Wednesday, November 28, 2012

Constructivizing the Common Core, II

Vague guidelines dictated from on high tend to empower rather than challenge the Powers that Be. In the world of education, the Powers that Be are those pushing Constructivism, a teaching ideology at great odds with empirical findings about how children learn. And the vague guidelines are the Common Core Standards for K12 education. As I and others have noted (most recently Barry Garelick at the, the new Common Core Standards already appear to be enabling further penetration of Constructivism into America's classrooms.

A number of people who commented on Barry Garelick's article took issue with this, defending the Common Core as not favoring any particular educational ideology. But what matters is actual, not potential interpretation--and specifically interpretation by those in power.  For this, one need look no further than the most recent Education Week.

Consider, for example, Edweek's article on the Common Core language arts standards, which call for an emphasis on reading and writing in all academic subjects.

What the Common Core Standards for English and Language Arts actually say in terms of goals for interdisciplinary literacy is mostly innocuous, unless you find these disturbing in their extreme obviousness: the ability to cite textual evidence, determine central ideas, follow multi-step directions, understand key terms, distinguish facts from speculation, and (drumroll!) read at grade level in all subjects.

Just a few goals show Constructivist influences: integrating verbal information with information from charts or diagrams (Constructivists love "visual representations"), and analyzing the author's organization and purpose (Constructivists are obsessed with making students write about authors' intent).

But, when it comes to the Constructivists and the Common Core, author intent may be totally irrelevant.  The Edweek article opens with the following Common Core-inspired practices:

The 4th graders in Mason A. Kuhn's classroom recently wrapped up an unusual assignment: Write a science-themed book and make the target audience not their teacher but 2nd graders at Shell Rock Elementary in northeastern Iowa. One student wrote and illustrated a cartoon about a feline named Space Kat trying to figure out how to power up her rocket ship to get back home. Along the way, the story explored concepts such as gravity and friction.

At Lewis County High School in Vanceburg, Ky., science teacher Sara M. Poeppelman asks her chemistry students to closely read and analyze an essay Albert Einstein penned in 1946 for a popular science magazine.
It's one thing to make sure students understand their science textbooks; quite another to take time away from science for drawing cartoons about science concepts for 2nd graders and writing about science writing. Is this what the authors of the Common Core Standards for English and Language Arts intend?

If not, it is their responsibility to look at what's happening and say so.

Monday, November 26, 2012

Left-brain meditation, II: the distractions of the usual variety

Meditation and mindfulness don't work for me. I find it extremely difficult, and perhaps impossible, to empty my mind of words. To the extent that I succeed in being "in the moment" and not thinking tangential thoughts, in seep anxieties and broodings.

When I wish to sooth my mind, I prefer what I've called a "left-brain meditation" that operates by deep, narrow, all-absorbing distractions.

A new book called "Encyclopedia Paranoiaca," by Henry Beard and Christopher Cerf, reviewed in this weekend's Wall Street Journal, validates my sense that standard meditation isn't all it's cracked up to be. Quoting the review, quoting the book, meditation:

has been known to produce a grisly array of symptoms including, according to one expert, "uncomfortable kinesthetic sensation, mild dissociation, feelings of guilt . . . and psychosis-like symptoms, grandiosity, elations, destructive behavior, and suicidal feelings."
It seems to me that suicidal feelings, in particular, are much more likely to arise when your mind isn't distracted by something aborbing, but instead is offering that vaccuum that nature abhors.

Saturday, November 24, 2012

Math news roundup-- 11/24/12

Barry Garelick's piece on the Common Core Standards, just out this week, is here.

Meanwhile, over in Montogomery County Maryland, hundreds of parents have signed an online petition to restore ability-based math groupings:

The online petition strikes me as a great way to combat the tendency of schools to divide and conquer parental concerns by turning every problem into a problem between a particular parent/child and a particular teacher. ("If your child is bored in math, talk to your child's teacher about it.")

Since the Common Core, as Barry Garelick points out, is threatening to dumb down math instruction even further, it would be nice to see more of these parental petitions beginning to circulate.

Tuesday, November 20, 2012

The sad legacy of Everyday Math

Twice this past week I saw shocking examples of the cumulative effects of Everyday Math. Last Thursday I visited a nearby private school with sliding scale tuition and a diversity of students. For years the school had used Everyday Math, but recently, with the encouragement of a friend and colleague of mine who advises schools on math curricula, they’d begun to use Singapore Math. They’re phasing it in gradually, however, and currently don’t introduce it until 4th grade. For the first few grades, like nearly every other school in Philadelphia, they use Everyday Math.

