Well, no. (Short Takes and Snarks)

The items below would take me a good eight months to write about in full (I made that number up), and most of them would drop off the table for the dog to snatch up (I don’t have a dog). How can someone who writes as slowly as I do still write so much?

So briefly (yes, laugh), while working on memory and math and wondering if Corona del Mar has successfully buried its cheating incident, I read many sentences that made me go “Well, no.”

1. “Even if that was necessary to success — and it’s not — surely she’ll have plenty of time later to agonize about putting a foot out of place.”–Megan McArdle, chastising America for forcing a tenth grade student to think she needs straight As.

   Well, no. For kids with no legacy, no sports, no ethnic desirability (that is, lacking URM status), and no real money, a GPA less than 4.0 puts them out of contention for a top 30 school, certainly, and probably a top 40 school as well. Now, I agree that success can be achieved from almost any starting point, but for any smart kid with strong ambition, a top-30 school should be a reasonable goal. But many kids are out of the game by freshman year, despite excellent brains, challenging transcripts, and sterling test scores, simply because they don’t obsess about grades the way that sophomore does. The problem isn’t the fear of failure, but the corrupt admissions process that has put GPA ahead of everything else. I’m a big fan of Megan McArdle, but when she shows empathy by offering up her devastation at having to settle for 7th-ranked Penn, she’s out of touch with reality—unless her column is meant as no more than a self-help guide for wealthy parents.

2. “Google attracts so much talent it can afford to look beyond traditional metrics, like G.P.A.”–Thomas Friedman, on his key insight after a free trip to the Googleplex.

   Well, no. First, as far as I’m concerned, Google just flat-out lied to Friedman. Specifically, according to Bock himself, Google does require GPA and transcripts for recent college grads. In previous years, Google demanded them from all applicants, no matter how much work experience. Less specifically, Google implies that you should just be a good, creative, humble person and they’ll take a serious look at your resume with its BS in Cognitive Science from Chico State. Please don’t believe that. Quite the contrary: you could be a really good, smart, creative person with a recent degree from Chico State and Google will laugh at your hubris in thinking you could work with God’s Chosen Few. Daniel Willingham raises his eyebrows at Google’s “purported” (ooooh, delicate, that) practices and says “Everything Bock says is probably not true, and if it were true, it would not work well in organizations other than Google.” Indeed.

3. “For context, KCPS is a system where 70 percent of students are below proficient and the average ACT score is a tick above 16.“–Ethan Gray, CEO of CEE, posting at Eduwonk.

   Well, no. That’s not context. You can’t have test score context without race.

   The Kansas City Public School district is 59% black, 26% Hispanic. The bulk of these students are also poor. The average black ACT score is 16.9, average Hispanic score is 18.8

   Considering that most blacks and most Hispanics aren’t poor, the simple truth is that Kansas City schools are probably neither better nor worse than any other urban, high poverty, black and Hispanic school district.

   But boy, it sounds sooooooo dramatic. Like, you know, the teachers are doing a bad job and if they’d just let the reformers come in, they’d have those high poverty kids at a 20 ACT score in no time.

4. “While middle school and high school may have brought a few more male teachers into the mix, the truth is, the teaching profession was and really still is, dominated by women.”—Amy Mayhew of the Tri-County Times.

   Well, no. As the article itself observes, ” male educators make up 2.3 percent of the overall pre-K and kindergarten teachers, while male elementary and middle school teachers constitute 18.3 percent of the teaching population. It evens out a little more at the high school level with men representing about 42 percent of the teachers overall.”

   Perspective: Law enforcement is roughly 20% female, federal and state combined, but the specifics vary both by agency and
   city. Meanwhile, 4% of firefighters are female, or at least were in 2008.

   So preschool and kindergarten teachers are predominantly female, just as firefighters are predominantly male. Elementary and middle school teachers are as male as cops are female, more so in many cases. And what, exactly, is the problem with the gender balance in high school? You all have got to stop treating it as one occupation.

   If you need to point and sputter at a female profession, try nursing.

