kitchen table math, the sequel: 7/1/12 - 7/8/12

Saturday, July 7, 2012

math & fractions

"Academic Music"

No idea what to make of this, but I don't rule it out. Temple always used to say that music was the precursor to language. She may actually have said that music is language for some animals...I don't recall now.

"Brain in the News"

Don't think I've ever mentioned the Dana Foundation's Brain in the News. I'm a fan.

Free subscriptions here

I've just discovered they have a "Neuroeducation" page, too. Looks interesting.

define "lesson"

more from the Times:
Last month I asked my students to take a pro or con position on the topic of genetic engineering; one student vociferously announced, “I completely disagree with it. We don’t know how it’s going to affect us in the long run!” The boy next to her replied, “Ally, they use genetic engineering to manipulate bacteria to make human insulin. I’m diabetic; that insulin keeps me alive.” Other students thrust their hands into the air anxious to share their point of view, while others simply blurted out their ideas – our classroom was intellectually alive and I was the moderator.

When asked why they were so engaged in the lesson one student replied, “It affects our future. We want to help build it.”

The other students clapped in agreement.
What is a good teacher worth?
Ok, number one: No actual teenaged person ever spoke the words "They use genetic engineering to manipulate bacteria to make human insulin."

No adult ever spoke the words "They use genetic engineering to manipulate bacteria to make human insulin." Not unless the adult was giving a lecture from notes.

"They use genetic engineering to manipulate bacteria to make human insulin" is not the way people talk.

Number two: No teenaged person ever said "It affects our future. We want to help build it," either.

Number three: Structurally speaking, the student who has diabetes is given the last word, which means s/he wins the point. I object. If this isn't a class where 'critical thinking' means 'adopt politically liberal positions re: science policy,' then both the discussion and the paragraph need to be handled differently. I.e.: some contrarian points of view need to be raised by the teacher.

Or maybe students could, you know, read something about the precautionary principle before they get so fired up they're thrusting their hands into the air and blurting out their ideas.

Which brings me to Number four: How is a bull session on genetic engineering a "lesson"?

(And, just out of curiosity, how does a bull session on genetic engineering, absent any engagement with the literature on the subject, help build the future?)

update 4:28pm: High school students preparing for a debate.

again with the critical thinking

Well, thanks to Texas Republicans including the words "critical thinking" in a statement no one outside a tiny group of public school obsessives actually understands (or cares to understand, apparently), we now have precious NYTimes real estate going to the celebration of non-memorization in schools.

Here, courtesy of the Times, we have the thoughts of a recipient of the Presidential Award for Excellence in Math and Science Teaching and the Distinguished Fulbright Award in Teaching:
I’ve worked for many years with students of varying demographics and learning abilities and what I’ve learned over and over is that nearly all kids love to learn – even those who would like us to believe they hate school. But what they need from their education is more than the memorization of facts – they need great teaching, foundational knowledge, problem solving skills, and the understanding of current issues.

What is a Good Teacher Worth?
July 6, 2012, 10:03 AM
So they're going to acquire "foundational knowledge" but they're not going to memorize any facts. Or not many.

How exactly do you pull that off?

And please don't tell me 'they construct their own knowledge.'

Speaking as a writer, I have constructed knowledge any number of times -- and then promptly forgotten what it was I constructed. For nonfiction writers, forgetting your own ideas is a common occurrence and an occupational hazard. That's why writers keep notebooks.

I do recall, I think, Willingham once saying that we remember knowledge we've figured out for ourselves somewhat better than we do knowledge we've been told by someone else. Assuming that's the case, I surmise that the mechanism is the amount of time you spend trying to figure something out, which amounts to a form of practice or rehearsal as well.

I know for a fact that 'discovering' and 'constructing' your own knowledge is absolutely no guarantee that you will recall your own knowledge later on.

Not even close.

