muriel and Scott Carter brought to my attention to a recent paper in Science, The Advantage of Abstract Examples in Learning Math, by Jennifer A. Kaminski, Vladimir M. Sloutsky and Andrew F. Heckler. It appears to make quite a splash. From abstract:
Undergraduate students may benefit more from learning mathematics through a single abstract, symbolic representation [...]
Archive for April, 2008
Quite a splash
Posted in Uncategorized on April 27, 2008 | 2 Comments »
Linear independence
Posted in Uncategorized on April 27, 2008 | Leave a Comment »
Linear independence over of numbers
is equivalent to uniqueness of decomposition of integers into a product of prime numbers. This observation, apparently, belongs to Harad Bohr.
When Language Can Hold the Answer
Posted in Uncategorized on April 23, 2008 | 2 Comments »
An enrerteining paper in the NY Times:
SCIENCE | April 22, 2008
When Language Can Hold the Answer
By CHRISTINE KENNEALLY
Does language shape what we perceive or are our perceptions pure sensory impressions?
An excerpt:
Elizabet Spaepen, a doctoral student at the University of Chicago, examined [...]
Escheresque art long before Escher
Posted in Uncategorized on April 22, 2008 | 1 Comment »
M.C. Escher was not the first who invented patterns of interlocked fish and birds.
The British Museum’ description of this object:
Length: 30.500 cm, Width: 24.300 cm, Height: 6.200 cm
Gift of Dr Bernhard Landan
Asia JA 1946.10-12.1.a-c
Lacquer document box, From Japan, Edo period, 19th century AD
The interlocking design of black crows and white egrets is very unusual, and [...]
History, Philosophy and Culture of Mathematics Seminar
Posted in Uncategorized on April 19, 2008 | Leave a Comment »
Date and time: May 15th at 4.30 for a 5pm start!
Venue: University of Manchester, Simon Building,
Brunswick Street (off Oxford Road), second floor seminar room (2.57)
Christian Greiffenhagen will present an aspect of his recent research:
Video analysis of scientific practice? An attempt to study a ‘thinking’ science.
This paper will report on my ongoing project of developing a [...]
Didactic Transformation
Posted in Uncategorized on April 19, 2008 | Leave a Comment »
The paper Mathematics, mathematicians, and mathematics education by Hyman Bass [Bull. Amer. Math. Soc. 42 no. 4 (2005) 417–430] contains a remarkably compact formulation of what makes mathematics education so special among other disciplines:
Upon his retirement in 1990 as president of the ICMI (International Commission on Mathematical Instruction), Jean-Pierre Kahane spoke perceptively of the intimate [...]
Induction over prime numbers
Posted in Uncategorized on April 18, 2008 | 5 Comments »
This was a question which intrigued me when I was a student: is there a meaningful mathematical statement about finite fields which is proven by induction on the characteristic of a field?
Finally and many years later I got a partial answer: a meaningful statement about prime numbers proven by induction on the size of prime [...]
Donald Knuth: Calculus via O notation
Posted in Uncategorized on April 14, 2008 | 47 Comments »
Continuing the theme of alternative approaches to teaching calculus, I take the liberty of posting a letter sent by Donald Knuth to to the Notices of the American Mathematical Society in March, 1998 (TeX file).
Professor Anthony W. Knapp
P O Box 333
East Setauket, NY 11733
Dear editor,
I am pleased to see so much serious attention being given [...]
Shut up and calculate
Posted in Uncategorized on April 12, 2008 | 6 Comments »
An extreme Platonist manifesto which reached me via Samizdat: Max Tegmark (MIT), Shut up and calculate, arXiv:0709.4024v1 [physics.pop-ph] 25 Sep 2007. One quote:
I argue that our universe is not just described by mathematics — it is mathematics.
Confluentes Mathematici
Posted in Uncategorized on April 11, 2008 | 1 Comment »
A new (paper) journal, Confluentes Mathematici, will specialize in transversal articles (touching at least two distinct mathematical disciplines) and survey papers. It is scheduled to be launched in March 2009.
A very good idea. A growth in highly specilaised journals is disturbing.
