Friday, February 28, 2014

Math problems of the week: 4th grade 1920s math vs. Everyday Math

The final problem set in the 4th grade curriculum for each book:

I. Hamilton's Essentials of Arithmetic:



II. Everyday Mathematics Student Math Journal, Volume 2:



Wednesday, February 26, 2014

Aiming for mediocrity

The largest school district in Maryland, the Montgomery County Public Schools, has unrolled a new grading system for elementary school. The scale now runs from N to ES:

N: Not yet making progress or making minimal progress toward meeting the grade-level standard  
I: In progress toward meeting the grade-level standard  
P: Meets the grade-level standard by demonstrating proficiency of the content or processes for the measurement topic   
ES: Exceptional at the grade-level standard
At one school, officials explained the new system via the following analogy:
N - cannot ride a bike  
I - rides a bike with training wheels  
P - rides a bike with two wheels  
ES - rides a Pogo stick
“Ride a Pogo stick? What does that mean?” This was one of many recent reactions on a Listserv for parents of gifted kids. Nor is it this parent's only concern. When the new grading system was first unveiled, she was told that an "ES" was no longer a realistic expectation and that all kids should, in the words of a school flyer proclaimed, “Aim for a P.”

“P” as in proficient, that is; not “P” as in “Pogostick.”

What does it take to propel oneself from “P” to “P”—i.e., to “ES”? It’s not so clear. One parent asked her daughter’s teacher what grade a 73 out of 100 would translate into. “Answer: P.” How about a 93 out of 100? “P” as well. Another teacher said that getting 100 on every math test doesn’t guarantee an “ES.” And one parent whose son's reading measured at an "S" level (end of fourth grade) in the first quarter of third grade received an "I" in Reading.

When one parent asked for examples of what it would take to earn an ES in math, the teacher wrote:
I cannot send home examples of students' work on how to answer an ES opportunity question. Part of demonstrating exceptional understanding of the content is being able to independently apply the content learned and independently develop and explain the math reasoning used to solve the problem. It is through this independence and understanding that a student demonstrates his/her exceptional ability. There isn't direct instruction on how to answer an ES opportunity question.
In other words, teachers aren’t teaching to the ES-level; only to "P". It’s entirely on the students to figure out what they need to do to get an ES—or even that there is something out that they need figure out. The ball is in entirely their court, and most of them don’t know it.

Some parents have figured out that writing more than an assignment literally asks for can earn you an ES. But not always. One parent reports that the “payoff” for extra details in writing has recently been a P+.

Results of Montgomery County’s new system include:

--smart kids who hardly ever got ES’s, some of whom, their parents report, aren’t any less intelligent than older siblings who got As under the old system.

-- unmotivated kids who see no reason to try to get more than 73 out of 100—or to “write a paragraph along with every arithmetic problem” for the sake of an ES.

--parents who don’t know how well their kids are doing in school unless they see the raw scores (73 out of 100? 93 out of 100?), and, in particular, if their kids have truly mastered the material or are struggling with it or slacking off.

This last issue strikes me as yet another way in which feedback loops are disappearing from today’s schools. I’ve written here, here, and here about ways in which students are getting hardly any feedback on their work; with this kind of grade compression, in which nearly everyone gets a P, there's even less feedback, not only to students, but also to parents and schools, about what, if anything, is working in public education today.

Friday, February 21, 2014

Uncommon Students in the Common Core

My piece in how special ed students are faring under the new Common Core Standards just went up on The Atlantic:




Math problems of the week: 4th grade 1920s math vs. Everyday Math

Two approaches to multidigit multiplication:

I. From Hamilton's Essential's of Arithmetic, First Book, published in 1919:


II. From the Everyday Math 4th grade Student Math Journal, Volume 1, published in 2002:

Wednesday, February 19, 2014

RULER or Roughhousing: what's better for bullying prevention?

Two recent articles present two different strategies for reducing bullying.

In one, an opinion piece in this past week's Education Week entitled Preventing Bullying With Emotional Intelligence, authors Marc A. Brackett and Susan E. Rivers of the Yale Center for Emotional Intelligence present their program, RULER, as the panacea for bullying.

The authors begin by citing "the results of six meta-analyses" which "confirm that current anti-bullying programs are not working." They then state that these programs aren't working because they fail to address the "underlying causes." These, the authors inform us, "likely include a lack of emotional intelligence—a set of skills for understanding, communicating about, and regulating feelings."

