in the old days teachers were smart women who couldn’t get other jobs, and now we’re all idiots.”

“In fact, teacher ability has been pretty constant. While it’s true that fewer really smart women become teachers, a whole lot of reasonably smart men did, along with the existing reasonably smart women.”

“And you’re right. It has always been this way. In the very early days, teachers were taught content. But for sixty years or more, prospective teachers have spent a year or so thinking and reading about pedagogy, six to ten weeks student teaching, and then entered the classroom.”

“All so America could invent the Internet and go to the moon.”

“Win World War II, outlast Communism, make AIDS a manageable disease, and elect a black president. But yeah, faced with the choice of accepting cognitive ability or pretending that teachers are ludicrously unprepared for the classroom, it’s an easy pick: spend billions on a useless training program for new teachers.”

“And so here we are.”

“Well, be happy Linda Darling Hammond didn’t get her way. She wants teachers train for three years after graduation before getting a job. And she’s a liberal!”

“What the hell? Here’s what I don’t get. Teaching isn’t that hard…well, it is hard. But it’s not hard in a way that training helps. It’s incredibly difficult but….exciting.”

“Well, of course.  Teaching is a performance job. Teachers have an audience. And as any actor can tell you, facing a hostile audience is a hellish proposition. Facing a hostile audience every day, eight hours a day, can’t long be borne. Facing a hostile audience of 30 or more children? Sane people run screaming if they can’t do the job.”

“So teaching has its own quality control built right in.”

“Exactly. If you are completely inept, you will quit or be fired in the unlikely event you made it past student teaching.”

“But you’re not saying everyone is a great teacher.”

“No. Everyone who continues teaching is at least an adequate teacher. And beyond adequate, no one can agree on the attributes of a great teacher. Manifestly, great teachers aren’t necessary. Adequate to good teachers are sufficient.”

“But we could do better. I mean, I would have loved to have talked to you before I started work, to get a good idea of what I was facing.”

“You wouldn’t have believed me. In fact, you didn’t believe me! Remember when I gave you that assessment test to give your kids the first day, and you were shocked because it was pre-algebra? These were geometry kids, you said. They’d finish it in 20 minutes. Um, no, I said, they’d need at least 45 and my guess more. You were polite, remember? Like who is this crazy loon.”

Bart was chagrined. “My god, you’re right. I doubted you back then. And then the test took them an hour and the average score was thirty wrong.”

“You still doubt me! You shouldn’t, of course, but teaching is hard to believe until you do it. Which is why induction is a waste.”

“Well, at least they pay you to do this. I do it for free!”

“Yep. Teaching is pay to play. Anyway, it’s seven. Let’s send this off and hope it pleases the bureaucrat.”

****************************************************

(It didn’t. The bureaucrat demanded more nonsensical changes. I wrote a cranky note.)

 

 


Realizing Radians: Teaching as Stagecraft

Teaching Objective: Introduce radian as a unit of angle measure that corresponds to the number of radians in the length of the arc that the angle “subtends” (cuts off? intersects?).  Put another way: One radian is the measure of an angle that subtends an arc the length of the circle’s radius.  Put still another way, with pictures:

How do you  engage understanding and interest, given this rather dry fact?  There’s no one answer. But in this particular case, I use stagecraft and misdirection.

I start by walking around a small circle.

“How far did I walk?”

“360 degrees.”

“Yeah, that won’t work.” I walk around a group of desks. “How far did I walk?”

“360 degrees.”

“Really? I walked the same distance both times?”

“No!” from the class.

“So what’s the difference?”

It takes a minute or so for someone to mention radius.

“Hey, there you go. Why does the radius matter?”

That’s always an interesting pause as the kids take into account something they’ve known forever, but never genuinely thought about before–the distance around a circle is determined by the radius.

“Yeah. Of course, we knew that, right? What’s that word for the distance around a circle?”

“Circumference!”

“Yes. And how do you find the circumference of a circle?” There’s always a pause, here. “OK, let me tell you for the fiftieth time: know the difference between area and circumference formulas!”

“2Πr” someone offers tentatively.  I put it up:

6bitcircform1

“So the circumference is the difference between this small circle” and I walk it again “and this biiiiigg circle around these desks here.” Nods. “And the difference in circumference comes down to radius.”

Pause.

“Look at the equation. 2 Π is 2 Π. So the only difference is radius. The difference in these two circles I walked is that one has a bigger radius.”

“So the real question is, how does the radius play into the circumference?”

“Well,” it’s always one of the better math students, here: “The bigger the radius is, the farther away from the center, right?”

“So then…you have to walk more around…more to walk around,” some other student will finish, or I’ll ask someone to explain what that means.

“Right. But how does that actually work? Can we know exactly how much bigger a circle is if it has a bigger radius?”

“A circle with a radius of 2 has a circumference of  4Π. A circle with a radius of 4 has a radius of 8 Π. So it’s bigger.” again, I can prompt if needed, but my class is such that the stronger students will speak their thoughts aloud. I allow it here, because they can never see where I’m going. See below for what happens if they start with spoiler alerts.

“Sure. But what’s that mean?”

Pause.

I pass out pairs of circles, cut from simple construction paper, of varying sizes, although each pair has the same radius.

“You’re going to find out exactly how many radius lengths are in a circle’s circumference using the two circles. Don’t mix and match. Don’t write annoyingly obscene things on the circles.”

“How about obscene things that aren’t annoying?”

“If you can think of charmingly obscene comments, imagine yourself repeating them to the principal or your parents, and refrain from writing them, too. Now. You will use one of these circles as a ruler. All you have to do is create a radius ruler. Then you’ll use that ruler to tell me how many times the radius goes around the circumference.”

“Use one of the circles as a ruler?”

“You figure it out.”