There's only one route to Carnegie Hall.

instructivist weighs in

Friday, July 6, 2012

support this

In the Times:
In just five months, the Obama administration has freed schools in more than half the nation from central provisions of the No Child Left Behind education law, raising the question of whether the decade-old federal program has been essentially nullified.

On Friday, the Department of Education plans to announce that it has granted waivers releasing two more states, Washington and Wisconsin, from some of the most onerous conditions of the signature Bush-era legislation. With this latest round, 26 states are now relieved from meeting the lofty — and controversial — goal of making all students proficient in reading and mathematics by 2014. Additional waivers are pending in 10 states and the District of Columbia.

“The more waivers there are, the less there really is a law, right?” said Andy Porter, dean of the University of Pennsylvania’s Graduate School of Education.


In exchange for the education waivers, schools and districts must promise to set new targets aimed at preparing students for colleges and careers. They must also tether evaluations of teachers and schools in part to student achievement on standardized tests. The use of tests to judge teacher effectiveness is a departure from No Child Left Behind, which used test scores to rate schools and districts.


Instead of labeling all struggling schools as failing, the waivers direct states to focus most attention on the bottom 5 percent of low-performing schools. “With the waiver we can focus on those schools that really need a lot of help,” said June Atkinson, North Carolina’s state superintendent of public schools.


The waivers also free up about $2 billion in annual federal funding that No Child Left Behind required low-performing schools to use either to transfer students to other schools or for tutoring services.

Maria Campanario, interim principal at Rafael Hernández School, a dual-language kindergarten-to-Grade 8 school in Roxbury, a Boston neighborhood, that has missed its federal targets four years running, said parents were often confused by the offer to transfer to another school.

“I have parents who come in who are English-language learners, and they would say: ‘What does this mean, we can go to another school? You don’t want us to be here?’ ” she said. “They would say, ‘But we like the school and think it’s fine.’ ”

Ms. Campanario said she welcomed the discretion to use the funding for “professional development that is going to support the whole school.”

“If you give me that money,” she said, “ I will put it to excellent use.”

‘No Child’ Law Whittled Down by White House By MOTOKO RICH
Published: July 6, 2012
More professional development.

I'm sure that will work.

By the way, when did 'support' become the all-purpose word for what schools do. I hear 'support' constantly in the edu-world these days. Hear it and read it. Struggling students need support, struggling teachers need support, struggling schools need support. Everyone needs support, and everyone else seems to be getting and/or providing support. It's all about support!

Thursday, July 5, 2012


The real horror, however, was on a one-page sheet – this was not on the agenda and was meant to be buried — titled, “Summary of January 2011 Regents.” The sheet had a very simple chart showing results of the Regents Exams — the tests taken by all New York State high schoolers, many of which have to be passed for graduation. Easy to read: Exam subject, number of students who took the exam, number of students who passed: 41 kids took Integrated Algebra and only 10 passed; 27 took Global History, 5 passed. Of the ten exams given that fateful January day, only 34 of the 129 students who took them (26%) passed. And this was before any budget crisis. “We’ll look into it,” said the Super.

Field Notes: Wake Up and Smell the Smoke - or Not
by Peter Meyer

palisadesk on full inclusion

On the subject of full inclusion, palisadesk writes:
The full inclusion movement in my district definitely evolved from three separate trends that coalesced in a perfect storm, so to speak. It didn't arise out of a belief system about inclusion or discovery-based learning or any of that. I followed the process very closely at the time (between about 1992-2002) because I was then teaching special ed (LD) and had a keen interest in providing appropriate programming to kids with reading disabilities, other LD or language impairment. The impetus came from above and had three prongs:

(1) Cost. There was a major effort to cut costs in some areas (senior administration not one of them, coincidentally), and Special Education was a target -- small classes, highly trained teachers, aides, paraprofessionals et alia were all very expensive. The research data (longitudinally) on self-contained sped programs for most students was also very disappointing. Inclusion was seen as a way to save money and still look egalitarian, socially equitable and all that. Our CEO had a public meeting about the issue where he was very frank that this was about money, but opined that our wonderful teachers would make the new inclusion work. We did not share his optimism (and still don't). Naturally, some SPED programs remain but they are very limited and the hoops to jump through for parents or teachers to refer students for these programs are daunting and endless. Currently, I'm told, a student has to be 4 years below grade level in all areas to qualify for a LD class.

