Wednesday, April 30, 2014

Other parents and other children, II

While I’m ready at the drop of a hat to advocate for the unmet needs of precocious children (albeit mostly blogging about those who are precocious in math, programming, and hard science), I have to admit that I don’t always find myself feeling quite so charitably towards certain of their parents.

I wrote about this earlier after engaging with a very proud dad who goes by the name of Physicist Dave--in what was one of the most maddening e-exchanges I've ever had. As I noted then, what really bugs me about this certain subset of parents is what I perceive as:

(1) a lack of sympathy for the needs of other children: children who may be reasonably intelligent in many ways, but, compared with their own kids, are (at least in certain respects) less precocious and less driven, or simply less privileged.

(2) a lack of appreciation and sympathy for the concerns of these other parents vis a vis these other children.

I aired some more of my grievances in a recent comment thread, which I’ve decided to repost here, elaborated a bit and edited for clarity:

It’s hard for parents who are gifted readers, and/or whose kids are gifted readers, to put themselves in the shoes of average or struggling readers.
It’s hard for people who have never had to worry about their own kid’s reading skills and who haven’t spent time in regular language arts classrooms in today’s public schools or time tutoring typical kids extracurricularly to see just how deficient reading instruction in schools has become and how this plays out in later grades for non-gifted readers.
It’s hard for parents whose kids are natural sponges for information and have plenty of extracurricular opportunities to learn things to appreciate that many reasonably intelligent children are different. It's hard for these parents to recognize that many reasonably intelligent kids, whether from distractibility or self-absorption or narrow obsessions or anxiety, frequently tune things out or lack the levels of curiosity that drive others to know everything about everything--or are simply less privileged and lack extra-curricular opportunities for learning. And it's hard these parents to appreciate how much more the parents of these other kids therefore depend on schools to teach them the vocabulary and core cultural and historical knowledge that becomes increasingly crucial for later reading comprehension. Not having to depend on schools to do this for their own kids, such parents can, in addition, be blissfully unaware of how deficient today’s schools are in teaching this core knowledge in ways that lead to long-term knowledge retention.
It’s hard for people whose kids read copiously on their own to see just much less other kids are reading on their own—even ones whose parents read great books to them every day and take them to the library once a week and keep screen time to a minimum and give them books, rather than video games, at every gift-giving occasion.  
And it’s hard for people who haven’t thought deeply about what goes into language comprehension and reading comprehension to appreciate the subtle challenges faced by non-gifted readers, including the many reasonably intelligent kids who have had, for all the above reasons, to depend much more on school-based instruction than their own kids have, as well as the different levels of incomplete comprehension that may slow progress or subtly turn kids off to reading.
Is my frustration out of line? Do others share it? Please weigh in.

Monday, April 28, 2014

What reading comprehension means in the digital age

A propos of a lengthening comment thread on my last post, here, via Joanne Jacobs, are some excerpts from an article in the Washington Post containing a bunch of testimonials from college students and other adult readers on what it's like to read classic (and popular) novels in the digital age.

From a 35-year-old graduate student in creative writing at American University:

“It’s like your eyes are passing over the words but you’re not taking in what they say,” she confessed. “When I realize what’s happening, I have to go back and read again and again.”
Then there's Brandon Ambrose, a 31-year-old Navy financial analyst:
His book club recently read “The Interestings,” a best-seller by Meg Wolitzer. When the club met, he realized he had missed a number of the book’s key plot points. It hit him that he had been scanning for information about one particular aspect of the book, just as he might scan for one particular fact on his computer screen, where he spends much of his day.
Then there's Ramesh Kurup, aged 47:
Working his way recently through a number of classic authors — George Eliot, Marcel Proust, that crowd — Kurup ... discovered that he was having trouble reading long sentences with multiple, winding clauses full of background information. Online sentences tend to be shorter, and the ones containing complicated information tend to link to helpful background material.
Then there's Maryanne Wolf, a Tufts University cognitive neuroscientist and one of the pre-eminent scholars of reading skills:
After a day of scrolling through the Web and hundreds of e-mails, she sat down one evening to read Hermann Hesse’s “The Glass Bead Game.”
“I’m not kidding: I couldn’t do it,” she said. “It was torture getting through the first page. I couldn’t force myself to slow down so that I wasn’t skimming, picking out key words, organizing my eye movements to generate the most information at the highest speed. I was so disgusted with myself.”
Wolf worries "that the superficial way we read during the day is affecting us when we have to read with more in-depth processing." She reports that:
Several English department chairs from around the country have e-mailed her to say their students are having trouble reading the classics.
“They cannot read ‘Middlemarch.’ They cannot read William James or Henry James,” Wolf said. “I can’t tell you how many people have written to me about this phenomenon. The students no longer will or are perhaps incapable of dealing with the convoluted syntax and construction of George Eliot and Henry James.”
If this is what's going on in college English departments, we should wonder all the more about the ability of college-bound 7th graders to handle The Jungle and Beowulf. Is the problem that kids aren't being assigned difficult enough texts in grade school? Or is it that they aren't being assigned books that are within their current reach for comprehension? And that they aren't being held accountable for their depth of understanding both of the books as wholes, and of the more complex sentences and passages within these books, with their unfamiliar words, structures, and references?