"Likely" quickly becomes universal certainty:

What all children need instead is an education in emotional intelligence. This will help prevent children from resorting to pushing, picking on, or hurting peers as an emotional release. And for the moments when bullying is inescapable, it will help targets of bullying and bystanders develop the skills they need to manage their fear and anxiety, communicate their needs, and get support.
And emotional intelligence quickly becomes
the ability to recognize emotions in the self and in others; understand the causes of emotions and their consequences for thinking and behavior; label emotions with a sophisticated vocabulary; express emotions in socially appropriate ways; and regulate emotions effectively.
...which, via , acronymity, turns out to be none other than RULER.

But wait, there's more:
Fortunately, emotional intelligence can be taught just like math or reading. It is easily integrated into the standard academic curriculum and can improve classroom instruction and school climate. The result includes a better school, with happier and more effective educators and students and a decline in bullying. But there is a catch: Adults need training, too.
And, fortunately for the Yale Center for Emotional Intelligence, training costs money. For the cheaper option, onsite training at Yale, you've got:

Phase 1 $1800/ participant
Phase 2 $1500/ participant

For Phase 3, "different packages are available to support your rollout."

The rest of the article is an infomercial for RULER, which I blogged about earlier. It includes:

--An emotional intelligence charter: "Written collaboratively, the charter provides the backbone for creating an emotionally supportive learning environment."

--A mood meter, which "builds emotional self-awareness, helping everyone gauge their feelings throughout the day, set goals, develop self-regulation strategies, and realize learning objectives."

Research, apparently, supports all this:
A recent meta-analysis on social- and emotional-learning programs like RULER confirms that teaching emotional intelligence is the common feature among schools that have safe, caring, and productive learning environments. The best outcomes occur when lessons are taught regularly and with high quality. Indeed, in these schools, not only does bullying decrease, but mental-health indicators and academic scores also go up.
And, therefore, taxpayer dollars should supplement participant dollars:
We believe evidence-based SEL programming deserves federal funding. One House bill, the Academic, Social, and Emotional Learning Act of 2013 (HR 1875), would give the U.S. Department of Education the authority to allocate funds and establish programs to address children's social and emotional needs. If it passes, and we are hopeful that it will, it will provide federal support for teacher-preparation programs which integrate social-emotional learning into their curricula.
After all, the stakes couldn't be higher:
Neglecting the emotional education of children and adults risks leaving children at the mercy of every emotion they feel and every aggressor who comes along. This neglect has created a gap in our educational system, one through which bullies and their targets have slipped. 
A second article, forwarded to me by a reader of this blog, proposes an alternative approach to bully reduction--namely, ridding schools of recess rules. Naturally, this hasn't happened here in the litigious U.S., but down under in New Zealand.

Again, a university--actually two of them--was involved, but their venture was more experimental than self-promotional. In a two-year-long experiment at Swanson Primary School in Aukland, all recess rules were completely eliminated, and kids were allowed to (shudders!) play tag, climb trees, ride skateboards, slide on mud, and play around in a pit containing wood, tires and an old fire hose. The result?
The school is actually seeing a drop in bullying, serious injuries and vandalism, while concentration levels in class are increasing.
As one observer reports:
"The kids were motivated, busy and engaged. In my experience, the time children get into trouble is when they are not busy, motivated and engaged. It's during that time they bully other kids, graffiti or wreck things around the school."
So take your pick: pay thousands to Yale for training in emotional intelligence charter drafting and mood meteorology, or eliminate boredom and let kids run around without adult interference.

Monday, February 17, 2014

Who speaks for reading, writing and literature?

“Do you call reading work? I don’t even remember how I learned. When it was too hot to play, Grandfather would take me into his library where it was dark and cool, and read to me out loud from his books, and later I would sit beside him and read to myself while he studied."
The Witch of Blackbird Pond is one of many novels featuring smart heroes or heroines who learned how to read and/or write without formal instruction. Given that the authors are themselves smart, linguistically gifted people who may likewise have learned language arts informally, with an ear for language naturally tuned for polished prose by their typically avid reading habits, this isn’t surprising.

But what’s problematic is when the highly articulate messages of the small minority of self-taught readers and writers—messages emanating through actual or fictionalized versions of their personal experiences—are generalized to the population as a whole. Most kids won’t learn to read simply by being read to and by being surrounded by interesting books; and most kids won’t become good writers simply by writing a lot and participating in student-centered writer’s workshops. Most kids need intensive instruction in phonics and extensive feedback from discerning adults on their sentences and paragraphs, as well as extensive guidance and practice in revision.