(2) Change in parental attitudes, overall. At one time parents of children with disabilities were happy to see their children enrolled in a program geared to their needs, and in my district at least the teachers of many of these programs were specially trained and the programs well-resourced and effective. More and more, there has been a shift in attitudes. At least, we are now seeing a majority of parents refusing SPED services or classification, and insisting on their right to have their child in the general ed classroom. There are quite a few powerful and well-organized parent lobby groups that are politically active and support full inclusion, even for severely disabled students. To answer Steve H's question, can they demand full inclusion in high school, the answer is yes, they can in many cases. They can refuse to let their child be enrolled in a lower track or ability-level class even when the student clearly cannot possibly do the work and will fail. In effect, they have the right to ensure their child will fail. Which s/he does, and eventually either does go to a lower track or drops out (I have seen this phenomenon so often I have lost count).

We have students who in an earlier era would certainly have been placed in SPED whose parents refuse sped classification and services. The school cannot, except under extraordinary circumstances, place a child in sped without the parent's consent. Having a child with an exceptionality in my extended family, I have some idea of how the parents often feel: it may take them years to come to grips with the child's needs and limitations on a realistic basis. Even the parents of children with developmental disabilities (and very low IQs) in my former school were often uinwilling to accept that Junior would not be going to college, and should perhaps focus on learning life skills. In my family I saw the progression (somewhat like the phases of the grief process) whereby denial and magical thinking gave way to desperate search for "cures," to hope for a sudden breakthrough, to gradual acceptance and more realistic planning for the child's future. This can take years, however. And the child may be in an inclusive setting all this time, whether it is best or not.

3) Legalities. Although courts have occasionally upheld the rights of school disctricts to place students in a special setting over the parents' objections, this can take years and whopping legal fees. Most often, the parent wins. My district has lost several major appeals regarding sped placement, based on allegations of cultural or racial insensitivity and discrimination. Thus, there is no eagerness to press for segregated programs for minority children. Even with very violent and disruptive students, the process and documentation required to remove them from the least restrictive environment is daunting and very time-consuming. It can take YEARS.

In our case, the requirements for differentiation and inclusion flowed from the top down, and were a response to the gradual dismantling of sped services and offloading to the neighborhood school. I don't hear any chorus of believers here that this is a system that works better for most children -- especially where teaching of foundation skills and sequential mastery is required -- but we are obliged to do our best with what we have. "Differentiation" is constantly trumpeted as the solution, but I have yet to meet any school-based staff who think that it is the answer. Inclusion could work much better if it allowed for "Joplin plan" -type flexible grouping by achievement or instructional level, and adequate staff (aides, paraprofessionals, resource teachers) to provide targeted instruction to the high-needs kids. There never has been a golden era when everyone was better served, but I think that both our most vulnerable kids AND our potential high-flyers are disadvantaged by the current model. "Every classroom a one-room K-8 schoolhouse" doesn't seem like a worthy 21st century model to me.

Do teachers believe in full inclusion and differentiated instruction or is it just a big front?

From what I learn from teachers in different states and districts, it is quite possible that many in your district (and certainly in some others I know of) are totally gung-ho on differentiation and inclusion. There are "true believers" out there.

But there's also an incredible range of opinion, beliefs, knowledge and skills among K-8 teachers across the country. I wasn't aware of it myself until I got active on listserves for teachers starting in the mid-90's. That was a revelation. There are vast differences in practice, philosphy, organization, attitudes.

