A couple days ago, I non-responded to the release of the 2023 PISA results (because, this). In a comment on that post, Tony Gardiner referred to a paper he had written for ICME10, held in 2004. In that paper, Tony claims, he “worked really hard … and totally failed” to make sense of “mathematical literacy”, one of the core nonsenses of PISA. Failure or otherwise, I think it’s a great paper, and Tony has kindly given permission to reproduce it here (and the PDF is here).
What is mathematical literacy?
University of Birmingham, UK
Freedom is the freedom to say that two plus two makes four.
If that is granted, all else follows. (George Orwell, 1984)
My goal is to explore the relationship between
Mathematics and “mathematical literacy”
in a way that might provoke a critical analysis of the many appealing, but often rather vague, claims made by the advocates of “mathematical literacy”. My hope is that this might help those in other countries to avoid some of the pitfalls that have characterized developments in England in the last 25 years, where a similar paradigm-shift occurred after the publication of the Cockcroft report (Cockcroft, 1982).
Mathematics is more permanent than perhaps any other human cultural activity. In contrast, in many western democracies concern about “mathematical literacy” (ML) is of relatively recent origin. Mathematics and mathematics education inhabit different worlds. The mathematical universe may be more permanent than that of mathematics education, but mathematicians have to accept that its principles and insights need to be mediated in various ways before they can become an effective part of the world of mathematics education. Similarly, if mathematics education in general – and ML in particular – are to benefit from their association in the public mind with the objective universe of “mathematics”, they are obliged to represent that universe faithfully when mediating its subject matter for the more pragmatic world of schools, of teachers and students, of politicians and bureaucrats, of curricula and examinations. Thus, in seeking to find improved approaches to elementary mathematics, we are not “free” to replace its objective character by something more “user-friendly”, but are obliged to respect the fundamental nature of the discipline.
In Peter Shaffer’s play Amadeus, Mozart represents God (or here Mathematics, the eternal), while Salieri represents Mammon (for us “mathematical literacy” – the transient). Salieri is “flavour of the month”, but his influence is short-term and superficial. In contrast, Mozart represents the nearest that Man can come to God. In Shaffer’s play Salieri understands this contrast perfectly well, and resents it bitterly:
“God needed Mozart to let himself into the world.
And Mozart needed me [Salieri] to get him worldly advancement.”
Salieri consistently exploits his temporal influence to cut the “God” Mozart down to size:
“What use, after all, is Man, if not to teach God his lessons?”
Salieri clearly understands the perfection of Mozart’s art and the relative crassness of the world’s judgement. After the first performance of The Marriage of Figaro he muses:
“Could one catch a realer moment? …
The disguises of opera had been invented for Mozart …
The final reconciliation melted sight.
Through my tears I saw the Emperor yawn.”
Emperor [coolly]: “Most ingenious Mozart. You are coming along nicely.”