April 26, 2012

Conference: Fixing mathematical education

[Permission to link to author slides is being asked. Stay tuned, but do not expect too much] Meanwhile, check out Simon Leys (aka Pierre Rickmans) "Le studio de l'inutilité" (or The Hall of uselessness), with a special attention to Leys' talk on 8 Nov. 2005 at l'Université catholique de Louvain, with its nice quote to Flaubert: "I have always tried to live in an ivory tower; but a tide of shit is beating at its walls, threatening to undermine it."

"Modeling is a life skill" (Solomon Garfunkel)  

"To be able to use maths at a certain level, it is necessary to learn it at the next level" (Alexandre Borovik)

 On April 4h, 2012, a meeting held in IHP, Paris. Under the motto: How to fix our math education (Comment réparer l’enseignement des mathématiques ?). The main incentive was Solomon GARFUNKEL (COMAP Inc., Boston) and David MUMFORD (Brown University) paper "How to fix our math education", New York Times, August 28th, 2011. The paper was translated in French in Le Monde (14 septembre 2011) by Jean-Michel Kantor under the same title: Comment réparer l’enseignement des mathématiques ?. Motivated by some prominence of mathematics, and bad results of France in PISA benchmarks, the conference aimed at answering the following questions:
  • does our education system answer the needs of newly opened areas in the scientific and technical realms?
  • how do we can train citizens on the present century?
Two talks were given by Sol Garfunkel (What Mathematics Do Educated Citizens Need To Know?)  and Alexandre Borovik (What do children learn when we teach them mathematics?), chaired and translated by Jean-Michel Kantor.

Both conferences were profound, lively, though provoking and entertaining, in a different style. Sol explained the motivations behind the NYT paper: the U.S. education was local to the extreme, with highly varying levels between states, counties, and even neighborhoods. Two great 4-letter sticker acronyms (NCLB: no child left behind, under G. Bush, and RTTT: race to the top, under B. Obama) have tried, and are trying, respectively, to change this local situation, by establishing nation-wide standards. The resulting goals reside in showing that mathematics are honestly (in the meaning of the honnête homme) useful and in ensuring the availability, in the future, of mathematicians and scientists. Mathematics provide a greater ability to understand (or model) the  world: "Modeling is a life skill" (SG). Sol reminded that cellphones and MRI are as much as engineering as maths. He also pointed out how operational research, computers, statistics used to belong to math departments, and have now grown into self-owned fields. He advocated the use of real-life examples graphs through mail delivery, Voronoi cells and bisectors via *** pizza delivery from Bengladesh call centers and rain falls in Colorado. Indeed, teachers tend to provide students with answers for questions they do not ask for. Looks like the following quote, inspired by Plotin, attributed to J. Lacan:  « l’amour  est  donner  ce  qu’on  n’a  pas  à quelqu’un  qui  n’en  veut  pas ». So students (and forthcoming adults) need an ability to estimate. Maths are a necessity for survival.

Alexandre Borovik drove a useful comparison between rhythm-impaired people (because of a drunk and noisy music teacher) and people who could not understand maths. Both are survivors. He considers (following Heinrich Neuhaus "the art of piano playing") that learning is an accumulation of neurological damages, reaching a threshold level. Some of us as only survivors. In a sort of Pareto-law, he tells that 95% of the population has no ideas on how 95% of the everyday stuff works, as a follow-on to the division of labor (Adam Smith, Frederick W. Taylor). He suggests re-branding maths into a tool for personal development and spiritual enhancement. Like music, not a profession, but a personal life-style. Teachers should thus be bound to the Hippocratic oath: do not arm. Which other school (mathematics including computer science) teaches "substitution of terms", at work in simple Excel sheets that provoke bracket overload (or in French "surcharge parenthétique") when three opening brackets and cell-depending operators confuse most people. Maths should be both interesting AND difficult, remember the "Law of excessive learning of mathematics": "to be able to use maths at a certain level, it is necessary to learn it at the next level".
He finally suggests teaching math bits at certain ages: maybe basic algebraic structures at 6-9 when kids are natural question-asking machines, leaving set-theoretic abstractions for teen-age, where sex hormones drive some appeal to pure idealities.

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