Saturday, April 26, 2014

Trivializing reading comprehension, II

Seventh graders at our local public school are divided into two levels based on perceived ability. Here are the opening passages of two of the books that the upper-level 7th graders were assigned to read this year. First, from Seamus Heaney's translation of Beowulf:

So. The Spear-Danes in days gone by
and the kings who ruled them had courage and greatness.
We have heard of those princes' heroic campaigns.
There was Shield Sheafson, scourge of many tribes,
a wrecker of mead-benches, rampaging among foes.
This terror of the hall-troops had come far.
A foundling to start with, he would flourish later on
as his powers waxed and his worth was proved.
In the end each clan on the outlying coasts
beyond the whale-road had to yield to him
and begin to pay tribute. That was one good king.
Afterwards a boy-child was born to Shield,
a cub in the yard, a comfort sent
by God to that nation. He knew what they had tholed,
the long times and troubles they'd come through
without a leader; so the Lord of Life,
the glorious Almighty, made this man renowned.
Shield had fathered a famous son:
Beow's name was known through the north.
And a young prince must be prudent like that,
giving freely while his father lives
so that afterwards in age when fighting starts
steadfast companions will stand by him
and hold the line. Behaviour that's admired
is the path to power among people everywhere.
Shield was still thriving when his time came
and he crossed over into the Lord's keeping.
His warrior band did what he bade them
when he laid down the law among the Danes:
they shouldered him out to the sea's flood,
the chief they revered who had long ruled them.
A ring-whorled prow rode in the harbour,
ice-clad, outbound, a craft for a prince.
They stretched their beloved lord in his boat,
laid out by the mast, amidships,
the great ring-giver. Far-fetched treasures
were piled upon him, and precious gear
I never heard before of a ship so well furbished
with battle tackle, bladed weapons
and coats of mail. The massed treasure
was loaded on top of him: it would travel far
on out into the ocean's sway.
They decked his body no less bountifully
with offerings than those first ones did
who cast him away when he was a child
and launched him alone out over the waves.
And they set a gold standard up
high above his head and let him drift
to wind and tide, bewailing him
and mourning their loss. No man can tell,
no wise man in hall or weathered veteran
knows for certain who salvaged that load.
Second, from the opening of Sinclair's The Jungle:
It was four o'clock when the ceremony was over and the carriages began to arrive. There had been a crowd following all the way, owing to the exuberance of Marija Berczynskas. The occasion rested heavily upon Marija's broad shoulders—it was her task to see that all things went in due form, and after the best home traditions; and, flying wildly hither and thither, bowling every one out of the way, and scolding and exhorting all day with her tremendous voice, Marija was too eager to see that others conformed to the proprieties to consider them herself. She had left the church last of all, and, desiring to arrive first at the hall, had issued orders to the coachman to drive faster. When that personage had developed a will of his own in the matter, Marija had flung up the window of the carriage, and, leaning out, proceeded to tell him her opinion of him, first in Lithuanian, which he did not understand, and then in Polish, which he did. Having the advantage of her in altitude, the driver had stood his ground and even ventured to attempt to speak; and the result had been a furious altercation, which, continuing all the way down Ashland Avenue, had added a new swarm of urchins to the cortege at each side street for half a mile.
This was unfortunate, for already there was a throng before the door. The music had started up, and half a block away you could hear the dull "broom, broom" of a cello, with the squeaking of two fiddles which vied with each other in intricate and altitudinous gymnastics. Seeing the throng, Marija abandoned precipitately the debate concerning the ancestors of her coachman, and, springing from the moving carriage, plunged in and proceeded to clear a way to the hall. Once within, she turned and began to push the other way, roaring, meantime, "Eik! Eik! Uzdaryk-duris!" in tones which made the orchestral uproar sound like fairy music.
"Z. Graiczunas, Pasilinksminimams darzas. Vynas. Sznapsas. Wines and Liquors. Union Headquarters"—that was the way the signs ran. The reader, who perhaps has never held much converse in the language of far-off Lithuania, will be glad of the explanation that the place was the rear room of a saloon in that part of Chicago known as "back of the yards." This information is definite and suited to the matter of fact; but how pitifully inadequate it would have seemed to one who understood that it was also the supreme hour of ecstasy in the life of one of God's gentlest creatures, the scene of the wedding feast and the joy-transfiguration of little Ona Lukoszaite!
Heaney's translation of Beowulf runs to over 100 pages; The Jungle spans 413. The 7th graders are supposed to "annotate" each text with underlines and comments. They also read other texts, including an article about post modern literary theory.

Back in my day, we 7th graders were reading books like To Kill A Mockingbird:
When he was nearly thirteen, my brother Jem got his arm badly broken at the elbow. When it healed, and Jem's fears of never being able to play football were assuaged, he was seldom self-conscious about his injury. His left arm was somewhat shorter than his right; when he stood or walked, the back of his hand was at right angles to his body, his thumb parallel to his thigh. He couldn't have cared less, so long as he could pass and punt.
When enough years had gone by to enable us to look back on them, we sometimes discussed the events leading to his accident. I maintain that the Ewells started it all, but Jem, who was four years my senior, said it started long before that. He said it began the summer Dill came to us, when Dill first gave us the idea of making Boo Radley come out.
I said if be wanted to take a broad view of the thing, it really began with Andrew Jackson. If General Jackson hadn't run the Creeks up the creek, Simon Finch would never have paddled up the Alabama, and where would we be if he hadn't? We were far too old to settle an argument with a fist-fight, so we consulted Atticus. Our father said we were both right.
Being Southerners, it was a source of shame to some members of the family that we had no recorded ancestors on either side of the Battle of Hastings. All we had was Simon Finch, a fur-trapping apothecary from Cornwall whose piety was exceeded only by his stinginess. In England, Simon was irritated by the persecution of those who called themselves Methodists at the hands of their more liberal brethren, and as Simon called himself a Methodist, he worked his way across the Atlantic to Philadelphia, thence to Jamaica, thence to Mobile, and up the Saint Stephens. Mindful of John Wesley's strictures on the use of many words in buying and selling, Simon made a pile practicing medicine, but in this pursuit he was unhappy lest he be tempted into doing what he knew was not for the glory of God, as the putting on of gold and costly apparel. So Simon, having forgotten his teacher's dictum on the possession of human chattels, bought three slaves and with their aid established a homestead on the banks of the Alabama River some forty miles above Saint Stephens. He returned to Saint Stephens only once, to find a wife, and with her established a line that ran high to daughters. Simon lived to an impressive age and died rich.
Children of my generation read less on their own than kids a generation earlier, and the quantity and difficulty of our reading assignments--as well as our verbal SAT scores--reflected this.

