Posted by: Alexandre Borovik | September 29, 2013

Photos from the FMSh

Some illustrations to my paper in The De Morgan Journal,  Free Maths Schools”: some international parallels


Mikhail Lavrentiev shows fluid mechanics experiments in a lecture for the Summer School: this rotating ring of smoke will fly across the lecture theatre without experiencing any detectable by eye resistance from the air.


The audience enthusiastically catches the rings. I am among of onlookers.


A staged publicity photograph. One of the boys is now a plasma physicist at the Columbia University.


And another one. The writing on the blackboard is taken from the mimeographed lecture notes of our physics course taught by Evgenii Bichenkov (the photographer asked us to write something  frightening).  The equations on the blackboard describe forced vibrations with damping, this is quite a canonical stuff in elementary mechanics. In the PhMSh parlance, it was called “колебалка с затухалкой”.


Evgenii Bichenkov invigilates an examination in physics.

I am present at all these photographs with the exception of the very first one.

Posted by: Alexandre Borovik | August 5, 2013

Montessori’s worst nightmare

Among horrors proudly shown at a recent conference on use of computers in mathematics education was a software package for primary school where pupils were supposed to enter numeric answers by moving, with a computer mouse, beads on a virtual number rack (two-string abacus) on the computer screen. Maria
Montessori introduced number rack for enhancing pupils’ TACTILE perception of number!

Posted by: Alexandre Borovik | July 4, 2013

Learning of mathematics is all about delayed gratification …

From Metafilter:

An old Stanford study famously found that preschoolers who could leave a marshmallow alone for 15 minutes in order to gain a second one would go on to do better at life. A new study suggests that the important factor here may not be the self control of the child, but the child’s level of trust that the second marshmallow would ever appear.

Actually, according to Wikipedia, the prequel to the original Stanford marshmallow experiment was already quite revealing:

Origins: The experiment has its roots in an earlier one performed on Trinidad, where Mischel noticed that the different ethnic groups living on the island had contrasting stereotypes of one another, specifically, on the other’s perceived recklessness, self-control, and ability to have fun. This small (n= 53) study of male and female children aged 7 to 9 (35 Black and 18 East Indian) in a rural Trinidad school involved the children in indicating a choice between receiving a 1c candy immediately, or having a (preferable) 10c candy given to them in one week’s time. Mischel reported a significant ethnic difference, large age differences, and that “Comparison of the “high” versus “low” socioeconomic groups on the experimental choice did not yield a significant difference”.  Absence of the father was prevalent in the African-descent group (occurring only once in the East Indian group), and this variable showed the strongest link to delay of gratification, with children from intact families showing superior ability to delay

And learning of mathematics is all about delayed gratification … 

Posted by: Alexandre Borovik | June 18, 2013

The Faulty Logic of the ‘Math Wars’

A brilliant opinion piece by ALICE CRARY and W. STEPHEN WILSON in the Opinion Pages of the New Your Times. A highlighted message:

Mastering and using algorithms involves a special and important kind of thinking.

Read the whole paper. It also contains a great quote from  John Dewey: the goal of education

“is to enable individuals to continue their education.”


[With thanks to muriel]

Posted by: Alexandre Borovik | June 16, 2013

Comparative linguistics, circa 1860

От того, что так много на французском языке говориться и много было хорошего писано, язык выработался очень хорошо: на нем можно выразить такие мелочные, вежливые и пустые тонкости, каких не скажешь на прямом, строгом, сильном языке, которым говорит вся Русская Земля.

Мир Божий: Руководство по русскому языку для приготовительного класса [военно-учебных заведений] / Сост. А. Разин. Спб., 1860.

Posted by: Alexandre Borovik | June 16, 2013

Mathematics Lecture in Gezi Park

Mathematics Lecture in Gezi Park

Ali Nesin is giving a mathematics lecture in Gezi Park, Monday 10 June 2013. And more photographs from Gezi Park:

Posted by: Alexandre Borovik | June 15, 2013

The origin of the Russian tradition in mathematics education

Surprise surprise, it appears to be Leonard Euler’s “Universal Arithmetic”, written by him in St Petersburg and published there in 1768 in Russian translation produced by his students:


It clearly set out standards of quality of mathematical content and enshrined the propaedeutics principle so visible in the Russian tradition: a textbook was supposed to be a stepping stone to further more advanced study.

Posted by: Alexandre Borovik | June 4, 2013

A professional skill: parsing







I am proud that, after marking 220 examination scripts in first year linear algebra , I was still able to locate, at a glance, an error in this picture — thanks to skills in parsing of meaningless symbolic input developed over many years of teaching mathematics.

Posted by: Alexandre Borovik | April 29, 2013

Andrei Zelevinsky 1/30/1953 – 4/10/2013

Andrei Zelevinsky 1/30/1953 – 4/10/2013

Posted by: Alexandre Borovik | November 25, 2012

Reading and doing arithmetic nonconsciously

Asael Y. SklarNir Levy , Ariel GoldsteinRoi MandelAnat Maril, and Ran R. Hassin, Reading and doing arithmetic nonconsciously, Published online before print November 12, 2012, doi:10.1073/pnas.1211645109,   PNAS November 12, 2012


The modal view in the cognitive and neural sciences holds that consciousness is necessary for abstract, symbolic, and rule-following computations. Hence, semantic processing of multiple-word expressions, and performing of abstract mathematical computations, are widely believed to require consciousness. We report a series of experiments in which we show that multiple-word verbal expressions can be processed outside conscious awareness and that multistep, effortful arithmetic equations can be solved unconsciously. All experiments used Continuous Flash Suppression to render stimuli invisible for relatively long durations (up to 2,000 ms). Where appropriate, unawareness was verified using both objective and subjective measures. The results show that novel word combinations, in the form of expressions that contain semantic violations, become conscious before expressions that do not contain semantic violations, that the more negative a verbal expression is, the more quickly it becomes conscious, and that subliminal arithmetic equations prime their results. These findings call for a significant update of our view of conscious and unconscious processes.

See a popular exposition in New Scientist.

« Newer Posts - Older Posts »