5. “As for the school board, what it should do is feel ashamed for once again putting students, families and educational achievement at the bottom of its priority list.”—LA Times Editorial, on LAUSD’s refusal to renew two Aspire charters.

   Well, no. LAUSD rejected the charters because they refused to join the district’s special ed services group, or SELPA, opting instead to pay El Dorado County a small fee to basically funnel their state funds right back to them, with a much smaller haircut than LA takes. Which sounds reasonable, except California takes a $2 billion loss every year providing IDEA-mandated services that the feds don’t pay for (hi, unfunded mandate!), and much of that loss is passed on to local districts. Both San Diego and Los Angeles lose millions each year paying for mandated special education services, and they spread that cost among all the kids. But California gave charters in region the ability to pull out their kids, thus increasing the cost to all the other kids in the district who don’t go to charters. El Dorado, presumably, doesn’t take a bath on special education, so is able to do nothing except give charter funds a hair cut and send them right back. So not only do LA charters have fewer special education students, but they also aren’t required to pay for all the special ed students in the region, like all the other district schools are. (I suspect the charter schools that stay with the district do so because it’s more cost effective, and no, I don’t know why.) Special education is expensive and frustrating, and I understand why any school, any district, would get out from under its thumb. But it’s very, very weird that El Dorado gets to sit back and collect money from charters who just want to escape the costs that everyone else in their district shares. However, the shame here points directly at the LA Times. There’s all sorts of additional reporting to be done on this story, but they can’t be bothered to even really investigate how much money is funneled through El Dorado County, or why charter students are allowed to skate the burden of regional special education. Because the district kids are suffering under a bigger share of the costs, while the LA Times is bleating on behalf of the lucky lottery winners who, as the paper points out, won’t lose their schools despite all the sturm und drang.

6. “In truth, the well-off kids went to far better “common” schools. The less well-off and minority students went to schools that didn’t give them an equal shot in life. “—Andrew Rotherham and Richard Whitmire, on the reformer’s dream “common schools”.

   Well, no. It’s not the schools and teachers that didn’t give students an equal shot, but rather the students’ cognitive ability, their parents’ income, and their peers. The only one of those that schools can mitigate, somewhat, is the peer group. That, not higher quality teachers or a better curriculum, remains the appeal of charter schools, private schools, and districts with well-protected zipcodes. Tracking and a better understanding of the impact of low incentive kids would give public schools much better weapons to fight the problems caused by mixed ability and mixed incentives. Alas, the feds keep threatening public schools if their discipline records aren’t racially balanced. Meanwhile, highly sought after charter schools often expel undesirable students, often free from scrutiny, although taken in total, charters and publics have roughly the same suspension and expulsion rates. And no one wants to talk about tracking. Peer environment remains the huge unmentionable.

In Teaching, Even Caitlin Flanagan Has Her Uses

In my Saturday enrichment class, I wrote the opening paragraph to Caitlin Flanagan’s The Dark Power of Fraternities on the board:

(1) One warm spring night in 2011, a young man named Travis Hughes stood on the back deck of the Alpha Tau Omega fraternity house at Marshall University, in West Virginia, and was struck by what seemed to him—under the influence of powerful inebriants, not least among them the clear ether of youth itself—to be an excellent idea: (2) he would shove a bottle rocket up his a** and blast it into the sweet night air. (3) And perhaps it was an excellent idea. (4) What was not an excellent idea, however, was to misjudge the relative tightness of a 20-year-old sphincter and the propulsive reliability of a 20-cent bottle rocket.(5) What followed ignition was not the bright report of a successful blastoff, but the muffled thud of fire in the hole.

The class, the same students I’ve been teaching weekly since September, were finishing up a brief assignment as I wrote. You are wondering, perhaps, why I didn’t just print out the passage, but that question gives me more credit for planning than I am due.

