Common Core math: deep or dull?

According to a New York Times article by Motoko Rich, parents and students are finding Common Core math not only confusing but tedious and slow.

To promote “conceptual” learning, many Core-aligned textbooks and workbooks require steps that may be laborious for students who already get it. A second-grade math worksheet, pictured in the article, includes the question: “There are 6 cars in the parking lot. What is the total number of wheels in the parking lot?” To answer the question, the student drew six circles with four dots within each. (Actually, this doesn’t seem new; it reminds me of “New Math” and “constructivist” math.)

One nine-year-old, apparently weary of this kind of problem, stated that she grew tired of “having to draw all those tiny little dots.”

Students with good understanding may be put through steps that seem redundant to them. If they skip those steps, they may be penalized.

“To make a student feel like they’re not good at math because they can’t explain something that to them seems incredibly obvious clearly isn’t good for the student,” said W. Stephen Wilson, a math professor at Johns Hopkins University.

One reason for emphasizing “conceptual” learning is that employers apparently are demanding critical thinking. Several questions remain to be answered, though: (a) whether Common Core math–in its current forms–really is promoting conceptual learning; (b) if so, whether it also promotes math proficiency; (c) whether the current approach is benefiting students at the upper and lower ends–and those in between, for that matter–or holding them back; and (d) whether this is the kind of “critical thinking” that will serve students well in college, the workplace, and elsewhere.

I will comment briefly on the first question; I welcome others’ insights.

Tedium and depth are not the same. One can go through a long explanation of a problem without gaining any understanding; one can solve a problem quickly and come to understand a great deal.

In sixth grade, in the Netherlands, I learned mental arithmetic: I learned to add, subtract, multiply, and divide double-digit numbers in my head, using all kinds of tricks that the teacher taught. Those tricks enhanced my understanding of what I was doing. I enjoyed the swiftness and ingenuity of it; I would have detested it, probably, if I had to write it all out, step by step, and illustrate the steps with circles and dots.

Detailing and explaining your steps is a worthwhile exercise. But part of the elegance of math has to do with its mental leaps. Sometimes, when you do steps in your head, or when you figure out which steps in a proof are assumed, you not only understand the problem at hand, but also see its extensions and corollaries. Sometimes this understanding is abstract, not visual or even verbal.

There seems to be an unquestioned assumption that one comes to understand math primarily through applying it to real-life situations; hence the Common Core emphasis on word problems. While word problems and practical problems can lead to insights, so can abstract reasoning, and so can models that bridge the abstract and the concrete, like the multiplication table.

Yes, the multiplication table–horrors, the multiplication table!–abounds with concepts. If you look at it carefully (while committing it to memory), you will see patterns in it. You can then figure out why those patterns are there (why, for instance, any natural number whose digits add up to a multiple of 3, is itself a multiple of 3). (Something similar can be said for Pascal’s triangle: one can learn a lot from studying the patterns.)

In other words, conceptual learning can happen in the mind and away from “real-life situations”; it need not always be spelled out at great length on paper or illustrated in terms of cars and wheels. Nor should students be penalized for finding shortcuts to solutions. Nor should memorizing be written off as “rote.” Yes, it’s good to understand those memorized things, but the memorization itself can help with this.

In ELA see a similar tendency toward laboriousness (that likewise long predates the Common Core). Students are required to “show their thinking” in ways that may not benefit the thinking itself. For example, they may be told to explain, at great length, how a supporting quotation or detail actually supports their point–even when it’s obvious. Students with economy of language (and, alas, clarity of thought) may lose points if they don’t follow instructions. Instead of being at liberty decide whether an explanation is needed, they receive a message along the lines of “Explain, and explain again, and then explain that you have explained what you set out to explain.”

Critical thinking is important–and one should think critically about how it is conveyed and taught.

Back to Balanced Literacy in NYC?

To those familiar with the history of New York City schools, this should come as no surprise: NYC schools chancellor Carmen Fariña is pushing for a return to Balanced Literacy, which she has long supported and which she sees as compatible with the Common Core.

Some dispute her claim; a New York Times article by Javier Hernández  quotes Common Core architect Susan Pimentel, who says that part of the Balanced Literacy philosophy is “worrisome and runs counter to the letter and spirit of Common Core.” Later, it states that she sees the two as potentially compatible. Compatibility aside, is this return to Balanced Literacy a good idea? I say emphatically no–and will give two reasons that weren’t mentioned in the article. It was in large part my objection to Balanced Literacy (as dogma) that spurred me to write Republic of Noise.