But the children of the wired world are reading even less. Thanks to this diminished reading, as the College Board has recognized, their vocabularies are smaller than ever. Similarly smaller than ever, as textbook companies have recognized, is their capacity to handle complex sentences, particularly archaic sounding ones. And also thanks to today's reading habits, along with the failure to hold kids responsible for substantive bodies of factual information in social studies, students today are acquiring less historical background knowledge than ever before.

So how is it that these particular kids--bright though they surely are--are able to make sense scores of pages of Beowulf or of 100s of pages of The Jungle? Or of academic essays in literary theory? The more I wonder about this, the more I see a parallel between:

(1) the assumptions about reading comprehension seen in the Common Core Standards (and in Common Core proponents), and

(2) the assumptions about reading comprehension seen in certain "rigorous" English classes.

After various exchanges with the Common Core enthusiasts vis-à-vis how accessible certain passages are to students with language comprehension challenges, I had already started to wonder what people today mean by "reading."

As far as comprehension goes, reading should mean the same as listening: i.e., attending to entire sentences, phrase by phrase, and making complete sense of them. Of course, it's not clear that people really even listen any more. Willingness to sustain attention, even in everyday conversation, seems always to be at a record low.

As for "reading," perhaps all it amounts to these days is letting the words flow over you, taking in (or underlining) certain key words and maybe making a few text-to-self connections in the margins. Then, when you have to write a paper--or do a project--about something you've "read," you do Internet "research," looking up the plot and characters on SparkNotes, and seeing the movie if one is available.

In the process, all of these high expectations backfire. What I wrote in my Atlantic article about special needs students:
Forcing all students into the same, age-pegged standards deprives atypical students of optimized learning opportunities and attainable goals at their level of developmental readiness. Far better for an eighth grader who is four years behind in language to read texts with vocabulary and sentence complexity just above her current skill level than to struggle through 67-word sentences in Tom Sawyer using story boards as crutches.
applies, with a few minor word changes, to students in general:
Forcing all students to meet above-grade-level expectations deprives most students of optimized learning opportunities and attainable goals at their level of developmental readiness. Far better for a student to read texts with vocabulary and sentence complexity and assumed background knowledge just above her current skill and knowledge level than to struggle through college-prep level texts using SparkNotes (whoops, I mean "Internet research") and movies (whoops, I mean "cinematic texts") as crutches.

Thursday, April 24, 2014

Math problems of the week: rectangles in Reform Math vs. Singapore Math

The final rectangle area problems in 4th grade Investigations Math vs. Singapore Math:

Investigations Math (Student Activity Book, Unit 4, p. 68):

Singapore Math (Primary Mathematics 4B workbook, Review 5, p. 184)

Tuesday, April 22, 2014

Trivializing reading comprehension, Part I

It should be a noncontroversial point: a significant number of kids don't comprehend texts at reading levels based on their calendar age and would do better with reading assignments that meet them at their Zone of Proximal Development.

And yet this point has become the bull's eye for a critique published last week on the Huffington Post by three people affiliated with the Harvard Graduate School of Education, including one whose work "focuses on education policy related to students with disabilities" and one who is the Silvana and Christopher Pascucci Professor of Practice in Learning Differences.

Their critique forms the basis for the claim expressed in the title of their article, "Don't Believe the Hype: Students With Disabilities Should Benefit From the Common Core," and for their claim that one source of this "hype," namely, my recent Atlantic article, is based "on anecdotes and misleading and false information."

They claim, first, that I way overestimate the percentage of kids with significant learning disabilities; second, that "most students with disabilities can meet high academic standards when provided with effective inclusive instruction and appropriate accommodations and supports," third, that "most major disability rights organizations support the Common Core standards," fourth, that the CCSS are "internationally benchmarked to enable students to compete in the global economy," fifth, that "imposing systematically lower expectations can make it difficult for students who are struggling academically to keep pace with their peers and meet the requirements for high school graduation," and sixth, that "lower expectations for some students... disproportionately impact poor and minority students."

Notably absent from this article is any mention of the benefits of basing reading assignments on ability level or Zone of Proximal Development; any appreciation of the variety and prevalence of impairments that affect reading comprehension; any mention of my discussion of the limitations and downsides of "accommodations and supports" for reading comprehension; and any mention of the specific CCSS sample passage I discuss as posing reading comprehension challenges for those who don't read at the calendar-aged-based grade levels assumed by the Common Core. Given that all three authors are supposed to be education experts and at least two of them are supposed to be disability experts, these omissions are rather astounding.

Furthermore, as their Argument by Appeal to Authority suggests, it would appear that many other disability "advocates"/"experts" share their lack of appreciation for the variety of ways in which different disabilities can affect reading comprehension, and for the variety of disabilities that that are implicated in reading comprehension difficulties--not to mention the numerous reports from special education teachers, parents of special education students (I am one of them) and special ed students themselves about just how frustrating and limiting these CCSS standards are proving to be in the actual field.

