December 26, 2014

The law of excessive gardening in education

Once upon a time. the term proletarian (or a Latin equivalent) used refer to  a Roman citizen who was so poor that he only had his children considered as his property. The term proles stands here for descendants (or litter). The term evolved through Marxism, to workers without capital or production means, who should sell their own work-force. The term can be somehow extended to the loss of knowledge of the production tools. An example lies in the comparison between the craftsman or artisan, who masters his tools, and may even be able to repair them, and manages a series of processes, as opposed to the factory worker, whose work has been taylorized and who lacks of knowledge in the whole meaning of the chain, or the functioning of the robots he "controls".

The concept of proletarianization has been used more recently by Bernard Stiegler (Ars Indutrialis), to describe a pauperization, not in terms of wealth, but in terms of ability to do, to make and to live. An externalization and therefore a loss of knowledge and memory. 

I believe proletarianization, in that sense, is rampant, and pervades all strata of the society: at every level of work, at least in institutions or companies, there is a loss of sense and understanding about the way stuff works. A corollary to Peter's principle. To make a long story short, strategic visions have progressively been replaced by indicator-based management. In science evaluation, the infamous impact factor or h-index are examples of such indicators. Stock-value and quality-based management are other examples. 
Peter's principle: (success>advancement)^n>failure

The top of proletarianization spread was given by Alan Greenspan, the former chairman of the Federal Reserve, who once told the CNBC that he did not fully understand the scope of the subprime mortgage market until well into 2005 and could not make sense of the complex derivative products created out of mortgages. Alan Greenspan, the chief banker of the world, was mystified...

So what's got the maths to do with it?

About two years ago, in April 2012, there was a conference called Fixing mathematical education. There i learned the effective law of excessive learning in mathematics from Alexandre V. Borovik:
To be able to use maths at certain level it is necessary to learn it at the next level
A week ago, Alexandre Borovik sent me a link to his preprint, Calling a spade a spade: Mathematics in the new pattern of division of labour:
The growing disconnection of the majority of population from mathematics is becoming a phenomenon that is increasingly difficult to ignore. This paper attempts to point to deeper roots of this cultural and social phenomenon. It concentrates on mathematics education, as the most important and better documented area of interaction of mathematics with the rest of human culture.
    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. 
The pdf is here. Alexandre claims that "The communist block was destroyed by a simple sentiment: If they think they pay me let them think I am working. Mathematics education in the West is being destroyed by a quiet thought (or even a subconscious impulse): If they think they teach me something useful, let them think I am learning." My experience as a part-time teacher is that it is increasingly difficult to have students learn things. Most of them are especially disgusted by the concept of "learning by heart" (wait, everything is in the Internet, isn't it?). While they could just try to understand. 

For a long time,  people could have proudly claimed that "I have never been good at mathematics, but I live happily without it". The XXth century has been rich in discoveries that have both pervaded the society (basically, from the transistor to the mp3). The pitfall is many users have no idea about the way these technologies work, and happily put their agenda, thoughts, entertainment time and finally life (pictures, films) in those hands. 

The world seemingly grows a local era where data becomes important (a new gold, a novel oil?) and big data or data science are slowly emerging as potentially disruptive technologies. Then, Alexandre states that "the West is losing the ability to produce competitively educated workers for mathematically intensive industries". It is high times to rethink (mathematical) education, as its changes may be much slower than the present evolution of technologies. 

Nota bene: and Igor, just for you, there is a phase transition ("The crystallisation of a mathematical concept (say, of a fraction), in a child's mind could be like a phase transition in a crystal") and an aha moment ("An aha! moment is a sudden jump to another level of abstraction")