I don't see any rah-rah support of full inclusion or differentiation, in my area, and I've been in both middle and k-8 schools over the last 15 years or so. In general, teachers - like most parents I talk to - support inclusion in principle, but with reservations. Inclusion for whom? For what purpose? With what support? With what assurances that the needs of other students will not be compromised?(etc.) As for "differentiation," so far it is perceived as just another top-down mandate that must be complied with. Teachers have always individualized to some extent, at least in the elementary grades; this is just a more formal and paperwork-intensive way of doing that. To the extent that it deflects attention from providing special needs kids the services that really are needed, we are skeptical, even suspicious, of it.

Because of the financial climate, we don't really anticipate any improvement in services to the sped kids in the immediate future, so we get on with it. Stupid mandates have been part of the ed biz for as long as I can remember; most of them die a natural death over time only to be (as Catherine pointed out) reincarnated with a different moniker.

On some of my teacher discussion groups these issues get bruited about a lot, and those who post tend to be more critical of these trends than not. But there are some who wax prolix in their enthusiasm for inclusion and differentiation -- so your local observation is probably quite accurate. It isn't necessarily similar in other districts, though.

Recently I had an extended conversation with a teacher in a district quite similar to mine and was amazed by the totally different attitudes, ethos and philosophies informing the teaching staff and administration, given that phenotypically the school milieux were similar. Instead, the differences were staggering.

I'd like to see a mix of inclusion for the less-academic subjects combined with focused, small-group instruction for the special needs kids at their instructional level. I know from my experience in LD back in the day that many of these kids could be effectively taught and eventually reintegrated into general ed classrooms without IEPs, but that will NOT happen in the present scheme of things. As for keeping our opinions secret -- in our contract, it specifically states we may not publicly criticize the policies of the district (as individuals). We can -- and I have done this -- join with others and make submissions to the school board, etc. to address our concerns about poicies such as sped, inclusion and the like, and suggest modifications or alternatives. This works about as well as parent input -- sometimes an effect, often not.

When asked (by parents, generally) I try to point out the limitations of inclusion and look for ways the parent can make the system work for the child, or what resources they can access outside the system if need be. I also encourage them to let their elected representatives know about the issues. One problem is it sounds like motherhood and apple pie -- who can be "against" inclusion? You have to reframe the issue as one of providing effective instruction for all students, not just a seat in the classroom.

shouts and murmurs

As I would learn in my five years on the board, there are no absolute victories and no deafening defeats in the land of education governance; just the constant hum of the bureaucracy trying to control the flow of information and—if you’re lucky—the shouts and murmurs of the “the people” complaining.

Five Lessons from Five Years on the School Board
by Peter Meyer

being there

At some low point in my tenure on the board of education in my small school district, a friend advised, “Don’t worry. You are like gravity. They always know that you are there.”

Five Lessons from Five Years on the School Board
Peter Meyer

abstract: bullying

Bullying and Victimization: The Role of Conduct Problems and Psychopathic Traits
Kostas A. Fanti1,*, Eva R. Kimonis2
Article first published online: 7 JUN 2012
Journal of Research on Adolescence

Bullying and victimization occurring in adolescence can have a long-lasting negative impact into adulthood. This study investigates whether conduct problems (CP) and dimensions of psychopathy predict the developmental course of bullying and victimization from ages 12 to 14 among 1,416 Greek-Cypriot adolescents. Results indicate that initial levels of bullying were highest among adolescents scoring high on narcissism, impulsivity, or CP—particularly for those also showing high callous-unemotional (CU) traits. Bullying behaviors were also more stable among youth scoring high on narcissism. Further, youth high on impulsivity showed more stable victimization by peers across development. Importantly, adolescents high on CP+CU were at greater risk for engaging in bullying across development compared with those scoring lower on CU traits or CP.
This is a case of synchronicity.

