kitchen table math, the sequel

Thursday, January 29, 2015

Question: When can you trust your intuition?

Answer: When you possess knowledge stored in long-term memory, not on Google.

I'm semi-beavering away on the writing exercises for Ed's textbook (with Katie Beals) and on Eric Hollander's & my book on the compulsive-impulsive dimension, which has meant long stretches away from Kitchen Table Math (frustrating!)

Trying to organize my collection of articles on the basal ganglia, the orbitofrontal cortex, associative learning, OCD, ADHD, addiction, impulsivity, compulsivity, the cognitive unconscious, intuition, cognitive biases, cognitive heuristics, Go/NoGo (I'll stop here), I came across this:
When should I trust my gut? Linking domain expertise to intuitive decision-making effectiveness
Erik Dane, Kevin W. Rockmann, Michael G. Pratt
Organizational Behavior and Human Decision Processes 119*2012) 187-194

ABSTRACT: Despite a growing body of scholarship on the concept of intuition, there is a scarcity of empirical research spotlighting the circumstances in which intuitive decision making is effective relative to analytical decision making. Seeking to address this deficiency, we conducted two laboratory studies assessing the link between domain expertise (low versus high) and intuitive decision-making effectiveness. . . . Across both studies, and consistent with our overarching hypothesis, we found that the effectiveness of intuition relative to analysis is amplified at a high level of domain expertise. Taken together, our results demonstrate the importance of domain expertise in intuitive decision making and carry a number of theoretical and practical implications.


While theory suggests that people may perform well using intuition . . . , we expect that the benefits of intuition are most likely to be realized by certain individuals -- those who have acquired a substantial degree of expertise in the focal domain (Kahneman & Klein, 2009; Klein, 1998; Salas et al., 2010). Domain experts are well equipped to capitalize on the potential benefits of intuition because they possess rich bodies of domain knowledge that foster the rapid and sophisticated associative processes that produce accurate intuitions (Dane & Pratt, 2007). Although little work has demonstrated just how much expertise must be accrued before the benefits of intuition begin to take hold, the benefits of intuition are generally most evident - and most striking - among those who have engaged in intense, repetitive practice for a number of years, or even decades (Dreyfus & Dreyfus, 2005; Ericsson & Charness, 1994; Simon, 1987).

By the same token, we expect that intuition is likely a poor or misguided decision-making approach for those with very little domain expertise (i.e., domain novices). On this point, research suggests that the intuitions of domain novices are generally based on relatively simple, context-insensitive heuristics (Dane & Pratt, 2007; Tversky & Kahneman, 1974). These intuitions tend to be biased and thus inaccurate (Bazerman, 2006; Hammong, Keeney, & Raiffa 1998).

Wednesday, January 21, 2015

If you want your children to sit in rows, you have to pay extra

Reading David Cutler's "The Private-School Stigma," I came across this:
In a Washington Post opinion piece last year about their book, the coauthors also wrote that private schools too often use their autonomy from state regulations to teach in such a way that may please parents but isn’t effective for learning. In the piece, the Lubienskis wrote:

For example, private school students are more likely than their public school counterparts to sit in rows, complete math worksheets and believe that mathematics is 'mostly memorizing facts'—a narrow view that captures neither the breadth of the discipline nor the reasoning that is central to it. In contrast, public schools have moved beyond traditional, repetitive exercises, and more often ask students to solve complex, real-world problems and to learn geometry, data analysis, and early algebra ideas, in addition to basic arithmetic.
So it's official.

If you want your children learning inside a teacher-centered classroom, you have to a) make enough money to pay for private or parochial school; b) live in an area that has a decent private or parochial school or two; c) hope your kids get in.

Can you spell 'hegemony,' part 2

The private/parochial school option may not be long for this world.

For one thing, the National Association of Independent Schools seems to come down on the side of progressive education, no surprise given that many private schools were founded as progressive alternatives to public school in the first place, at least here in New York:
The 70-odd private schools in or near Manhattan are a varied lot, but with few exceptions they share one notable quality: age. They have the mystique of wood-paneled privilege that is hard to manufacture anew and that continues to radiate the glamour that makes even pop divas like Madonna aspire to Scottish castles and English nannies. Many of these schools are housed in fine, old Upper East Side buildings or ivy-covered campuses; students often wear uniforms, including blazers or kilts; they honor traditions like teas and Founder's Days; they may even call teachers "Sir." History has given each of these institutions a unique character. Towne and Allen-Stevenson are small, traditional schools with a neighborhood tone; Little Red Schoolhouse and Trevor Day have a staunchly 1920s left-wing feel; Grace Church, Marymount, and Sacred Heart have proud religious affiliations.

