kitchen table math, the sequel: 8/2/09 - 8/9/09

Saturday, August 8, 2009

linguistics, sign language and writing

With my previous post on a "phonetic basis" to language, I should make it clear that I consider signed languages to be close analogues to spoken languages. (From what I know, this is a commonly-accepted fact among linguists.)

However, one thing that linguistics hasn't really provided a unified theory is explaining cognitively what happens for sign language -- part of the problem is that a lot of people still perceive sign languages as proxies for spoken language, or an alternative to speaking, that is, taking signed systems to be like writing systems. This doesn't bode well for scientific attention or funding...

We know sign language systems are very similar to phonetic systems, and in fact can be analysed like a phonetic system as far as dynamics like sound change, lexical diffusion, acquisition, etc. goes, and signs can be broken down into equivalents of phonemes, etc. -- the most pertinent difference generally is that a signed language is often capable of much more co-articulation than a spoken one. (Co-articulation is very common in all spoken languages, but we can usually co-articulate sound elements only if their places of articulation are far enough apart. The /t/ in "tea" for example, is a co-articulated phoneme, composed of a consonant not unlike the Spanish [t] and aspiration [h].) Sign language is not ideographic either. The fundamental permitted gestures in a sign language do not represent "ideas" -- like phonemes, by themselves they are often meaningless, until combined together. The gestures obey the recombination principle -- if you make one gesture and then another to form a word, that word is not necessarily releated in meaning to either gesture, much like "party" is not a semantic fusion of the concepts "par" and "tea".

Signed languages are so similar to phonetic languages that they are often used as alternate means to research child language acquisition, especially in crosslingual settings, often because it's very common for the parents of deaf children not to be native speakers/signers of the language the child learns to speak/sign. (The other research sources that have been useful in the field are migrant families and pidgin-creole communities.)

Similarities include a critical window for sign language -- children who learn it early invariably become fluent signers, excepting cases like those with neurological disorders; children who hit puberty before learning to sign generally never become native-level signers except with intensive study. And even then, errors are frequent and signing is more jerky and less fluid.

A deaf infant, instead of babbling, will instead do the equivalent with his hands. In fact, the timeline for sign language acquisition among children is so similar to spoken language acquisition -- e.g. we can expect a six-year-old signer to be very fluent, replete with different inflections, conjugations, declensions, irregular constructions and syntactical phrase-shifting -- that biologically the mechanism for sign language acquisition must be very similar to the mechanism for spoken language acquisition.

Even signed languages obey all the rules of Chomsky's Universal Grammar. I won't go into hardcore syntax here, but the idea is that there are universal rules that govern language, where expressions can be analysed as sets of verb phrases and noun phrases, with embedding rules and phrase-order rules, and in the way the order of a phrase can be shifted in different situations. An example that gets used frequently for English-speaking audiences for the principle of shifting word orders is when you ask a question -- which verb and subject do you invert? When being asked to turn a sentence with a relative clause like, "The goat that is in the garden is eating the flowers" into a question, invariably all the young children fluent enough to understand the sentence invert the right phrases. They do not form constructions like "goat the that is in the garden eating the flowers" or "is the goat that in the garden is eating the flowers?" -- and Chomsky argues this must be a consequence of a natural rule of universal grammar, known as the argument of the poverty of the stimulus. For one, children learning language-specific rules generally demonstrate their acquisition of the rules in stages, just as we regularly observe young children saying "he hitted her!", "I bringed juice for doggie" or "she giggled me!" -- evidence that they haven't completely learnt the rule. But we observe no children making wrong inversions. There are other arguments too -- like how children would learn such an elaborate algorithm, and use it so fluently and automatically?

Teenage and adult learners of sign languages, however, generally commit many violations of universal grammar, probably because they are not using their L1 cognitive machinery to process the language, which would automatically organise words into phrases (e.g. mentally organising like "goat that is in the garden" into a noun phrase, or NP) and clauses -- just like learners of spoken languages. The ability to analyse a sign language along noun-phrase / verb-phrase lines isn't necessary for an ideographic system; try telling a linguistics student to find the noun phrase or a verb phrase in a picture, painting or musical score and you will get protests about the silliness of the effort. Computer language isn't organised along VP/NP lines.... and not even veteran computer programmers can "think" in the computer languages they know well; it's always "code" and generally not a very effective medium for thought for humans, even though computers do very well, performing vast amounts of symbolic operations in it.

Sign languages can be generated spontaneously, and are capable of undergoing a process called "creolisation" like spoken languages. It's the spontaneous origins of many sign languages that make their study useful to many linguists working in spoken languages -- it sheds light on the origin of language in general. Children, when exposed to a stimulus composed of ungrammatical or pidgin language (e.g. migrant parents on a plantation, a colony composed of many ethnicities speaking each other's languages brokenly, non-native parents who sign imperfectly), without a good competing grammatical stimulus, will spontaneously generate corrective rules. The resulting language they produce obeys a grammar, complying with all the rules of universal grammar -- and is as complex and full-fledged as any other language. It's a good example of how grammar, though it may be culturally transmitted, is a partial consequence of universal biology. However, for spontaneous language generation to occur, you need at least two people -- a baby raised by wolves will not generate his own language, while there exist many documented cases of a secret grammatically full-fledged language, spoken between two close twins.

