kitchen table math, the sequel: 1/3/10 - 1/10/10

Saturday, January 9, 2010


average cost of 1 DC voucher: $6,600
cost of sending 1 DC student to DC public schools: $28,170

DC Vouchers Solved?

strategies not content

The proposed English-Language Arts “college and career readiness” standards (which we are told are not high school graduation standards) are largely a list of content-free generic skills. Rather than focusing on what English teachers are trained to teach (quality literature), the drafters seem to expect English teachers to teach reading strategies presumed to help students to cope with biology or economics textbooks.

Alternative Needed to Common Core: An Additional Consortium for ‎Common Standards
Williamson M. Evers and Ze'ev Wurman
If you want a reading "strategy" that works, buy a copy of Eugene Schwartz's How to Double Your Child's Grades in School and/or read Carolyn Johnston's posts on Schwartz:
I like SQ3R, too.

American Educator issue devoted to reading comprehension
Six-Way Paragraphs
SQ3R chart

Bill Evers has a blog

How did I not know this?


Guided reading is scripted.

Miss Brave:
Before I actually became a first-year teacher, I was all about the workshop model. I thought it would be helpful, as a new teacher, to have a script of sorts to follow. After all, every mini lesson sounds a little something like this, but with all the blanks filled in:

"Boys and girls, we have been working hard on _____. Today I want to teach you that ____. Let me show you what I mean. ________. Boys and girls, did you see the way I ______? Now let's try it together. Turn and talk to your partner about _______. Boys and girls, today and every day I want you to remember that _______. Now off you go!"

A month and a half into the school year, the workshop model is pretty much the bane of my existence. Remembering the script and keeping the mini lesson to a scant 10 minutes is not as easy as it sounds. Neither is trying to shoehorn all the aspects of my lesson into the workshop model framework. I'm used to teaching in a style where I ask lots of questions of my students and invite lots of discussion. During the workshop model mini lesson, there are no questions allowed from the students and no discussion (except during the active engagement); it's all the teacher, all the time. I see my students raise their hands with these hopeful looks on their faces because they have something they want to share or something they have a question about, and it breaks my heart to keep saying, "Hands down, it's my turn now."

I think the workshop model probably does work for the population of students in the school where I teach. After all, taking advantage of those "teachable moments" that lead the lesson astray can be really confusing for students whose native language is not English, like the students at my school. But at the same time, the workshop model feels really one-sided. I can tell that there are kids who are confused, who aren't getting it, and I'm supposed to pull those kids for a 2-minute "re-teach" at the rug instead of changing tack and trying a different method?

This weekend, I took two New York State teaching certification exams (because my teaching license is from another state, I have to pass New York's exams to get my New York license). Mostly they were a joke, but they included lots of samples of class discussions -- and I realized that's something I miss. In my workshop model lessons, there's no back and forth, no "What do you think?", no "Who else has an idea about this?" I don't get to invite my students' opinions, their knowledge, their ideas. All I get to do is tell them how to punctuate their sentences and then eavesdrop on them while they try it. And even though I allegedly have more freedom as a cluster teacher, I've still been told by the powers that be that every class I teach should start with a mini lesson. It's hard enough being a first-year teacher as it is, but trying to shoehorn every lesson into a framework I'm not all that comfortable with is overwhelming.

Apparently the workshop model is mandated for use in schools throughout New York City, so...I should use it or lose it, I guess? Or I should, as someone suggested, plan two lessons: one to be taught the way I want to teach, and one workshop model to pull out when I'm being observed.

I don't think I'm ready to be that much of a renegade just yet.

Can we conclude from this that 'it's scripted' isn't the real objection the education establishment has to Direct Instruction?

Friday, January 8, 2010

an Iraqi, English spelling, and a bit of English historical linguistics

I had an Iraqi roommate this summer. Let's call him Ali. His cultural story is interesting and comes with all sorts of other-than-linguistic things to muse about; he's very humble and is a sous-chef for one of the eateries on Grounds here. He was going to enter engineering school in Germany when the war broke out. He speaks broken German, more fluent Turkish and some Kurdish -- and very impressive English for two years of immersion.

Ali, trying to go back to school and enter the American college system what with its SATs and all, entreated me for help on reading, writing and speaking. I do think his progress in two years is very laudable -- some other members of the refugee community have been here for a year or more, yet cannot speak more than a smattering of English.

"My biggest problem is reading," he once said, struggling to pronounce that "-ng" sound. "English is a hard language to learn, harder than Turkish, German or Arabic. In Arabic, you spell the words like they are pronounced. Like this..." He writes out an example for me, which I struggle to read.

