Students will make and investigate mathematical conjectures

from New York state Education Department Geometry standards (pdf standards):

Now that Jeanette has finished inventing the rule to find the measure of an angle in a regular n-gon, maybe she'll have time to invent the wheel.

help desk - variables and expressions

from Glencoe Algebra 1 Skills Practice (pdf file):

the difference of 17 and 5 times a number

How do you write this?

17 - 5n

I don't think I've seen a number problem worded that way.

do students learn to read from beginning to end?

from the math and reading thread, EM reports:

I have in fact encountered quite a few SAT students who quite literally don't understand what it is that they're reading.

It has nothing to do with them not producing a particular answer that a teacher has arbitrarily deemed "correct" but rather is a result of their inability to unpack complex syntax, infer meanings that aren't literally spelled out for them, and, astonishingly (at least I was astonished the first time it happened - now I've been desensitized), to read an entire sentence from beginning to end, paying attention to every word, rather than "skimming" it in such a way that they only pick up random words that bear no apparent relationship to one another. If asked to summarize the gist of a reading in their own words, they're often completely lost.

Did I mention that some of these kids have attended elite Manhattan private schools since kindergarten?

At least from what I've seen, the problem isn't as bad as most people think. It's actually a lot worse.

I assume some of the problem can be attributed to balanced literacy reading instruction, which teaches students to move their eyes around the text as they seek clues to help them decipher unknown words. But I don't know, of course.

Thoughts?

Must get palisadesk on the case---!

Here is Arthur Whimbey making the same observation.

'the most important fact about IQ'

Garret Jones slides (pdf file) 
National IQ and National Productivity:
The Hive Mind Across Asia (pdf file)
Garett Jones
Center for Study of Public Choice
Department of Economics
George Mason University
January 2011
[Published in Asian Development Review, June 2011]

sitters

Susan Cain's op-ed in today's Times reminds me of Katharine's book:

But shyness and introversion share an undervalued status in a world that prizes extroversion. Children’s classroom desks are now often arranged in pods, because group participation supposedly leads to better learning; in one school I visited, a sign announcing “Rules for Group Work” included, “You can’t ask a teacher for help unless everyone in your group has the same question.” Many adults work for organizations that now assign work in teams, in offices without walls, for supervisors who value “people skills” above all. As a society, we prefer action to contemplation, risk-taking to heed-taking, certainty to doubt. Studies show that we rank fast and frequent talkers as more competent, likable and even smarter than slow ones. As the psychologists William Hart and Dolores Albarracin point out, phrases like “get active,” “get moving,” “do something” and similar calls to action surface repeatedly in recent books.

Yet shy and introverted people have been part of our species for a very long time, often in leadership positions. We find them in the Bible (“Who am I, that I should go unto Pharaoh?" asked Moses, whom the Book of Numbers describes as “very meek, above all the men which were upon the face of the earth.”) We find them in recent history, in figures like Charles Darwin, Marcel Proust and Albert Einstein, and, in contemporary times: think of Google’s Larry Page, or Harry Potter’s creator, J. K. Rowling.

In the science journalist Winifred Gallagher’s words: “The glory of the disposition that stops to consider stimuli rather than rushing to engage with them is its long association with intellectual and artistic achievement. Neither E=mc2 nor ‘Paradise Lost’ was dashed off by a party animal.”

We even find “introverts” in the animal kingdom, where 15 percent to 20 percent of many species are watchful, slow-to-warm-up types who stick to the sidelines (sometimes called “sitters”) while the other 80 percent are “rovers” who sally forth without paying much attention to their surroundings. Sitters and rovers favor different survival strategies, which could be summed up as the sitter’s “Look before you leap” versus the rover’s inclination to “Just do it!” Each strategy reaps different rewards.

IN an illustrative experiment, David Sloan Wilson, a Binghamton evolutionary biologist, dropped metal traps into a pond of pumpkinseed sunfish. The “rover” fish couldn’t help but investigate — and were immediately caught. But the “sitter” fish stayed back, making it impossible for Professor Wilson to capture them.

[snip]

Next, Professor Wilson used fishing nets to catch both types of fish; when he carried them back to his lab, he noted that the rovers quickly acclimated to their new environment and started eating a full five days earlier than their sitter brethren. In this situation, the rovers were the likely survivors. “There is no single best ... [animal] personality,” Professor Wilson concludes in his book, “Evolution for Everyone,” “but rather a diversity of personalities maintained by natural selection.”