The armchair quality of this cluelessness also appears in the comments that one of the authors made in response to my follow-up comments:

Essentially, your argument is that it is preferable for students who struggle to read to focus on the remediation of their perceived “deficits” rather than using reasonable accommodations to access high level content. This is the sort of ablest perspective that keeps students with language-based learning disabilities from developing the high order skills they will need to succeed in post-secondary education and the labor force.
The best estimates suggest that approximately 1 out of every 100 children have the types of cognitive disability that preclude them from successfully working at grade level.
I love it: I'm an ablest! As I wrote in response:
Language comprehension disorders that significantly impede comprehension of passages like the Twain passage are far more prevalent than you suggest. Autism alone, according to the CDC, affects 1 in 68 kids, and receptive pragmatics is universally impaired in autism. Then there is Specific Language Impairment, which affects 7 percent of all children. This, too, significantly affects language comprehension. Even ADHD (over diagnosed though it is!) has been implicated in impaired comprehension of complex language.
These issues, again, are subtle, and require a deep understanding both of these (rather prevalent) language challenges, and of the linguistic and cognitive issues that underpin language comprehension, which range from syntactic parsing and working memory to receptive pragmatics and social inferencing, as well as subtle deficits in assumed cultural background knowledge that differentially affect those who tune into the world in non-neurotypical ways.
Beyond all this, it's also important to consider the reading comprehension challenges of those "uncategorized" children who are either ELL students, or have gotten behind in reading comprehension for other reasons (inadequate reading instruction; inadequate instruction in core background knowledge). These children, too, will fail to reach their potential if placed at calendar-age-based reading levels.
The more I look around, the more "education experts" I see who seem to be unable to put themselves in the shoes of developing readers with various challenges that subtly affect comprehension. At the very least, educators should be using standardized, normed assessments to place children at instructionally appropriate levels. Even better would be if at least some of these people showed at least some curiosity about the linguistics of reading comprehension.

To be continued...

Sunday, April 20, 2014

More from the NY Times on why people hate the Common Core

First it was Jennifer Finney Boylan; now it's David Brooks. Each shoots down an army that consists mainly of straw men. Boylan's opponents are those who fear that the Common Core State Standards will indoctrinate their children and make them smarter than they are. Brooks' opponents also include indoctrination worriers, but his main target are those who fear that the CCSS amount to a top-down straight jacketing of education, and those who fear (not being straw men) that the standards put too much pressure on teachers.

Brooks argues:

It is true that the new standards are more rigorous than the old, and that in some cases students have to perform certain math skills a year earlier than they formerly had to learn them. But that is a feature, not a bug. The point is to get students competitive with their international peers.
Both ignore the more substantive arguments that I and many others have made. Here, for example, is my take on those "more rigorous" yet "flexible" standards:
[The CC] tells [schools and teachers] what the reading level has to be and leaves it up to them to somehow figure out what "supports" or "intervention methods" or "materials" will somehow give all students meaningful access to texts at this reading level...
Imagine being told: "You need climb this 200 foot cliff, but don't worry, we're giving you all the flexibility you want, because we're not telling you how to do it or providing you with any specific materials."
To those in actual classrooms, this is a bug, not a feature.

Then there are all the pedagogical biases that make the Common Core so problematic, which I blogged about earlier:
The bias towards lofty, everyone-can-do-it, one-size-fits-all goals; the bias towards an abstract version of “higher-level thinking” that probably doesn’t exist; the bias towards the supposed virtues of explaining in words one’s reasoning in math problems; the bias towards an abstract, information-aged, multi-media conception of “text”; and finally, via its abstract goals and its leaving up to schools and teachers how to meet these goals, the de facto bias towards the dominant pedagogical philosophies of the Powers that Be in education.
Beyond these concerns, there are all the ways in which the Common Core undermines the education, in particular, of special needs students, which I wrote about in my recent piece in the online Atlantic.

While Brooks and Boylan ignore the special needs population entirely, several special-needs professionals recently published a piece on the Huffington Post critiquing my article. More on that later; you can read an exchange between me and one of the authors in the comments section.

Friday, April 18, 2014

Math problems of the week: Rates problems in Chicago Algebra vs. 1900s algebra

I. From the "Rates" section of the "Division in Algebra" chapter (Chapter 6) of The University of Chicago Mathematics Project Algebra: [click to enlarge]:

II. The rates problems in the "Simple Equations" chapter (Chapter 2) of Wentworth's New School Algebra [click to enlarge]:

Wednesday, April 16, 2014

Casualties of "balanced" literacy, years later

pra sno vla pni smu gra

These are some of the nonsense syllables that students in the after school program I teach in were recently asked to read aloud. This list was part of a French language literacy test, and the point of this test was to assess the kids’ French skills (many of them have French-speaking parents). But what was most revealing about the results of this particular test component had nothing to do with French.

The kids did ok with two other lists of syllables: ones that consisted of consonant vowel combinations (ta, le…) and vowel consonant combinations (ame, ette). But when it came to the consonant clusters in the above list (pr, sn, vl, pn, sm, and gr), they stumbled. Invariably, if they pronounced the second consonant at all, they placed it at the end of the syllable, such that “pre” became “par”; “sno” became “son,” etc.

In other words, these students, now in 3rd and 4th grades, were totally stumped by consonant clusters. What does this mean for their ability to read words like “presque” and “pneue”?

As it turns out, none of these students can read any French. As for English, while they are able to read it, they do so less fluently than an unsuspecting person might predict, given how many years they’ve attended ELA classrooms. How would a new word like “protracted” or “gravely” sound in their mouths?

The difficulty these kids have sounding out single syllabus with consonant clusters has nothing to do with their unusual backgrounds, and everything to do with the continued de-emphasis on phonics instruction in America’s K12 classrooms. I didn’t get to test the older kids, but I’m guessing that they, too, had problems with “pra,” “sno,” etc. If you never learn how to sound out arbitrary consonant clusters, you’d think this would get only marginally easier over time.

In fact, it would be really interesting to take a random sample even of high students and see how they would do sounding out random nonsense syllables with consonant clusters. Let alone erstwhile SAT words like "phlegmatic" and "punctilious."