"English is kinda written as it is pronounced," I try to reassure him, struggling to summarise the vast body of work linguists and philologists have done over the years. "It's just that the pronunciations have changed over the years, and many spellings have yet to be updated. You know Arabic dialects, right? Aren't they spoken much differently than Standard Arabic is? It's kinda like that." It's like speaking those dialects but writing them in the system of formal Standard Arabic.

But I already knew there were complications with this analogy. Often, the colloquial dialects -- if they are written at all -- are transcribed exactly the way the sound. This was the case with the Vulgar Latin's descendants -- the Romance dialects, that diverged into the Romance languages like (Old) French, Italian and Spanish. (Modern French writing is an interesting story and shares some parallels with English.) With the Chinese languages, many characters are in fact, composites of other characters, where some characters have been borrowed for sound rather than meaning. After that, the borrowed character and the word being represented diverge in sound in some dialects -- and incongruence develops à la English. Often some of the diverging dialects will simply adopt different characters -- but elsewhere other dialects will keep the original (but incongruent) analogy; and of course the most conservative dialects do not even see an incongruence at all.

An immediate concept that helped Ali, but wasn't taught very often in ESL classes, was the concept of stress. At first this didn't have anything to do with reading or writing -- simply the way he pronounced the words that made him hard to understand.

"Sometimes, you say the words correctly... correct vowel and everything, but you don't put the correct stress on the word, so it sounds as though the vowel isn't there. And sometimes you say the stress correctly, but you use the full vowel on unstressed syllables or the reduced vowel on stressed syllables."

This was new to him, because in the two years of ESL help he had received, "stress" was a concept that had appeared to escape ESL teachers' minds. A fundamental concept in English phonology, it's kind of hard to teach both fluency and reading/writing if you ignore it. Stress, you see, is a historical innovation in the history of the English language. Unlike many other languages, it's neither predictable (i.e. it's phonemic) but neither is it explicitly marked in writing (as is the case with Spanish).

But don't worry -- stress is something easy to memorise, because the stress of each word is usually memorable. Many grammatical function words like "the", "a", "of", or affixes "-ing", "-er" etc. have no stress at all. Ali, I discovered, had already internalised many stresses -- he just didn't know it was that important. If you randomly quizzed him on the stresses of "bigger", "party", "telephone", "ambulance" or "reduce," he would get it right, down to the primary and secondary stresses. This is because stress is something that is quite easy to memorise and he had already done it unconsciously, even as a non-native speaker.

There are complications of stress, like the fact that the relative strength of a word's stress compared to other word's stresses will change depending on where it is in a sentence (syntactical stress), but that was for a more advanced lesson. Some words' syllables can be stressed when emphasised, such that when you quiz them in isolation, they become stressed, e.g. the "re-" in "reduce" or "the" gets pronounced with an "-ee" (/i/) sound rather than a reduced vowel -- but are usually unstressed when you use them in a sentence. But I told Ali not to worry for now -- it's not a big error for a second language learner to sound extra emphatic.

Stress came in handy, I discovered, because Ali had a real trouble with the letter "e". It can be pronounced like the "e" in "me" (/i/), the "ei" (/e/) in "weigh", the "e" (/ɛ/) in "bed", the reduced vowels /ə/ and /ɪ/ (when unstressed, I treated them like the same phoneme for Ali's sake, but some English dialects -- including mine -- do not merge them). And oh yeah, if you want to be really finicky, there's the stressed rhotic /ɝ/ (like in "rehearse") as opposed to the unstressed rhotic /ər/, but I didn't go there.

And oh yeah. That silent-e issue, which Ali had learnt functionally but still had trouble with because his ESL teachers had taught him the rule imperfectly. But wait, stress can come to the rescue...

Long vowels, when pronounced long, are almost always pronounced stressed. That is, you rarely see unstressed long vowels. Plus, conjugations of verbs and their gerunds tend to preserve the stress of their parent verbs.

"Biking" preserves the stress of "bike" and is not pronounced "bick King"
"Corner" had the stress on the first syllable, so the e's in "cornered" cannot be stressed, and also cannot be pronounced "corneared".
"Cornea" in contrast has two stresses (primary and secondary). It's a good example of a word with syntax-dependent stress, because it is pronounced with three syllables when the second syllable is stressed (during emphasis, like if a med school lecturer distinguishing the cornea versus the sclera), but the secondary stress can be dropped to form a two-syllable word.

This got us into diphthongs and glides (when vowels get compounded together and one of the vowels get reduced). When not emphasised, the /i/ in "cornea" is reduced to a glide (/j/; it behaves like a consonant), and consonants cannot be stressed in English.

There are also "exceptions" that really aren't. For example, I gave this stress-based rule: Stressed terminal -y is pronounced like the vowel in "tie" -- e.g. fly, fry, why, rely, retie, deny
Unstressed terminal -y is pronounced like the vowel in "free" -- e.g. belly, patty, hearty

The reason why terminal -y is pronounced /i/ even in unstressed positions (like "party") has a historical reason behind it, because terminal -y doesn't come from historical "e" but historical "i", which historically split into /ɪ/ (bit) and /aɪ/ (bite) during the Great Vowel Shift.