Spontaneous language generation can fuse different source languages -- the most prominent examples are creoles like Haitian Creole, combining elements from French, Spanish, African and indigeneous languages into a new grammatical system; I speak a creole called Singlish, with elements from Hokkien/Teochew Chinese, Malay, English, among others. With signed languages, the most prominent example is the emergence of a single "Nicaraguan Sign Language" (LSN) from the pooling together of home sign after the first schools for the deaf were opened in Nicaragua in 1979. Suddenly, previously isolated deaf children were pooling signs on playgrounds, schoolbusses, classrooms, and then becoming fast friends and signing to each other in each other's homes... However, this LSN was like the pidigin language that parents of immigrant children speak, a mixture of the various languages of their new environment; the conventions were often irregular, with jerky, non-fluid signing, and trends rather than real grammatical rules. The younger children exposed to LSN weren't content; they took it and transformed it into Idioma de Señas de Nicaragua (ISN), spontaneously standardising many of the grammatical rules and making many patterns that were previously mere trends obligatory. The new language also simplified many of the common constructions like a native language would, and had all the classic signs of assimilation rules found in natural spoken language. How a group of 4- to 8-year-olds achieves such efficient consensus on a matter like creating a unified "fusion" language has to be pretty fascinating if you ask me; the process is probably unconscious and memetic. I imagine a single child having a particularly ingenious way of signing something; some other child sees it and with excited eyes gestures something to the effect of "oh that's such a cool sign!" and then soon everyone's copying it. It's such a good meme that it outcompetes all other signing patterns for the same concept or grammatical rule; some signs occupy a slightly different niche (slightly different connotations, etc.) and they survive, becoming the signed equivalents of synonyms. Repeat for each convention. The process of creolisation is effectively identical for speaking children, only with spoken words.

There's a good argument to make for the idea that objectively, all languages have equal difficulty to the infant, and ultimately have all the same complexity and are biologically constrained to be that way. Latin has a mediumly-complex inflection system that tortures high school students, but on the other hand it only has a collection of word order rules that are not very strict and relatively simple phonology; Chinese languages have little inflectional grammar but have complex syntactical and phonological rules; when English dropped the sheer majority of the gender, case and conjugation systems, it converted other previously-normal words into grammatical auxiliaries and suddenly gained a complex word order system, and when English dropped vowel length distinction, it also started recognising a large degree of other vowel phonemes that previously didn't exist, and as such, English has a large amount of vowels compared to most other languages. English vowels are a torture for Arabic speakers, who have only 3 vowel qualities, yet an abundance of exotic consonants. In fact a general rule I'd like to propose is when a language is undergoing a change that will simplify or add complexity to its grammar, it must also undergo a complementary change that will compensate for the added or removed complexity in the opposite direction -- in a different area of course.

So that would imply signed languages must be as equally complex as spoken languages -- just extracting grammatical information from the secondary visual cortex rather than say, the auditory cortex. Curiously, the frontal cortex, auditory cortex and visual cortex converge roughly around the Sylvian Fissure, along which are located several important sites for language processing (though recent research suggests we've misidentified the actual locations of Broca's and Wernicke's areas -- partially because of the imprecision of the 1800s). Research into signed languages may have implications for phonics and children who learn spoken languages, and learn to read and write in them, because it shows the brain can process visual information grammatically. It is not the case however, that the visual information in sign language can be processed as a direct representation of symbolic thought and ideas: damage the same language centres that speaking people use, and sign language ability goes with it. In fact, Google tells me there's some good research out there on "sign language aphasia".

However, there's some further complexity for neuroscientific research into linguistic processing and the shared machinery that spoken and signed languages would both use because of the concept of neurplasticity. If you damage or lesion the areas commonly regarded as Broca's Area and Wernicke's Area in a child that is young enough (e.g. a large fall at two weeks of age), the child will probably grow up into a normal, healthy, fast-talking young child. Why? The appropriate neural tissue couldn't develop in the place it usually develops, so it develops somewhere else, sometimes in radically different areas (and later the remnants of these lesions show up 30 years later on medical imaging scans in an otherwise neurologically-normal patient). But neuroplasticity is also probably part of the mechanism for native-level sign language processing; if a language centre is supposed to be receiving signals from the auditory cortex but isn't (or isn't receiving enough signals, as with a damaged ear or damaged auditory cortex), some neuroplasticity mechanism probably has it adapt to processing from the visual cortex instead, and growing and sending out networks and pioneer neurons accordingly. Notably, the degree of neuroplasticity is greatest in children -- if being fluent in a language requires your language processing centres to send out pioneer axons (or even new neurons or networks) to the appropriate auditory or visual cortex and vice versa, and you're 13 years old ... well, hard luck.

writing as a phonetic system

Without some context, you might be puzzled (or misinterpret) what exactly Bloomfield's quote means in the passage cited by Catherine...

The question raised is: Can a marking that conveys a general idea be called writing, or must all writing represent specific units of speech?