So the 4th graders I observed had only been using Singapore Math since September. Their teacher was walking them through a topic in the 3rd grade Singapore Math curriculum: how to multiply and reduce fractions. And no one in the class who tried to answer the teacher’s questions got a single answer right. They didn’t know how to find ¼ of a 20, and they didn’t know how to reduce 5/20.

The next day I spent my first session of the school year with a group of children of French African immigrant parents who had enrolled them in an after school enrichment program I’m involved with. They were four Everyday Math-educated 5th graders, and I was exploring their mastery of addition and subtraction. Addition went fine: they know how to stack numbers and carry from one digit to the next. Subtraction was another story.

Heartened by their success adding two three-digit numbers, I asked them how to do 1000 - 91. All but one of the five students were stumped. Most got the same number: 1011. Two things had stumped them: 0 - 1, which they thought was 1, and how to borrow across more than one digit. So I gave them an easier problem, 100-71--and they were equally stumped, again getting answers that were larger than the number they were subtracting from. So I began the tricky process of teaching them how to borrow across more than one digit.

The great thing is that they were hooked. When I asked them whether their answers should be bigger or smaller than the number they were subtracting from, they all answered “smaller.” When I then asked them whether their answers were, in fact, smaller, they looked down at their sheets, and then up at me, and I had their undivided attention. These are good kids: they want to learn. And they like math.

You can’t blame the mathematical deficiencies of these 4th and 5th graders on their parents: both the private school and the after school program select for parents who care about education. You can’t blame it on the kids: my kids, who clearly wanted to learn, and had been admitted in part based on their behavior; in the private school classroom I saw, they were very well behaved. You can’t blame it on class size: the classes I observed contained between 7 and 12 students. You can’t blame it on the teachers: the teachers I saw seemed well above average in their ability to engage their students in the material at hand.

No, I’m afraid there’s only one thing we can blame here, much as the developers of the Everyday Math monolith would like to claim otherwise.

Sunday, November 18, 2012

Home schooling update, November 2012

It’s been longer than I can remember since I wrote up my last homeschooling update. Home school tends to lack clear beginnings and endings, with some stuff continuing on into the summer, and with milestones spread throughout the year. But we’ve just hit a big one: H has finished her last Singapore Math book: Challenging Word Problems for 6th grade, and has moved on to algebra.

Yes, that’s it for Singapore Math. Much as I loved the elementary school curriculum, based on what I've seen and heard about what comes next (New Elementary Math), I'm somewhat ambivalent about continuing. So I’ve selected the best beginning algebra book currently in my possession--my fragile copy of Wentworth’s New School Algebra, published back in 1898, excerpts of which I’ve frequently posted in my problems of the week. H has just finished the first chapter, calculating the value of such expressions as:

a(b+c)÷(ac-d) where a=4, b=3, c=7, d=8

She’s had a good foundation for beginning algebra, as a number of the more challenging of the Challenging Word Problems cried out for algebraic solutions, which I helped guide her through. And she seems comfortable with variables and order of operations--probably because these were covered periodically throughout latter half of the Singapore Math elementary school curriculum.

In other subjects she’s reading and summarizing the Arabian Nights, Lives of Saints, Wrinkle in Time, Watership Down, and Story of the World, III. She’s half way through French in Action and has started the ALM French Level II (a 2nd year college level French textbook). She’s working her way through a World Geography book, taking notes and copying maps. And she’s been doing a lot with sentences: combining them in Sentencecraft, unscrambling them in exercises Catherine Johnson has created for her writing class and generously forwarded to me, and, in a series of writing exercises I’ve been developing, constructing passive and active counterparts pairs to slot, as appropriate, into paragraphs.

For “extracurriculars,” there’s music every day--listening as well as practicing. H has a violin lesson on Tuesday, a piano lesson on Wednesday, duo practice on Thursday (violin duets, piano duets, and violin-piano duets), an organ lesson on Friday, and trio practice on Saturday. In the chronological survey of classical CDs that we began nearly 2 years ago, we’ve reached Prokofiev and Janáček.

Besides music, there’s horseback riding (and, shortly, cartooning) on Mondays, creative writing class on Wednesdays, pottery on Fridays, and girl scouts every other Friday evening.