These four boys: smart, engaged (even Francis, who still hugs the wall when I let him), fluid writers, ready readers. A joy. When I refuse to let them have “word banks”, they thrive on the challenge. When I turn over discussion to them, I get three boys eagerly arguing for their interpretation of events, individuals, authorial intent. (I have to noodge Francis). Dino is still the leader, the punky Korean kid with cowlick and attitude to spare, but Arthur and Bruce are more than willing to stand up for their own ideas. I would be happier if they remembered paper and pencil more often (here, Francis shines, always prepared, always lending out supplies, whereas I snark at the others routinely for their failure to live up to the stereotype), but in all other ways, a dream class.

Example: Our previous book was Hound of the Baskervilles. After we’d finished the book, I gave them a prompt in which I asserted my opinion, that the women of the book were opportunistic whiners, morally inferior in every way to the men, that they were weak ninnies who cared only for their own interests. They were to agree or disagree, using specific characters and their actions to support. Dino generally agreed with my position, citing Laura Lyons’ betrayal of Sir Charles, and Beryl Stapleton’s rage upon realizing her abusive husband had been cheating on her. Bruce and Arthur sympathized with the women, pointing out that they had very little control over their lives. Francis agreed with the “no choice” position, but used Mrs. Barrymore, who I honestly hadn’t even considered in writing the prompt, pointing out that she was entirely dependent on her husband to help her brother—all she did was cry about it.

So how to step it up? Last week, I dug up some of the vocabulary and grammar workbooks we keep around, and gave them each one.

“But these words are easy,” sniffed Dino.

“I haven’t seen any of them in your essays,” I noted.

“Oh,” said Arthur, always the one to see pedagogical intent. “We are working on writing?”

“Yes, I’ve been mulling the best way to challenge you, to keep this class a step beyond just an acceptably interesting way to spend Saturday afternoon. You are all effective readers who understand the importance of content knowledge. I trust you’re going to continue to build on that. So I decided you’re going to focus on writing quality. We’re going to study grammar and vocabulary in part to incorporate the deeper knowledge of vocabulary and sentence structure, and in part to give you a means to focus in on the act of writing—not the ideas and content, but the expression itself.”

So it’s a week later, and I’d told them to write three sentences using any three vocabulary words, using the structure of Subordinate Clause, Independent Clause. I had originally planned to put them on the board, go through the “work/glue” routine (more on that in a minute), and then have them rewrite.

But just then, I thought of the Flanagan piece. Like I said, not much of a planner.

The kids had finished up while I was writing, and I could hear the rustle of shock as they figured out the gist.

“This paragraph opens an article by Caitlin Flanagan on fraternities, and for now, it’s not important if you don’t know what they are. In journalism, the opening paragraph is known as the lede; when your English teachers talk about the hook, they’re describing the same thing in an annoying way.”

“Why would she write about an idiot?” asked Dino, ever the challenger.

“How did someone so stupid get to college?” Bruce wanted to know.

“Both worthy questions, but not what I want you to focus on. Anything else you notice?”

Pause.

“She doesn’t seem very sympathetic,” offered Arthur. Francis, the Clarence Thomas of my class, still silent.

“You are all focusing on the content. I knew you would. That’s a big part of my point. Not one of you ever considered the quality of the writing. How many sentences do you see, if you count the colon break as a sentence?”

“Five.”

I marked them out (as you see now).

“What do you notice?”

Pause again, but this time they examined the sentences, not the content.

Arthur: “So, okay, I don’t know if this is what you mean, but the first sentence is really, really long.”

Dino: “Yeah, and then the next one, what he’s going to do” (they giggle) “is short. And….specific. Like, you have to kind of figure out what the first sentence is about, but the second one is, like…..” he searches for a word. “blunt.”

Me: “Brutal, even.”

“The shortest sentence is the third one,” Bruce: “Which is weird, because it’s not an excellent idea.”

“Nice,” I said. “It’s almost like a bridge, a pause, to the second half of the paragraph. Go back to the first sentence, again. Dino has a good point—it’s a meandering sentence, in a way. What is it saying?”

“He’s stupid.”

“He’s young,” Francis stepped up.

“What does inebriant mean?” I asked.