But it is what Victoria Goldman, co-author of The Manhattan Family Guide to Private Schools, calls the Baby Ivies that are the million-dollar prize of this Survivor game. These are the crème de la crème, the Harvard, Yale, and Princeton of the K-12 set. Decades ago, these schools could easily be divided into two broad categories. The coed, progressive schools—Dalton, Fieldston, Friends Seminary, Horace Mann, Riverdale, and St. Ann's—appealed to New York's artistic and intellectual elite. The unisex traditional schools—Buckley, Collegiate, St. Bernard's, and Trinity (now coed) for boys or Brearley, Chapin, Nightingale-Bamford, and Spence for girls—educated the children of the Protestant establishment, at least until adolescence, when many of the boys went on to board at Groton and Choate. (St. Bernard's and Buckley still only go up to ninth grade.) These days, all the schools pride themselves on a progressive, multicultural curriculum that counts as today's conventional wisdom; you would be just as likely to find a first-grade "interdisciplinary project" on Eskimos at Collegiate as at Dalton and a tenth-grade African-American literature course at Spence as at Fieldston. All of them "respect different learning styles." Yet despite the trendy veneer, the curricula remain fairly rigorous, and the schools still turn out graduates who know the difference between a Van Gogh and a Vermeer, speak French, and play decent tennis.

Survivor: The Manhattan Kindergarten by Kay Hymowitz
And then there are the forces of hegemony, which are pervasive and powerful, and which explain why every reform is the same non-reform all over again, for the most part. The hegemon never quite wins, so the battle never (quite) ends.

That's one theory.

Hirsch has a different take on the one hundred years' war:
The history of American education since the 1930s has been the stubborn persistence of illusion in the face of reality. Illusion has not been defeated. But since reality cannot be defeated, either, and since it determines what actually happens in the world, the result has been educational decline.
And this:
In a conflict between ideology and reality, reality always trumps.
I think that's true.

"Reality always trumps" explains why our schools grind on and on, innovating and disrupting, disrupting and innovating, adopting open classrooms, and flipped classrooms, and station classrooms--any permutation they can dream up--but nothing ever sticks, and the conflict never ends.

Tuesday, January 20, 2015

Station math, part 2

Julie writes:
My 7th grader, who was in an accelerated math class this year (in GA) experienced these same math stations. He said it was like being in elementary school all over again.

This same teacher "flipped" her classroom by making videos of her reading the textbook and examples aloud. He was expected to watch the videos each night before doing homework problems...but he couldn't stand it. He wanted to just read the book to himself and get the homework done.

Same teacher wanted parents and students to follow her on Twitter to keep up with daily son has no interest in using Twitter.
Part of what is going on in my district, and I imagine in Julie's district, is that administrators here are focused first and foremost on "infusing technology into the curriculum." This is the prime directive.

Just how to infuse technology into the curriculum remains a mystery, however, so the district has elected to buy a bunch of stuff and have teachers "innovate."

Which reminds me of a funny conversation. (Not funny ha-ha, I'm afraid.)

A fellow dissident here in the district invited me to a meeting she had scheduled with the high school principal re: flipped classrooms. As we sat down, the principal, who is new to the district, told us he "believes in" flipped classrooms.

"I encourage teachers to take risks," he said.

Having spent years of my life chewing over this and related issues, I had a response at the ready: "You're taking risks with other people's children," I said.

"Teachers have tenure and a union, they're not the ones taking the risk. The kids are taking the risk, and they haven't been asked whether they want to take the risk you're forcing them to take."

(I actually said these sentences, out loud. I didn't just think of saying them later on and wish I had. Very satisfying!)

The principal, who seems like a very nice guy, looked horrified. Clearly, it had never crossed his mind that "teachers taking risks" could be construed as anything other than an unalloyed good--let alone a borderline abuse of his authority as head of school, which is pretty much what I was suggesting.

Since then the administration has gotten a bit of an earful on the subject of experimenting with other peoples' children.

But the experiments continue apace.

"Station math" is, I gather, another effort to infuse technology into the curriculum, I guess because one of the stations has movies, and movies are technology.

So....time flies. I'm old enough to remember when SMART Boards were technology.

My district has beaucoup SMART Boards. We had to buy one for every classroom because we had a SMART Board equity gap.

Maybe the problem is presenters....

I've just come across a blog by Raymond Johnson, who writes:
I hold some grudges when it comes to the topic of research to practice in education. A few highlights: A principal who (probably rightly) thought I was struggling to engage my students told me to watch Barbara Streisand's performance as a college professor in The Mirror Has Two Faces and "do what she does, because her students love her." The question, "Which academic journal did she read that in?" sarcastically crossed my mind, and no, I never watched the movie. At a state conference presentation about RtI, a presenter told us to only use research-based intervention strategies. When a teacher at my table asked, "How do we know if a strategy is research-based?" the presenter responded, "I figure if it's something you find in writing, and didn't just make up by yourself, then it's research-based."
Schneider's From the Ivory Tower to the Schoolhouse, Chapter 1: Bloom's Taxonomy
I guess Wikipedia counts.

Monday, January 19, 2015

Kai on teachers writing curriculum

Kai writes:
Wasn't Englemann the same one who said (paraphrased), "Making curriculum and teaching it at the same time is like building the airplane as you try to fly it...".