Balanced Literacy, which traces back to initiatives of the 1970s and 1980s, rests on the premise that children learn best when allowed to teach each other and themselves. The teacher is a “guide on the side,” not a “sage on the stage”; students have frequent opportunities to choose their own books; and most lessons involve small group work (or sometimes independent work). The program was extensively developed in NYC schools in the 1990s. Mayor Bloomberg and Chancellor Klein mandated it throughout NYC schools in 2003. It is the foundation of the Reading and Writing Project, founded by Lucy Calkins.

While certain elements of Balanced Literacy, applied prudently, could be part of good teaching anywhere, the program as a whole has dangerous weaknesses. Many critics have pointed to the lack of curricular focus and the implied disparagement of direct instruction. The NYT article quotes Robert Pondiscio, who became an eloquent and passionate critic of Balanced Literacy as a result of teaching it in the South Bronx:

“One of the best things you can do to build reading proficiency is to build a strong base of background knowledge,” said Robert Pondiscio, a senior fellow and vice president at the Thomas B. Fordham Institute, a research organization. “When you have 24 kids reading 24 books, you’re not accounting for that.”

Indeed. Moreover, when there’s no specific content that the students are learning together, what do they get instead? Strategies, strategies, and more strategies. Reading strategies, writing strategies, strategies for remembering your strategies. In the absence of content, such strategies become vapid. Forget about holding a candle; they can’t even hold hot air to subject matter. Also, some of these “strategies” involve sidestepping the text–for instance, a teacher might encourage students to figure out unfamiliar words (that is, to figure out what they actually are) by looking at the pictures.

Here’s my contribution to the discussion: Balanced Literacy is to be distrusted because it is an all-encompassing pedagogical package that comes with both a worldview and a fever. Moreover, its emphasis on group work discourages high-level, sustained, and original work and thought. [Read more...]

Jindal and the irony of local control

Governor Jindal is determined to pull Louisiana out of the Common Core. He wants “Louisiana standards and a Louisiana test” for Louisiana kids. But here’s the rub: Louisiana’s top education officials aren’t having it. According to the Times-Picayune,

Education Superintendent White and board President Chas Roemer dismissed Jindal’s rejection of Common Core as a dramatic but meaningless gesture. They said the state’s 714,000 students will continue lessons aligned with the national academic standards and its associated tests.

So, in the name of local control, Jindal wants out, but local officials are pushing back. This brings up the question: what is local control?

I find much of the Core implementation dismal (and consider the standards themselves partly to blame)–but question the claim that the main problem  is federal overreach. Those making this claim cite a long tradition of “local control,” which, in their view, should remain. What do they mean by that?

If “local control” is state control, well, I’d be happy with local control in Massachusetts but somewhat worried in Kentucky, say.

If “local control” is district control, great–if I live in a district with a liberal curricular tradition (“liberal” in the sense of “liberal education,” not necessarily liberal politics). In a weak district, or a district with strong religious or ideological biases, there’s a much greater chance of fads, poor curriculum, upheavals, and so on, in which case a counterbalance of power could potentially do good.

If “local control” is control at the school level, good for you, if your school has a strong staff, a good curriculum, adequate resources, and wise leadership, or at least some of these. If not, you’re out of luck.  School-level control may be liberating in some cases and confining in others.

Beyond that, within any of these definitions of “local control,” a hierarchy exists. The person in charge (for instance, Jindal) might see things one way, and those directly below him might disagree. Who, then, controls the local control? “Democratic process,” some may say–but democratic process doesn’t always uphold local control.

My point is not to bash local control. In many ways I support it. I am just observing its conceptual fuzziness and practical contradictions.

It’s not PC or censorship

Common Core State Standards “and standardized testing are trying to make teachers into KAPOs, a Nazi concentration camp prisoner who was given privileges if they would supervise work gangs,” wrote a reader commenting on Diane Ravitch’s blog. She goes on to reference Schindler’s List and her relatives killed in the Holocaust.

When readers objected to the analogy, Ravitch wrote: “I find this argument to be a form of political correctness that is used to censor opinion. If anyone wants to use an analogy to make a point, that is their choice.” She defended the posting on Twitter as a free speech issue.

This isn’t about political correctness or censorship, responds Daniel Willingham.

First, he writes, the analogy trivializes enormous suffering. Test takers are not in any way like Holocaust victims just as students asked to perform public service are not comparable to slaves.

If a reformer said schools are concentration camps where teachers brutalize their students . . . It’s insulting, isn’t it?

Willingham also disagrees that it’s censorship to tell people you think their analogy is “ill-considered and offensive.”