Monday, April 14, 2014

The lost arts of listening and learning

In this week’s New York Times Education Section, we see a continuation of the love affair between education journalists and “interactive” classrooms that minimize extended reading and listening. In Ten Courses with a Twist Laura Pappano characterizes such instruction as “inventive,” explaining that it treats students not just as “sponges soaking up content,” and citing an expert to elaborate further:

They apply lessons to life, says C. Edward Watson, director of the Center for Teaching and Learning at the University of Georgia. He adds that “faculty are trying to be more engaging in the classroom” because, for one, “competition is greater than it used to be.”
Why are these changes occurring now? Usually people cite “21st century skills,” claiming that today’s world requires “real-life” skills rather than the core knowledge and academic skills that, for centuries, have formed the basis for intelligent thought and effective communication. But Pappano instead cites the rise of online courses and the decline in listening skills:
The proliferation of online content means in-person courses must offer more than just another lecture “video.” Professors also face challenges in getting and keeping the attention of students raised on quick takes. Some weave in ways for students to use restless fingers and splintered focus; every few minutes during Prof. Perry Samson’s “Extreme Weather” lecture at the University of Michigan, students must respond to questions by phone or laptop. Others design courses with gaming features.
The less experience people have attending to real-live lectures, the worse their listening skills become, and the more they tend to assume, as Pappano does, that listening is passive, that live lectures are as canned as canned lectures are, and that lecturing precludes q & a and other interactions between lecturers and audiences. As I noted earlier:
Each year that a teacher opts out of exerting the energy needed to hold students’ attention for major chunks of class time, whoever teaches these students the next year will find this even harder.
These concerns aren’t shared by writers at the Education Times, who shift their focus elsewhere:
We looked around the nation for courses with buzz, according to campus newspapers, higher education experts and enrollment numbers. Students still file into lecture halls and classrooms, but once they’re seated, it’s clear that these courses are different. They mess with the old models. And they give students an experience that might change how they think, what they care about or even how they spend their lives.
Thus, in the Introduction to Cultural Anthropology at Kansas State University:
The … class is broken into groups of indigenous peoples and colonizers. They get bins of limited supplies and must trade for other items to make weapons, following rules they devise in advance. Colonizers typically get blowgun-like tools to launch marshmallow-tipped straws while indigenous peoples may only use rubber bands.
Jordan Thomas, who took the course in 2012 and is now a teaching assistant, felt the impact of being colonized and made to string marshmallows on rubber bands. When you get “taken over and are forced to sit around and assemble and manufacture a necklace for the entire hour, you engage in the emotions that come with that,” he says, adding that this was something he never would have gotten from a book.
But what drove the professor to teach this way wasn’t the desire for students to experience emotions that they “never would have gotten from a book,” but frustration with their attitudes:
Dr. Wesch started the simulations in 2004 after growing frustrated that most student questions were about grades and how much something was worth on a test. “Those are terrible questions,” he says. “I realized I needed to change everything.” Yes, there is a final exam, but it’s only one question: Why are you here? (He’s expecting you to tell the 12,000-year history of mankind and what you plan to do for the planet.)
One finds a similar de-emphasis of core content knowledge in another of the Times’ picks: Professor Samson’s Extreme Weather class at the University of Michigan. Here, anecdotes about extreme weather prevail (a car being bounced across a highway when to close to a F4 tornado), and all exams are “open book, open computer, call a friend.”

Another of the Times’ pics is Professor Monger’s Introduction to Oceanography at Cornell, where:
a third of the course is activism. Dr. Monger keeps a website for the course, (sample post: “Why you should avoid eating shrimp”), and a listserve of 1,700. “I want to stimulate these guys to raise their voices,” he says. “I tell them, ‘That ocean is as much yours as anybody else’s.’ ” The final assignment is to write Congress, though students are not required to mail the letters.
And no, I’m not worried about indoctrination; I’m worried about how much students are actually learning and retaining.

Relatedly, in his World Regions class at Virginia Tech:
Mr. Boyer wants students to “get excited about the world” and lets them choose how they engage. Students participate through Twitter, in-class smartphone surveys and old-fashioned microphones. They earn a course grade by doing assignments with point values; collect 1,100 points for an A, 1,000 will get you a B. They also decide what class will cover (this spring, it’s the Middle East, Russia and China), and Skype with international figures.
When he put up a map to talk about Egypt and the Arab Spring, someone said, “How come Jordan doesn’t have anything going on?” His reply: “Maybe we should ask someone from Jordan.” Less than six hours after a YouTube appeal to King Abdullah II of Jordan, the king’s office responded.
In another of the Times’ Top Ten, the Global Jam Forum at the Berklee College of Music:
Students jam with [prison] inmates, put inmate poems to music and respond musically to art, poetry and even health issues like malaria in Africa. Caili O’Doherty, a pianist, says the class “changed the way I think about music,” adding: “I think about playing for those different audiences. We are playing for them, not for ourselves. The music isn’t about me.”