Curriculum is hard. At one of my schools I spent 30 hours over the summer just making a scope and sequence with four other people. "Making your own curriculum" is just shorthand for non-systematic throw it against the wall and see what sticks.
Building the airplane while you try to fly it---I love that!

I don't remember reading that before.

Let me tell you: 30 hours to write a scope and sequence with four other people sounds fast to me.

That reminds me!

Daniel Kahneman has a fabulous curriculum-writing story in Thinking, Fast and Slow:
A few years after my collaboration with Amos began, I convinced some officials in the Israeli Ministry of Education of the need for a curriculum to teach judgment and decision making in  high schools. The team that I assembled to design the curriculum and write a textbook for it included several experienced teachers, some of my psychology students, and Seymour Fox, then dean of the Hebrew University's School of Education, who was an expert in curriculum development.

After meeting every Friday afternoon for about a year, we had constructed a detailed outline of the syllabus, had written a couple of chapters, and had run a few sample lessons in the classroom. We all felt that we had made good progress. One day, as we were discussing procedures for estimating uncertain quantities, the idea of conducting an exercise occurred to me. I asked everyone to write down an estimate of how long it would take us to submit a finished draft of the textbook to the Ministry of Education. I was following a procedure that we already panned to incorporate into our curriculum: the proper way to elicit information from a group is not by starting with a public discussion but by confidentially collecting each person's judgment. ... I collected the estimates and jotted the results on the blackboard. They were narrowly centered around two years; the low end was one and a half, the high end two and a half years.

Then I had another idea. I turned to Seymour, our curriculum expert, and asked whether he could think of other teams similar to ours that had developed a curriculum from scratch. This was a time when several pedagogical innovations like "new math" ha been introduced, and Seymour said he could think of quite a few.


He fell silent. When he finally spoke, it seemed to me that he was blushing, embarrassed by his own answer: "You know, I never realized this before, but in fact not all the teams at a stage comparable to ours ever did complete their task...."

This was worrisome; we had never considered the possibility that we mint fail. My anxiety rising, I asked how large he estimated that fraction was. "About 40%," he answered. By now, a pall of gloom was falling over the room. The next question was obvious: "Those who finished," I asked. "How long did it take them?" "I cannot think of any grow that finished in less than seven years," he replied, "nor any that took more than ten."


Our state of mind when we heard Seymour is not well described by stating what we "knew." Surely all of us "knew" that a minimum of seven years and a 40% chance of failure was a more plausible forecast of the fate of our project than the numbers we had written on our slips of paper a few minutes earlier. But we did not acknowledge what we knew. The new forecast still seemed unreal, because we could not imagine how it could take so long to finish a project that looked so manageable. ... All we could see was a reasonable plan that should produce a book in about two years....


We should have quit that day. None of us was willing to invest six more years of work in a project with a 40% chance of failure. Although we must have ended that persevering was not reasonable, the warning did not provide an immediately compelling reason to quit. After a few minutes of desultory debate, we gathered ourselves together and carried on as if nothing had happened. The book was eventually completed eight(!) years later. By that time I was no longer living in Israel and had long since ceased to be part of the tam, which completed the task after many unpredictable vicissitudes. The initial enthusiasm for the idea in the Ministry of Education had waned by the time the text was delivered and it was never used.

This embarrassing episode remains one of the most instructive experiences of my professional life.
Planning fallacy

Auntie Anne and Anonymous on teachers writing their own curriculum

Anonymous writes:
When I was a new teacher I would have croaked if I had had to write curriculum. And it would have failed miserably. What I did develop over time was the ability to extend curriculum in some realms. But I was glad to have a logical, tested curriculum for Grade 1 Reading. It's too important to be left to multiple teachers winging it.

My ideal writing team, where curriculum is concerned, is a classroom teacher working with a disciplinary specialist. Classroom teachers have pedagogical content knowledge, mathematicians have the curse of knowledge, et voilà, at least potentially: real math kids can actually learn and comprehend.

(I'd always heard that the Singapore Math series was written by math teachers partnered with mathematicians, but Barry tells me that story is apocryphal.)

The only reason teachers can't write curriculum is that they already have a job teaching.

Auntie Anne:
But these days, "our own curriculum" is often the teacher spending 5 or 10 minutes googling for a worksheet--this was our kids' 6th grade math from start to finish.

Our school likes to say that the curriculum they buy (formerly EM, now moving over to SM) isn't their "curriculum," they just use that as the basic outline and go from there.

Now, there are some websites I love for worksheets ( is my favorite,) and good sites for information and explanations ( for example), but nothing compares to a carefully constructed, brick-by-brick textbook for completeness, coherence, and consistency.

Here in these parts, the curriculum is becoming Google.

Onward and upward: Station math

I learned this week that our 6th-grade math teachers have adopted a new way of teaching math.

One day a week, they teach the whole class.

On the other four days of the week, students are given a menu of options, each one of which corresponds to a station in the classroom. Some stations have videos.

Children select a station and spend the class doing whatever it is they do at math stations while the teacher circulates the room "working one on one." 

In the beginning, students were told they couldn't ask the teacher questions because she would be too busy to answer. That's: no questions at all. Not even three before me

That rule has now been rescinded, it seems.