Unfortunately, just as the kinds of people who didn’t need extensive math drills—i.e., math professors—are also, some of them, among the most convincing spokespeople for eschewing math drills (they’re math professors; surely they know what it takes to learn math!), the kinds of people who didn’t need extensive language arts drills—i.e., articulate writers and speakers—are, some of them, the most convincing (i.e., articulate) spokespeople for eschewing language arts drills.

Articulate writers and speakers also tend to be very well read, and therefore self-educated, in key content areas like history, geography, politics, and current events. As a result, they may not appreciate of the degree to which most kids depend on a systematic, content-rich curriculum at school. And, especially if their reading doesn’t extend to cognitive science research, they may become convincing spokespeople for the idea that schools should focus more on “higher level skills” rather than specific content—and/or the idea that all you have to do is encourage kids to be curious and read a lot and they’ll learn what matters on their own.

Genetics being genetics, these highly articulate but wrong-headed spokespeople also often have kids that take after them in their avid reading habits and ears for writing. As a result, they are never directly confronted with the inadequacies of the trends in education to which they so happily give verbal support, or with how rapidly everyone else’s verbal skills are declining.

Surely these people recognize how unusual their talents are, and how special their kids are (don’t all parents?). But somehow when it comes to K12 education, they forget to consider how others might differ. Or, espousing an egalitarianism that confuses equality of ability with equality of opportunity, they deliberately suppress such considerations, blissfully unaware of how many kids they’re leaving behind in the dust.

Saturday, February 15, 2014

Flipping home and school vs. homeschooling

Flipped classrooms are all the rage these days. Kids doing homework type problems at school and watching recorded lectures at home: at first, it sounds like a great idea. Why have teachers deliver live lectures when recorded lectures can be podcast? Why not have teachers instead play more active roles in helping students through assignments?

But devils lurk in the details. The best classroom “lectures” are highly spontaneous and interactive, resembling Socratic dialogs more than Shakespearian soliloquys. Lecturers instinctively adjust when listeners tune out, and would-be mind-wanderers know they might not get away with it. With canned, prerecorded lectures, inherently less engaging (no matter how many canned jokes they contain) and accessible (canned lecturers tending not to respond to requests for clarification), tuning out is both more likely to happen and easier to get away with. And there are more ways to do it. You can’t fast-forward through live lectures or skip ahead to the conclusion. But you can raise your hand and ask questions.

Homework at home, on the other hand, is an opportunity for students to be fully independent, and to enjoy freedom from the supervising eyes that, though making independent tasks more oppressive, make live lectures more engaging.

In home school, of course, flipped classrooms are impossible: except for field trips and extra-curriculars, most everything happens at home. What’s distinct here, instead, is the ratio of “lecture” to homework. Except when I briefly go over her work with her, or briefly introduce a new math concept, or when we watch a science or French video, my daughter is doing what could easily be called homework. Sometimes my supervising eyes are there; sometimes they’re elsewhere, and I’m nearly always available to clear up confusion or dialogue Socratically. But most of the time she’s working independently, and most of what she listens to isn’t a teacher up in front, but music in the background.

Thursday, February 13, 2014

Math problem of the week: Disentanglement Puzzles

Earlier, I blogged about how you make math fun not by making math more like art or dance, but through actual math problems that scratch the puzzle-solving itch. And one of the key puzzle-solving strategies I mentioned was simplification. Something looks horribly messy, like one of those disentanglement puzzles:


And your job is to figure out a clever way to simplify it. It might be a tremendous struggle, but when you figure it out, there's an equally tremendous satisfaction. And a confidence-boosting sense of your own cleverness.

But for simplification, you need complication. And for complication, you need harder math than many kids are exposed to, which in turn would require unfashionable drills in calculation and symbolic manipulation. So puzzle math (along with all the special satisfaction and feelings of cleverness) is a vanishing treat.

...Except if you’re home schooling and have the luxury of going back in time, say, to 1900s math. Here are some simplification problems my daughter has been working on this week:


While non-mathematical disentanglement puzzles are alive and while, nowhere in America’s contemporary Reform Math Algebra texts do we find any mathematical disentanglement puzzles approaching this level of complexity.

Tuesday, February 11, 2014

Home schooling update

I’m long overdue for a home schooling update (the last one was back in May). Since we’ve just reached a harmonic convergence of endings and new beginnings, this seems a particular appropriate moment.