To this question, the great linguist Leonard Bloomfield apparently gives his answer when he states, "Writing is merely a device for recording speech."

Bloomfield was addressing several questions of his day. Before Bloomberg, linguistics was sort of like a slightly more holistic version of philology, which might be found as a subset of some philosophy or history department. Certainly that was the sort of linguistics I perceived the field to be before I got interested passionately obsessed with it -- dry, pedantic stuff. Today, linguists are slightly more confident about some of the questions today -- thanks to cognitive science, psycholinguistics, documentation of creoles, cross-cultural studies, study of child language acquisition, the acoustics of phonetics, modern evolutionary synthesis, game theory, and 100 other disciplines that emerged in the 20th century. As an aside, I will say that I think true potential of linguistics is still in its infancy, despite the advances of this century. We still don't really know a whole lot about language -- in both its social and biological aspects.

Anyway, Bloomfield was probably commenting on the idea of an ideographic writing system, or even an ideographic language -- a communication system that doesn't ultimately have sound as its foundations. For those in the dark about the meaning of "ideographic" -- there's a popular conception of the Chinese writing system as an organised system of pictographs, with each character standing for an object or an idea, and the characters interacting with each other as though they were abstract symbols, functions and variables performing operations on each other. For example, when a Sinophone expresses "I love forest(s)" in Chinese writing, the ideographic viewpoint would analyse the writing as a graphically-symbolic representation of the ideas contained in such a statement, as though the written statement was an abstract depiction of the first person hugging several trees. (At least I think the character's origin is that of hugging, based on the old ancient seal script way of writing the character 爱 -- ai, or to love. I'm probably very wrong though.)

But of course, the ideographic viewpoint is all wrong. There's a fairly good essay on why exactly the ideographic viewpoint is wrong in an article called "The Ideographic Myth". Victor Mair -- a linguist, sinologist, a professor at the University of Pennsylvania -- has also blogged a few posts about it on Language Log. The basic summary of the arguments is that the Chinese writing system is not actually pictorial, in as much as we do not mean an ox's head every time we write the letter A, which has its origins in the Proto-Canaanite symbol Aleph. (I do not dispute however, that knowing such origins make characters more fun or easier to learn.) On top of that, only a minority of characters in the Chinese writing system have pictorial origins -- frequently, other characters, representing semantically-unrelated meanings, are borrowed and then combined with a few other radicals to form a new character to represent some word. Why? The character that was borrowed simply carried the same (or even just similar) sound. One complication that often makes this less obvious today is that the spoken language has changed since the Chinese writing system was first invented, on top of the fact that the characters themselves evolve, so words with initially the same pronunciation might diverge, not to mention the divergence of the characters themselves. This can often obscure the Chinese writing system's highly phonetic nature. Like English and French, the Chinese writing system doesn't do a good job of updating itself with the spoken language. In fact, it would be rather hard to do that today, because Old Chinese has since diverged into a plethora of mutually-unintelligible language families (colloquially known as "dialects"). Such divergence shows further evidence of the necessity of a phonetic basis in a writing system, because each Chinese language has a "colloquial writing system", with different character sets, different vocabulary frequencies, different idioms, different word orders for different constructions. However, because the Chinese writing system itself is fairly stable, you can occasionally say, write a Mandarin phrase using Chinese characters and have a Cantonese speaker be able to interpret it -- but the effect is rather like reading Latin. Sometimes, speakers of different Chinese languages cannot interpret each other's writing at all!

Bloomfield posed more general arguments. He was arguing that as far as communication goes, the foundation of it is based on spoken language. Sure we can perform all sorts of symbolic operations in our heads, but when we fluently communicate such operations, we must use a system based on spoken language.

The mechanisms of reading and writing are pretty wondrous biologically -- they take advantage of the fact that we're capable of repeating sounds in our heads. There are various theories of memory based on this, as well as various theories of reading and language processing, and some exploration of the different types of working memory that might be involved linguistically -- as well as long-term acquisition of grammar and vocabulary (at an L1/native level -- second language learning is a bit more complicated). Some concepts that might be interesting to people working in phonics include Baddeley's model of working memory, including concepts like a "phonological loop". Of course the theory is highly incomplete, but it's a good place to start, and there are many experimental precursors to the model that demonstrate the necessity for a phonetic basis to reading.

For a writing system to express precise and fluent thoughts, it must be dependent on sound -- because that is the basis of communication. Sure there's art and music ... but you can't really communicate fluent and precise ideas with them, only gists. Could you communicate something like Newton's laws of physics to someone who didn't know them based on a picture, or a series of pictures? Take for example, the former practice of some of the Plains Natives to draw symbols on teepees for communciation -- such systems were really imprecise, and used for communication purposes that didn't have too many symbolic operations -- like "need bow-wood, twine; offer leather" or "off to river 3 days" as well as various artful depictions. In contrast, look at the complexity of many Native American languages, such as Cherokee and Sioux. Known as polysynthetic languages, they have high levels of inflection and morphological agreement, with agreement between subject, verb, direct and indirect objects, clauses. Certainly quite complex enough to express instructions on the precise order of steps to take to cook a buffalo recipe, explain the finer principles of riflemanship to a young child, suggest how you should take this flank to corner Custer and cut him off from the other Union troops, or argue why we need to stop the practice of counting coups because the situation dictates that our survival is dependent on seizing every defensive advantage possible.