So parents are hiring tutors, and some parents have asked that their children be switched to "Academic Intervention Services" so they can have a teacher who actually teaches. 

The board wasn't alerted to the change, and it's not clear how much parents even know that their children are now receiving only one day of direct instruction per week. The parent I spoke to knew about it because she picked up on a line in a Back to School Night handout and put two and two together.

None of the administrators admits to having anything to do with it. 

Somehow, the entire 6th grade math program turned into a writers workshop for math without anyone's being the wiser. 

Another wrinkle: accelerated math placements aren't made until January of grade 6. Since mine is a nominally high-performing district, the goal in placement decisions is to keep as many kids out of accelerated classes as possible -- which, according to my source, has meant that parents of the mathematically talented kids have had to suck it up, hire tutors, and keep their opinions to themselves. 

A child who is having trouble learning math at stations is a child who's not getting the nod.

Vanishing act....

My book is due May 1 and Katie's and my writing curriculum, which accompanies Ed's textbook, is due now, plus I made ONE New Year's resolution, which is to completely and totally de-clutter my office ....

Not exactly sure how blogging fits in there -- !

Miss you guys!

Friday, January 9, 2015

Wrong again: noise in the classroom

Progressive educators seem to like noisy classrooms, I've noticed.

Here's Carmen Farina:
“Once I was about to visit a principal,” [New York City Schools Chancellor] Ms. Fariña said, “who told me, ‘You’re going to love coming here because you can hear a pin drop.’ I said, ‘I better not come because that isn’t going to make me happy.’ ”

Schools Chancellor Brings Joyful and Fierce Style
And here's reality:
...[E]merging research suggests that quieter noises can have varied effects on student learning and memory.


Low or barely perceptible sound—be it from a lecture in the classroom next door, a heating system that keeps turning on and off, or even a classroom aquarium filter—can increase stress and interfere with memory and learning....

“You can’t depend on the kids to complain,” said Ruth M. Morgan, a speech pathologist at Ephesus Elementary School in Chapel Hill, N.C. “Kids generally go with the flow, and they wouldn’t let you know there’s too much background noise.”

How Loud Is Too Loud?

Noise is measured in decibels on a logarithmic scale; every 10 decibels marks an increase in sound that is twice as loud. Normal conversation is usually in the range of 60 to 65 decibels, and children often speak more softly than adults, as low as 35 decibels.


...In a 2013 study in the Journal of Urban Health, a publication of the New York Academy of Medicine, 8- and 9-year-old students who had higher “ambient” noise levels in school performed significantly worse on standardized tests in mathematics and French language, after controlling for their socioeconomic backgrounds. A difference of 10 decibels of regular background noise was associated with 5.5-point-lower scores on average in both subjects.

Similarly, a prior study found students were highly distracted by a television playing in an adjoining room, even when it was barely audible, but they were unable to identify why they were having trouble concentrating.


The results don’t surprise Ms. Morgan in Chapel Hill. She noticed that while the classroom didn’t seem particularly loud, both she and her students seemed to be having trouble following conversations during sessions in which students worked in groups.

“So much of class now is the children speaking to each other, doing buddy reading,” she said. “And children’s voices are softer; I was having difficulty hearing them.”

Some sounds are also more vulnerable to distortion: s-, sh-, and ch- sounds in speech are particularly easy to mistake when competing with low-frequency mechanical sounds, such as the hum of a computer fan or heating system.

Ms. Morgan said she thinks her school’s noise issues may be common in older schools, where former “open concept” classrooms were later closed in with walls that typically have less noise insulation than new construction, allowing students to hear more lectures and mechanical sounds in other rooms.

Low-Level Classroom Noise Distracts, Experts Say

Thursday, January 8, 2015

Can teachers write their own curriculum?

A few years ago, our then-assistant curriculum director, a terrific woman and an advocate for children whom I miss to this day, explained to the school board that our math curriculum was not Math Trailblazers.

I was in the audience at the time, and I was annoyed, because our curriculum most certainly was Math Trailblazers.

"People say our curriculum is Trailblazers," she said, "but it's not. We write our own curriculum."*

At the time, I was somewhat regularly in touch with a parent who had worked as an editor for a textbook publisher. Apprised of the 'we write our own' exchange, she was aghast.

In the world of publishing, where curricula actually do get written and published, writing a curriculum is a massive undertaking that consumes months of effort and multiple bodies playing multiple roles.

Not here. In my district writing-our-own-curriculum meant giving teachers two-week stipends over the summer to meet with a Trailblazers specialist from Bedford (the only other district still using Trailblazers, everyone else having dumped it) and be briefed on tweaks.

Trailblazers finally disappeared last year, but the curriculum situation has not improved. It's probably worse; the old-time curriculum adoption process seems to have been scuttled in favor of unilateral decisions made by the central executives. And our current curriculum director's new Powerpoint, titled "Teaching for Understanding," includes the observation that "Conventional linear (text-book [sic] driven) scope and sequence is a major impediment to developing understanding."