Every once in a while I flirt with the possibility of the somewhat local K-8 French International School for 7th and 8th grades. But besides wondering whether H's French will be good enough by then and how the school's overall curriculum* compares with what we're doing, I think of how much harder it would be for her to keep up all those extra curriculars if she were to return to an actual school.

*The school's curriculum, taught half in French and half in English by middle school, partly follows the French national curriculum (good); and partly follows the Pennsylvania State Standards (not so good).

Wednesday, November 14, 2012

Refining your thoughts: the diminishing feedback loop

“Have any of your children ever come home with a marked up essay draft that they were supposed to revise and turn in for additional feedback?” I’ve been asking this question lately of parents of school-aged children.

I was thinking of the feedback I used to get a generation ago at my public junior high and high school in my medium income school district: those elaborates and explains on literature papers; those hows, whys, justifys, and much to generals on history essays; the gigantic question marks that sometimes appeared next to particular sentences and paragraphs; and perhaps the best prose-tightening advice I ever got: “this paragraph can be reduced by about 50% without losing any actual content.” The feedback was often quite elaborate and precisely targeted at specific sentences, but left it up to me to identify the precise problem and deal with it. If it persisted in my next draft, there’d be more feedback about it, and perhaps a one-on-one conference with my teacher. These teachers seemed to know implicitly what recent studies have been showing empirically: that one of the best ways to learn is through regular feedback and self-correction.

Of the various interdisciplinary deficits in today’s schools, perhaps the most troubling is the decline in the feedback that students receive on their thoughts. How well have they have they expressed, organized, and justified these thoughts? Are they relevant to the given assignment? Do they collectively answer the question they were supposed to address? As you might have guessed if you are the parent of a current student, none of the parents I’ve queried so far about marked up drafts has answered “yes.”

What feedback students get today appears to be a combination of “peer editing” and teacher comments on final drafts. In the case of peer editing, you’re getting feedback from non-experts, much of which is skewed by the peer pressure (or is it the societal pressure?) to be positive rather than critical. As for teacher comments on final drafts, even the most critical of these, as far as I’ve seen, focus more on global factors like organization and overall argumentation and creativity and less on the building blocks: the individual sentences, the specific thoughts they express, and their linkages to other sentences. If what I’m hearing is representative of what’s going on generally (in private as well as in public schools) revising marked up drafts is totally passé. There’s little targeted feedback, and what feedback there is doesn’t loop.

The loop is missing from more than just essays. A generation ago and before, geometry students proved theorems from axioms. Filling out the steps in our two-sided proofs gave us implicit feedback on whether each next step in our reasoning was warranted. Similar, but more compelling, was the feedback we’d get in writing our own computer programs. Back when people used relatively basic programming languages that didn’t do most of the debugging for us, we’d write basic routines, run them, debug them, rerun them, etc. Today there are actually fewer true programming courses than there used to be: “computer science” now often means Power Point, Photoshop, and web development. Students who write actual programs are mostly using higher-level programming languages that are less logically challenging and are generously forgiving of inconsistencies and syntax errors. Geometry proofs, replaced by “hands-on inquiry,” have gone the way of the Dodo.

In my earlier post on students’ diminished ability to sustain attention, I worry about a resulting decline in the ability to comprehenend, or express, ideas that are beyond a certain level of complexity. Yet another obstacle is the minimum amount of critical feedback students get on any of their thoughts.

Monday, November 12, 2012

Autism Diaries, XLI: the test

Thanks to the efficiency with which the dysfunctional network of state agencies responsible for supplying services to special needs children summarily dropped the ball on us and thousands of other Pennsylvania families over the past year, J has been attending classes without the 1:1 support that he had received ever since he was 3. It’s now been four weeks sans support, and we’re keeping our fingers crossed.

As soon as I learned that this was about to happen, I tried to milk it for what it was worth. “J,” I said, “Your behavior has been very, very good this year. Better than ever. And so we’re going to test you. We’re going to see how you do without any tss.”

Instantly his eyes lit up and a beautiful smile spread across his glowing face. He was not just flattered, but utterly delighted. For several years now he’d been hoping to rid himself of what, to him, was an increasingly irritating interference in both his autonomy and in his attempt to be just like all the rest of his classmates.

The “test” began, and he’s been playing the role of “normal” student well—astoundingly well, given how mischievous and out of control he was in his early years, with absolutely no sense of classroom rules or teacher authority. Now he follows his roster, walks calmly down the hallway, stays in his seat, and copies down things from the blackboard. He participates in class—particularly in math, where he knows the answer, or in chemistry, where he’s extremely curious about where things come from and how they work.

