kitchen table math, the sequel: 1/10/10 - 1/17/10

Saturday, January 16, 2010

"one strongly confirmed impact on math ability in a negative direction"

Cato@Liberty quotes from the new Head Start study:
Head Start improved children’s language and literacy development during the program year but not later and had only one strongly confirmed impact on math ability in a negative direction. (For the 3-year-old cohort, kindergarten teachers reported poorer math skills for children in the Head Start group than children in the control group.)
If they'd gone with Siegfried Engelmann in 1966, things would be different.

Thursday, January 14, 2010

Anniversary Edition of Liping Ma's book out this month

You can now pre-order from Amazon, here's what the review says it includes:
The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.
It's a great book, a must have, I'm looking forward to getting my copy.

Tuesday, January 12, 2010

against strategies, part 2

from Dan Willingham:
I have written (on this on this blog and elsewhere) about the importance of background knowledge and about the limited value of instructing students in reading comprehension strategies.

To be clear, I don’t think that such instruction is worthless. It has a significant impact, but it seems to be a one-time effect and the strategies are quickly learned. More practice of these strategies pays little or no return. You can read more about that here.

Knowledge of the topic you’re reading about, in contrast, has an enormous impact and more important, there is no ceiling—the more knowledge you gain, the more your reading improves.

In a recent email conversation an experienced educator asked me why, if that’s true, there has been such emphasis on reading strategies and skills in teacher’s professional development.

There’s a temptation to say “Oh, Americans don’t value knowledge; they don’t think that people need to know stuff.” But I rarely run into a teacher or administrator who believes that, and I actually have (as yet unpublished) survey data to support that impression. So I don’t think that’s behind it.

Doubtless there is more than one reason, but as a researcher, I have a hypothesis: People think strategies are important because most of the reading research is on strategies. But that’s an accident of the way research is done.

Behavioral research (and educational research in particular) is a more conservative enterprise than you might think. When a researcher decides to conduct a study in classrooms, he or she typically commits at minimum two years of his or her life to the project. What if nothing much happens?

A researcher is therefore motivated not to conduct studies that break utterly new ground, but rather to conduct studies in which one is fairly confident that something will happen.

One takes an intervention that has worked in the past, and adds an interesting tweak.


[T]o be competitive for funding the proposal has to be something for which there is already evidence that it will work.
Now consider what it takes to do research on strategy instruction versus knowledge instruction. Teaching children reading strategies is quick. A research project might call for 10 or 20 lessons in total, each lasting 30 minutes or less. One can imagine getting a school administrator’s permission to do such a study in his or her district.
But the hypothesis for knowledge instruction is that it takes years to make a broad impact on students’ knowledge.
Willingham: The Zeitgeist of Reading Instruction
The Answer Sheet

teaching content is teaching reading

Monday, January 11, 2010

IPA English vowel chart, oriented towards learners (not documentation)

So this is basically the IPA chart I used with Ali, just that it looks cleaner and there's less scribbling. (Click for larger version).

In my opinion (as in not backed by double blind clinical trials, rigourous empirical evidence or anything but simply my own intuition and experience with others), IPA charts are useful. They provide a "skeleton" in which to arrange the seemingly vast array of English vowel sounds.

I have not really been happy with the way the English vowel system is generally presented to learners, both native children and ESL learners. For one, the vowels are often presented in random lists, and learners aren't told how the vowels are related to each other. An IPA-based vowel chart is organised by two physical traits often used to classify vowels (among others): vowel height, and vowel backness.

Here, height and backness are relative. If you look up the IPA vowel chart on Wikipedia, you find distinctions like "mid-open", "mid-front", etc. but those are w/respect to "absolute" cardinal vowels defined by phoneticians -- and there is no single language that uses all of them. Most languages distinguish 2 or 3 heights, and distinguish 2 or 3 levels of backness. There are always exceptions -- but languages that distinguish 5 heights for example, may only have a handful of consonants, etc. It's a trend you find among the world's languages -- complexities in one area tend to be compensated by simplifications elsewhere.

The more "open" a vowel is, the higher its F1 formant frequency is (more close ==> lower F1 formant frequency). F2 formant frequencies are primarily influenced by vowel backness (more front ==> higher F2 formant frequency). Formant analysis in phonetics goes all the way to formants like F9 ... but their effects are more subtle. And of course formant frequencies have interfering effects on each other, but there are compensating functions to do that -- and I won't discuss any more phonetics because I really want to discuss literacy.