Naturally the words "we write our own curriculum" make me crazy because, as an adjunct who actually does write her own curriculum, not to mention an author who writes her own books, I know exactly how time-consuming writing a curriculum is.

Writing a curriculum takes forever.

Here's Siegfried Engelmann on the subject of writing and time:
As part of the endorsement of whole language, the ["Report Card on Basal Readers"] concludes that teachers should throw out basal readers and teach without them, using literature. The baseless are seen as an evil that deprives reading specialists of their right to make instructional decisions.

There are several problems with this solution: The first is that teachers are typically slaves to instructional programs and follow them very closely (even when they tell other that they don't). The second is that there is no evidence to support the assertion that typical reading specialists are capable of designing instruction that is effective (and a lot of data to suggest that they aren't). The third and most serious problem is that a reading specialist who designed even one grade-level of a program that worked well with the full range of kids, wold have to work on it no less than 6 hours a day for a minimum of two years.

War Against the Schools' Academic Child Abuse by Siegfried Engelmann, p 24
Six hours a day, five days a week, for two years.

Sounds about right to me.

Full disclosure: I am writing part of a textbook.

It's taking forever.

Later on one of our school board members, whom I had lobbied heavily on the subject of Singapore Math, took to calling our curriculum "Irvington math."

Wednesday, January 7, 2015

Je Suis Charlie

Charlie Hebdo website back up

Charlie Hebdo, RIP

UGH: NY Daily News CENSORS image of Hebdo’s Muhammad Cartoon in report on attack

Ed just spoke to a French friend whose mother lives on the same street as the Charlie Hebdo offices.

She says she grew up reading the writers who were killed. She can't believe they're gone.

Still here...

Thanks to Palisadesk, Surfer is still with us!

Of course, now he has a tumor the size of a grapefruit on his spleen, so .... it's always something.

I love our vet.

He told me: "As your vet, I have to tell you to remove his spleen. But as a person, I don't think I would."

Then he told me his wife is a vet & she would smack him if she heard him give me that advice because "she whips spleens out of dogs all the time."

Our vet is hugely entertaining. I like that in a vet.

He's also a good soul.

Two days after Thanksgiving, Abby (the Labrador) had a near-death experience. Blood all over the basement floor, emergency room, bladder infection, all of it leading to -- surprise! -- liver failure.

I don't know whether bladder-infection-to-liver-failure is a Thing, and neither did my vet, though I have since heard from the mother of one of C's friends that her own aged dog recently went through the same sequence.

Two Monday's after Thanksgiving, Abby was so sick she looked like the photographs I remember seeing of starving people in Biafra, or in the death camps. One of her liver enzymes was supposed to be 200-ish; that day it was 12,000 and rising. The vet said he'd never seen a number that high.  She was dying.

He kept her in the office all day, on IV fluids and antibiotics. Later on, he told me he'd expected to put her down that day, but by evening she was still alive, and a bit restored.

Which created a new problem: she was still desperately ill and, by rights, needed to spend the night in the hospital. Probably several nights.

The vet called & danced around the problem. He said he would drive into the office in the middle of the night to check on her, but otherwise, if she stayed there, she would be alone.

That's what I call a good soul. He doesn't live close to his office; he has young kids get to school first thing in the morning. Waking up in the middle of the night to check on a possibly dying dog who has already lived longer than the norm for her breed is above and beyond.

I said I'd keep her home overnight & bring her back the next morning.

When I arrived to pick her up, our vet took her down the stairs to the parking lot himself, then pointed out she'd walked them on her own, which she hadn't been able to do that morning.

Then he lifted her into the back of my car. The vet's aide was there, too, standing with us in the parking lot, but the vet lifted her himself.

Abby survived.

She is amazingly restored: chipper, tuned in, and hungry as only a Lab can be. She was no longer eating or drinking

Her poor legs are done for, and she seems awfully thin. She's probably done for, too, but she has a vet who will get up in the middle of the night and drive 20 miles just to look in on an old dog, and that has made all the difference.

Happy New Year!

Wednesday, December 31, 2014

Frederick Hess: Common Core tests were the fix for NCLB

Frederick Hess writing in National Affairs:
In 2001, the No Child Left Behind Act marked a dramatic win for standards-based reform — but at the price of abandoning the push for "national" standards. NCLB required states to adopt standards in reading and math, administer annual tests geared to those standards, use tests to determine which students were proficient, and analyze the outcomes to determine which schools and systems were making "adequate yearly progress" — including the absurd requirement that 100% of students be proficient by 2014. Schools and systems that didn't perform adequately were subject to federally mandated sanctions. The crucial compromise was that states could set their own standards and tests. In fact, NCLB specifically prohibited national testing or a federally controlled curriculum.

What followed was not difficult to anticipate. The possibility of sanctions gave more than a few state leaders reason to adopt easy tests and lower the scores required for proficiency. A "race to the bottom" was soon underway, prompting an effort to combat the gamesmanship.