Silence.

“So you ever heard of someone being inebriated?”

“Oh, is he drunk?” asked Arthur.

“Hey, ether is an alcohol, too!” from Bruce.

“So being young is like being drunk.”

“But he was drunk, too.”

“She never used the word drunk,” observed Dino. “My English teacher always tells us to be clear, not use big words just to use them.”

“Good point. Flanagan, the author, wrote this for the Atlantic, so was directing it to a highly educated audience. But you bring up an interesting point: when are writers using appropriate synonyms, bringing in the full richness of the English language, and when are they just ‘using big words’? ”

“It’s weird, too, because she’s real direct after the colon,” Arthur observed.

“Hey, excellent point. After all that lyrical description of youth and alcohol, suddenly we get the brutality.”

Dino smacked the desk. “Contrast!”

“There you go.”

“Oh, I see” Bruce leaned forward. “She kind of leads you in, it’s a nice night, he’s drunk but kind of in a nice-sounding way, and he’s young, so he has an idea.”

“Francis?” we all waited. And waited. And waited.

“It’s like the short sentence in the middle stops it.”

“Interesting. What do you mean?” we all waited some more. Dino wanted desperately to talk; I waved him down.

“Like, not telling you what happened…”

“..yet. I totally agree.” Dino could wait no longer. “It’s like she’s giving time to process what this idiot did before going on to say what happened.”

“And then she tells us what happened, and both sentences are different from the first three.” Arthur pointed out.

“What do you notice?”

“It’s like…parallel? The 20-year-old hahahahaha, um, and then the 20-cent bottle rocket.” Bruce pushed back his glasses. “So she tells you why things went wrong (eww).”

“Nice. Notice at the end, the use of two general terms that convey exactly what happened: ‘successful blastoff’ and ‘failure to launch’.” They all laughed. “So first she explains why things went wrong, then she tells you what happened, generally, and your imagination fills in the details.”

“Eww.”

“Good discussion; you’ve talked about how her writing achieved her goals. What you haven’t mentioned one way or the other is the quality of the writing.”

“I don’t know what good writing is.” from Arthur.

“Look at the board.”

They looked again, and were quiet.

“I could give you some of the technical ways in which it’s great. Remember the many times we’ve discussed working words and glue words? Let’s go through it again.

(Note: C. Edward Good’s oops book transformed my writing a decade or so ago. Good gives full credit for work/glue concept to the originator Richard Wydick, but Wydick didn’t get specific the way that Good does. I teach a modified form of Good’s structure.)

“So how much glue do you see?”

Silence.

“Wow. Not much.”

“Remember, glue is not a matter of bad or good. Articles are essential, as are conjunctions and pronouns. She uses the simple word ‘it’ to great effect. And starts a sentence with ‘And’!, which some teachers say is wrong, but they’re wrong. She opens with ‘a young man named’, when ‘Travis Hughes’ would do nicely. It’s not all about following rigid rules.”

“She uses ‘to be’ as a main verb, too.”

“Right, another thing that shouldn’t be taken to excess but is used beautifully here. And let me tell you something: I am not a fan of Caitlin Flanagan’s ideas. If she’s against fraternities then I’m strongly tempted in favor of them. But if I ever wrote an essay that’s half as evocative, as rich, as this five-sentence paragraph, I’d count it as a good day. So now, look down at your three sentences.”

They all groaned. I laughed.

“No, I’m not trying to make you feel inadequate! That’s not the point. Here’s the question: how much work did you put into crafting them? How much time did you spend choosing words, thinking about active verbs, how much did you think about how much weight each word could pull?”

“None.”

“Right. You just wanted to get the assignment done. Well, this is what I mean by our new focus on writing. When I ask you to write sentences, using a particular style, I don’t want you to just get it done. I want you to think about the words, form a picture in your head of what you want your sentence to do, or the idea you want to communicate. It’s easier at first to work with images or actions, but over time, you want to spend the same time making your ideas as vivid. But the point here is the quality of your writing, not simply putting together a grammatically correct sentence. You all have the stuff to become strong writers.”

