Susan M. C. Mac Donald: Euclid Transmogrified: A National Scandal

As the title suggests this book details a national scandal centred on Euclidean geometry in schools.Specifically, the book is concerned with changes to the geometry syllabus for the Inter.Cert.and later the Junior Cert.from the 1940s to the late 1980s and how these changes were influenced by the opinion of the Department of Education inspectorate rather than professional mathematicians and teachers.What is particularly surprising is the length of time these problems were allowed to persist across two syllabuses from the mid 1960s to the late 1980s with ramifications that extend to the present day.Mac Donald has split the book into four sections: Setting, Phase One, Phase Two, and Aftermath.The first of these, Setting, places a recently independent Ireland in a changing world mathematically when it comes to geometry education.At the time Ireland was primarily promoting the education of the Irish language and had separate Intermediate Certificate mathematics for boys and girls, with the girls' syllabus called 'Elementary Mathematics (for girls only)' and of a lower standard than the 'Mathematics' syllabus for boys.I found this to be a very interesting and accessible introduction to the state of education in Ireland post-independence.Some aspects of this will be familiar to many readers but that does not detract from the book and undoubtedly there will still be something new for everyone.At the time, an international debate was taking place about how to reform the mathematics syllabus in secondary schools.Some mathematicians endorsed models that sought to 'fix' Euclid such as Hilbert's axioms, whereas others sought to replace the geometry of Euclid with a linear algebra based approach.Georges Papy was a prominent figure in the latter movement.The Phase One section of the book outlines how the Department of Education inspectorate reacted to these international developments and the policy of the government of the day.The resulting syllabus, which Mac Donald calls Syllabus II, had some positive aspects: it removed 'Elementary Mathematics (for girls only)', it ran at a lower and higher level ensuring girls had access to the more advanced material, while less able boys could take the lower level.This also happened at a time when secondary education became free to Leaving Certificate level, and a common Intermediate Certificate was introduced for secondary and vocational schools.However, for the geometry content of Syllabus II, the inspectorate developed a hybrid system where existing aspects of Euclid ran alongside parts of Papy's mathematics.Syllabus II was met with a large number of teachers who were unfamiliar and unprepared to teach this new mathematics, while no textbook in English was available to teachers of Syllabus II until two years after its introduction.This resulted in a lot of confusion for teachers and for students.