As the school’s special ed specialist puts it, he’s become very good at acting like a student. But his greatest weaknesses persist: language comprehension and tuning in to speech (the two, of course, are related). He takes notes without attending to meaning, once transcribing “region” as “religion.” He faces the teacher without taking in much of what he or she says (or of what his classmates contribute in response). Without an aide to prompt him to focus, his grades are starting to drop.

Luckily all the key stakeholders—except, of course, for J—are all on the same page. We agree that what he needs is no longer behavioral support, but a school district-supplied academic aide. Where the state of Pennsylvania has let us down, the school district of Philadelphia, cash-strapped though it is, must pick up the slack—as J’s new IEP now requires.

At the IEP meeting I heard various confirmations of how J’s behavior has improved. Just a couple of years ago a major disruption meant throwing a tantrum that rung through the whole building, or menacing a classmate by raising a chair over his head, or eloping to the teacher’s lounge to grab the chocolate syrup from the refrigerator and “chocolate his way back to his seat”; now it means excitedly getting out of his seat to “correct” his chemistry teacher when the teacher pretends to be about to make an egregious mistake in setting up an experiment.

How long it will take the cash-strapped School District of Philadelphia to get J an academic aide is one question. Another is how best to spin it to J. I tossed out one idea at the IEP meeting. J has been—through no encouragement whatsoever from us—increasingly interested in getting his learner’s permit. Taking advantage of his overall cluelessness (another function of not paying attention), we’ve told him that you can’t get a learner’s permit until you get straight A’s in all subjects but English, and at least B in English (even that would be a real stretch for J.)

So how about if I tell J that because his grades are dropping, he needs an academic aide in order to help him, so that he will have a better chance of getting his learner’s permit? The special ed specialist thought this was a great idea. But, remembering how just half a year ago he was still charging through the crowded hallway to get from one class to the next before anyone else did, she also said, “The day J gets his learner’s permit, I’m moving out of the state.”

Saturday, November 10, 2012

Math news roundup

In reverse order of appearance: Barry Garelick’s article in the online Atlantic on why not just writing instruction, but also math instruction, needs a revolution/
Barry Garelick’s excellent critique in Ed News of the Common Core math standards. 

Reform Math schools in Pennsylvania that were recently reprimanded by the state for not achieving “Adequate Yearly Progress” (courtesy Leigh Liberman).

An award-winning classroom math volunteer was turned away by the superintendent after months of service for his perceived opposition to the Reform Math curriculum (courtesy Leigh Liberman).

Thursday, November 8, 2012

Math problems of the week: 5th grade Investigations vs. Singapore Math

I. The first factors problem set in the 5th grade TERC/Investigations Student Activity Book, from the very beginning of the book [click to enlarge]:

II. The first factors problem set in the 5th grade Singapore Math Primary Mathematics 5A Workbook, from the very beginning of the book [click to enlarge]:

II. Extra Credit

Which approach helps lay more of a foundation for early algebra?

Tuesday, November 6, 2012

Attending to complex thoughts

As a college and graduate-level instructor, I’m constantly surprised by how much difficulty my students have with reading comprehension and with writing clear sentences. I place the blame, however, not on a failure to master the English language, but on difficulties sustaining attention, whether it’s in reading long, complex sentences or in keeping track of the long, complex sentences they themselves sometimes attempt to write. For various reasons that are visible, audible, and palpable (vibrating in our palms or pockets) all around us, it’s harder and harder for all of us to sustain attention in the course of our daily lives. Exacerbating matters, many young people haven’t developed the discipline necessary to sustain attention even when distractions are minimal.

This is particularly true of reading. As Anonymous points out in my last post on this subject, fewer and fewer kids are reading in their free time. As Auntie Ann points out, schools are assigning easier and easier texts with shorter and shorter sentences. Exacerbating things further, many reading assignments distract students with “text-to-self” or “text-to-world” connections rather than requiring them to immerse themselves in subtleties of the text itself.

This is also true of attention-demanding subjects like math, where Reform Math’s watered-down, concrete, “real-world,” problems require less and less focused, step-by-step reasoning. And it’s more generally true across the disciplines, where those group-centered activities that eat up so much of class time further distract rather than foster focused attention. Teachers (as a recent study reports) are quick to blame increasing attention deficits on video games; it doesn’t occur to them that current fads in classroom instruction may be equally to blame.