Then there’s The Art of Walking at Centre College:
Wear comfortable shoes because this environmental studies class covers serious mileage. Walks take several hours and typically cover 15 to 25 miles. Readings include philosophers like Martin Heidegger and are discussed during nonwalk days. Dr. Keffer, who began teaching the course in 2002, has offered it on campus in Danville, Ky., and as part of Centre’s study abroad program.
Last January, in Strasburg, Germany, students walked 17 miles between two villages in the Black Forest, what he calls “Heidegger’s office.” There is nothing goal-oriented or prescribed in the walks; students don’t phone or text (it’s not banned, they just don’t). Covering distance by foot, Dr. Keffer says, opens “a temporal branch of environmental studies.”
Meanwhile, in courses in Philanthropy at Princeton and the University of Virginia:
Having real money, and a deadline for giving it away, lets students feel both the power and the challenge of charitable donations. Since 2011, the Once Upon a Time Foundation has provided some $2.5 million for hands-on learning at 13 campuses, including the University of Virginia and Princeton. Fueling the trend, Warren Buffett’s sister Doris began an online course last year through her Sunshine Lady Foundation in which participants give away $100,000.
At Princeton, Dr. Katz’s freshman seminar is as much about learning to reach a consensus with 14 others as it is about tackling big questions. “Some of the disagreements are quite profound,” says Dr. Katz, whose students research charities and must persuade classmates to align with them. “Some students feel it makes no sense to give a gift in the United States,” while others find value only in “giving gifts close to home.” Last fall’s class had $25,000 to give away.
Last but not least in Self-Theories at Stanford:
Prepare to take on your demons in this freshman psychology seminar. Dr. Dweck’s groundbreaking research has helped shape current wisdom about success and achievement — that failure and recovering from it are more valuable than sticking with what you already know how to do. Dr. Dweck tells students to tackle something “they have never had the guts to try.”
A student belted out “The Phantom of the Opera” on a public bus; another struck up conversations with strangers in San Francisco. Ricardo Flores, a self-described introvert, challenged himself to run for dorm co-president and, though filled with anxiety, give a campaign speech. He spoke, and won the election. For his next task, Mr. Flores is honing his salsa skills in hopes of performing with Los Salseros de Stanford.
When it comes to the lost art of listening in education, Diana Senechal has posted some wonderful comments on Joanne Jacobs' recent post  about an OILF post:
The people who aggressively disparage the “sage on the stage” don’t realize what a mess they are causing. Students, too, are getting the message that they shouldn’t have to listen to the teacher (or, for that matter, to anything or anyone). Sometimes the message is subtle, sometimes direct–but it’s there.
The “achievement gap” is in many ways a listening gap. The kids who will fly off the handle if they aren’t given something concrete to do every minute–these tend to be the ones who do poorly. (There are exceptions: students who focus and listen but don’t do well, and students who seem perennially distracted but somehow ace their courses and tests.)
Guess who’s more likely, overall, to get into a good college and do well there? The student who can listen. Not because this student is “docile” or “passive”–but because he or she has developed the discipline of focus and attention, which are essential for most intellectual fields.
It’s inadvisable for a K-12 teacher to teach by lecture exclusively. Even in college, lectures are complemented by discussion sections, labs, etc. But the campaign against “teacher talk” is misguided and destructive. Not only does the teacher have something to convey, but the student benefits from learning to take it in.
Senechal adds:
What worries me is the “turn and talk” impulse–the tendency of many students to start talking to their neighbors at random moments (about anything at all). Students who do that are rarely focused on the subject, in my experience; they’re more concerned about what’s going on socially in the room.
I don’t see this as their fault entirely; they are receiving many messages that the classroom is a place for socializing.
If it were established that students should listen in class, then much of the problem would disappear (not all, but a lot). Unfortunately, teachers are told over and over to avoid talking and to have students constantly “turn and talk.” That feeds the problem, unless the discipline of listening is already established.
Sadly, the dying art of listening applies to adults as well: if only more people would listen to Diana Senechal!

Saturday, April 12, 2014

No, it's not a therapist, it's a "teacher-researcher"

"Can you let me in to what's going on? Into your thinking?"
No, this isn't a therapist talking; it's a "teacher-researcher." As the opening paragraphs of a recent article in Edweek (Teachers May Need to Deepen Assessment Practices for Common Core) explain:
For Olivia Lozano and Gabriela Cardenas, team teachers at the UCLA Lab School in Los Angeles, understanding what each of their students know and can do at any point in time is so integral to their practice that they call themselves "teacher researchers."
Over the 10 years they've worked together, the two have put formative assessment at the center of their instructional routines. Each day during workshop time, they pull students aside one-on-one or in small groups to ask open-ended questions about the lesson at hand and to gain insight into each 1st and 2nd graders' thinking.
And as one of these teacher-researchers tells us:
"I have a conferencing binder where I'm taking copious notes on each individual student. I analyze their work and see where they're at."
Known as formative assessment, this process potentially improves student learning, so long as:

1. It doesn't consume too much instructional time.
2. It is used *only* to inform and tailor instruction, and not to determine report card grades.

(As I've argued earlier, report cards should be based on what students can do on their own at the end of a given unit, not on their works-in-progress or their thought processes. Report cards should measure a student's degree of ultimate mastery of instructed material, not how they got there or vague things like the "depth" of their thinking, or how "critical" or "exploratory" of "creative" that thinking was.)

Transforming teachers into so-called "teacher-researchers" risks unwarranted intrusions into student's thought processes. Some intrusions--forcing students to share personal reflections that they might rather keep private--violate privacy and provoke anxiety. Other intrusions--making students who can do math automatically and nonverbally in their heads (which should be the ultimate goal!) fake their way through verbal "translations"--make things tedious, decelerate learning, and disadvantage kids with language delays.