We had friends over for the fourth of July, and I was trying to remember what I'd read about kids who are bullied more than other kids.

I still don't remember, but I found this today while I was looking for something else.

Tuesday, July 3, 2012

brain memory is different

Larry Summers, economist:
Suppose the educational system is drastically altered to reflect the structure of society and what we now understand about how people learn.
Richard Clark, Paul Kirschner, & John Swellers, psychologists and education researchers:
Our understanding of the role of long-term memory in human cognition cognition has altered dramatically over the last few decades. It is no longer seen as a passive repository of discrete, isolated fragments of information that permit us to repeat what we have learned. Nor is it seen as having only peripheral influence on complex cognitive processes such as critical thinking and problem solving. Rather, long-term memory is now viewed as the central, dominant structure of human cognition. Everything we see, hear, and think about is dependent on and influenced by our long-termmemory.
Putting Students on the Path to Learning
Richard E. Clark, Paul A. Kirschner, and John Sweller
American Educator | Spring 2012
Here's a thought.

Before Larry Summers writes a NY Times op ed invoking "what we now understand about how people learn," he should do a little nosing around and find out what we now understand about how people learn.

Hint: what we now understand about how people learn turns out NOT to be that in a world where the entire Library of Congress will soon be accessible on a mobile device with search procedures that are vastly better than any card catalog, factual mastery will become less and less important.

Long-term memory is a biological entity with cognitive functions.

Internet archives are storage facilities.

Those two things are not the same.

P.S.: A Commenter reminded me of the Clark/Kirschner/Sweller article the other day, when I was trying to recall where I'd read the passage about long-term memory having a cognitive and biological function that Google does not. Unfortunately, I can't remember who it was, but thank you!

Larry Summers has a really bad idea
Look it up

Monday, July 2, 2012

David Mulroy on 'critical thinking' in the late Middle Ages & 'looking for bias'

The "critical thinking" discussion brought David Mulroy's The War Against Grammar to mind.

I remember Mulroy making an argument that what we call critical thinking today corresponds in some sense to "disputation" and "logic" in the Middle Ages. Mulroy is on grammar's side of grammar, obviously.

Unfortunately, looking at my copy of Mulroy's book, I see that I'm going to have to do more than skim my underlinings and notes to reconstruct exactly what he's saying.

So, for the time being, here is one of my favorite passages from the book: Mulroy on "interpretation by free association" ("making connections," presumably) versus "precise interpretation of the meaning of complex statements." [boldface added in the passages below]
The tendency of modern teachers to disparage the importance of literal meanings reinforces and is reinforced by the low status of grammar, since the rules of grammar play an indispensable role in establishing the literal meanings of statements. Grammar and literal meanings have both become pariahs, and this fact lies at the root of several troubling tendencies.

To a teacher in the humanities, the most obvious of these tendencies pertains to reading comprehension. We increasingly encounter students who can speculate about the "hidden meanings" of literary texts but miss their literal sense. To gauge the extent of this problem, I recently asked members of one of my large mythology classes to produce brief paraphrases of the first sentence of the Declaration of Independence
When in the Course of human events it becomes necessary for one people to dissolve the political bands which have connected them with another and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
I was looking for a restatement of the proposition expressed in the main clause, that respect for public opinion makes it necessary for parties who are abandoning an established union to explain why they are doing so. It was disconcerting that of sixty-one students who tried to paraphrase the sentence, none seemed to recognize its source. Some thought that it had to do with ending a romance. I estimated that twenty-five comprehended the gist of the sentence. 

Most disturbing, however, were a large number of students who responded to the assignment with misguided enthusiasm.

It doesn't matter where you came from. In the end we are all human beings. Humans are at the top of the food chain, but it doesn't mean we shouldn't respect nature. Because we have one earth, learn to preserve it.
I was taken aback by how poorly the students had done on this test and repeated it twice with essentially the same results. Most recently, in November 22002, I offered the paraphrase exercise as an opportunity for "extra credit" on a mythology test. Sixty-four students of 228 attempted it. Thirty-three seemed to have grasped the essential thought. Among the others war e some more vivid examples of interpretation by free association.

