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Mathematics, imagination and reality. The legacy of Emma Castelnuovo

Mathematics, imagination and reality. The legacy of Emma Castelnuovo

Last April 13, Emma Castelnuovo, aged 100, a leading mathematics educator, passed away. In order to present the legacy of Emma Castelnuovo’s thought, ResearchItaly has interviewed Nicoletta Lanciano (in the picture), her disciple and collaborator, a professor in Science Education at the Sapienza University in Rome and a member of the Movement of Educational Cooperation.

Emma Castelnuovo's ideas and experiments have inspired new important methods to teach mathematics, since the late 1970s. Her study activity has been intertwined with her intense personal life, also during the darkest moments of the Twentieth Century.
Being of Jewish origins, Emma was born in Rome in 1913. Graduated in Mathematics, under the racial laws she was fired by the University of Rome. After surviving persecutions, following Liberation Day, she chose to commit to teaching at junior high schools, as well as to research and investigation in the field of education that culminated in a rich publishing and congress activity as well as international assignments.

Prof. Lanciano, Emma Castelnuovo conceived learning as an experimental and operative process that proceeds from the concrete to the abstract. In this perspective, does study activity share common features with research and investigation activity?

Emma Castelnuovo’s perspective, regardless of formalisms, allows children to freely build their own knowledge by using individual direct observation, fantasy and imagination. In this perspective, school encourages children to use a process similar to that used by mathematicians in their research, where the “ability to see” always precedes any systematization processes. At Emma Castelnuovo’s school, work in the classroom starts with the observation of concrete shapes, moving objects – e.g. shadows moving on the classroom floor guided by sun rays traveling through the window – and leaves children free to imagine, giving them time to follow their thoughts and to continue unbridled along a path that brings them to a dead end, as it sometimes happens during research activity, or to an unexpected outcome, e.g. the “discovery” of an unknown property, before someone else tells them about it.

The link between mathematics and reality is a key topic developed by Castelnuovo that is still up-to-date. Mathematics is considered as an abstract discipline by most people. But its applications in a number of research fields – from medicine to engineering, to space – have a direct impact on our lives... Don’t they?

Applications of mathematics have not only an impact on, but also roots in, everyday life. From this point of view, Emma Castelnuovo’s school is a school of the truth where questions are asked about things students are interested in, because they rise from the observation of the surrounding world – environment, art, architecture – seen through different eyes.
An example? Studying the forms of a monument like the Pantheon, that is considered as a giant mathematical object made by a cylinder and a hemisphere or... bridges, that are very much present in the architecture of Rome. Emma Castelnuovo paid great attention to how the shapes of these structures, and their constituent elements, have changed over the various ages, according to the way they were built and the materials used.

In Italy, the percentage of graduates in scientific disciplines is lower than the European average and the number of Italian researchers is lower than that of the big industrial economies, as recently highlighted in the Anvur Report. In order to invert the course, how shall we revise the way science is taught at school?

As I see it, this can be achieved by avoiding to propose a pre-set knowledge and leaving students free to use their imagination and think by themselves. This is a challenging job for teachers who, in order to serenely address all the changes the society puts in front of them, must count on an adequate training, not feeling alone, but supported by reference groups within which they can consult and compete.
It is crucial to enchance the social role of teachers who are the cornerstone of school and education in an ever-changing world.

Publication date 04/29/2014