“Writing is thinking, you always say.”

“That’s right. That’s stage one. That’s what everyone has to understand first. You’ve got that part down, all of you. Now it’s time to craft your thoughts, make them compelling, think about presenting those thoughts to their greatest advantage.”

I’ve been teaching English longer than I’ve been teaching math, really, although not in public school. Math, at its core, has a procedural, structural component rarely found in the study of either composition or literature, once you get past grammar. Writing or literary analysis doesn’t involve procedures, but an approach, a quality of thought.

I started into a full jeremiad against English high school instruction today, but decided against it. I don’t know enough about what goes on in the average classroom. Suffice it to say this: from what I see, we spend almost no time in high school English teaching students how to write well, or how to analyze literature to the extent of their ability. No, Common Core won’t fix this.

In math, improvement doesn’t count until the kid gets The Right Answer. Writing and literary analysis both have a big advantage in that respect: all improvement counts. I’ve taught ACT classes in which I’ve taken low ability kids from single incoherent paragraphs to five paragraph essays—still weak in language and grammar, but considerably improved from where they began and infinitely greater in self-expression. I’ve watched students with sixth grade reading skills suddenly realize that in two chapters of his memoir that cover Haiti, Rick Bragg barely mentioned that the oppressors and the oppressed were all black, and wonder why he avoided direct mention of this key fact, leading to great discussions of audience and ideology. None of the kids ended with significantly stronger reading skills or much more in the way of vocabulary—although they usually retain a much stronger understanding of grammar. However, they all improved in using the skills they had to think and express their ideas.

Best of all is when you get smart kids who understand what’s on offer. I can’t give them procedures. I can give paths, methods, considerations, advice. But not a flowchart on how. Sorry, Don Hirsch. It’s not all about content.

Of course, that’s what makes it so fun.

Math Instruction Philosophies: Instructivist and Constructivist

Harry Webb has been on a tear about discovery vs. traditional explanations. The hubbub has pulled the great god Grant Wiggins, originator of backward design, which is a bible of ed schools as a method for developing curriculum.

Now, let us pause, a brief segue, to reflect on those last two words. Developing curriculum. I’m talking about teachers, yes? Teachers, building their own unit lessons, their own tests, their own worksheets. As I’ve written, teachers develop their own curriculum and, to varying degrees, have intellectual property rights (I would argue) to their material. So when reformers, unions, politicians, or whoever stress the importance of curriculum, textbooks, and professional development in implementing Common Core, there’s a whole bunch of teachers nationwide snorfling at them.

So Wiggins and Jay McTighe wrote Understanding by Design, which describes their framework and approach to curriculum. It is, as I said, a bible of ed schools. I have a copy. It’s good, although you have to look past their irritating examples to figure that out.

(Note: See Grant Wiggins’ response below. I’ve reworded this slightly and separated it to respond to his concerns. Also throughout, I changed “direct instruction” to some other term, usually instructivism.)

The book clearly states that there’s no one correct approach for every situation, that arguing between instructivism and constructivism creates a false dichotomy. So I was jokingly sarcastic before, but my point is real: it’s hard to read Grant Wiggins and not think that, so far as K-12 curriculum goes, he leans heavily towards constructivist. As one example, in a text section that discusses the fact that there’s no one right approach, he includes this table on the activities dominant in each approach. When I look at this table, I see a clear preference for constructivist approaches. I also see it in this highly influential essay and much of his writing. But as Wiggins states in the comments, and in the book, he clearly denies this preference. However, Wiggins’ book is the bible of ed schools for a reason, and it’s not for its categoric embrace of all things instructivist. So put it this way: what he says are his preferences and what any instructivist would take away from his preferences are probably not the same thing. I say this as someone who periodically rereads his work because of the value I find in it once I shift my focus away from the trappings and focus in on the substance. I encourage anyone who agrees with my impression of Wiggins’ preference to read him closely, because he’s done a lot over time to inform my approach to curriculum development.