The real power of standards lies in their ability to change what is tested, and thus to change how curricula and textbooks are written, how teachers teach, and how students learn. As Finn and Petrilli put it, the standards are ignored, and "[e]ducators instead obsess about what's on the high-stakes test." This is why advocates are so impassioned and why critics are justified in fretting about the implications of the Common Core. When coupled with tests, accountability systems, and teacher evaluation, the Common Core becomes the invisible but omnipresent foundation of American education.


[T]he Common Core is neither necessary nor sufficient for fixing the problem it was designed to solve. The critical rationale for the Common Core was concern that states had gamed and manipulated testing under NCLB. But a more modest solution was already available. Every state has long participated in the National Assessment of Educational Progress, which tests students in reading and math (and sometimes in other subjects) in grades four, eight, and twelve under carefully controlled conditions and provides a rock-solid means for comparing performance. In fact, NAEP results were already being used to flag states that appeared to be gaming their NCLB tests. Common Core advocates, however, thought that relying on NAEP was an unsatisfactory, makeshift solution. Instead, they embraced the Common Core standards.

Solving the "race to the bottom" problem would have required the Common Core tests to replicate NAEP's careful protocols. However, perhaps recognizing that states might not have signed on if they were subject to transparent coercion, Common Core advocates were remarkably laid back about what states would actually be required to do when it came to policing test conditions, accepting mandatory passing scores, or establishing strong oversight boards. Thus, advocates failed to build in controls to prevent states from manipulating outcomes. States can administer the Common Core-aligned tests much later in the school year than is recommended (thus inflating measures of student learning), ignore guidelines on testing conditions, and set their own proficiency scores. The only "safeguard" against any of this is state officials' inclination to do the right thing — which is precisely what it was before the Common Core. Meanwhile, many Common Core states have decided not to use the program's new tests at all; as a result, barely 40% of students are currently slated to be tested with one of the two new Common Core tests, and at least 19 different tests will be used nationwide next spring. Given the critical role of the tests for maintaining standards, this undermines the purpose of the Common Core — and in a fashion that seems unlikely to lead to purposeful experimentation or rethinking. Within a few years, testing may be only slightly less fragmented than before the Common Core, and many established tests will have been jettisoned for slapped-together replacements.

How the Common Core Went Wrong
Common Core was all about the tests.

NCLB had failed -- so the thinking went -- because (some) states gamed the system by writing easy tests (or writing hard tests but setting easy cut scores).

So Common Core would create common standards and, hence, common tests. Hard tests.

Like Jason Zimba, I might have thought, a few years back, that changing the tests would do the trick. Create good tests, let the schools take it from there.

But having sent three children through public schools, and having read some of the literature on foreign aid and its many debacles, I now have a much greater appreciation for the slipperiness of reality.

Or the slipperiness of culture, more like.

I'm extremely tardy getting Barbara Oakley's op ed & new book posted, and it looks like I won't get to it today, either.

But I do want to quote her passage on culture:
Today's Common Core approach to teaching STEM is at least superficially appealing. The goal of placing equal emphasis on conceptual understanding, procedural skills and fluency, and application is laudable. But as with any new approach to teaching, the Common Core builds on the culture that's already there. And the culture that has long reigned in STEM education is that conceptual understanding trumps everything. So bewildered math teachers who are now struggling to teach the Common Core are leaning on the old thinking, which has it that if a student doesn't understand—in the "ah-ha," light-bulb sense of understanding—there's no way she or he can truly become expert in the material.

True experts have a profound conceptual understanding of their field. But the expertise built the profound conceptual understanding, not the other way around. There's a big difference between the "ah-ha" light bulb, as understanding begins to glimmer, and real mastery.

How We Should Be Teaching Math
Like NGOs disbursing foreign aid, the Common Core had to build on the culture that was already there.

The culture that's already there inside public schools pits "knowledge" against "thinking," "problem solving," and "understanding," with knowledge the loser. Here in my district, in fact, our curriculum director has produced a new Powerpoint, titled "Teaching for Understanding," which poses a rhetorical question:
Is it possible to have a great deal of knowledge but limited understanding?
Harder tests aren't going to raise student achievement inside a culture whose denizens believe that knowledge is an impediment to understanding.

Auntie Ann points out the obvious

Lot of these studies about the problems with reading on screens--including amount absorbed and lack of sleep--need to get through to schools that putting everything on electronic media instead of good old books is a bad idea.

Yes, carrying 3-4 textbooks home every night is like lugging a backpack full of bricks, but there has to be some happy medium out there somewhere.
Thank you!

Can't believe I didn't think of that.

(I did think of it where my own kids are concerned. I've been bugging Chris to get off his laptop in the evening, and I've been asking myself whether I have what it takes to pry Andrew* from his.)

Put together the finding that e-readers affect circadian rhythms with the fact that teenagers' circadian rhythms are already delayed ....


* For passersby, Andrew is 20 years old and autistic.

Jason Zimba teaching his children math

For passersby, Jason Zimba is one of 3 writers of the Common Core math standards.
Every Saturday morning at 10 a.m., Jason Zimba begins a math tutoring session for his two young daughters with the same ritual. Claire, 4, draws on a worksheet while Abigail, 7, pulls addition problems written on strips of paper out of an old Kleenex box decorated like a piggy bank.

