Posted by: Alexandre Borovik | August 22, 2012

News from Chile re: Boris Weisfeiler’s disappearance

From Olga Weisfeiler:

Today brought big news from Chile regarding my brother’s disappearance. After many many years of frustration, arrest warrants have been issued for 8 police and military officers for the kidnapping and enforced disappearance of my brother, who went missing in 1985.

A briefing should be up on NYT shortly.
For more information on the case itself, please see http://boris.weisfeiler.com
For all those who have supported the efforts over the years, a very big thank you!
best,
Olga

 

Posted by: Alexandre Borovik | July 22, 2012

Women in the violent world of mathematics

I refer to my old post Women and mathematics in relation to the caustic comic strip by Zach Weiner. Both my post (which later became a section in my book Mathematics under the Microscope) and Weiner’s cartoons are about the place of a woman in the violent world of mathematics and about men’s perception of women’s place. If you think that this is an exaggeration then read comments to my post, like this one, from a female colleague:

As one of the few female mathematicians in Alexandre’s field I think he is correct.

You probably have to be a research mathematician to understand what he is saying about being bold, needing intellectual independence, the psychologically charged and tense discourse and everyone looking and acting as if they are going to get into a fist fight any moment.

This is typically not how women behave and when a woman does act like this (learned or natural) she gets all sorts of criticism for not being the sweet docile soft person she looks like. And all too often the criticism is from other women, not just from men.

Or this comment, sent to me in response to my book and published in the Addenda and Comments:

Part of my anger and frustration at school was that so much of this subject
that I loved, mathematics, was wasted on what I thought was frivolous or
immoral applications: frivolous because of all those unrealistic puzzles,
and immoral because of the emphasis on competition (Olympiads, chess, card
games, gambling, etc). I had (and retain) a profound dislike of
competition, and I don’t see why one always had to demonstrate one’s
abilities by beating other people, rather than by collaborating with them.
I believed that “playing music together”, rather than “playing sport against
one another”, was a better metaphor for what I wanted to do in life, and as
a mathematician.

Indeed, the macho competitiveness of much of pure mathematics struck me very
strongly when I was an undergraduate student: I switched then to
mathematical statistics because the teachers and students in that discipline
were much less competitive towards one another. For a long time, I thought
I was alone in this view, but I have since heard the same story from other
people, including some prominent mathematicians. I know one famous category
theorist who switched from analysis as a graduate student because the people
there were too competitive, while the category theory people were more
co-operative.

It may be worth mentioning that I am male. In other words, a dislike of competitiveness is not confined to women. The
statistics department I entered as an undergraduate, for example, had no
women in it, yet was much less competitive than the pure mathematics
department (which had once been headed by a woman). I think it is
disciplinary tradition rather than gender that is the key factor here.

I am now a Computer Scientist. I have also found differences in the competitiveness of people in different sub-domains of CS.
To generalize greatly, I have found people in Artificial Intelligence (AI)
much less macho and competitive than those in (say) Algorithm and Complexity
Theory. Within AI, people in (say) Argumentation are generally much less
macho and competitive than those in Game Theory and Mechanism Design. In each
case, the more formal and mathematical the domain, the more competitive it
tends to be. It could be that these domains have acquired their cultures
from mathematicians, while the other domains have been less influenced by
the culture of mathematics.

Press release from Association for Psychological Sciences:

From factory workers to Wall Street bankers, a reasonable proficiency in math is a crucial requirement for most well-paying jobs in a modern economy. Yet, over the past 30 years, mathematics achievement of U.S. high school students has remained stagnant — and significantly behind many other countries, including China, Japan, Finland, the Netherlands and Canada.

A research team led by Carnegie Mellon University’s Robert Siegler has identified a major source of the gap — U. S. students’ inadequate knowledge of fractions and division. Although fractions and division are taught in elementary school, even many college students have poor knowledge of them. The research team found that fifth graders’ understanding of fractions and division predicted high school students’ knowledge of algebra and overall math achievement, even after statistically controlling for parents’ education and income and for the children’s own age, gender, I.Q., reading comprehension, working memory, and knowledge of whole number addition, subtraction and multiplication. Published in Psychological Science, a journal of the Association for Psychological Science, the findings demonstrate an immediate need to improve teaching and learning of fractions and division.