A brief vowel chart orientation (an initiation to IPA). In IPA, /j/ is used preferentially for the "yod" (as in yogurt), since /y/ is used for a vowel sound (that English doesn't use). English has (more or less) eight pure vowels:

æ -- "bad"
ɛ -- "bed"
ɪ -- "bid"
ʊ -- "good"
ɔ -- "law"; for people who make the cot-caught distinction. This pure vowel does not exist by itself in my dialect (New England rhotic)
ɑ -- "father"
ə -- "kernel"
ʌ -- "bud"

Now long vowels. Long vowels aren't actually pure vowels, though they used to be. They are actually diphthongs. A diphthong is a combination of vowel + semivowel (aka vowel-like consonant). Not all combinations of two vowel-like sounds are diphthongs. For example, if you pronounce "towel" with two syllables, there are three-vowel like sounds in there, but there is only one diphthong and there is no "triphthong". My rule of thumb:

1. A diphthong has to occupy the time length of one syllable. The semivowel component is generally shorter and more "clipped" than the vowel, thus the VV sequence is really behaving like VC. The preferred syllable structure in English (if not universally) is the structure CVC, which lasts for the length of one standard syllable. Deviations from this structure generally result in compensation.

For example: the word it. Kinda simple, but you never knew you implemented so many phonological corrections when you used this word! If you use it by itself (just say it to yourself), notice how, the /ɪ/ phoneme is stressed, and is slightly longer than say, the word in "sit". But put a consonant before it -- like in a sentence, and "it" will actually pull a consonant off your preceding syllable, and /ɪ/ will revert back to being an unstressed vowel of normal length. Thus, "make it so" can be analysed as: /mɛj.kɪt.sɔ w/; all three syllables have the structure CVC. This is part of what we usually regard as "fluency" -- our mind is so automatic and flexible, we unconsciously rearrange phonemes around based on sound laws we don't even think consciously about. These sound rules will also make consonants appear out of thin air:

by themselves: "you" "can" "see" "it" -- /jʊw/ | /kɛ~n/ | /sɪj/ | /ɪt/ [note stresses in bold]
in a sentence: "You can see it." /jʊw.kɛn.sɪj.jɪt/ (extra consonant suddenly duplicated from previous syllable: length compensation!) [stresses in bold, extra consonant italicised]

You can observe this as a rule in children. Young children and toddlers have incomplete length compensation -- the result is a sort of sing-song sentence structure we associate with two-year-olds. But analyse the sound structure of a six-year-old or an eight-year-old, and many elaborate sound rules suddenly appear.

Okay, that was a rather long aside. Second rule of thumb:

Diphthongs generally "obscure" their component sounds. Only by conscious analysis do you realise that the sound in "ay" (like stay) is made up of ɛ (like in bed) and the yod (the consonant of yogurt). Same goes for "how" (æ+w). I include rhotics in here too, because they have a tendency to change the vowel, but you can also make an argument for excluding them.

So here are the diphthongs of English:

æw -- "how"
æj -- "my"
ɛj -- "bake"
ɪj -- "bee"
ʊw -- "moose"
ɔw -- "bow"
ɔj -- "toy"
ɑw -- "sock"
ɑr -- "far"
ɑwr -- "war", "core" **
ər -- "wicker"
ʌr -- "kernel", "rehearse" **

** There's further discussion about these diphthongs but it would make this post too long.
There's also nasal vowels (like the vowel in sand) but I've decided to skip that for now.

IMO, this is better than the traditional short-long vowel system often presented, because that system really only allows for ten vowel phonemes and the rest of the vowels are randomly placed. Was always confused about the vowel system from day 1 when it was presented in first grade, until grade 10, which is when I learnt phonetics.

A pure vowel / diphthong contrast can be used to explain English spelling, whereas it's not apparent with a short-long system. So you have to explain why silent-e often generates diphthongs ("long vowels"). OK. Short answer: It's related to length compensation, like the syllable exercises we've been doing above. But why does double-o ("long o") not actually sound like a long "o" (like in stone)? Can you actually make sense of English spelling? Ah, that is for an upcoming post on the Great Vowel Shift.

cross-pressured individuals of the world, unite!

Beth wrote:
First of all, real progressives hate what's going on in the public schools as much as anyone. "Progressive" shouldn't mean "mushy."

We've talked about this before; political opinion re: our public schools does not break along party lines. In fact, I have the impression that education politics are the single most bipartisan issue we have. (Is that true?)

The most useful explanation I've found of public school ideology is E.D. Hirsch on progressive education's roots in romanticism. Ultimately, though, Hirsch doesn't tell me why 'everyday liberals' and 'everyday conservatives' should see eye-to-eye on so many issues when it comes to K-12.

Then, a couple of days ago, I came across two studies of public opinion that struck me as relevant:
  • The Nature of Political Ideology in the Contemporary Electorate by Shawn Treier and D. Sunshine Hillygus | Public Opinion Quarterly 2009 73(4):679-703
  • Value Preferences and Ideological Structuring of Attitudes in American Public Opinion by Brendon Swedlow and Mikel L. Wyckoff | American Politics Research |Volume 37 Number 6 | November 2009 | 1048-1087
Both argue that political opinion is multidimensional. Thus the liberal-conservative dimension fails to capture a rather large percentage of the public. (62%?)