And they do. Most of them figure it out independently; a few covertly imitate a nearby group that got it. Folding up one of the circles into fourths (or 8ths) exposes the radius.

radian1

Folding up one circle exposes the radius.

It takes most of them a bit more time to figure out how to use the radius as a ruler, and sometimes I noodge them. It’s so low-tech!

radian2

Curl the folded circle around the edge of the measured circle. 

But within ten to fifteen minutes everyone has painstakingly used the “radius ruler” to mark off the number of radius lengths around the circumference, and then I go back up front.

 

“Okay. So how many times did the radius fit into the circumference?”

Various choruses of “Over six” come back, but invariably, someone says something like “Six with and a little bit left over.”

“Hey, I like that. Six and a little bit. Everyone agreed?” Yesses come back. “So did everyone get something that looks like this?”

6bitcirclewradius

“Huh. And did it matter what size the circle was? Jody, you had the big two, right? Samir, the tiny ones? Same difference? Six and a little bit?”

“So no matter the circle size, it appears, the radius goes into the circumference six times, with a little bit left over.”

No one has any clue where I’m going, usually, but they’re interested.

“‘Goes into’ is a familiar term, isn’t it? I mean, if I say I wonder how many times 2 goes into 6, what am I actually asking?”

Pause, as the import registers, then “Six divided by two.”

“Yeah, it’s a division question! So when I ask how many times the radius goes into the circumference, I’m actually asking…..” The pause is a fun thing. Most beginning teachers dream of using it, but then get fearful when no one answers. No. Be fearless. Wait longer. And, if you need it:

“Oh, come on. You all just said it. How many times does 2 go into 6 is 6 divided by 2. So how many times the radius goes into the circumference is…”

and this time you’ll get it: “Circumference divided by the radius.”

“Yeah–and that’s interesting, isn’t it? It applies to the original formula, too.”

6bitcircform2

“Cancel  out the radius.” the class is still mystified, usually, but they see the math.

“Right. The radius is a factor in both the numerator and denominator, so they can be eliminated. This leaves an equation that looks like this.”

6bitcircform4

“The circumference divided by the radius is 2Π. Well. That’s good to know. Does everyone follow the math? Everyone get what we did? You all manually measured the circumference in terms of radius length–which is the same as division–and learned that the radius goes into the circumference a little bit over six times. Meanwhile, we’re looking at the algebra, where it appears that the circumference divided by the radius is 2Π.”

(Note: I have never had the experience where a bright kid figures it out at this point. If I did, I would kill him daid, visually speaking, with a look of daggers. YOU DO NOT SPOIL MY APPLAUSE LINE. It’s important. Then go to him or her later and say, “thanks for keeping it secret.” Or give kudos after the fact, “Aman figured it out early, just two seconds before figuring out I’d kill him if he spoke up.” Bright kids learn early, in my class, to speak to me personally about their great observations and not interrupt my stagecraft.)

And then, almost as an aside: “What is Π, again?” I always ask it that way, never “what’s the value of Π” because the stronger kids, again, will answer reflexively with the correct value and they aren’t the main audience yet. So the stronger kids will start talking yap about circles, and I will always call then on a weaker kid, up front.

“So, Alberto, you know those insane posters going around all the math teachers’ walls? With all the numbers?”

“Oh, yeah. That’s Π, right? 3.14.”

“Right. So Π is 3.14 blah blah blah. And we multiply it by two.”

6bitfinal

That’s when I start to get the gasps and “Oh, MAN!” “You’re kidding!”

“….so 3.14 blah blah times 2 is 6.28 or…..”

“SIX AND A LITTLE BIT!” the class always shouts with joy and comprehension. And on good days, I get applause, too, from the stronger kids who realized I misdirected them long enough to get a deeper appreciation of the math, not just “the answer”.

******************************************************

So a traditionalist would just explain it, maybe with power point. I don’t want to fault that, but I have a bunch of students who would simply not pay any attention. They’ll take the F. I either have to figure out a way to feed them the math in a way they’ll remember, or fail more kids than I’m comfortable failing.

A discovery-oriented teacher would probably turn it into a crafts project, complete with pipe cleaners and magic markers. I don’t want to fault that, but you always get the obsessive artists who focus on making a beautiful picture and don’t care about the math. Besides, it takes forever. This little activity has to be 15-20 minutes, tops. Remember, there’s still a lot to explain. Radians are the unit measure that allow us to talk about circles in terms akin to similarity in polygons–and that’s just the start, of course. We have to talk about conversion, about the power that radians gives us in terms of thinking of percentage of the entire circle–and then actual practice. I don’t have time for a damn pipe-cleaning activity.

As I’ve written before somewhere between open-ended, squishy discovery and straight discussion lecture lies a lot of ground for productive, memorable teaching. In my  opinion, good teachers don’t just transmit information, but create learning events, moments that all students remember and can use as hooks for further memories of learning. In this case, I want them to sneak around the back end to realize that  Π is a concrete reality, something that can actually be counted, if not exactly.

 

Teaching as stagecraft. All the best teachers use it–even pure lecture artists who do it with the power of their words (and an appropriate audience).  Many idealistic teachers begin with fond delusions of an enthralled class listening as they explain math in terms that their other soulless, uncaring teachers just listlessly put up on the board. When those fantasies are ruthlessly dashed, they often have no plan B. My god, it turns out that the kids really don’t find math interesting! Who do I blame, myself or them?

I never had the delusions. I always ask my kids one simple question: is your life better off if you pass math, or if you fail?  Stick with me, and you’ll pass. For many, that’s a soulless promise. To me, that’s where the fun starts. How do you get them interested? How do you create those moments? How do you engage kids who don’t care?

It’s not enough. It’s never enough.

But it’s a good way to start.