The potential consequences of all this are pretty alarming. As many have noted, there’s an intimate connection between reading, writing, and thinking. If you don’t read well, you miss much of the subject-specific content you need to take in in order to think clearly and critically within a particular subject. If you don’t read well and can’t sustain attention across longer, more complex sentences, you miss out on the immersion in good models of written language that helps students develop good writing skills. You can't produce, let alone revise, coherent complex sentences of your own.

When people, especially today’s education professionals, discuss the connections between thinking and writing, they tend to focus on the importance of “critical thinking.” Help students become better thinkers, and improved writing skills will come along automatically for the ride. There’s a lot of truth to this, but it’s not the end of the story. First of all, as cognitive scientist Dan Willingham pointed out, you can’t teach critical thinking in a vacuum; critical thinking is subject-specific and depends on mastering subject-specific content. Secondly, thinking clearly and critically about subject X doesn’t guarantee an absence of sentence fragments, comma splices, and dangling modifiers in your essay on subject X.

What many people, especially today’s education professionals, tend to ignore is the other direction of causality. Assuming a sufficiently challenging writing assignment (particularly one requiring multiple revisions), writing improves thinking. Having to put pen to paper (or fingers to keyboard) and write an essay on a challenging topic helps you clarify your ideas. Only then do certain gaps in your understanding come to light, inspiring you to think through them more carefully as you attempt to express things fully and coherently. Deciding how to slot things into main clauses or subordinate clauses, and how to order the phrases within a sentence, and how to connect one sentence to the next in a paragraph, and when and how to begin the next paragraph, forces you to focus on the relative importance of different concepts and all the different ways they relate to one another. In fact, as you read and revise what you’ve written, there’s a complex feedback loop at work that involves writing, reading, and thinking.

There’s also an intimate connection between ideas and written complexity. Some ideas are so complex that they can only be expressed in a series of complex sentences. Sentences beyond a certain level of complexity can only be fully digested in written form, where readers can take them in at their own pace and reread as necessary. If you aren’t able to sustain the attention it takes to parse such sentences in all their complexity, or to develop the skills it takes to write them, you are shut off from whole worlds of ideas, across all sorts of disciplines, from economics to psychology; from chemistry to literary analysis.

Combined with the distractions of today’s world, the decline in challenging, focused reading assignments, sentence-focused writing instruction, analytical essay writing, and multiple-revisions requirements may have consequences that are further reaching than any of us, even those of us who still think in complex sentences, can possibly imagine.

Addendum-- Here's one of the Ballot Questions that confronted me in the voting booth today:

Shall The Philadelphia Home Rule Charter be amended to authorize the creation by ordinance of requirements for additional information to be submitted with the annual operating budget, annual capital budget, and capital program, including, but not limited to, information about the cost of performing specific functions, the effectiveness of such functions, and the costs versus benefits of proposed expenditures, and to require the Finance Director to provide such information?

Sunday, November 4, 2012

Autism Diaries XL: Text-to-Self connections

Speaking of writing from a prompt about Of Mice and Men, here’s something J produced a few weeks ago in English class.

George feels mad about his siblings in charge. He lives in the house with the family. His house has 0 ceiling fans. He does something, eats food, goes to school, grows up, and rides a car. I am the only child and I live with my parents. My hose is small, 0 ceiling fans, no internet, and only 1 big gedroom, The kitchen is tiny, 1 burner, small oven, and a tiny refrigerator. I want to get a ceiling fan but my parents have no money. I also want a wii. There are no stores in my town and there is only 1 blackberry plant in my backyard. My grandparents send me food sometimes.
What you see here is J’s minimal understanding (and misunderstanding) of the story, followed by his version of a “text-to-self” (personal) connection: a series of lies about his home life. If he’d been asked to start a sentence beginning “Although George,” who knows what he’d come up with.

On the other hand, if he’d been asked write a sentence about hydrogen and oxygen that began with although, he’d have demonstrated full mastery of the meaning and usage this not particularly esoteric element of the English language.

Friday, November 2, 2012

Math problems of the week: 5th grade Investigations vs. Singapore Math

I. The first number puzzles in the 5th grade TERC/Investigations Student Activity Book, from the very beginning of the book [click to enlarge]:

II. The first number puzzles in the 5th grade Singapore Math Primary Mathematics 5B Workbook, from the very beginning of the book [click to enlarge]:

III. Extra Credit

Compare the relative challenges of figuring out the directions vs. doing the math in each of the problem sets.