For example:
Mankind is in a state of separation. There will come a time when all will be forgotten, and man will be one with mother earth.

These responses seem to me to exemplify a kind of higher illiteracy. The students who suffer from this are proficient in spoken English and can express their own thoughts in writing adequately. They lack the tools, however, for the precise interpretation of the meaning of complex statements. This kind of illiteracy boils down to an ignorance of grammar. If a student interprets the first sentence of the Declaration of Independence a an exhortation to "preserve the earth," then how can you demonstrate the error? There is no way to do so that does not involve grammatical analysis: the subject of the main clause is respect to the opinions of mankind, the main verb is requires, and so forth.
Mulroy goes on to connect "a-grammatical interpretation by free association" with what he sees as a focus on ad hominem argument in many state standards:
By far the worst effect of interpretation by free association, however, is the legitimation of ad hominem arguments. Of all the associations that are attached to statements by reflective judgments, those having to do with the speaker's or the author's motives are the most common. In a culture in which interpretation is typically based on free association, people have inevitably lost sight of the fact that speculation about motives is an invalid method of argumentation, a well-known logical fallacy....Most discouraging, however, is the fact that new state academic standards in the language arts actually encourage students to engage in ad hominem arguments. In Wisconsin, for example, a standard for grade 12 under the heading of "Effective Participation in Discussion" reads: "Detect and evaluate a speaker's bias." And later: "Appraise the purpose of discussion by examining their context and the motivation of participants." California's Listening and Speaking Standards for grade 8 include this: "Evaluate the credibility of a speaks (e.g., hidden agendas, slanted or biased material)." In Kansas, fifth-graders are supposed to perceive an author's "purpose"; eighth-graders, his "point of view"; eleventh-gradesr, his "point of view or bias."

This is not the way to train students to participate in serious discussions. Charges of hidden agendas or biases and raising the question of motives are sure ways to turn conversations int o shouting matches. Students should be exhorted, when engaged in serious discussion, to analyze the meaning of statements according to the rules of lexicography and grammar and then to test their truthfulness according to the rules of logic and evidence, while disregarding extraneous associations. One arrives at truth and maintains civility by obeying well-grounded rules, not through exhortations to be sensitive and certainly not by trying to psychoanalyze one's opponent. We cannot have good conversations in our society unless we attend to the literal meanings of what we say to one another, and we cannot do that without greater emphasis on understanding grammar.

Or so it seems to me.
Until the moment I read Mulroy, I had simply taken for granted that 'looking for bias' was an OK thing for students to do.

Mulroy opened my eyes. Then, when I visited the Cambridge Pre-U course, I saw the fallacy of "looking for bias" in action. "Looking for bias" when you lack background knowledge easily turns into an exercise in being - or becoming - biased yourself.

One group of students in the class, whose Google search had turned up an article in Haaretz, the liberal Israeli newspaper, reported that: "Since this is an article in a newspaper in Israel, it might be biased against Arabs."

No one present challenged this reasonable-sounding observation, including the two teachers, and I remember feeling distinctly uncomfortable. Is it OK to assume that any news article written by any Israeli reporter should be suspected of bias against Arabs?


The answer seemed to be 'yes,' and to me that 'yes' comes pretty close to being an expression of (unintended) bias against Israelis.

So I'm off the boat when it comes to looking for bias, etc. Looking for logical fallacies and the like is another matter -- although I suspect it's more valuable for students to look for logical fallacies in their own work than in the work of others.

Setting aside the basic question of civil discourse, however, Mulroy is right: students need a great deal of help throughout their educations in reaching a precise interpretation of the meaning of complex statements.

I suspect most college-level instructors, not to mention SAT critical reading tutors, would agree.