You can't do this with teepee writing. There's just not enough complexity, or even vocabulary. The Chinese writing system probably evolved from a pictorial convention not unlike teepee symbols -- representing things for sale, things for buying, common objects, weather, etc. But as you wanted to use the system for more and more things, you got bogged down with the picture aspect. Really, try a convenient arrangement of symbols to symbolically depict the idea that Charlie tried to intercept a letter sent from Alice to Bob, but that Alice and Bob already know of his intentions and have come up with a plan to trick Charlie. The eureka moment was when the system switched from depicting ideas to depicting sounds. Sure, you're still using a little drawing of the sun to represent the word for sun, but now you can also use it for words with unrelated meanings (an English equivalent would be using a symbol for "sun" for the word "asunder", or combining it with a radical element related to "math" to make the word "sum"). The system exploded with the sudden possibilities. The side effect is that since you were now representing sounds and not ideas, you could drastically simplify many of the characters. Characters with elaborate depictions of mountains, trees and fields were reduced to series of short quick strokes to the extent that often you can't figure out what the character originally depicted.

There are some who argue that language is essentially a learned social construct, and this argument was probably in vogue during Bloomberg's day (the era also spawned the Sapir-Whorf hypothesis). If you can make a language on a phonetic basis -- why not one on an ideographic basis, or one that exists only in writing? But scientific evidence shows a huge biologically-determined component to language. Granted there is a huge memetic (culturally-transmitted) aspect, which is what makes it so fascinating to study (especially from an evolutionary dynamics standpoint), but an interesting thing to note is that the children of all the world learn their native language at around the same timelines. Indeed, intralanguage variance (for the time it takes for a child to learn to speak fluently) generally exceeds interlanguage variance by far. It's strong evidence that many aspects of language are human universals and are biologically/genetically constrained.

Thursday, August 6, 2009

Angela's Ashes

When I look back on my childhood, I wonder how I survived at all. It was, of course, a miserable childhood: the happy childhood is hardly worth your while. Worse than the ordinary miserable childhood is the miserable Irish childhood, and worse yet is the miserable Irish Catholic childhood.

People everywhere brag and whimper about the woes of their early years, but nothing can compare with the Irish version: the poverty; the shiftless loquacious alcoholic father; the pious defeated mother moaning by the fire; pompous priests; bullying schoolmasters; the English and all the terrible things they did to us for 800 long years.
Angela’s Ashes by Frank McCourt, page 11

We go to school through lanes and back streets so that we won’t meet the respectable boys who go to the Christian Brothers’ School or the rich ones who go to the Jesuit school, Crescent College. The Christian Brothers’ boys wear tweed jackets, warm woolen sweaters, shirts, ties and shiny new boots. We know they’re the ones who will get jobs in the civil service and help the people who run the world. The crescent College boys wear blazers and school scarves tossed around their necks and over their shoulders to show they’re cock o’ the walk. They have long hair which falls cross their foreheads and over their eyes so that they can toss their quaffs like Englishmen. We know they’re the ones who will go to university, take over the family business, run the government, run the world. We’ll be the messenger boys on bicycles who deliver their groceries or we’ll go to England to work on the building sites. Our sisters will mind their children and scrub their floors unless they go off to England, too. We know that. We’re ashamed of the way we look and if boys from the rich schools pass remarks we’ll get into a fight and wind up with bloody noses or torn clothes. Our masters will have no patience with us and our fights because their sons go to the rich schools and, Ye have no right to raise your hands to a better class of people so ye don’t.
Angela’s Ashes by Frank McCourt, page 272-273

Frank McCourt,Whose Irish Childhood Illuminated His Prose, is Dead at 78
Published: July 19, 2009

Frank McCourt dies at 78: late-blooming author of 'Angela's Ashes'
LA Times

Only a Teacher: Teachers Today interview with Frank McCourt

Wednesday, August 5, 2009

how did this happen?

Lynne Munson at the Common Core blog:

New York City’s Board of Regents has chosen David Steiner as New York’s new education commissioner, EdWeek reported earlier this week. Steiner’s move to Albany comes after four years as dean of Hunter College’s School of Education.

Why are we happy with the regents’ pick? Because Steiner is widely known for his commitment to a rigorous, comprehensive curriculum, and he has published quite a bit on the subject.

Don’t take our word for it, though – read how Steiner describes his schoolboy days:

“I read the classics as they were then understood—Austen, Brontë, Chaucer, Conrad, Dickens (not a favorite), Eliot, Hardy, Lawrence, Milton (sampled, and put aside for years to come), Mann, Kafka, Tolstoy, Dostoyevsky, Turgenev, Flaubert, Zola—and many authors of the second rank. I recall Trollope, Webster, Spencer, “modern” novelists of every hue—Fitzgerald, Roth, Updike, Nicholas Monsarrat, Storm Jameson (a close family friend), John le Carré—and so many others lost to memory.”