Classically speaking, she’s just finished Genesis, encountering a few lewd concepts in the process, and is starting Exodus as I write this. She’s also just finished D'Aulare's Book of Greek Myths and starts Nathaniel Hawthorne’s retellings in A Wonder Book next week.

She’s also just moved on from The Diary of Anne Frank to The Witch of Blackbird Pond and from Tom Sawyer to Huck Finn. In the wonderful Tween Book Club for Girls run by her much beloved local aunt, she’s moved on from Alice in Zombieland (OK, not exactly a classic; the girls chose it) to The Book Thief (also chosen by the girls). Alice in Zombieland, though pretty trashy, educated my daughter on text message abbreviations (she just got an iPhone as a birthday present) which she’s now enumerated for herself on index card cheat-sheet.

Aside from the creative writing she does on her own, her prose mostly involves daily reading summaries. But now that she’s learned how to type, we’ve factored in repeated revisions. She types out a draft, I boldface stuff that’s awkward or unclear; she goes back and revises. With the ease of revision afforded by word processing (and perhaps also inspired by her earlier work with Sentence Craft), she’s also revising a lot of her sentences before I even see them, producing some quite complex but elegant ones in the process.

In math, she’s still working her way through Wentworth’s New School Algebra, most recently simplifying complex and compound fractional expressions. I’ll post an excerpt as this week’s problem of the week. A first this year was a math proof, the proof of The Factor Theorem. I walked her through the steps every morning, structuring it like a traditional geometry proof, gradually having her do more and more of it on her own. Learning it involved a combination of rote practice and conceptual understanding, two tactics that so many contemporary education experts assume are at odds with one another rather than being mutually reinforcing.

In science, in addition to the activities I blogged about last week, she’s been working through some interactive web-based materials on animal taxonomy provided by a generous curriculum developer, most recently classifying mammals by dental features.

In Social Studies, or, rather, history, she’s now two thirds of the way through Story of the World Part IV, where she continues to outline chapters. Employing the Premack Principal, she’s rewarding herself after each completed paragraph with a problem in Level IV Grid Perplexors. Combined with the summarizing she’s doing in “English and Language Arts” and the chart creation she’s doing for science, she’s now processing information in three distinct ways.

In French, she continues to work her way through ALM Level II and the LuLu series, as well as a few other short French books for young French children. But we’ve just finished French in Action, so now I’m trying to track down French language movies. It’s hard to get ones without English subtitles, so my current strategy is to have her watch the movie once with subtitles, and then do a second viewing with tape over the bottom of the screen where the subtitles appear. So far we’ve only watched one movie, the rather risqué (though not as much so as Genesis) 17 Filles, which, among other things, provides a good lesson in the virtues of nonconformity.

For art, she continues to take drawing and pottery classes at our local after-school arts center. At home, an ongoing, systematic house cleanup has unearthed a number of art kits, including a knitting set with an instructional CD more informative than her non-knitting parents can possibly be. She started that last weekend.

For music, she continues with piano, organ, and violin, including Beethoven’s Piano Sonata # 10 in C minor, Bach’s Little Fugue in G minor, and the Bach A minor violin concerto, as well as various duo, trio, and orchestra pieces.

This summer, she’ll do another two-week stint at our local theater camp, and then off to France for a 12-day summer music camp that will consist mostly of French teenagers and German counterparts wanting to improve their French. The universal language of music will unite them all.

Sunday, February 9, 2014

Autism Diaries: Quotables

A text exchange with Mommy, who somehow misplaced the lettuce she'd shredded for salad:

Did you find the lettuce?
No. Please clean up your room.
I sometimes have the same problem with homework, I thought I did it but I realized I didn't. 
In response to a query about why his paper was loose in his backpack rather than in its assigned folder:
Looks like I put it in the water instead of the boat.

Friday, February 7, 2014

Mah problems of the week: 4h grade Everyday Math vs. Singapore Mah

Two approaches to multidigit multiplication and estimation in 4th grade math.

I. From the 4th grade Everyday Math Student Math Journal, Volume 1 [click to enlarge]:



II. From the 4th grade Singapore Math, Primary Mathemaics 4A Workbook [click to enlarge]:

Wednesday, February 5, 2014

Ah-hah moments in unexpected places

My daughter has done science experiments, science kits, science projects, and interactive science activities; she's read science books filled with fancy photographs and diagrams; she's watched stunning nature videos created with state-of-the-art technology. But she's never before had a real ah-ha moment--a moment in which she actually gasped out loud--until yesterday.

