kitchen table math, the sequel: 6/23/13 - 6/30/13

Friday, June 28, 2013

"Wasting time in school"

Have just this moment stumbled upon a UK education blog: Wasting Time in School."

Check out this post.


This reminds me of that business idea we all had a while back, doing school projects for beleaguered parents.

Thought experiment: since the parents are already doing the projects & everyone knows it....wouldn't a School Project Business be legit in a way a term-paper business is not?

I think it might.

Gone fishing (and did NCLB work?)

In Princeton, NJ, waiting for our room to be ready.

While I wait I'm looking at NAEP scores, and wondering.

Are we seeing evidence that No Child Left Behind worked?

  • Compared to the first assessment in 1971 for reading and in 1973 for mathematics, scores were higher in 2012 for 9- and 13-year-olds and not significantly different for 17-year-olds.
  • In both reading and mathematics at all three ages, Black students made larger gains from the early 1970s than White students.
  • Hispanic students made larger gains from the 1970s than White students in reading at all three ages and in mathematics at ages 13 and 17.
  • Female students have consistently outscored male students in reading at all three ages, but the gender gap narrowed from 1971 to 2012 at age 9.
  • At ages 9 and 13, the scores of male and female students were not significantly different in mathematics, but the gender gap in mathematics for 17-year-olds narrowed in comparison to 1973.

About NAEP
NAEP Summary

Tuesday, June 25, 2013

the "triple dissociation" and slow and fast readers

re: We can see just 7 or 8 letters at a time

The NYU reading-speed study, which has come up a couple of times on ktm, found a "triple dissociation" amongst three contributors to reading speed:
  • Decoding by phonics (62% of reading speed)
  • Whole-word recognition (16% of reading speed)
  • Word-prediction via knowledge of grammar and context (22%)
"Triple dissociation":
Surprisingly, the effects of the knockouts on reading rate reveal a triple dissociation. Each reading process always contributes the same number of words per minute, regardless of whether the other processes are operating.
I've just this moment realized the implications of the triple dissociation they found:
  1. If students don't know phonics, they can never read quickly enough to do college-level reading,  which requires at least 200 wpm. 
  2. Students who don't know the grammar of written English well, will be significantly slower readers than students who do. ("Know" in the procedural sense of being able instantly to comprehend grammatical structures such as appositives and relative clauses and anaphora and the like.)
  3. Until you have substantial background knowledge in a subject, you will be a slow(ish) reader in that content area. 
I'd love to know how that 22% is distributed between grammar and background knowledge. The researchers did not test to see how grammar and background knowledge

Parts, Wholes, and Context in Reading: A Triple Dissociation by Denis G. Pelli mail, Katharine A. Tillman

We can see just 7 or 8 letters at a time

I've always wondered about this:
Let us consider the behaviour in which you are currently engaged – namely, reading these words. What exactly is your brain is doing right now? What kind of behaviour is reading and what must the brain do in order to achieve it?


Reading, when reduced to the rather prosaic level of motor actions, depends on the brain’s ability to orchestrate a series of eye movements. Now, as you read these words, your brain is commanding your eyes to make small but very rapid (about 500° per second) left-to-right movements called saccades (right-to-left or up-and-down for some other written languages). You are not consciously aware of it, but these rapid movements are frequently interrupted by brief periods when the eyes are fixed in position. Watch someone reading and you will see exactly what I mean. You’ll notice that the eyes do not sweep smoothly along the line of text, rather they dart from one fixation to another. It is only during the fixations, when the eyes dwell for about a fifth of a second, that the brain is able to examine the text in detail. Reading is not possible during the darting saccadic movements because the eyes are moving too quickly across the page. You are not aware of the blur and confusion during a saccade because fortunately there is a brain mechanism that suppresses vision and protects you from visual overload.

Reading is only possible between saccades, not only because the eyes are then stationary but also because gaze is centred on the retina’s fovea. The fovea is the only part of the retina specialized for high acuity vision (see Chapter 5), but it scrutinizes a very small area of our visual world. As a literal rule of thumb, foveal vision is restricted approximately to the area of your vision covered by your thumbnail held at arm’s length. It is a small window of clear vision within which you are able to decipher just 7 or 8 letters of normal print size at a time. The task for the brain is to generate a precise series of motor commands to the eye muscles which ensure that at the end of each saccade your high acuity vision is fixed on that part of the text you need to see most clearly next. As your eyes approach the end of a line, the brain generates a carriage return. Of course the return saccade must be to the left, of the correct magnitude and associated with a slight downward shift in gaze in order to bring the first word on the next line onto the fovea.

I have considered only the simple case of the brain directing eye movements alone, as if nothing else affects gaze direction. But of course the relative positions of the eye and page are affected continuously by head, body, and book motion. Thus the brain must continually monitor and anticipate factors affecting the future position of your eyes relative to the text. The fact that you can effortlessly read on a moving train while eating a sandwich is evidence that your brain can solve this problem quite easily. Importantly, it is done automatically and on an unconscious level without you having to think through every step. If you had to consciously think about the mechanical process of reading, you would be illiterate!

Our lack of conscious awareness of underlying brain processes can also be illustrated by reflecting on the subjective experience that the comprehension of written material represents. While reading we are not conscious of the fragmented nature of comprehension imposed by underlying move—stop—move—stop activity of the eyes I’ve just described or by the fact that only 7 or 8 letters can be deciphered at each stop. On the contrary, our strong subjective impression is that comprehension of the text flows uninterrupted and moreover that we can read several words or even whole sentences ‘at a glance’. That this is not the case can be illustrated by reading a sentence containing a word that has more than one meaning and pronunciation. For example, the word tear has two very different meanings and pronunciations in English – tear the noun of crying and tear the verb of ripping apart. Clearly such word ambiguity complicates the brain’s task of providing you with an uninterrupted comprehension. If for instance the word tear occurred at the beginning of a sentence its meaning might remain ambiguous until the subject of the sentence appears later. Because you cannot read the whole sentence at a glance your brain may be left with no option but to choose one of the alternative meanings (or sounds, if you are reading aloud) of a word and hope for the best.

While we cannot read whole sentences at a glance, the brain does recognize each word as a whole. What is quite surprising however is that the order of the letters is not particularly important (good news for poor spellers). That is why you will be able to read the following passage without consciously having to decode it.
I cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdgnieg. It deosn’t mttaer in waht oredr the ltteers in a wrod aer, the olny iprmoatnt tihng is taht eth frist dan lsat ltteer be in the rghit pclae. The rset cna be a taotl mses and yuo can still raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Amzanig huh?
The Brain: A Very Short Introduction by Michael O'Shea

The NYU study of reading speed (found that reading happens at 3 levels:

  • Decoding (phonics): 62% of reading speed
  • Whole word: 16% of reading speed
  • "Sentence or story context": 22% of reading speed

And see:
How many words can readers predict?