We’ll be watching with interest.

Boy. Me, too.

Steiner was on the board of the Core Knowledge Foundation, he did the ed-school syllabus study a few years ago, and he worked with Uncommon Schools, KIPP, and Achievement First to create Teacher U at Hunter College.

Steiner's appointment has happened at the precise moment I was gearing up to lobby for adoption of the Core Knowledge curriculum here in Irvington. The precise moment. Ed says we should see if he'll come to town to give a talk.

The press release describes Steiner as "a bold and provocative education reformer."

That's something you don't see every day.

what do linguists think?

My copy of The Roots of Phonics: A Historical Introduction A Revised Edition by Miriam Balmuth just arrived, and on page 11 I find this:
The question raised is: Can a marking that conveys a general idea be called writing, or must all writing represent specific units of speech?

To this question, the great linguist Leonard Bloomfield apparently gives his answer when he states, "Writing is merely a device for recording speech." This statement narrows writing down to only those markings that are directly related to spoken language. It reflects the attitude of linguistic theoreticians from the mid-nineteenth to the mid-twentieth century.
How do linguists define 'writing' today?

Monday, August 3, 2009

michellem needs tips!

MichelleM said...
Hi there. I love this blog, I've been reading for a few months.

I'm a mom of a very bright kindergartner, he starts this week. The good news is his school uses Saxon Math curriculum.

I'm wondering if the wise posters of Kitchen Table Math have tips for the moms of kids just starting their elementary schooling adventure.

Thanks so much.

well, can we distill anything down for someone just entering the school system? Other than Abandon All Hope, of course :)

guerilla instructivism, part 3

from Exo:
Yes, we cover up. I taught in NY, middle school. Workshop model prescribed, word walls, bulletin boards, not more than 20% of premade or teacher-made posters, the rest -students work... No seats in rows! No teacher talking longer than 10 minutes! Teach the whole child, not the subject.. etc, etc, etc. I was shushed by my more experienced and well-meaning fellow teachers from even saying "direct instruction" aloud. So when talking to my principal about what I do, and writing up the course descriptions I used "problem-solving", "case study method", guided discovery" to cover for my very direct teaching. Well, since my results in regents passing were good, the principal seleted to ignore my classroom when walking around the building, but I was warned beforehand about any external visitors so I could move the desks from rows into groups, and do a lab...

from Redkudu:
Not only does guerilla teaching live, but I'm required to have my lesson plans in a binder on the desk for any passing visitations by admin.

And, due to past experience, I now have a system of code in which my lesson plans look one way (constructivist), but the lesson goes another. Never yet had anyone complain because, I think, they truly don't know what they're looking at.

Coalition for World Class math on Twitter


Here's the Facebook page.

CA World Class Math

Web site is up this morning.

You may want to sign the letter.

CA Coalition for World Class Math
CO Coalition for World Class Math
CT Coalition for World Class Math
NJ Coalition for World Class Math
PA coalition for World Class Math
United States Coalition for World Class Math
Parents' Group Wants to Shape Math Standards

Common Core Standards: Who Made the List?

6.30.2009 Parents Group Wants to Shape Math Standards
Common Core Standards: Who Made the List?
‘Common Core’ Initiative: Who’ll Make Decisions? (Jill Gladstone, Timotha Trigg)
A Look at the Promises and Challenges of Common Standards—UPDATED
Transparency of Common-Standards Process at Issue

Core Knowledge: Voluntary National Standards Dead on Arrival

I've just gotten the Core Knowledge post re: the National Governors Association and the Council of Chief State School Officers standards from Robert Pondiscio:
Written By: Robert Pondiscio Blogger
Categorized in: Education

A draft of the newly developed common core state standards purports to offer “sufficient guidance and clarity so that they are teachable, learnable and measurable,” however the ELA guidelines offer almost no specific content and little that would be of use to teachers in planning lessons–or parents in understanding what their child is expected to know.

Copies of the draft, an effort spearheaded by the Council of Chief State School Officers (CCSSO) and the National Governors Association (NGA) have begun circulating among reviewers. A copy found its way to me without any restrictions on its use or circulation. I have posted the draft document here.

The draft insists that the voluntary standards be “coherent” but defines coherence to mean they “should convey a unified vision of the big ideas and supporting concepts within a discipline and reflect a progression of learning that is meaningful and appropriate.” Framed as a series of benchmarks students must reach “to be college and career ready,” the draft enumerates standards such as the ability to “determine what text says explicitly and use evidence within text to infer what is implied by or follows logically from the text.”

To put this as blandly as possible, this is neither a revelatory insight nor a meaningful standard. Educators hoping for guidance on what particular texts are expected to be taught, or how to get students to reach the bland and obvious standards will be disappointed. On specific “texts” the draft says merely:

The literary and informational texts chosen should be rich in content….This includes texts that have broad resonance and are referred to and quoted often, such as influential political documents, foundational literary works, and seminal historical and scientific texts.

“At first glance, these language standards are, despite the brave descriptors, very similar to the dysfunctional state standards already in place,” notes Core Knowledge founder E.D. Hirsch, Jr. “Like most state standards, they naively take a formalistic approach to language ability. They assume that the ability to understand literary and informational language is chiefly a how–to skill, whereas it is chiefly a topic-dependent skill that varies with specific topic familiarity.”

