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...]

Superfun sameness

In a New York Times op-ed, editor Pamela Paul points out a “farcical reversal” of our concepts of work and play: “schoolwork is meant to be superfun; play, like homework, is meant to teach.” Video games in particular have reversed (or mixed up) these roles; schools are making increasing use of video game technology in the classroom, while many recreational video games come packaged with a purported educational purpose. This ends up compromising both study and play:

Many of the games marketed as educational aren’t as much fun as video games children would play if left to their own devices. But the added bells and whistles still make it harder for them to focus on plain old boring work sheets and exams. Imagine how flat a work sheet would seem after a boisterous round of Zap the Math From Outer Space.

I agree with Paul but would call this “superfun sameness” instead. Study and play have become more and more alike–especially when “driven” by computer games. What’s more: they are alike in a disturbing way: hyped up, cloyingly interactive, and oh, so much fun. The result: students lose tolerance for things that seem slightly boring at first.

This happens on many fronts (not only with video games). Students get the message that their studies are supposed to be immediately gratifying and tailored to them. I often hear students (not at my school specifically, but in many places) complain that this or that book isn’t “relevant” to their lives and that they don’t enjoy it. What they’re really saying is that they haven’t learned to exercise patience and stretch the imagination.

I haven’t tried this experiment, nor do I plan to do so, but I’m willing to bet on the outcome: Give a high school class a unit on Hamlet. One group gets just the book (and a few video clips of performances); the other gets an interactive Hamlet video game, where they get to take photos of their friends and dress them up as the characters, follow the ghost around the castle, reenact the final swordfight, etc. Each group is aware of the other. One week into the project, students are given a survey on their interest levels and their desire to remain in their current group. The survey is repeated at the completion of the unit and then a year later. I imagine the first survey would show many students wishing to switch from the book group to the video group (but not vice versa); the second survey would have a less pronounced result, and the final survey would show a preference for the book group.

In other words, if you can persuade kids to stick with something that’s initially difficult or not palpably fun, you see their interest grow over time. But if you give up, you encourage the “relevance” crutch: you feed their demand for studies that feel good and seem to meet their needs and wants, right now. “Relevance” and “fun” are not exactly the same, but in their shallowest form they become close to synonymous. When omnipresent, they become that shallow.

It takes a lot of energy to get students to stick with something in their studies that doesn’t immediately grab them–but it’s worth the struggle. Then they become capable of a larger range, and they overthrow the tyranny of relevance.

In contrast with Paul (or seeming contrast), I see many instances where play could be educational (for instance, working with an electronics kit) and study could be fun (for instance, learning songs in Russian). The problem lies not in the overlap but in the homogeneity, the cutesiness, and the appeal to a lazy part of the mind and character.

Big role of test scores in New York teacher evaluations

Last year, the New York State Legislature passed a measure that allowed 20 percent of a teacher’s evaluation to be based on students’ scores on standardized state tests.

Now student test scores will account for as much as 40 percent of the evaluations, according to an article in today’s New York Times. This means they will count more than any other single measure. The new regulations are expected to be enacted on Monday by the state’s Board of Regents.

This change is likely due to pressure from Governor Andrew M. Cuomo, who, according to the New York Times, said that a high-quality evaluation system had to be in place before he could support Mayor Bloomberg’s push to end seniority protection in layoffs.

But is this a high-quality evaluation system? It gives a great deal of power to tests that we don’t even have yet (as they are being revised) and to a value-added formula that has turned up many eccentricities, to put it mildly.

It is especially dangerous as a means of determining who should and shouldn’t be laid off. Teachers will be compared with each other by means of measures that haven’t stood the test of time yet (and that leave much to be desired). Principals will have little power to go against value-added ratings, even if they are clearly wrong.

New York State is still reeling from the disclosure that its state tests had gotten easier over the years. It is in the midst of revising its assessments and adopting the Common Core State Standards. The outcome of all of this is uncertain. In the meantime, the value-added formula used in New York City has numerous problems. Andrew Gelman, professor of statistics and political science at Columbia, demonstrates that when teachers are graded on a curve in this manner, a few students (in a large class) doing a little better on a test can bring a teacher from the 7th to the 50th percentile. (See all the comments on his post–they are interesting.)

Why, at this uncertain juncture, would the governor choose to make state test scores such a large part of teacher evaluations? Why the push for something clearly flawed?

Seems not only unwise and reckless, but weird.