“We suspected that early knowledge in these areas was absolutely crucial to later learning of more advanced mathematics, but did not have any evidence until now,” said Siegler, the Teresa Heinz Professor of Cognitive Psychology at Carnegie Mellon. “The clear message is that we need to improve instruction in long division and fractions, which will require helping teachers to gain a deeper understanding of the concepts that underlie these mathematical operations. At present, many teachers lack this understanding. Because mastery of fractions, ratios and proportions is necessary in a high percentage of contemporary occupations, we need to start making these improvements now.”

The research, supported by grants from the U.S. Department of Education’s Institute of Education Sciences and by the National Science Foundation’s Developmental and Learning Science Group at the Social, Behavioral, and Economic Directorate, was conducted by a team of eight investigators: Siegler; U.C. Irvine’s Greg J. Duncan; the University of Michigan’s Pamela E. Davis-Kean, Maria Ines Susperreguy and Meichu Chen; the University of London’s Kathryn Duckworth; the University of Chicago’s Amy Claessens; and Vanderbilt University’s Mimi Engel.

For the study, the team examined two nationally representative data sets, one from the U.S. and one from the United Kingdom. The U.S. set included 599 children who were tested in 1997 as 10-12 year-olds and again in 2002 as 15-17-year-olds. The set from the U.K. included 3,677 children who were tested in 1980 as 10-year-olds and in 1986 as 16-year-olds. The importance of fractions and division for long-term mathematics learning was evident in both data sets, despite the data being collected in two different countries almost 20 years apart.

“This research is a good demonstration of what collaborations between psychologists, economists, public policy analysts and education scientists can create,” said Davis-Kean, associate professor of psychology at Michigan. “Instead of relying on results from a single study, this study replicates findings across two national data sets in two different countries, which strengthens our confidence in the results.”

Rob Ochsendorf, program officer for special education research at the U.S. Department of Education’s Institute for Special Education Research added, “This study is critical for providing empirical and general confirmation of the crucial role of division and fractions proficiency for long-term success in mathematics for all students. The results provide important cues to educators and researchers regarding the skills that are ripe for intervention in order to improve overall mathematics achievement in the U.S.”

For more information, watch this short video of Siegler discussing the study and its implications:http://youtu.be/7YSj0mmjwBM.

###

For more information about this study, please contact: Robert S. Siegler at rs7k@andrew.cmu.edu.

The APS journal Psychological Science is the highest ranked empirical journal in psychology. For a copy of the article “Early Predictors of High School Mathematics Achievement” and access to other Psychological Scienceresearch findings, please contact Anna Mikulak at 202-293-9300 or amikulak@psychologicalscience.org.

With thanks to muriel

Posted by: Alexandre Borovik | June 6, 2012

About learning by heart

Vladimir Radzivilovsky:

The brain is like the stomach: it can digest only stuff which is already inside.

 

Posted by: Alexandre Borovik | April 11, 2012

Recommend

  http://www.thebigquestions.com/2012/03/26/loose-ends/
Posted by: Alexandre Borovik | April 1, 2012

Felix Klein, who did for the bottle …

A bizarre phrase in an otherwise quite sensible article in the NYT:

Felix Klein, who did for the bottle what August Ferdinand Möbius had done for the strip …

[With thanks to muriel]

Posted by: Alexandre Borovik | March 22, 2012

Liar’s paradox

From a letter from a colleague:

I am reminded of a commentary on logic puzzles of a certain kind; it
was perhaps in a letter to Martin Gardner, reprinted in one of his
books. The puzzles are those about getting about on an island where
each native either always tells the truth or always lies. You reach a
fork in the road, for example, and a native is standing there, and you
want to learn from him, with one question, which way leads to the
village. The “correct” question is “If I asked you if the left way
led to the village, would you say yes?” But why should the native’s
concept of lying conform to our own logical ideas? If the native is a
liar, it means he wants to fool you, and your logical trickery will
not work. The best you can do is say something like “Did you hear
they are giving away free beer in the village today?” and see which
way the native runs. You follow him, even if he says something like
“Ugh, I hate beer!” since then he probably really is lying.