From Treier and Hillygus:
...Although political rhetoric today is clearly organized by a single ideological dimension, we find that the belief systems of the mass public remain multidimensional, with many in the electorate holding liberal preferences on one dimension and conservative preferences on another. These cross-pressured individuals tend to self-identify as moderate (or say "Don't Know") in response to the standard liberal-conservative scale, thereby jeopardizing the validity of this commonly used measure. Our analysis further shows that failing to account for the multidimensional nature of ideological preferences can produce inaccurate predictions about the voting behavior of the American public.

I can't pull a copy of their article just now, so I don't know the nature of the dimensions they see as characterizing American public opinion. I have been able to skim Swedlow and Wyckoff, who say that political opinion is organized along two dimensions:
  • order vs equality/caring
  • high freedom vs low freedom
From their article:
In this study, we investigate four attitudinal structures (including liberal, conservative, and libertarian configurations) associated with two ideological dimensions among American voters and demonstrate that these attitudinal structures are related in expected ways to differential preferences for the values of freedom, order, and equality/caring. Liberals are inclined to trade freedom for equality/caring but not for order, whereas conservatives are their opposites—willing to trade freedom for order but not for equality/caring. In contrast, libertarians are generally less willing than others to trade freedom for either order or equality/caring (although they probably prefer order to equality/caring). The fourth ideological type is more willing than the others to relinquish freedom, preferring both order and equality/caring. Depending on how our results are interpreted, this fourth type may be characterized as either communitarian or humanitarian. These findings help close the gap between unidimensional conceptions and multidimensional evidence of ideological organization in political attitudes by demonstrating that value structure and attitudinal structure are strongly related in two ideological dimensions.
Swedlow and Wyckoff duplicate Treier and Hillygus' finding re: self-identified "moderates":
When asked to identify their ideological orientation, nearly half (45% to 48% in both groups) of those with libertarian and communitarian political attitudes identified themselves as “moderates.” Similarly, when we recompute percentages by rows instead of columns, we find that just more than 60% of those identifying themselves as moderates on the self-identification scale are classified as libertarians or communitarians in our attitudinal typology. Those with libertarian and communitarian attitudes were also more likely not to respond to the self-identification question at all (4.6% and 8.6%, respectively). The bulk of libertarians and communitarians, to their credit, seem to know that they are not liberals and conservatives.* Meanwhile, though less than perfect in their ability to match attitudes with ideological labels, those with liberal and conservative attitudes are by comparison noticeably less likely to select the “moderate” or “don’t know” categories, and when they pick one of the other two ideological labels, they are usually correct.

Swedlow & Wyckoff, p. 1056

Cross-pressured individuals who "don't know" their political orientation: that's a pretty fair description of my own plight when it comes to choosing between Door A and Door B.

The reason the grid strikes me as possibly relevant to public schools is that the "Communitarian" option -- low-low on freedom -- is one way to describe what it is that is not 'liberal' about public schools, whose employees are generally identified with the Democratic Party and with liberal politics. And I think you can use this grid to visualize why a real progressive like Mary Damer and a real conservative like Martin Kozloff can be so naturally allied. Neither is a communitarian.

By which I mean that individual freedom is a core value for liberals and conservatives alike, although in different realms, which is not the case for the people running our public schools. All too often, public school culture is distinctly illiberal.

They do what they do.

Michael Kinsley on Democrats, Republicans, libertarians and conservatives
And what is the opposite of libertarianism? Libertarians would say fascism. But in the American political context, it is something infinitely milder that calls itself communitarianism. The term is not as familiar, and communitarians are far less organized as a movement than libertarians, ironically enough. But in general communitarians emphasize society rather than the individual and believe that group responsibilities (to family, community, nation, the globe) should trump individual rights.

The relationship of these two ways of thinking to the two established parties is peculiar. Republicans are far more likely to identify themselves as libertarians and to vilify the government in the abstract. And yet Republicans have a clearer vision of what constitutes a good society and a well-run planet and are quicker to try to impose this vision on the rest of us. Now that the Republican Party is in trouble, critics are advising it to free itself of the religious right on issues like abortion and gay rights. That is, the party should become less communitarian and more libertarian. With Democrats, it's the other way around.

Very few Democrats self-identify as libertarians, but they are in fact much more likely to have a live-and-let-live attitude toward the lesbian couple next door or the Islamofascist dictator halfway around the world. And every time the Democrats lose an election, critics scold that they must put less emphasis on the sterile rights of individuals and more emphasis on responsibilities to society. That is, they should become less libertarian and more communitarian. Usually this boils down to advocating mandatory so-called voluntary national service by people younger than whoever is doing the advocating.

Libertarians and communitarians (to continue this unjustified generalizing) are different character types. Communitarians tend to be bossy, boring and self-important, if they're not being oversweetened and touchy-feely. Libertarians, by contrast, are not the selfish monsters you might expect. They are earnest and impractical--eager to corner you with their plan for using old refrigerators to reverse global warming or solving the traffic mess by privatizing stoplights. And if you disagree, they're fine with that. It's a free country.

Libertarians Rising
by Michael Kinsley
TIME Thursday October 18, 2007

* I love it!

small-d democracy and its discontents

Middle School Mathematics Institute: msmi2010

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