The opening quote falls mostly into the latter category. Here's its context:
The common standards are asking students to do that and more. They are aimed at "building childrens' [sic] capacity to think, and analyze, and communicate, and reason," said Margaret Heritage, the assistant director for professional development at the National Center for Research on Evaluation, Standards, and Student Testing at UCLA. "We need to know if [students are] grappling with complex ideas," said Heritage, who mentored Lozano and Cadenas. "Where are they? Is the idea beginning to consolidate? What do I need to do to go deeper and really help them get this?"
All of that may be tough to measure with quick-answer questions or exit slips. Instead, to get a full picture of student understanding, teachers need to ask open-ended questions and push students to explore ideas aloud, the UCLA educators say. "When [students are] solving problems mathematically, they say, 'I did it in my head,'" said Cardenas. "And you ask, 'Can you let me in to what's going on? Into your thinking?'" 
With the common standards, "classrooms will look different," said Heritage. "We'll need a lot more talking, more focus, more discourse, more depth."
Cardenas and Lozano spend conference time asking guiding questions and posing strategies to help lead students toward an answer—and to get them talking about their thinking. "You're developing their metacognition skills, helping them think about 'What kind of a learner am I? What's going to help me learn better?'," Lozano explained. "It helps to give them a voice."
[Nancy] Frey of San Diego State University tells teachers that, when listening closely to students, "The question you have to ask yourself is not whether the answer is correct or incorrect, but rather what is it likely that that student knows and doesn't know in this moment in time that would lead him to that response?"
Rather than asking multiple-choice questions or scanning quickly for right and wrong, teachers will need to be attuned to what students are saying during those discussion and debate sessions. "If you're walking around with a clipboard or notebook as kids are working through application, you're hearing, are they using mathematical thinking? Are they attending to precision? How well are they using the mathematical practices?" said Pecsi.
Notice how all of this is being justified by the supposedly pedagogically neutral Common Core Standards.

These Standards, apparently, justify thought-process intrusions not just by teachers, but also by peers:
Another technique for potentially deepening assessment practices—and complying with the new standards' focus on collaboration and communication—is to have students assess each other.
Amanda Pecsi, director of curriculum at the Washington, D.C.-based Center City Public Charter Schools, pointed out that one of the mathematical practices required by the common standards is to "construct viable arguments and critique the reasoning of others." She said this may lead to teachers using more peer review during their lessons. well as a shift of responsibility from teachers to students:
"Ideally we want to be moving into a place where students are doing that heavy lifting and their formative assessment is how they evaluate someone else and how they talk about it." well as a tremendous inefficiency in math instruction that risks leaving American students even further behind than they already are with respect to the developed world:
In light of the math common standards' emphasis on performance tasks and constructing arguments,... Pecsi said teachers will need to begin using more inquiry-based problem-solving. That might entail "20 minutes of students digging deep into one problem and debating," she said. "Ideally that could be an entire lesson eventually." well as an expansion of the Educational Testing Industrial Complex, in which ever more money flows from impoverished school districts to the testing companies whose consultants comprised the majority of the authors of the Common Core State Standards:
Meanwhile, the two main common-core assessment groups—the aforementioned Partnership for Assessment of Readiness for College and Careers and the Smarter Balanced Assessment Consortium—are planning to support teachers with formative assessment.
Smarter Balanced is putting out a "digital library," which Chrys Mursky, the group's director of professional learning, emphasized is "not a test bank of items" but a group of digital resources aimed at helping teachers build their own formative assessments. The library will be available by the time the Smarter Balanced assessments are ready to use, but only for teachers in states that purchase the full suite of tests.
PARCC plans to have adaptive, online "non-summative" tests for students available to all teachers in PARCC states. However, Bob Bickerton, co-chair of the PARCC non-summative working group, said the consortium is still currently looking for a vendor for some of the formative tools, so those will not be available until the 2015-16 school year.
 ...all of it, of course, for the sake of those "teacher-researchers" and, ultimately, the guinea pigs populating their laboratories--um, classrooms.

Thursday, April 10, 2014

Math problems of the week: word problems in 1900s vs. 2000s algebra

Word problems with one or more unknown, following systems of equations practice.

 I. From Wentworth's New School Algebra, published in 1898: the Problems chapter immediately following the the Linear Systems chapter:

II. From College Preparatory Mathematics, published in 2000: the Cumulative Review section at the end of the Graphing and Systems of Linear Equations chapter:

Tuesday, April 8, 2014

Deconstructing the sample Keystone Exam, continued

I've been mulling over some great comments I received on my most recent post on the sample algebra exam for Pennsylvania's new Keystone tests. As I commented in response, I'm intrigued by the idea that these problems are each intended to measure a particular skill rather than, say, the general skills of setting up word problems algebraically and manipulating the resulting expressions to solve find solutions. It makes sense that the test-designers are attempting to align particular problems to particular Standards, and also that they are trying to ensure that students who failed to master skills from pre-Algebra and below are still able demonstrate that which they can nontheless do.

However, it seems to me that there's a significant overlap in what these 10 problems measure, and that the skills they measure boil down to:

1. passively recognizing the correct set up of an equation
2. correctly plugging in numbers and doing the arithmetic
3. using estimation to rule out unlikely candidates
4. knowledge of ordinal pair conventions
5. understanding of the inequality sign
6. facility with arithmetic

This list, unfortunately, includes few, if any, of the core skills of first year algebra.

I've ended up with a more cynical take on what, at least in part, is going on here. To most people, unless they actually sit down and do the problems, this sample exam looks to be testing much more advanced skills than the 6 I've listed above. It looks like we have word problems that need to be set up; systems of equations to solve algebraically; expression upon expression to manipulate symbolically; possibly complex relationships involving ordered pairs, or vertical and horizontal distances. In other words, it looks like a student's performance on this test is a function of how well he or she mastered first year algebra. Or, using ordered pair notation: (test score, mastery of Algebra I).

This gambit will quickly appease many people will might otherwise worry about what students are learning--or not learning--in today's schools. Enough kids will do OK, and it will look like they're thinking deeply and critically about algebra.

I'm reminded of the few problem sets in Math Investigations that appear at first glance to actually involve complex calculations, and that only on closer inspection clearly involve none. Consider, for example, this one, excerpted from one of my Problems of the Week.

STOP. Don't start yet. Star problems that may have odd answers.
× 7


× 65
× 37





Sunday, April 6, 2014

Word problems in a sample in Keystone Algebra exam--deconstructed

In an earlier post, I posted some word problems from a sample exam for Pennsylvania's new Common Core-inspired tests (the Keystone Tests). I found these problems vaguely troubling, but hadn't taken the time to figure out what was bothering me.

