CTK Insights

27 Apr

Poincaré And Standardized Testing

Henri Poincaré (1854-1912) was a teenager during the Franco-Prussian war. He taught himself German in order to keep abreast of the news [Ayoub, 17-18]:

Opponents of standardized tests would be interested to know that after achieving fame, he agreed to take the Binet test whose use was becoming more widespread; he performed abominably!

According to E. T. Bell, Poincaré's test performance was that of an imbecile. Speaking for himself, Poincaré (whom E. T. Bell identified as the Last Universalist) freely admitted [Ayoub, 22] to being absolutely incapable of doing addition without mistakes.

Poincaré had a life-long interest in psychology and philosophy of science. In a 1908 lecture L'invention mathématique whose translation form the second chapter in Musings of the Masters, Poincaré a mathematician's road to invention, mainly from his own experience. But he starts with wondering "How does it happen that there are individuals who do not understand mathematics?" He further writes:

That not everyone is capable of invention is not in the least mysterious. That not everyone can retain a proof that they once learned is also understandable. But that not everyone can understand a mathematical argument when we explain it, that is what is most surprising if we think about it. Besides, those who cannot follow this reasoning except with great difficulty are the majority (the emphasis is mine, AB): that is undeniable and the experience of secondary school teachers would certainly not contradict me.

What is significant to me in this quote is that the difficulty of the majority of students in studying mathematics has been observed more than a hundred years ago. It's not a new phenomenon at all. New educational policies come about regularly, with unflinching authority. The process goes on for more than a hundred years (math associations began cropping up late in the 19th century with the purpose of improving math education). One question I have not seen addressed is why there is no coherent reports of effects a particular twist in math education had on students performance. Moreover, it appears that positive experiments, like those of Harold Fawcett and Louis Benezet, continue to be ignored by the subsequent generations of educational policy makers.

Instituting high stakes tests and stringent algebra requirements seem to me as the proverbial attempts of beating a dead horse. Among the present day experiments is the success of the educational reform in Finland that, too, I am afraid, are going to be unheeded by our educators and politicians.


  1. E. T. Bell, Men of Mathematics, Touchstone Books, 1986
  2. R. G. Ayoub (editor), Musings of the Masters, MAA 2004

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