A sample scientific text on covalent bonds in the draft document, Hirsch notes, is a “a good illustration of this general point. Will it be more useful for understanding such texts to spend class time teaching some will-o-the-wisp language proficiency or to impart a good general education in science and the humanities?

“One begins to despair,” Hirsch concludes.

Speaking as a parent who has had to enroll her son in a Jesuit high school to provide him a liberal education, I do not want to hear that E.D. Hirsch is beginning to despair.

Disciplinary specialists, of whom E.D. Hirsch is one, need to be writing these standards.

too much knowledge

Comment on Curriculum Matters:
My problem with any of these standards is that they are too focused on knowledge learned rather than basic learning process skills. Learning these 100 things about algebra or these 100 things about American history is not the point and just forces kids to learn a bunch of stuff that they may not be interested in, or that prevents them from learning other stuff they might be interested in.

Meanwhile Core Knowledge has apparently called the draft "Dead on Arrival," though you can't read the post because the Core Knowledge blog is down.

I'm taking my cues from E.D. Hirsch.

Sunday, August 2, 2009


To the Editor:

Your June 17, 2009, article on national standards discusses the virtual exclusion so far of the National Council of Teachers of Mathematics, the National Council of Teachers of English, and the International Reading Association from the Common Core State Standards Initiative. But the exclusion of other key stakeholders also must be addressed.

First is the exclusion of authentic subject-matter groups from the “Common Core” decisionmaking process that determines what is in the final document. Anyone proposing to create mathematics and English-language-arts standards must enlist and pay heed to the expertise of true subject-area experts. Members of the American Mathematical Society, the Mathematical Association of America, appropriate engineering societies, and the Association of Literary Scholars and Critics should be allowed to provide input.

In addition to being true experts in their fields, college and university professors are in the best position to inform standards-writing committees about what high school graduates need to know and be able to do for success in credit-bearing college-level courses. It is well documented that community colleges nationwide have freshman remediation rates of more than 70 percent in math and English. Clearly, the community college stakeholders must have a seat at the standards-writing table.

Tax-paying parents are another important stakeholder group absent from the Common Core project. Yet the ultimate responsibility for ensuring that children receive a proper education rests with them. It is they who must closely monitor the success of students and schools, and it is they who must pay the price—in dollars and in anguish—when inadequate standards leave children ill-prepared for college or the workplace. Dozens of grassroots parent groups have sprung up in the past decade to advocate for improvements in mathematics education in the public schools. Our group, the United States Coalition for World Class Math, is just one of these.

Before mathematics standards for K-12 are finalized, the National Governors Association and the Council of Chief State School Officers should make room at the table for one of the most important education constituencies in the country: the parents of children in our public schools.

Amy Flax
Westfield, N.J.
Jill Gladstone
Bridgewater, N.J.
Sarah-Kate Maskin
Ridgewood, N.J.
Renata Pestic
Oradell, N.J.
Timotha Trigg
Chadds Ford, Pa.

The writers are co-founders of the United States Coalition for World Class Math.

Vol. 28, Issue 36, Pages 26-27

CO Coalition for World Class Math
CT Coalition for World Class Math
NJ Coalition for World Class Math
PA coalition for World Class Math
United States Coalition for World Class Math
Parents' Group Wants to Shape Math Standards

Common Core Standards: Who Made the List?
Education Week coverage:
6.30.2009 Parents Group Wants to Shape Math Standards
7.1.2009 Common Core Standards: Who Made the List?
7.14.2009 ‘Common Core’ Initiative: Who’ll Make Decisions?
Transparency of Common-Standards Process at Issue

1.12.2007 how politics work

guerilla instructivism, part 2

[A parent] wouldn't know of "guerrilla instructivists" because if they WERE known, they would be disciplined, transferred, or fired (or all of the above). I doubt if a single parent of the hundreds of students I've taught in the last 10 years would regard me as a guerrilla instructivist, nor do any of them, in all likelihood, know that I am using DI and other non-approved practices and curricula. I use the same lingo as everyone else, reporting on "shared reading," "making meaning" and whatnot, but I mean different things by those terms and use empirically-validated materials and methods to achieve the goals.

If I were to "come out," I would certainly be disciplined, probably moved to a position where I couldn't do any of the things I am doing.

....The fact is that methods, materials, instructional practices and use of teaching time is often prescribed at the district level, with no teacher input, even down to the last minute, and classrooms are searched for materials that are deemed inappropriate. Teachers have very little say in what and how to teach. They certainly can't do things like, junk Guided Reading and do DI (pdf file) instead. Teachers must follow the established protocols. They are lower-level employees, not independent contractors.

....Small districts tend to be more responsive to their clientele.* The real edu-nazis are in large urban districts, where they have a population that they can manipulate, ignore or work around, and who rarely are politically active and almost never in an effective manner. The administration runs the show. Teachers, like me, who strongly disagree with what is being done have to fly under the radar. Kind of like being in the Underground in WW2. You need a good "cover," and you must under no circumstances let on what you are actually doing.