As Auntie Ann pointed out:

1) They're wordy.
2) They give you far more information than necessary. If kids really are supposed to understand this stuff, why does almost every problem write out the equation for the student? Why not have them generate it themselves? Shows a lack of faith that the kids *have* actually learned what to do.
Indeed, all cases, the expressions are set up for you. Furthermore, as I noticed upon going through these problems and doing them myself, no algebraic manipulations are necessary in order to solve any of them.

Here, again, are the problems, with my commentary below:


All that’s involved here, obviously, is a passive identification of the correct setup. Actively translating words into algebra is significantly more challenging.


Here, not only is the equation already set up, but the variables are explicitly defined. All you have to do is map the equation to word problem to determine what the coefficients stand for, and then apply your knowledge of the conventional x, y ordering of ordered pairs.


This one is not really a word problem: you can answer the question without even reading through the scenario. Since the four choices for x are all easily plugged into each equation with the resulting values for y easily calculated (from the second equation) and checked (via the first equation), the correct value of x can be determined by guess and check alone—i.e., by simple arithmetic—along with simple realization that the second equation is easier to start with.


Here, you’re given the equations and told what the variables stand for. You can determine the answer by seeing which one of a handful of obvious whole number pairs works for the first equation. What works for the first equation, (4,3), also works for the second equation.

Here, there’s just one variable, and what it stands for is obvious from the given scenario. Choices b-d look suspicious (it would be a coincidence if 185 is also the value of b; more likely, the 185s here are red herrings). Choice a is easily confirmed by plugging in 204 and doing some simple arithmetic.

Here again, not only is the problem set up for you, but the variables are also identified for you. All you have to do is plug in the pairs of values in the different choices until you find one that works. Again, the problem boils down to simple arithmetic.

Problem 18 involves passively picking out the correct expression; choices c and d can be eliminated instantly because the intervals are obviously too large, and choice b can be eliminated because the constant term (75 times 4453) is obviously too large. In problem 19, the equation is set up, the variables are defined, and the correct answer is readily determined by a quick inspection of the only plausible choices: c and d.

Assuming an understanding of similar triangles and simple ratios, the answer to this problem is obvious (and the triangle diagram, as with the scenario in problem 12, is a pointless distraction).

Here again the equation is already set up and the variables defined; one simply recognizes that x equals 0 when the machine is full, and that one can therefore eliminate x and solve for y.

Facility with algebraic manipulation is crucial for calculus. The idea that one can get sail through the Keystone algebra test by passively interpreting someone else's algebraic expression, and by plugging numbers into them, is deeply disturbing. What incentive is there left for algebra teachers to prepare students for higher-level math?

Friday, April 4, 2014

Math problems of the week: word problems in Chicago Math vs. traditional algebra

I. From the review section of Linear Systems, the 11th chapter (out of 13)in the University of Chicago Mathematics Project Algebra book (2002), p. 702 (out of 823 pages) [click to enlarge]:

II. From the middle of the word problems at the end of Fractional Equations, the 10th chapter (out of 27) in Wentworth's New School Algebra: (1898), pp. 166-167 (out of 420 pages) [click to enlarge]:

III. Extra Credit:

Write your own word problem eliciting simultaneous equations that relate the page number, percentage of the way through chapters, and the textbook's date of publication to the estimated number and difficulty of word problems per problem set.

Wednesday, April 2, 2014

"I did it all by myself!"

Few phrases capture the joys of childhood better than this one.

...And one of the most troubling results of today’s trends in education is how little opportunity today’s kids get to experience this in school: the joy of mastering things on their own, and of demonstrating this mastery to others.

More and more, they work in groups and turn in group assignments. More and more, teachers de-emphasize closed book, calculator-free, in-class tests in favor of “formative” assessments of portfolios and projects that, even if they are mostly the work of individual students, may also involve unacknowledged help from parents.

Increasingly rarely are students asked to engage, on their own and on the spot, with challenging tasks that gauge true mastery. And, as I discovered in writing my recent Atlantic piece, it’s our special ed students who have it the worst.

The most recent culprit are the Common Core State Standards. By holding special needs students to the same, one-size-fits-all standards as everyone else, they deprive such students of assignments tailored to their current ability levels. For those students who are below grade level in a particular subject, this practice ends up restricting them to assignments that they can only “complete” with what’s called “scaffolding” or “supports” or “accommodations.”

Here, I’m talking not about accommodations that create or improve access—e.g., to sound (sign language interpreters, FM systems), or to written texts (enlarged text, text to speech apps)—or that bypass fine motor impairments (keyboards and touchscreens). Instead, I’m talking about “accommodations” like simplified texts or story boards or movies (for those with reading comprehension impairments), or speech-to-text apps or word-predication software (for those with impairments in productive language). And I’m talking about the many instances of “scaffolding” in which the teacher or aide ends up walking over to the struggling student and, consciously or not, guiding him or her to through the task—essentially giving away the answer and moving on to the next lesson or unit before the student ever shows independent mastery. These are the sorts of accommodations that interfere with learning—and that easily become excuses not to teach.

Even for many neurotypical kids, many of the Common Core goals, and the tests and assignments they inspire, are too far out of reach to allow independent mastery.

It should come as no surprise that students learn much faster when given assignments at their Zones of Proximal Development (if you're skeptical, read this paper). But beyond cognitive benefits, think of all those socio-emotional goals we purport to have for our students: we want to grow their confidence, self-esteem, and grit: we want them to feel good about themselves, about what they can do independently, all by themselves; we want them to see how hard work and perseverance are what get them there.

In the name of a lofty, feel-good curriculum, we deprive students of opportunities to achieve their own, personal lofty goals and feel good about themselves--to experience, time and again, the wonder of "I did it all by myself."