Update: A few points of clarification:

The 40 percent would apply to those districts within the state that chose to use state assessments for the local-assessment portion of the evaluation. This would require the approval of the union in the district. So, on the one hand, it’s likely that many districts would choose to use local assessments for the local-assessment portion. On the other, the possibility of using state assessments would always be open, and districts might be under considerable pressure to take that route.

In New York Magazine, Chris Smith interprets this as a bargaining chip for Bloomberg: maybe the UFT will agree to a larger role for state tests if Bloomberg agrees to reduce the number of layoffs. It seems an ominous proposition, as the layoffs are (perhaps) a one-time deal, whereas the regulations will likely be in place for a long time.

The grand sacrifice of teaching

Is teaching supposed to be a great virtuous sacrifice for the sake of the poor? One might think so from reading Fernanda Santos’s article in today’s New York Times.

Samantha Sherwood had lofty aspirations when she settled on a family-studies major at the University of Connecticut, like redrawing welfare rules or weaving together a sturdier safety net for people in need. She figured that she could change the world in big, broad strokes, and that she might pick up a fancy title and ample salary along the way.

Instead, Ms. Sherwood, 25, joined up with Teach for America, the program that puts top college graduates into the nation’s most poverty-stricken schools, deciding that the best way to make a difference would be, as she put it on Monday, “to be there, where the rubber meets the road.”

I am not passing judgment on Ms. Sherwood; I don’t know her or her teaching. She sounds very dedicated. It’s the article that seems a bit strange. Santos mentions that Sherwood earns $45,000–presumably much less than she would or could have earned as a high-profile social worker.

Is it really that great a sacrifice to go into teaching? I would hope not; I’d hope that those who do it enjoy it enough that they don’t perceive it as a sacrifice. Yes, it’s tough, but it can be immensely rewarding too. Is a salary of $45,000 so bad? Well, it isn’t much money in NYC, but one can live on it, especially if one is 25 and doesn’t have major financial obligations.

The layoffs–which were really the point of the article–will hurt veteran and new teachers alike. They will hurt the classrooms. No layoff system will mitigate that. But one of the weakest arguments on behalf of the younger teachers is that they gave up possible fame and fortune for the sake of the kids.

Teachers on ed degree's value

Teachers discuss an education degree’s value (or lack thereof) on the NY Times’ Room for Debate blog. From Mark:

I am a 21-year veteran teacher who took a whole boatload of education courses in furtherance of my BA and MS degrees. They were utterly useless. The only thing that actually prepared me for teaching was student teaching. All of the other courses taught theory, but nothing practical.

Mark has mixed feelings on merit pay.

I am a very successful teacher, and parents and students alike have sought me out over my career. I make the same salary as another teacher who does nothing but shows movies in class all day. I spend my summers revising my work, creating new and interesting facets to the course. I make the same as the teacher who spends the summer not thinking one iota about the next school year.

Merit pay has some merit, it encourages certain behaviors and discourages others. What I am afraid of is that it will be used to reward the wrong people. If a teacher is mediocre, it is because they have been allowed to get away with it, their behavior empowered by administration. There is a great deal of cronyism in the business, and it skews the playing field.

A “frustrated early-childhood education teacher” calls for combining “pedagogy and a strong apprenticeship” program. What she doesn’t want is to sit through time-wasting professional development classes, such as a “five-hour session that culminated in making a caterpillar from an egg carton.”

Update: After qualifying for National Board certification, a veteran teacher was told he lacks enough credits for certification, reports WashPost columnist Jay Mathews. One phone call from Mathews got the bureaucrats to decide the teacher, who’s also a lawyer and Army vet, is qualified to teach.

Frank McCourt: Teacher and writer

Writer Frank McCourt, who died Sunday of melanoma at the age of 78, spent decades telling stories to New York City students as an English and creative writing teacher, reports the New York Times.  Those stories became Angela’s Ashes on his desperately poor Irish childhood, then ‘Tis and Teacher Man.

Gotham Schools quotes McCourt on his first teaching job at a vocational school on Staten Island. (He was rejected by several schools because of his thick Irish accent.) It was staffed by World War II vets who considered students “the enemy”  and young, Dewey-eyed teachers who wanted to meet the students’ “felt needs.”

From his second book, ‘Tis:

They don’t want to read and they don’t want to write. They say, Aw, Mr. McCourt, all these English teachers want us to write about dumb things like our summer vacation or the story of our life. Boring. Every year since our first grade we write the story of our life and teachers just give us a check mark and they say, Very Nice.