Of course many who want to teach effectively throw in the towel and go to the private sector. I have given this serious consideration from time to time, but am stopped by the realization that in the private sector I will not be able to serve the population I do now. Every year I rescue a few off the Titanic, in spite of administration, curriculum and other impediments. Their parents don't know, the admin doesn't know (everyone can chalk it up to sudden "development.")

But I know.

So I am still here. But if you were a parent in my school, you would not know that I was a guerilla instructivist. You wouldn't know who the others are, either.

This reminds me of my days writing for New Woman Magazine. I used to lace my articles with all manner of rupturous, pro-male sentiments, but I'd cloak my heresies in proper language and tone and I'd usually get away with it.

* not in my experience, but I haven't been able to discover whether my district is unusual

palisadesk on guerilla instructivism

You talk about a long list of readiness characteristics in your district, but what about ed schools? You talk about a long list of readiness characteristics in your district, but what about ed schools?

In my area the 2 major ed schools focus on "big ideas" like diversity, social justice and being a change agent. They don't concern themselves with any practicalities, like how to teach anybody anything.

I surveyed the new teachers and the army of student teachers coming into our school over the last decade and they all report learning nothing about assessment, classroom management, cognitive or behavioral science, early reading/literacy, communicating with parents or indeed much of anything of a practical nature. They study Paulo Friere, Jonathan Kozol, Sylvia Ashton-Warner,* and so on. The content is nearly all theoretical and philosophical, nothing empirical, evidence-based or useful on the classroom level.

This is not all that unusual a situation. In many areas it is the district that teaches new teachers what to do and provides workshops and non-credit courses on balanced literacy, how to administer the Developmental Reading Assessment, do Writers Workshop and Guided Reading, and so on. The mandate for these practices comes not from the Ed schools but from the district level and from the department of education level higher up. I haven't seen any evidence that ed schools set the agenda; they seem to be responsive to what the education bureaucracy wants -- in many cases, ed school staff are bureaucrats as well, sometimes on assignment for a 2-5 year stint at an ed school, other times they hold double assignments. It's one big cabal running both the ed schools and senior management in the bureaucracy.

An even more cynical blogger might take away that by pushing these literacy skills down to parents' responsibilities, it leaves teachers free to give Writer's Workshop instead.

I find that many parents and private citizens do not know this, so I will point it out: teachers are not, in most jurisdictions, "free" to give or not give Writers Workshop, or Guided Reading, or whatever curriculum practice is the latest craze. Most districts are quite prescriptive and require teachers to comply with very specific guidelines -- what materials they may (and may not) use, what practices they MUST employ (Word Walls, Writers Workshop, Readers Workshop, Guided Reading, Shared Writing, and so on). They may be specifically forbidden to do other things (teach standard algorithms, teach systematic phonics, hold students accountable for spelling, meeting deadlines, completing assignments). Many districts have "literacy police" (even "numeracy police") who go around inspecting classrooms and monitoring compliance. Teachers have very little freedom in most districts to choose their own methods or materials. That has both positive and negative consequences.

The infatuation with most of the practices so often deplored here (and elsewhere) does not come from teaching staff but from higher up in the bureaucracy. Indeed, surveys have shown almost as great a disconnect between what teachers want and think effective vs. what administrators and bureaucrats want/believe as the Public Agenda study "Different Drummers" showed exists between ed school faculty and the public at large, including teachers. There is a great divide, but the power is largely on one side.

Being a successful "guerrilla instructivist" requires camouflage and using the opposition's terminology and jargon to describe things totally incongruent with the prevailing philosophy. One can generally assume ignorance of instructional matters, research and cognitive science on the part of school and district administration, so unless you wave red flags in front of them they will not notice the details of what you do as long as you appear assertively compliant.

What would we do without palisadesk (and redukudu & Paul B & Instructivist & Concerned ....)?

That is not a rhetorical question.

What these teachers do for children, families, and for their country goes far beyond guerilla instructivism. I was about to invoke the samizdat, but that's not quite right, is it? This is America; palisadesk has a right to speak her mind, although if she were to do so using her own name she would put her job at risk.

I've just asked Ed whether there is a historical precedent for this kind of 'inside reporting.' He says that during the Ancien Regime there were members of the court who, using a pseudonym, wrote about court intrigues and the like.

But that's all he could think of on the spur of the moment.

The writings of guerilla instructivists make me wonder whether the internet really is something new and different: whether the internet has a "democratizing" effect in realms that have been anything but democratic.

We will see.

wedding dance

Vicky S just sent the link. I cried through most of the video.

That's because I have 3 kids. Back in Studio City I told my friend Debra, after the twins were born and I found myself mail-ordering goofy Christmas sweater knitting kits,* that once you have 3 kids you turn into the kind of person who cries over Hallmark ads. My mom had four kids and she always cried over Hallmark ads.

She didn't cry over real life.

She just cried over the ads.