(end major edits–I put the original text at the bottom)

So Wiggins reads all this hooha, and comes out with this outstanding description of lectures and why they are a problem. I agreed with every word of this post (there are two others), so much so that I tweeted on it. (Note: I agree for math. History’s a different issue.) As I did so, I was vaguely disturbed, because look, while I don’t write a lot about ed school per se (and even defend it, slightly), I spent a lot of time in class naysaying. And if they’d been saying reasonable things like this about lectures, what had I been disagreeing about?

And then Harry comes through brilliantly, answering my question and pointing out a huge hole in Wiggins’ 3-part series:

Wiggins writes of a survey of teachers in order to support his view that different pedagogies are required to achieve different aims. Unsurprisingly, the teachers give the right answers; the ones that they probably learnt at Ed School. However, the survey response that is taken to represent lecturing is called, “DIRECT TEACHING Instruction on the knowledge and skills.” Now, although I do not recognise my practice in Wiggins’ definition of lecturing, I do recognise myself in this definition wholeheartedly. And so I think we are being invited here to see all direct teaching – dare I say direct instruction – as non-interactive lecturing that lasts for most of a period.

Hey. Yeah. That’s right! Wiggins naysays the lecture in his essay, but the overall debate is between instructivism, of which lectures are just a part, and it’s , and it’s instructivism that has a bad name in ed school, not solely lectures. Harry says that he explains in classroom discussion, but rarely lectures. Which may sound like someone else.

Harry scoots right by this, because he’s all obsessed about the fuzzy math and constructivist debate, and it occurred to me that this area needs elucidation, because most people—and reporters, I am looking at you—don’t understand this difference.

So here it is: not all explanation is lecture, and not all discovery is constructivist.

In an effort to not turn all my posts into massive tomes (don’t laugh), I’m going to write about this difference later. Here, I’m just going to show you the difference through different teachers.

Before I start: labels are hard. Roughly, the terms reform, student-centered, constructivist, “facilitative” (Grant Wiggins’ term) all refer to the open-ended investigative approach. Instructivist, teacher-centered, traditionalist, direct instruction are all terms used to describe the approach where the teacher either tells you how to do it or wants you to figure out the way (not a way) to do it. (Note: I left “direct instruction” in here, because I believe it’s still an instructivist approach.)

Very few math teachers are pure constructivist. We’re talking degrees. I have no data on usage rates, but I’d be pretty surprised if 80% of all high school math teachers didn’t use traditional instruction-based approach for 90% of their lessons. I speak to a lot of colleagues who dislike pure lecture and would like to teach a more modified instructivist mode, but they aren’t sure how it works. However, most high school math teachers are instructivists who lecture. Full stop.

Constructivist Approach (aka investigation, reform)

Dan Meyer: Dan Meyer’s 3-Act Meatballs
Fawn Nguyen: Barbie Bungee
Fawn Nguyen Vroom Vroom
Michael Pershan: Triangles and Angles (he calls this investigation. I’d personally characterize it as “in between”, but it’s his call.)
Cathy Humphries: Investigation into Quadrilaterals

This is a partial list. Dan’s blog has links to all his various projects, as well as other bloggers committed to the investigative approach.

(By the way, I am dying to do the Vroom Vroom one, but I’m not enough of a mathematician to understand the math behind it. Neither does Fawn, apparently. The math looks quadratic. Is it?)

I’m not a fan of the open-ended reform approach, but I like all sorts of the activities the constructivists come up with. I just modify them to be more instructivist.

Remember that both Meyer and Nguyen use worksheets, practice skills, and many other elements that are pure instructivist. Pershan rarely does open-ended activities. In contrast, Cathy Humphries is very close to pure constructivist math. Total commitment to reform.

Traditional Instructivism (Lectures)

Much MUCH harder to find traditionalists bloggers. I’ve included two of my “lectures” that have relatively little discussion, just to fill out the list:

Me: Geometry: Starting Off
Me: Binomial Multiplication and Factoring with the Rectangle

Dave at MathEquality is traditionalist, a guy who works hard to explain math conceptually, but does so for the most part in lecture form. However, it’s also clear he keeps the lectures fairly short and gives his students lots of in class time for work.

