“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!
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 …
Mastering and using algorithms involves a special and important kind of thinking.
“is to enable individuals to continue their education.”
[With thanks to muriel]
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.