The precipitating event? A stripped down, schematic, no-bells-and-whistles demonstration of convection currents in magma in the middle of a Direct Instruction Earth Science video series.

It's the kind of series that would strike many people--particularly in education--as intensely dull and rote, structured, as it is, as a series of stripped-down, step-by-step lessons in pressure, density, temperature, and basic terrestrial features and astronomy. It's filled with frequent, repetitive quizzes that occupy at least as much disk space as the lessons do. My daughter, though she enjoys the lessons, complains about how often she's quizzed. And yet I can tell she's learning a lot.

I am, too. Never before have I seen these foundational concepts explained in such depth, and I'm learning stuff I never knew, with never a moment of distracting confusion about unclear explanations or missing steps. Suddenly, a lot of things I've wondered about over the years have started making sense to me. (I should say that I stopped taking science courses after high school, and that the courses I took were pretty darn mediocre--perhaps as much so as they are today.)

Why, at a fundamental level, does hot air rise? How and when do changes in pressure cause changes in temperature? What's really going on with subduction?

The first 12 lessons alternate between lessons on the phases of matter; lessons on atmosphere, continents, oceans, continental vs. oceanic crusts, magma, and the inner and outer cores; lessons on the earth's rotation, orbit, and orientation with respect to the sun; and lessons on volume, mass, density, temperature, and static and dynamic pressure.

To some extent, it's supplementing what she's been reading about in a standard middle school earth science textbook, which I had had her set aside once I acquired this video series (from one of the Direct Instruction folks out in Eugene, Oregon). I had felt that the textbook, for all its pictures and flowcharts and lengthy chapters, didn't explain core concepts in sufficient depth.

Anyway, we working our way through the video to convention cells (I'd never learned about these before) and the relative densities of basalt vs. granite (ditto!), when all of a sudden there was a lesson on how convention cells created by dynamic pressure in magma pull apart the crusts at mid-ocean ridges and cause subduction where oceanic plates meet continental plates. And H, who'd already seen many illustrated descriptions and fancy charts about earth quakes and volcanos in her Prentice-Hall Earth Science textbook, said "Oh!" And "That's why...", and "Now I see..."--and various combinations of all three.

Suddenly everything was coming together in a way that it never had before--deeply, meaningfully, and memorably. And it was all thanks to a structured, stripped down, step-by-step, back-to-basics approach, complete with repetitive quizzes, for which Direct Instruction is so reviled by so many people.

I don't think she'll ever forget what she's learned--nor will I. And the great thing is, we have 23 more lessons to go.

Sunday, February 2, 2014

Autism Diaries: Slipping into Life... and Death

Some people invoke the Multiverse to explain how it is that the universe is tuned just right for planets, liquid H20, tidal forces, and … life. This preternaturally unlikely state of affairs is explained in a preternatural way: beyond our universe, there are multiple others—all possible ones, in fact. Even if our universe is just one in a multiple billion, we humans are in it because it’s (one of) the only one(s) we can be in.

J takes this a step further. What inspired him was a chapter in his American history textbook that described the Plymouth Landing. He wouldn’t normally have any more interest in this event than in any others—that is to say, hardly any at all—except for the fact that William Bradford happens to be his great-great-great-great....great-grand father.

We were reading about how Bradford’s first wife, Dorothy, slipped over the side of the Mayflower and drowned. What would have happened if Dorothy hadn’t slipped, it immediately occurred to me to ask him.

And, equally immediately, J grasped his personal stake in the matter, quickly expanding it to cosmic proportions. Maybe the multiverses include ones in which Dorothy didn’t lose her footing, but he has to be in one of the ones in which she did.

And that’s where Life (J’s life) comes from.

Death, too, has interested J recently--but here the trigger is a more immediate ancestor. Whenever the subject arises (often at J’s initation) of the death of his grandfather, he pulls a long face, lowers his voice, and says, with uncharacteristic earnestness, “When I saw Grandpa at Labor Day, I didn’t know he would die. I thought I would see him again at Christmas time.”

But, perhaps realizing the inevitability of it all, he’s also found a better way to spin things. “Do you think old people get tired of living?” he asks hopefully.

And a way to make light of it all. Shortly after learning the standard euphemism--“Why do people say ‘pass away'?”—he handed me a folded slip of paper. “Can you pass it to Daddy?” he asks. As soon as I do, he hollers: “You passed away!”

Taking back the slip, he unfolds it and holds it up. In his large, crude handwriting is scrawled a single word:

“AWAY.”