[snip]

...sitter children are careful and astute, and tend to learn by observing instead of by acting. They notice scary things more than other children do, but they also notice more things in general. Studies dating all the way back to the 1960’s by the psychologists Jerome Kagan and Ellen Siegelman found that cautious, solitary children playing matching games spent more time considering all the alternatives than impulsive children did, actually using more eye movements to make decisions. Recent studies by a group of scientists at Stony Brook University and at Chinese universities using functional M.R.I. technology echoed this research, finding that adults with sitter-like temperaments looked longer at pairs of photos with subtle differences and showed more activity in brain regions that make associations between the photos and other stored information in the brain.
Once they reach school age, many sitter children use such traits to great effect. Introverts, who tend to digest information thoroughly, stay on task, and work accurately, earn disproportionate numbers of National Merit Scholarship finalist positions and Phi Beta Kappa keys, according to the Center for Applications of Psychological Type, a research arm for the Myers-Briggs personality type indicator — even though their I.Q. scores are no higher than those of extroverts. Another study, by the psychologists Eric Rolfhus and Philip Ackerman, tested 141 college students’ knowledge of 20 different subjects, from art to astronomy to statistics, and found that the introverts knew more than the extroverts about 19 subjects — presumably, the researchers concluded, because the more time people spend socializing, the less time they have for learning.

THE psychologist Gregory Feist found that many of the most creative people in a range of fields are introverts who are comfortable working in solitary conditions in which they can focus attention inward. Steve Wozniak, the engineer who founded Apple with Steve Jobs, is a prime example: Mr. Wozniak describes his creative process as an exercise in solitude. “Most inventors and engineers I’ve met are like me,” he writes in “iWoz,” his autobiography. “They’re shy and they live in their heads. They’re almost like artists. In fact, the very best of them are artists. And artists work best alone ... Not on a committee. Not on a team.”
Shyness: Evolutionary Tactic?
By SUSAN CAIN
Published: June 25, 2011

Quiet: The Power of Introverts in a World That Can't Stop Talking




Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School

Susan Cain's blog

Bonnie on college student reading skills

from the Headsprouts thread:

Reading comprehension is a huge problem for my college students. The introductory CS textbooks are written using vocabulary and a sentence complexity that is way beyond them. I wish I had a better sense of their actual reading skills so I could do some vocabulary work with them. The gasstationwithoupumps blog has posted links to some excellent material on teaching students how to read technical material that I think I may use next semester.

"people love pizza"

Math lovers of the world unite

Envision or Math in Focus?

query from Peter Meyer

Any thoughts?

Newhart

Headsprouts reading comprehension program

abstract:
Teaching learners how to comprehend text remains a largely unsuccessful attempt in our school system. Drawing from the fields of learning sciences, education, instructional design, and performance improvement, we designed, tested, revised, and released to schools and homes an interactive online program that reliably teaches flexible, widely applicable reading comprehension strategies to children. This article describes the analysis and design processes involved in the development of such a program.
Comprehension by Design: Teaching Young Learners How to Comprehend What They Read (pdf file)
Marta Leon, PhD; Victoria Ford Hirofumi Shimizu, PhD; April Heimlich Stretz Jay Thompson Melinda Sota; Janet S. Twyman, PhD T. V. Joe Layng, PhD

Reading this tonight!

More Connected Math Woes, This Time in Pennsylvania

The Riverview School District enrolls about 1,100 k-12 students in Oakmont and Verona Boroughs, Pennsylvania.

From an online news blog, the Plum-Oakmont Patch

The Riverview School Board meeting on Monday had the largest attendance in years, according to school board members. Parents filled the high school library, and in a citizen comment session that lasted two hours, they discussed their concerns about the middle school Connected Mathematics 2 program.

The parents had a lot of familiar things to say:

Among the parents' concerns were the group work involved, the participation aspect of the class, the frequency of testing and the combination of students at different math levels in the same classroom.

Parent Joseph Knapp said his son struggled in the class because of the way it was structured.

"I, unfortunately, found the Connected Math program to be an unorthodox way of teaching students," he said. "It seemed like the students taught themselves, in theory.

"They have groups where they figure out problems and are encouraged to come up with the ideas on their own. I thought that was ridiculous. In sixth and seventh grades, you need instruction."

Parent Tim Lazor said his son usually did very well in math class until he took the class this year. Lazor said he doesn't think the program has the support of the students or the teachers who are teaching it.