If she gets the answer "lickety-split," as her dad says, she can check it off. If she doesn't, the problem goes back in the box, to try the following week.

"I would be sleeping in if I weren't frustrated," Zimba says of his Saturday-morning lessons, which he teaches in his pajamas. He feels the math instruction at Abigail's public elementary school in Manhattan is subpar — even after the school switched to the Common Core State Standards.

But Zimba, a mathematician by training, is not just any disgruntled parent. He's one of the guys who wrote the Common Core.

And four years after signing off on the final draft of the standards, he spends his weekends trying to make up for what he considers the lackluster curriculum at his daughter's school, and his weekdays battling the lackluster curriculum and teaching at schools around the country that are struggling to shift to the Common Core.


Zimba gave up an academic career in which he had the freedom to wonder about abstract physics problems in the peace and quiet of his Vermont barn. But, he says, "I'm now participating in a much more urgent problem."

That problem is how to elevate the academic achievement of American students, especially the most disadvantaged, so the country can maintain its competitive advantage in the global economy. These days, Zimba and his colleagues acknowledge better standards aren't enough.

"I used to think if you got the assessments right, it would virtually be enough," he says. "In the No Child Left Behind world, everything follows from the test."

Now, he says, "I think it's curriculum."

The Man Behind the Curtain
The theory behind CC was that common tests were the ticket.

Common standards would produce common tests would produce common curricula.

No more race to the bottom.

Monday, December 29, 2014

TimesWatch, Day 1

I need to stop reading education stories in the New York Times.

Because life is short.

Since I'm probably not going to stop reading education stories in the New York Times, I've decided to document the badness.

Or at least list it:
  • 12/19/2014 Raising Ambitions: The Challenge in Teaching at Community Colleges:"Data on what kind of teaching works most effectively at the community college level is scant. But what is known from learning theories generally is that constructivist methods, which prize active student participation over passive receipt of information, are intensely valuable." 
  • 12/26/2014 Colleges Reinvent Classes to Keep More Students in Science: "Hundreds of students fill the seats, but the lecture hall stays quiet enough for everyone to hear each cough and crumpling piece of paper. The instructor speaks from a podium for nearly the entire 80 minutes. Most students take notes. Some scan the Internet. A few doze....Multiple studies have shown that students fare better with a more active approach to learning...
  • 12/27/2014 Rage Against the Common Core: "Many teachers like the standards, because they invite creativity in the classroom — instead of memorization, the Common Core emphasizes critical thinking and problem-solving."
If you haven't read the stories, don't waste your time.

Instead, spend it listening to Education Next's pod cat with Guido Schwerdt:
More Lecturing, More LearningIn this podcast, Guido Schwerdt talks with Ed Next’s Paul Peterson about his new study finding that students learn more math and science when their teachers devote more time to lecturing and less time to problem-solving activities.

Today, on average, teachers spend more time on problem-solving activities than they do making lecture-style presentations. If teachers were to spend 10 percent more time lecturing, this would be associated with a rise in test scores comparable to about 1 or two months of additional learning in a year.

1 space after periods redux

I knew there was a reason why you're supposed to use just one space after a period when you're typing on a computer, but I couldn't remember what it was.

Turns out that, unbeknownst to me, my Downloads folder holds the answer, in a document entitled "Problems Noted on Student Writing":
This change occurred in academic writing as a result of the use of computers that have proportional fonts capable of adjusting the spacing as needed. This rule has been the standard in journalism and publishing since computers have been used for word processing purposes. 
Have I ever come upon a document I didn't download?

Sometimes I wonder.

Barry's Rifle Range on grit

In all my classes, I required my students to answer warm-up questions at the beginning of class. I used two types of questions:. One was a review-type question to apply what they recently learned. The other required them to some apply their prior knowledge –or what was familiar—in a new or unfamiliar situation. Some may view this as an inquiry-based approach, or an application of the “struggle is good” philosophy that adherents of Common Core seem to say is necessary to develop perseverance in problem solving, as well as the all-important and frequently undefined “grit”. I view a short amount of struggle as appropriate provided that explanation is provided shortly after. That way, even if students do not succeed in solving a problem, most are receptive to explanations that they might otherwise tune out.

Saturday, December 20, 2014
Conversations on the Rifle Range, 19: Grant’s Tomb Again, Alice in Wonderland, and the Eternal Question
Asking students to spend a few minutes applying prior knowledge to a new problem arouses curiosity.

That's a good thing because, according to Jaak Panksepp, curiosity is one of the seven core emotions driving all human behavior. He calls it "SEEKING."*

SEEKING may be the core emotion, in fact, the emotion without which the other six don't work.

So: arousing curiosity about math!

Good idea.

Panksepp's fantastic book: Affective Neuroscience: The Foundations of Human and Animal Emotions

And I see he published a new book in 2012!