 . . .  if she had asked the author to change the analogy or had refused to post the piece because of the analogy, I would not call that censorship. The author does not have a guaranteed right to post what she likes in Diane’s blog, a right that Diane would have been infringing. Diane was a offering a platform for this author’s voice, and obviously she offers that platform to voices she thinks are worth amplifying.

This situation is not comparable to that documented in The Language Police, in which enormous power was concentrated in the hands of few publishers. If an author wanted to publish a textbook they had to toe the line drawn by the publishers or give up on publishing the book. That power relationship does not exist in this case. This is the internet, for crying out loud.

He asks Ravitch to rethink her position.

I agree with Willingham. I’d add that the analogy is ridiculous and therefore unpersuasive.

Core standards: It’s not about the benjamins

Democratic state senators in Pennsylvania have come out against Common Core State Standards “without adequate state financial resources,” reports Ed Week.

It’s not about the benjamins, responds Marc Tucker on Ed Week‘s Top Performers blog. Some high-achieving countries spend substantially less per student than the U.S. “Top performers . . . redesign their school finance systems” to provide more resources for hard-to-educate students.

When Florida first proposed to raise its standards years ago, some people objected on the grounds that high standards would hurt the poor and minorities, who would not be able to meet them.  The standards were raised and the students whose scores improved the most were poor and minority students.  When Massachusetts set out to raise their standards, the liberals objected that the poor and minority students would be hurt, because they would not be able to meet the standards.  And–you guessed it–when the standards were raised anyway, the students who made the greatest gains were the poor and minority students.

Years ago, he asked parents in a focus group about standards.  An African-American single mother living on welfare said her middle-school son was getting A’s for coloring in a coloring book. “The kids in the suburbs have to work really hard for their A’s,” she said. “When my child graduates, all he will be good for is working the checkout counter at the grocery store.  I want my child to have the same opportunities they have.  I want him to have to do as well in school as they have to do to earn an A.”

It will be very hard for schools with low-income and minority students to meet the new standards, Tucker concedes. Spending more won’t be enough.

We already spend more money on average than every industrialized country except Luxembourg and Norway.  We will have to do what the top-performers everywhere have done: radically change our school finance systems, academic standards, curriculum, instructional practices and tests and exams.  Not least important, we will have to make big changes in teacher compensation, the way we structure teachers’ careers, the standards for getting into teachers colleges, the curriculum in our teachers colleges, our teacher licensure standards and the way we support new teachers.

Rejecting high standards isn’t an option, Tucker argues. Employers will enforce the standards when they decide who to hire. Selective colleges will enforce the standards when they decide who to admit.

Teachers hit computer-scored writing exams

New tests aligned to the new common standards will ask students to do more writing and provide quick feedback to teachers on their students’ skills. But that’s only cost effective, if students’ writing is scored by computers, writes Catherine Gewertz on Ed Week‘s Curriculum Matters. Not surprisingly, the National Council of Teachers of English think machines can’t evaluate writing.

In its statement, the NCTE says that artificial intelligence assesses student writing by only “a few limited surface features,” ignoring important elements such as logic, clarity, accuracy, quality of evidence, and humor or irony. Computers ability to judge student writing also gets worse as the length of the essays increases, the NCTE says. The organization argues for consideration of other ways of judging student writing, such as portfolio assessment, teacher-assessment teams, and more localized classroom- or district-based assessments.

If essays are scored by humans — usually teachers working over the summer — the costs will go way up, tempting states to require less writing.

Conservatives can like the Common Core

Conservatives should support the Common Core standards, write Kathleen Porter-Magee and Sol Stern, who describe themselves as “education scholars at two right-of-center think tanks” (Fordham and the Manhattan Institute).

Glenn Beck  calls the standards a stealth “leftist indoctrination” plot by the Obama administration. Michelle Malkin warns that they will “eliminate American children’s core knowledge base in English, language arts and history.”  Not so, write Porter-Magee and Stern.

Common Core State Standards . . . describe what children should know and the skills that they must acquire at each grade level to stay on course toward college- or career-readiness, something that conservatives have long argued for. They were written and adopted by governors—not by the Obama administration—thus preserving state control over K–12 education. And they are much more focused on rigorous back-to-basics content than the vast majority of state standards they replaced.

Common Core doesn’t force English teachers to drop To Kill a Mockingbird in favor of government manuals, they write.  All teachers — not just English teachers — will expose students to informational texts and literary nonfiction. That includes “foundational texts of American history—the Gettysburg Address, Common Sense, and works of thought leaders like Emerson and Thoreau.”