In a closet, McCourt found old student compositions going back to 1942.

The boys back then yearned to fight, to avenge the deaths of brothers, friends, neighbors…

… I pile the crumbling papers on my desk and begin reading to my classes. They sit up. There are familiar names. Hey, that was my father. He was wounded in Africa. Hey, that was my Uncle Sal that was killed in Guam.

When I read the essays aloud there are tears. Boys run from the room to the toilets and return red-eyed. Girls weep openly and console one another.

The old essays, written on brittle paper, are about to fall apart. The students agree to copy them by hand.

We are saving the immediate past of immediate families. . . . This is my father when he was fifteen. This is my aunt and she died when she was having a baby.

They are suddenly interested in compositions with the title, My Life, and I want to say, See what you can learn about your fathers and uncles and aunts? Don’t you want to write about your lives for the next generation?

McCourt was a thoughtful, creative, inspiring and original soul, writes NYC Educator.

Liberating languor

Over breakfast with New York Times reporter Susan Dominus, Chancellor Joel Klein waxed enthusiastic over the recent book of Terry M. Moe and John E. Chubb, Liberating Learning: Technology, Politics, and the Future of Education. According to Klein, this book shows how, “through distance learning and other individualized teaching approaches, we may be able to reduce the need in the future for teachers’ overall numbers and increase their pay.”

One might use online courses to supplement existing curricula. But it’s hard to see how they could replace teachers. What would count as an absence, and what would be done about chronic absences? How many students would drop out of contact and slip through the cracks? What would keep children from “learning” on the sofa with the TV on?

Nor would it be fair to use distance learning for the top students. They, too, need teachers in their daily lives. Intellectual advancement and self-sufficiency are not one and the same. Moreover, young people spend so much time online with their peers that they need a counterbalance: adults they must face, places where they must be.

There is no getting around it. Teachers are needed.

Failing in the suburbs

While some immigrant students are doing fine, others are choosing to join the “rainbow underclass,” writes Jason DeParle in the New York Times.  He looks at Hispanic teens in working-class suburbs, where “failing means fitting in.”

The problems of young people like Jesselyn are sometimes called failures of assimilation. But they can also be seen as assimilation to the wrong things: crime, drugs and self-fulfilling prophecies of racial defeat.

As Jesselyn tells it, she assimilated to the surrounding values of gangsta rap. Writing in her eighth-grade yearbook, she celebrated friends as “my nigga!” and labeled enemies “crackers,” “bamma” and “whyte.”

“If you’re Hispanic, people already expect you to steal, to fight, to be rude, to be ghetto,” Jesselyn said.

Jesselyn’s parents, immigrants from Mexico, have been unable to pass their work ethic on to their daughter.

If you’re feeling overly euphoric, read the whole thing.

Teaching niceness

“Social and emotional knowledge” can be taught in school “just like trigonometry or French grammar,” some psychologists believe. From the Boston Globe:

. . .  a typical teaching unit might include a role-playing exercise, or a set of diagrams breaking down the components of different facial expressions, or, in older children, a discussion of the subtle differences between disgust and contempt.

Some of this sounds like the social skills classes offered to kids with Asperger’s Syndrome and other forms of autism.

Around 10 percent of American grade school and high school students now go through some form of social and emotional learning curriculum, according to the Collaborative for Academic, Social, and Emotional Learning (CASEL), a Chicago-based emotional learning research organization. A handful of states have instituted emotional learning guidelines for their public schools – the most comprehensive is Illinois’s, which sets “self-management,” “social awareness,” and “interpersonal skills” benchmarks, among others, for kids at each grade level.

At high-scoring Scarsdale Middle School and elsewhere, empathy is showing up in the curriculum, reports the New York Times.

English classes discuss whether Friar Laurence was empathetic to Romeo and Juliet. Research projects involve interviews with octogenarians and a survey of local wheelchair ramps to help students identify with the elderly and the disabled. A new club invites students to share snacks and board games after school with four autistic classmates who are in separate classes during the day.

Los Angeles is using Second Step, which “teaches empathy, impulse control, anger management and problem solving,” in its middle schools.  Seven Seattle elementary schools are using Roots of Empathy.

I’m dubious about adding another responsibility — one traditionally handled by parents — on to teachers’ shoulders. It’s one thing to insist that students learn to behave in class; it’s another to take on their social and emotional development. Also, I know there’s little research backing the effectiveness of these programs in changing students’ behavior.

Teachers, what do you think? Should “relating” become the fourth R?