For various reasons, historical "i" in this unstressed terminal position didn't become /ɪ/ and remained /i/, while stressed "i" followed the sound change to "/aɪ/". It sounds like a mouthful to explain, but makes intuitive sense to children who already have an implicit knowledge of English phonotactics. Some vowels (vowel sounds) are never found by themselves at the end of words, or heck, open syllables (syllables that do not end in a consonant). English simply forbids them to exist (or more accurately, the historical pressure for their existence never ... existed). This includes vowels like /ɪ/, /ɛ/, /æ/ and /ʌ/. Try it for yourselves: the vowels in "bit", "bed", "bad" and "but" never end words by themselves.

The reason even comes down to universal trends seen in all languages: if there is length distinction involved, long vowels prefer to be in open situations (syllables that end in vowel), and short vowels prefer to be in "closed" situations (syllables that in a consonant). It's sort of a length compensation. After the historical Great Reorganisation of the English sound system, consonant length is no longer as noticeable, but can be noticed in the following examples:

The /t/ in the word "fitting" is likely to be pronounced longer than the /t/ in "fighting"

i.e. a transcription making note of this might note "fitting" as "fɪt.tɪŋ" (CVC.CVC) but "fighting" as "faɪ.tɪŋ" (CVV.CVC).

The /f/ in "riffle" is likely to be pronounced longer than the /f/ in "rifle", hence
/rɪf.fl/ and /raɪ.fl/

This gives us a historical basis for why double consonants (in terms of consonants found in writing) tend to convert long vowels in verbs to their short counterparts, hence the distinction between "writing" and "written". If you say "rifle" like "rife-fel" as opposed to "rye-fel", you won't technically be wrong, but you will sound slightly strange. These subtle details can be confirmed by taking spectrograms of native speakers' utterances.

At some point -- to distinguish letters from sounds -- I had to introduce Ali to IPA and the linguists' English vowel chart, for both our sakes. I'm surprised that it isn't used in schools -- because there are some overarching rules that follow from it that was a big "OH! it makes so much sense now" moment for Ali.

** At this point I should also mention various important laws of logic in analysing sound systems. Like causality. Situation X may imply sound type A, e.g. there is a correlation, but that doesn't mean sound type A implies situation X. Similarly, sound type B may imply situation Y, but the causality may or may not be bidirectional.

more fun with balanced literacy

from Miss Brave:
On an unrelated note, I love field trip days, because they let me get to see the best of my class. (i.e., my students are surprisingly enjoyable when I am not forcing the workshop model down their throats!)

against initiatives, too

Speaking of schools teaching strategies instead of knowledge (alert E.D. Hirsch!), an approach that requires fantastic levels of goal-mongering and running-record-keeping, I also stand foursquare against the obsessive "rolling-out" of "initiatives."

Take my district. (Please.)

Last year, not long after the crash, the monthly Superintendent's Letter included the following observation:
Excitement abounds throughout the district over recent and upcoming initiatives.
Jobs were disappearing, housing values were cratering, but in the high-flying world of our schools superintendent excitement was abounding. Excitement over initiatives.

Come to find out, there is a name for districts like mine:
Too often, the measure of success in schools has been the number of activities and innovations going on. Bryk, Sebring, Kerbow, Rollow, and Easton (1998) call schools like these "Christmas tree schools," a phrase they coined to describe schools undergoing school improvement where activity per se had run amok: "There were many new programs--not just a few--and a great deal of activity and hoopla surrounded them. Some of these new initiatives may have some real strength and integrity. But because they do not cohere as a group and may even conflict, their impact is minimal at best, and potentially negative" .... In the absence of a single-minded academic focus, educators are easy targets for the "innovation du jour," seldom finishing anything they start. The dean of American basketball coaches, John Wooden (1997), gave his playeres this advice, which is admirably suited for educators in Christmas tree schools: "Do not mistake activity for achievement."

10 Traits of Highly Effective School: Raising the Achievement Bar for All Students, p. 53 by Elaine K. McEwan
Guided reading and the workshop model: activity mistaken for achievement.

Thursday, January 7, 2010

against strategies

A few years and -- oh -- maybe 3 or 4 Directors of Pupil Personnel ago,* I noticed, while sitting in on another parent's CSE meeting, a liberal use of the word "strategies." As in: "We'll teach him some strategies for self-monitoring." Or: "We'll give him some strategies for managing his learning." It was strategies-this and strategies-that, all strategies all the time. Apparently our higher-functioning special needs students were being given strategies they could use to overcome their learning problems and work around their developmental disabilities. Check.