Posted by: Alexandre Borovik | March 19, 2012

Previously unpublished manuscript by Boris Weisfeiler

Boris WeisfeilerOn the size and structure of finite linear groups,  http://arxiv.org/abs/1203.1960

This is a nearly complete, previously unpublished manuscript by Boris Weisfeiler. The results were announced by him in August 1984. Soon after, in early January 1985, he disappeared during a hiking trip in Chile.

The investigation into Boris Weisfeiler disappearance is still ongoing in Chile, see http://www.weisfeiler.com/boris

Posted by: Alexandre Borovik | February 25, 2012

Girls’ Verbal Skills Make Them Better At Arithmetic

Another finding, which appears to contradict a previous post:

While boys generally do better than girls in science and math, some studies have found that girls do better in arithmetic. A new study published in Psychological Science, a journal of the Association for Psychological Science, finds that the advantage comes from girls’ superior verbal skills.
“People have always thought that males’ advantage is in math and spatial skills, and girls’ advantage is in language,” says Xinlin Zhou of Beijing Normal University, who cowrote the study with Wei Wei, Hao Lu, Hui Zhao, and Qi Dong of Beijing Normal University and Chuansheng Chen of the University of California-Irvine. “However, some parents and teachers in China say girls do arithmetic better than boys in primary school.”
Zhou and his colleagues did a series of tests with children ages 8 to 11 at 12 primary schools in and around Beijing. Indeed, girls outperformed boys in many math skills. They were better at arithmetic, including tasks like simple subtraction and complex multiplication. Girls were also better at numerosity comparison—making a quick estimate of which of two arrays had more dots in it. Girls outperformed boys at quickly recognizing the larger of two numbers and at completing a series of numbers (like “2 4 6 8”). Boys performed better at mentally rotating three-dimensional images.
Girls were also better at judging whether two words rhymed, and Zhou and his colleagues think this is the key to their better math performance. “Arithmetic and even advanced math needs verbal processing,” Zhou says. Counting is verbal; the multiplication table is memorized verbally, and when people are doing multiple-digit calculations, they hold the intermediate results in their memory as words.
“Better language skills could lead to more efficient verbal processing in arithmetic,” Zhou says. He thinks it might be possible to use these results to help both boys and girls learn math better. Boys could use more help with verbal strategies for learning math terms, while girls might benefit from more practice with spatial skills.

[with thanks to muriel]

Posted by: Alexandre Borovik | February 25, 2012

Alan Turing and Linear Algebra

2012 is Alan Turing Year but perhaps I have missed a chance to attract attention of my colleagues who, like me, teach undergraduate linear algebra to a significant fact in history of linear algebra which is worth mentioning to students:

LU decomposition of matrices (and, within the routine, systematic use of elementary matrices) was introduced in Alan Turing‘s paper [1948] which was motivated, in Alan Turing’s own words, by

“the advent of electronic computers“.

I told the story to my students in my lecture on Wednesday. Since the idea that

“The process of replacing the rows of a matrix by a linear combination of other rows may be regarded as left-multiplication of the matrix by another matrix, this second matrix having coefficients which describe the linear combinations required” [1948, p. 290]

comes forth at early stages of modern expositions of linear algebra, this semester’s courses are likely to pass the point when history of LU decomposition could be usefully mentioned. But maybe it is not too late to do that in linear algebra courses taught in the Autumn.

[1948] A. M. Turing, Rounding-off errors in matrix processes. Quart. J Mech. Appl. Math. 1 (1948), 287–308.

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