My new preprint:
I argue that new patterns of division of labour have dramatically changed the nature and role of mathematical skills needed for the labour force and correspondingly changed the place of mathematics in popular culture and in the mainstream education. The forces that drive these changes come from the tension between the ever deepening specialisation of labour and ever increasing length of specialised training required for jobs at the increasingly sharp cutting edge of technology.
Unfortunately these deeper socio-economic origins of the current systemic crisis of mathematics education are not clearly spelt out, neither in cultural studies nor, even more worryingly, in the education policy discourse; at the best, they are only euphemistically hinted at.
This paper is an attempt to describe the socio-economic landscape of mathematics education without resorting to euphemisms.
Alexander Shen, Основания теории вероятностей и колмогоровская сложность.
(Foundations of probability theory and Kolmogorov complexity).
“In the experiment, 288 community-college students enrolled in developmental math were randomly assigned, at the beginning of the semester, to read one of two articles. The control group read a generic article about the brain. The treatment group read an article that laid out the scientific evidence against the entity theory of intelligence. “When people learn and practice new ways of doing algebra or statistics,” the article explained, “it can grow their brains — even if they haven’t done well in math in the past.” After reading the article, the students wrote a mentoring letter to future students explaining its key points. The whole exercise took 30 minutes, and there was no follow-up of any kind. But at the end of the semester, 20 percent of the students in the control group had dropped out of developmental math, compared with just 9 percent of the treatment group. In other words, a half-hour online intervention, done at almost no cost, had apparently cut the community-college math dropout rate by more than half.”
An article by Peter Gray in The Independent. Full title: Give childhood back to children: if we want our offspring to have happy, productive and moral lives, we must allow more time for play, not less.
I’m lucky. I grew up in the United States in the 1950s, at the tail end of what the historian Howard Chudacoff refers to as the “golden age” of children’s free play. The need for child labour had declined greatly, decades earlier, and adults had not yet begun to take away the freedom that children had gained.
It tantalisingly hints at a possibility of analysis of socio-economic undercurrents that “take away the freedom that children had gained”.
Students in my class raised the issue of self-referential paradoxes, and the old classics came to my mind:
“Now is not the time for sound-bites. I can feel the hand of history on
(Tony Blair on TV, arriving in Belfast for the final stage of the Northern Irish negotiations, 8 April 1998
The most fantastic thing is that it was not a slip of tongue, it was written by Tony Blair a day before, as could be seen from Alistair Campbell diaries:
Tuesday, April 7, 1998
Mitchell finally tabled his paper around midnight . . . On the plane (to Belfast) we went through the paper in some detail . . . TB [Tony Blair] was a bit fed up with it because he and Bertie had not actually negotiated all this, but Mitchell insisted it was all in there . . . I drafted a few lines, but he pretty much did his own thing. This is not a time for sound bites but I feel the hand of history upon my shoulder.
Hell of a sound bite.
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.
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!