At the time, I took this as just another moderately annoying instance of edu-inanity.

But it's always worse than you think.

Reading Miss Brave, and I plan to read every last word Miss Brave has written and posted to her blog, I realize that "strategies" are yet another means of transferring responsibility from the school to the student, while also working your teachers into an early grave and providing employment for a cadre of Lucy-Calkins and/or Fountas-and-Pinnell-trained literacy specialists. Win-win.

Here is Miss Brave:
I've mentioned before that we're expected to make sure each of our students has three goals for each unit in reading, writing and math. While students are working independently after the mini lesson, we're supposed to meet with two small groups for strategy lessons to help them meet these goals.
And here she is again:
And again:

Question: How do you get to Carnegie Hall?

Answer: The answer is not 'strategies.'

Students need distributed practice in order to learn and progress, and it is the school's job to give them that practice, not tell them to remember 15 goals and 30 strategies when they are age seven.

Even if a child does manage to hold 3 reading goals in working memory, he's not going to have room for anything else.

* Recently I figured out that my district has had 5 assistant superintendents for curriculum, instruction, and technology in 6 years. That's a lot.

60 lessons a week



Lucy Calkins has a lot to answer for.

The good news: at least they're using phonics.

the mathematics in linguistics

In high school I was super-obsessed with linguistics. (I still am -- I just am less likely to burst out inappropriately into linguistic asides in casual conversation.)

In my childhood my father had always treated calculus like this esoteric and super-abstract thing that only erudites could know. It was a uselessly haughty attitude in retrospect; my father was kind of a weird character -- I remember at 7 or 8, I came home with the "we worked with fractions today!" excitement, and he gave me this dismissive, "Psh! With that excitement I thought you had learnt something truly enlightening, like calculus." My father piqued my interest in science, but he was also the type to leave the family when I was 10. My mother, who works in architectural drafting and currently designs ships for a defence contractor, has only the vaguest recollection of a derivative -- her knowledge of calculus is all procedural knowledge, like how to find shear stress or dead load, moment formulas for various geometric shapes, etc. AFAIK no one talks about the elegance of the Mean Value Theorem on the job.

So my father's leaving meant I became the mathy one in my family. Which was bad, cuz when I was 14, I basically failed my secondary two mathematics exam in Singapore with a score of 47%. (OK they also let me take a makeup exam and I passed, but it was none too glamourous.) I had lost most passion for mathematics, until I picked up this book called Fermat's Last Theorem. You mean .... there are active areas of research in mathematics? I was inspired to self-study ... in Singapore everyone has private tutors or something, even the lower middle class, but my single parent household was even below that. Now I can laugh at all those people who spent thousands of dollars a year on private tutoring ... when I spent an amazing amount of $0 using Google. This is why I don't really disagree with idea of an "Investigations" curriculum -- it's just implemented horribly, when there are so many more fascinating and intellectually-stimulating investigations one could use.

Like take linguistics.

It had come to pass that in high school I had become pretty fascinated with calculus and linear algebra. I was taking linear algebra via dual-enrollment, and was trying to wrap my head around things like vector spaces and determinants. "Yeah I get how to do this problem, and I get the fact that theorem X is proven, but I still don't get why it works." I made the mistake of treating it like a regular high school class, because apparently my constant question-asking had annoyed some of my classmates, and the Dean of Students came to me and was basically recommended a remedy of asking less questions.

This was around the same time I was really into historical linguistics and phonetics, and had discovered the real truth behind English "long" and "short" vowels, and suddenly English spelling made so much sense, especially since I was also working out sound changes between French, Latin and Spanish. I felt like a child again ...

But then came my beloved math teachers -- the last ones who I expected to ask, "Why are you studying all this math? You're going into linguistics, right?"

At that time I was totally caught off guard, and could only come up with replies like, "Well uh.... it's kinda interesting," or "It's good to know, if I ever switch fields..." or "There's so much physics in phonetics! Well, kinda...."

Well, I'm glad to report that the suspicions of my math teachers were wrong. Other than the fact that I suddenly became interested in materials science in college, there is so much abstract math in linguistics it's not even funny.

[the above is a CPG mutual-inhibition diagram for a nonlinguistic circuit, but I can't believe that some people -- math teachers of all people -- don't seem to get that in order to study acoustic signal processing, especially in the brain, you need to understand a) how to analyse a periodic function b) the general solution to the differential equation y'' = -ky]

Wednesday, January 6, 2010

are flyswatters better than the 3-cueing system?


Mary Damer posted a link to this video on the DI list, and it's well worth taking the time to watch -- especially the section starting at 3:42.

The lesson: reading is not naming.

Reading is unspelling.

Tuesday, January 5, 2010