"I don't think the teachers bought into this," he said. "That's a critical component.

Eight years to find a new curriculum?

Superintendent Charles Erdeljac said district officials had been looking for a way to improve the math curriculum for about eight years. He said to participate in the Math and Science Partnership of Southwest Pennsylvania, the district would have to implement Connected Math 2 or MathScape—the only two programs with the National Science Foundation's "stamp of approval."

Scores declined?

When asked by parents about Pennsylvania System of School Assessment Scores, principal Jay Moser said the scores of last school year's seventh graders dropped by 9 percent, according to primary figures from the state department of education.

Hmmn I guess math is different in small-town Pennsylvania.

Erdeljac said district officials are going to continue to monitor the program and data associated with it to ensure it is a good fit for students.

"On the one hand, we have to have fidelity to the program as it's intended to be taught, but on the other hand, we're Riverview," he said. "We need to find out how this program can be most successful here at Riverview…we're still in the process of making this program Riverview's Connected Math program."

gaps

From the reading and math, math and reading comments thread:

Erica writes:

You can tell C. that I beat him: 220 point gap between CR and math (800/580), and I actually knew a couple of people with even larger gaps (800/560, 800/490!).

Independent George wrote:

I scored a 420 on my Writing achievement test (waaaay back in 1994). I had a 720 on the SAT-Verbal, and a 5 on the AP English test, but I scored 420 on the writing test.

C. has a friend who got an 800 on reading and a 550 on math.

He's still only at 670 on writing, which is equally ridiculous! (Ridiculous because he's losing his points on the grammar section.) Erica's going to shape him up.

reading and math, math and reading

via Marginal Revolution:

To an economist, the most important fact to know about mental abilities is that across large populations, different mental abilities are positively correlated.1 In other words, people who are above average in arithmetic tend to perform above average in vocabulary tests, block puzzles, as well as in memorizing lists of numbers and then repeating them in reverse order. This positive correlation conflicts with the commonsense view that abilities are negatively correlated, that for instance while some people are good in math, others are good in verbal tasks.

This positive correlation is at the heart of the psychological concept of intelligence. Quantitatively, it is at the heart of psychometric methods that extract a principal component from a broad variety of mental ability subtests. This principal component is formally called g, or the g factor. Lay persons, and most routine psychological research, refer to IQ instead of g, but it is worth keeping the concept of g in mind. Across thousands of studies on the correlation across mental abilities across populations, no one has yet found a reliable negative correlation.

This fact should strengthen our priors when we come across new mental tasks and we ask ourselves, “Will high IQ groups be better than average at this new mental task?” For every mental task so far that involves any level of sophistication, the answer has been yes.
National IQ and National Productivity: The Hive Mind Across Asia
Garett Jones
January 2011
[Published in Asian Development Review, June 2011]

Serendipity!

Since last Thursday, I've been trying to explain to C. that a 190-point gap between your reading score & your math score is ridiculous. Ridiculous because a 190-point gap between a reading score & a math score is not consistent with the way a person's brain is built. On IQ tests, everything goes with everything; if you're good on one task, you're good on another.

C's math scores, I keep telling him, like my math scores when I was his age, are a measure of the math teaching and math curriculum he's had, not of his innate ability to do math. His math tutor told him the same thing this morning, but C. claimed later not to have heard. So I was in need of fresh ammunition, and now here it is.

I love the internet.

SAT grammar rules from Erica Meltzer

Complete SAT Grammar Rules

If we didn't have the SAT to prep for, C would never have learned what terms like pronoun case or pronoun antecedent meant. I'm convinced C. is going to develop more quickly as a writer because of it.

Hack the SAT on the writing section

Hack the SAT on tutoring the writing section:

The grammar portions [of the SAT writing test are far more important [than the essay]. And they're very easy to prepare for. In fact, there are only a handful of grammar rules that the SAT loves to test, and they repeat them over and over. So if you can just memorize the rules that we'll lay out in this section, you'll find that the actual test won't be that much of a challenge. During test prep, scores on the writing section tend to increase most reliably, and by the most number of points.
Hack the SAT by Eliot Schrefer
p. 159

I believe it.

Last week I skimmed an SAT roster for our high school from a couple of years back. I saw no 800s on math, one 800 on reading, and four 800s on writing. (Not sure how many students in that group -- perhaps 125?)

I think that's consistent with Schrefer's observation that the writing section is easiest to coach.