(Non-fiction reading can inspire creativity, writes an AP English teacher in Ed Week’s Teacher.)

On the math side, opponents argue the standards are “squishy, progressive and lacking in rigorous content.”  But the math standards are dominated by content, write Porter-Magee and Stern.

 Unlike many of the replaced state standards, Common Core demands automaticity (memorization) with basic math facts, mastery of standard algorithms, and understanding of critical arithmetic. These essential foundational math skills are not only required but prioritized, particularly in the early grades. The math standards focus in depth on fewer topics that coherently build over time.

“For decades, conservatives have fought to hold students accountable for high standards and an academic curriculum imbued with great works of Western civilization and the American republic,” conclude Porter-Magee and Stern. “This is our chance to make it happen.”

Common Core could lead to “federal control of school curricula,” writes Neal McCluskey on Cato’s blog.  Porter-Magee will serve on the U.S. Department of Education’s technical review panel vetting Common Core tests developed by “Department-selected consortia,” he adds. If the feds control the tests, they control what’s taught in schools, argues McCluskey.

The bigotry of low (teacher) expectations

Common Core Standards didn’t invent effective teaching, writes Julie Greenberg in  The bigotry of low (teacher) expectations in the National Council on Teacher Quality’s blog. She objects to step 5 in Six Steps to Teacher Development, a joint production of the Gates Foundation and the American Federation of Teachers.

Districts are encouraged to “Align teacher development and evaluation to the Common Core Standards.”

..while most teachers are adept at classroom management skills, teachers have long been taught to fit a lot of material in a short period of time, not to ask high-level questions or to engage students in rigorous discussions.

Greenberg taught secondary math for 13 years without being advised to ask low-level questions and avoid rigorous discussion. Nobody helped her improve her questioning or discussion techniques. Perhaps the new standards will do so, she writes.

But I’m also worried that districts will fall into the same old professional development trap they’re in now, paying some pricey “Common Core” consultants to portray  the need for better questioning and discussion techniques to teachers as breaking news without any follow-through on real improved practice.

Greenberg provides a caricature of teachers attending the typical professional development session. It’s all too close to reality, she writes.
 

Kindergarten, play and standards

Teachers are blaming new standards for taking the joy out of kindergarten, writes Deborah Kenny, a charter school founder in New York City, in the Washington PostKindergartners should learn by playing, she writes. But she thinks the standards are getting a bum rap.

Last year, as Harlem Village Academies prepared to open new elementary schools , our principals visited dozens of kindergarten classrooms. The upper-income schools focused mostly on active play, interesting discussions and crafts, including papier-mache projects that delighted children for hours. In the lower-income schools we saw regimented academics, reward-and-punishment behavior systems and top-down instruction. In one South Bronx classroom, the only time children spoke during the course of three hours was to repeat drills of the sounds of letters over and over.

Why the disparity? Many educators are placing the blame squarely on the Common Core — national learning standards recently adopted by 45 states and the District and supported by the Obama administration — and asserting that they lead to poor-quality teaching and take all the joy out of kindergarten.

The standards’ goals —  “teach students to think independently, grapple with difficult texts, solve problems and explain their thinking in a clear and compelling way” — are noble, Kenny writes. That can be done well or badly.

Take vocabulary, for example. The Common Core standards state that kindergarten students should be able to “distinguish shades of meaning among verbs that describe some general action (e.g., walk, march, strut, prance) by acting out the meanings.” Imagine a classroom full of 5-year-olds marching, strutting, walking and prancing for 10 minutes to different kinds of music while laughing and learning vocabulary. . . . So while some schools might choose to teach vocabulary in a rote, boring way, clearly the standards are not to blame.

Teaching to the new standards demands more of teachers, Kenny writes. Principals need to hire good teachers and then let them learn from each other, try different strategies, learn from mistakes and improve. Principals also need the power to fire teachers who aren’t up to the job.

Via Eduwonk.

This anti-CCSS math blog critiques the standards’ call for kindergartners to “decompose” numbers.

Core math adds coherence, rigor, focus

Common Core’s new math standards “have the potential to improve average student achievement” by adding focus, rigor and coherence, predict  William H. Schmidt and Nathan A. Burroughs in the new American Educator.

Common Core State Standards in math resemble the high-quality standards of high-achieving nations, they conclude.

Furthermore, states with standards similar to CCSS-M had the highest eighth-grade mathematics score on the 2009 NAEP. “The more similar the standards were to the CCSS-M, the higher student achievement.”