Ordering it now -----

The Archaeology of Mind: Neuroevolutionary Origins of Human Emotions by Jaak Panksepp and Lucy Biven

*It's probably more accurate to say that curiosity is a facet of SEEKING.

"About that mom who's not bragging about her kid"

A friend sent me a link to this essay on the subject of kvelling moms, and I'm passing it along.

Very nice.

Thursday, December 25, 2014

Back to books

I've decided to start turning off my laptop and my iPad at 6pm.


I see it is currently 6:28 pm.

So I'm going to post this, eat dinner, and pick up a book!

Light-emitting e-readers before bedtime can adversely impact sleep

Open the Book, Put Down the Tablet at Bedtime (behind pay wall)

Reading on electronic devices before bedtime can disrupt the body’s circadian clock, making it harder to fall asleep and become alert in the morning, according to a study from Brigham and Women’s Hospital in Boston.

Evening use of light-emitting eReaders negatively affects sleep, circadian timing, and next-morning alertness

I've been reading bad reports on eReaders and sleep for a while now, but it was the finding on next-morning alertness that finally got to me. Before I owned a laptop and an iPad, I never had trouble waking up in the morning.

Now I do.

I may have to re-up my subscription to the paper version of The New Yorker.

Sing-along: Il est né le divin enfant

Wednesday, December 24, 2014

Merry Christmas | Happy Chanukkah

From the annals of persistence:

Ed just spent ages figuring out how to watch The Interview on TV (via YouTube, via Roku, which turned out not to be plugged in. At all. As in, not plugged in to the TV or the wall socket. Things went downhill from there.)

This may have to become a Christmas Eve tradition.

I must say ... I'm enjoying the fact that this is the movie that stopped Sony in its tracks.

Good grief.

In other news, this is the first year we have ever had Christmas presents under the tree!

Meaning: this is the first year Andrew has been willing to leave Christmas presents under the tree unmolested. We used to have to lock wrapped presents in the car so Andrew couldn't get to them.

Needless to say, the Andrew menace led to a distinctly not-fun practice of wrapping all the presents Christmas Eve.

No more!

Another innovation: Andrew wrote out a Christmas list.

Monday, December 15, 2014

Advanced Math for Young Students

Phil Keller sent me a copy of his beautiful new book Advanced Math for Young Students.

(Here's his blog. And here's an early review!)

I told Phil, as soon as I laid eyes on the book, that it has the look and feel of an authored work, nothing like the many-authored splendor of a typical commercial textbook.

Plus (and I have to say this) the cover and pages are creamy and smooth, a throwback to the physical beauty of books pre-crash (although of late I've had the sense that decent paper may be making a comeback).

The book is so compelling I may have to buy a second copy to work through myself so the other one can stay on the coffee table.

From the Introduction:
For 26 years, I have been a high school physics teacher. I work in an excellent, well-regarded high school and I have been fortunate to have many talented students who soak up all the physics I can teach them, and more. But every year, I also teach students who struggle to master the topic, despite their great efforts and mine. And I know from discussions with colleagues, both within my school and arose the country, that we are not the only ones struggling. There is something getting in our way. Maybe this will seem obvious to anyone who has struggled in physics, but here's what I think: I think it's the math.

Physics applies math. It's all about finding relationships and solving the puzzles that the laws of physics present. For the most part, this work is done in the language of mathematics, and more specifically, the language of algebra. So to be comfortable learning physics, a student has to be fluent in that language. Algebra cannot just be a memorized set of procedures for finding 'x'. It has to be a symbolic way of representing ideas. But for many students, that level of fluency is not attained unjust one year of algebra--which is all that many students have had when they start studying physics. It's no wonder that some struggle.

It is not only physic students who struggle. For even more than 26 years, I have been teaching students how to prepare for the math portion of the SAT. What I have seen over the years is that most students are not fluent enough in algebra to successfully apply algebra on the SAT. One goal of my SAT course is to teach alternative, non-algebraic approaches to SAT problems. It is also a major theme of my math SAT book, The New Math SAT Game Plan. And I will tell you something you may find surprising (or even distressing): on the SAT, these non-algebraic methods work very nicely. They won't get you to an 800, but they will take you pretty far. And even my top scorers report that they like to mix in the non-algebraic methods along with the standard approaches (which, as top students, they also know how to use).

The non-algebraic methods, however, won't get you very far in physics. In fact, a student who does not really learn the language of algebra is going to struggle in all later math and science classes: physics, statistics, computer science and beyond. That STEM door is swinging closed because one year of algebra class did not lead to sufficient fluency. So why spend only one year? Why not start earlier?

I am not saying every 7th grader should be in a high-school version of Algebra I. But I am saying that every middle school student should, over the course of the middle school years, start learning about and thinking about the ideas of algebra (even some ideas that won't reappear until Algebra II or Pre-calculus). These are ideas that take some time to ponder.

Saturday, December 13, 2014

Happy 12/13/14!

I speak as a fan of 11:11 on digital clocks.

Speaking of digital clocks, several years back my neighbor told me her son couldn't read an analog clock.

Are schools teaching analog clocks these days?