CTK Insights

The news are sometimes overwhelming. The latest I read came from National Geographic Daily News. A new research by Satoshi Kanazawa, an evolutionary psychologist at the London School of Economics and Political Science, suggests “that human evolution may have a big influence on whether you’re liberal or conservative—not to mention how smart you are, whether you believe in God, or whether you’ve got a cheatin’ heart.”

As a result of their iconoclastic ancestry, he suggests, people with higher levels of intelligence are more likely to adopt social values and behaviors that are relatively new to human life—liberalism, atheism, staying up late, and (for men) monogamy, for example.

This is how the study was run:

The study used a picture-based vocabulary test to estimate the IQ of participating teenagers. Seven years later, the same people were asked about their religious and political beliefs.

People who later admitted to being “not at all religious,” and who classified themselves as “very liberal” politically had higher IQ scores as teenagers than those who were “very religious” and “very conservative.”

The disagreements concerning IQ scores as a measure of intelligence apart, I find it disconcerting that the new study did not apparently look into the correlation of IQ with mating habits. Just off the top of my hat, I would guess that the more liberal parents are the less likely they are to get into the playful mood in the course of Christmas festivities and, as a result, are less likely to produce an offspring with potential difficulties at school.

This appears as a plausible venue for the concealed ways of natural selection to act through.

A story in foxnews.com under the caption “Detroit School Leader Sends Wrong Message, Some Parents Say” tells of the president of the city’s school board who shockingly confessed that he can’t pen a coherent sentence.

Mathis, 56, of Detroit, has had difficulties with language as early as fourth grade, when he was placed in special education classes. His college degree was also held up for more than a decade due to repeatedly failing English proficiency exams required for graduation from Wayne State University, the paper reported.

Some parents wonder, “If this is the leader, what does it say about the followers? It explains a lot about why there’s so much confusion and infighting with the board and Robert Bobb.” Which seems like a very logical argument, does not it?

Other parents are simply worried that learning about Mr. Mathis’ disability may send a wrong message to the students. But it’s a white lie that a disability or a lack of a particular skill may stop a person from achieving his or her goals.

“Instead of telling them that they can’t write and won’t be anything, I show that cannot stop you,” Mathis told the paper. “If Detroit Public Schools can allow kids to dream, with whatever weakness they have, that’s something. … It’s not about what you don’t have. It’s what you can do.”

I remember the two-terms NJ Governor Thomas Kean once admitted to being dyslexic. This did not prevent him from being the most popular figure in the NJ political scene. He was President of Drew University for 15 years, Head of the September 11 Commission about which he co-authored (with L. Hamilton) a book.

Thinking about math education, I would wager that a major portion of the state and federal officials would not pass a high school proficiency test. The same officials would promote the “math for the 21st century” slogan and high stakes examinations. The sound bites like that, although stale, are hard to argue against. But the establishment that is based on this perversion is at the core of the systemic failure of education. It is much easier and appears more equitable to lump the goals into the “algebra for all” (say) slogans than promote the idea that the purpose of education should be helping every student to develop to the fullest his or her abilities.

In the Fall 2009, the Bill & Melinda Gates Foundation has given $45 million to six school districts, including Denver, for a two-year study of teaching. I’ll quote a response to this news from James D. Starkey, a retired teacher. The purpose of the study is a quest to find out the best teaching practices. During one telephone interview, Melinda Gates is reported to have said this: “What was the thing that works absolutely the best? At the end of the day, it is the teacher in the classroom.” Which made Mr. Starkey wonder “if you know what the answer is, why are you spending $45 million on research?” He anticipates the results of the research:

We’ll tell you what the research will reveal about effective teaching, and it has almost nothing to do with time on task, identifying objectives, administrative fiats, or the latest recycled fad (small-group instruction, large-group instruction, writing workshops, reading labs, concept attainment, modular scheduling, block scheduling, traditional scheduling-or, for that matter, following curriculum guides). Teaching and learning happen whenever significant adults interact with and direct children. You can’t stop it.

He writes further:

I’m talking about the effect a serious and interested and knowledgeable adult can have on a group of children. It can be a wonderful thing to see. In such an atmosphere, learning happens regardless of the curriculum, or the objectives, or the strategies. In any given school, on any given day, you could walk by rooms with master teachers doing their thing. One might be a lecturer, and every day students would go into her class, get out notes, and pay attention. Another might be totally committed to large-group discussion, and every day that teacher’s students would be seated in a circle talking to one another. The teacher next door might deal exclusively with small groups. The one next to him might be convinced that a writers’-workshop approach is the best.

There are as many classroom approaches as there are master teachers, but the one thing they all have in common is that students learn. They get higher test scores. When you walk by such teachers’ rooms, students will be smiling. There will be no one asleep (well, let’s not get too carried away). Their classrooms, though different from one another, are good places to be. They feel right. And none of those teachers learned how to create that feeling in a methods class, or from an administrator, or from some ground breaking research.

What can I say? I have a curious feeling that practically every educator will agree with Mr. Starkey’s opinion, except of course for the ones who made a career out of promoting a particular fad.

A recent article at MailOnline by Laura Clark made public the findings of a research conducted over the past 5 years by the experts at the Higher Education Policy Institute.

As many as 12,000 children a year miss out on university places because they were born in the summer, research shows.

Children born late in the school year are significantly less likely to go to university than their older classmates, a study found.

Just 28 per cent of August-born children went to university during the six years of the study compared with 32 per cent of those born in September, an analysis of university admissions by birth month showed.

This is especially significant because it is a long-observed trend that July, August and September are the months with the highest number of births.

Figures from 1998, for example, show that July had the most births – 8.9 per cent of the annual total – followed by September with 8.7 per cent and August with 8.6.

Experts at the Higher Education Policy Institute, who disclosed the figures yesterday, said it was stunning that birth month should have such a major impact on university prospects

What can I say? My advice to potential and aspiring parents is to become more statistically minded, especially between the Thanksgiving and Christmas time.

How to divide evenly 7 apples between 12 boys?

An obious answer is to divided each apple into twelve parts and give each boy seven of them.

But assume there is a restriction: one does not know how to divide an apple into more than 5 parts. What do you do then?

See Why 1/3 + 1/4 = 7/12?

Apparently it is quite possible to convince students that 1/3 + 1/4 must be equal 7/12 even before the operation of addition has been defined for fractions.

Wonderment at the identity

-1 = 1 + 2 + 4 + 8 + …

dwarfes the perennial question as to whether .9999… equals 1 or not. Still, it holds in exactly same sense as the limit of a convergent series. The sums of the successive powers of 2 converge in the 2-adic norm! Moreover, they converge to a negative 1.

See, p-adic Numbers and p-adic Expansions

Equilateral triangle is the largest among all inscribed into the same circle
http://www.cut-the-knot.org/triangle/InscribedEquilateral.shtml

arctan(1)+arctan(1/2)+actan(1/3)=π/2,
http://www.cut-the-knot.org/Curriculum/Geometry/ThreeSquares.shtml

arctan(1)+arctan(2)+arctan(3)=π,
http://www.cut-the-knot.org/pythagoras/PaperFolding/arctan123.shtml

Art in sand. No mathematics, but so beautiful.

In the Toads and Frogs puzzle the sequence of moves in the Toads and Frogs puzzle is always palindromic. To undertsand why this is so needs very little in case the number of toads is the same as the number of frogs. But this is also true even if the two numbers are different. Why?

Another look at the perennial stumbling block of whether 0.999… = 1 and what it actually may mean, see

http://www.cut-the-knot.org/WhatIs/Infinity/9999.shtml