But he’s the only one I can find. Right on the Left Coast appears to be a traditionalist, but he writes more about policy and his disagreement with traditional union views. (Huh, I should have mentioned him in my teacher blogger writeup of a while back.)

In order to give the uninitiated a good idea of what lecture looks like, three google searches are informative:

factoring trinomials power point

holt math power point

McDougall Litell math power point

Many high school teachers build their own power point explanations. Others just take the ones provided by publishers.

Still others use a document camera or, if they’re extremely old-school, transparencies.

What they look like is mostly this:

Khan Academy: Isosceles Right Triangles

Many teachers are really, really irritated at the fuss over Khan Academy because all he does is lecture his explanations—and not very well at that.

The most vigorous voices for traditional direct instruction comes from people who don’t teach high school math. That’s not a dig, it’s just a fact.

Modified instructivist

I’m not sure what to call it. There’s not just one way to depart from instructivist or constructivist. The examples here generally fall into two categories: highly structured instructivist discovery, and classroom discussions with lots of student involvement.

Me:Modeling Linear Equations
Me: Modeling Exponential Growth/Decay
Michael Pershan: Proof with Little Kids
Michael Pershan: Introducing Polar Coordinates
Michael Pershan: The 10K Chart
Ben Orlin: …999…. and the Debate that Repeats Forever.
Ben Orlin: Permutations and combinations

For a complete list of my work, check out the encyclopedia page on teaching. I likewise recommend Pershan and Orlin’s blogs.

A question for Grant Wiggins, and anyone else interested: what differences do you see in these approaches?

A question for reporters: when you write about reform or traditional math, do you have a clear idea of what the fuss is about? And did these examples help?

Question for Harry Webb: You sucked me into this, dammit. Satisfied?

If you have good examples of math instruction that falls into one of these categories, or want to propose it, tweet or add it to the comments. I’m going to write up my own characterizations of this later. Hopefully not much later.

*******

Here’s what I originally said in the changed paragraph:

So Wiggins and Jay McTighe wrote Understanding by Design, which describes their framework and approach to curriculum. It is, as I said, a bible of ed schools. I have a copy. It’s good, although you have to look past their irritating examples to figure that out. The book clearly states that there’s no one right answer, that arguing between direction instruction or constructivism creates a false dichotomy, but then there’s this table on the activities dominant in each approach. Cough. Okay, no one right answer, but a strong preference for facilitative/constructivist.

The Encyclopedia of Ed

It’s so weird. I thought I saw Old Andrew or Andrew Old or whoever publish a guide to the key posts on his site. Which gave me the idea. And now I can’t find it. Perhaps I hallucinated.

Anyway, for whatever reason, I thought it might be nice to categorize my essays by topic. So I did. Originally one big post. Then one big page, since I thought I might update the encyclopedia as time goes on. Then four pages, which Elegant Grunge, the theme of which I’m quite fond, wanted to put at the top of the page. I think I’ve convinced Grunge otherwise.

As I say in the intro:

Every so often I run across a forum conversation, in which one poster says “Hey, I remember reading a teacher who talks about HBD stuff” or “What’s the blog of that teacher who writes about IQ?” The answer always comes in a minute or two, and the answer is never not me. Like Michael Clayton, I ‘ve made a niche for myself. (I miss Sidney.)

So I’m the HBD teacher. But I write about a lot of stuff. Fox (sigh), not hedgehog. Occasionally, fans of one aspect of my work realize they were playing one of the blind men, with me as the camel. “Um, what? This awesome math teacher thinks immigration is bad for education?” (well, I might have made up the adjective.)

Hence the Encyclopedia, from Controversial to Universal.

They are on the sidebar. But what the heck, you’re here, so:

Part I: Things Voldemortean

Part II: The Players

Part III: Teaching

Part IV: Miscellany, Movies and Me