* Once you have 3 kids you also turn into the kind of person who doesn't manage to actually complete the Christmas sweater knitting kit.

le Mini Kit

On our next to last day in St. Romain en Viennois we went to the local Intermarché, where I purchased a Mini Kit Incassable in the school supplies section.

right triangle 45-45-90
right triangle 30-60-90

I'm pretty sure it is not possible to buy trigonometry paraphernalia in U.S. supermarkets.

I also scored a Travaux Pratiques for writing proofs and a Vocabulary Coach for memorizing Spanish & French vocabulary. Vocabulary Coach is very cool.

The Intermarché is a big-box Target-type store, like Meijer's in the Midwest.

When I get back to Springfield, IL in a couple of weeks, I'll see if Meijer's has right triangles idéal pour la trousse.

I'm guessing no.

the Academy

"Let no one ignorant of geometry enter here."

- inscription above the entry to Plato's Academy

(thanks to MagisterGreen)

First Principles of Algebra - 1912

downloadable from Google Books

In writing the First Principles of Algebra the authors have had constantly before them two chief aims:

(1) To provide a gradual and natural introduction to the symbols and processes of algebra.

(2) To give vital purpose to the study of algebra by using it to do interesting and valuable things.

Each of these aims leads to the same order of topics, which, however, differs somewhat from the conventional order.

If it is admitted that there should be a gradually increasing complexity of forms to be manipulated, it follows that factoring and complicated work in fractions have no proper place in the first half year. This book is arranged so that factoring may begin with the second semester and complicated fractions may come still later. Simple fractions are treated in Chapter V.

The pupil is introduced to the algebraic notation by recalling and stating in terms of letters certain rules of arithmetic with which he is already familiar. The simplicity of the algebraic formulas, compared with the arithmetical statement of rules known to the pupil, cannot fail to impress him with the usefulness and power of the subject which h is about to study. This impression will be deepened when, in Chapter VI [Literal Equations and Their Uses], rules which caused considerable trouble in arithmetic are derived with the utmost ease by algebraic processes.


For the development of skill in algebraic manipulation it is not sufficient to solve a certain number of exercises when an operation is first introduced. To fix each operation in the learner's mind, there must be recurring drills extending over a considerable period of time. These are amply provided for in this book. The fundamental operations on integral and simple fractional expressions, the solution of simple equations, and the representation of given conditions in algebraic symbols are constantly reviewed in the numerous lists of "drill exercises," many of which may be solved mentally. Factoring is practised almost daily throughout the second half year.

The principles of algebra used in the Elementary Course are enunciated in a small number of short rules--eighteen in all. The purpose of these rules is to furnish, in simple form, a codification of those operations of algebra which require special emphasis. Such a codification has several important advantages:

By constant reference to these few fundamental statements they become an organic, and hence a permanent, part of the learner's mental equipment.

By their systematic use he is made to realize that the processes of algebra, which seem so multifarious and heterogeneous, are, in reality, few and simple.

Such a body of principles furnishes a ready means for the correction of erroneous notions, a constant incitement to effective review, and a definite basis upon which to proceed at each stage of progress.

The authors gratefully acknowledge the receipt of many helpful suggestions from teachers who have used their High School Algebra

H. E. Slaught.
N. J. Lennes.
Chicago and New York,
April, 1912


Chapter VI: Literal Equations and Their Uses

102. Some of the advantages of algebra over arithmetic in solving problems have been pointed out in the preceding chapters. For instance, the brevity and simplicity of statement secured through the use of letters to represent numbers; the translation of problems into equations; and the clear and logical solution of these equations, step by step.

Another advantaged is set forth in the present chapter; namely, the opportunity offered in Algebra to summarize the solution of a whole class of problems by solving what is called a literal equation, thus obtaining a formula which may be used in solving other problems.

For example, in arithmetic we solved many problems obtaining the interest when the principal, rate, and time were given. We now see that all of these can be summarized in the one literal equation

i = prt.


104. In arithmetic a problem is said to be solved when a numerical answer is obtained which satisfies the conditions given. The solutions thus far found in algebra have, for the most part, been of this sort.

It is customary, however, to say that a problem has been solved in the algebraic sense when a formula is found which gives complete directions for deriving the numerical answer.

Thus, p = i/rt is a solution for the principal since it states precisely how to find the principal in terms of interest, rate, and time.

105. It is thus seen that from the literal equation i=prt we obtain the complete solution of every problem which calls for any one of these four numbers in terms of the other three.

In modern times machines are extensively used for computation. The algebraic solution of a literal equation gets the problem ready for the computing machine, that is, it gets the formula which the computer must use.

First Principles of Algebra: Elementary Course
by H.E. Slaught Associate Professor of Mathematics in the University of Chicago
N.J. Lennes Instructor in Mathematics in Columbia University
Boston ALlyn and Bacon 1912
pp. pp. iii - v; 92-93

One hundred years ago, mathematicians wrote math textbooks with the advice of math teachers. Today parents have to organize grass roots political movements to lobby for the inclusion of mathematicians in the design of national standards.

CO Coalition for World Class Math
CT Coalition for World Class Math
NJ Coalition for World Class Math
PA coalition for World Class Math
United States Coalition for World Class Math
Parents' Group Wants to Shape Math Standards

Common Core Standards: Who Made the List?