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, itsmyocean.org (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.
...as 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."
..as 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."
..as 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.