“The Play’s the Thing”: Mathematization as Dramatization

Mobilizing prevalent themes in the fields of mathematics education, literary criticism, and philosophy, this paper contextualizes ‘the mathematical’, ‘mathematical thinking’, and ‘mathematical pedagogy’ with respect to ancient Greek concept of mathesis, modern notions of mathematical agency, the Keatsian concept of negative capability, and the analogy of ‘staging’ a dramatic/mathematical ‘play’. Its central claim is that mathematization is dramatization—that learning mathematics (indeed, learning to learn, which is what the Greek mathesis actually means) is an activity of setting things up and (in this ‘set’ or ‘setting’) allowing things to play out (e-ducere). Beginning with Paul Ernest’s identification of the difference between absolutism and fallibilism in the philosophy of math education, and incorporating concepts from Pythagoras, Hippasus, Heraclitus (the ‘ancients’), Descartes, Kant, Keats (the ‘moderns’), as well as Freud, Heidegger, and Badiou (‘nos prochains’, to quote Klossowski ), we argue that ‘mathematical knowledge’ cannot be understood simply within the framework of logicism, formalism, or even simply as an epistemological articulation. Rather, we endeavour to show that the process of ‘learning mathematically’ allows us to gain insight into the foundations of ‘being’ itself (i.e. ontology). Learning to learn (mathesis) proceeds, as such, by way of staging and playing-out the half-known or unknown (the ill-seen and ill-said) in the hopes of uncovering the mystery (Greek myesis) at the heart of things.

The Jesuit Roots of Spanish Naval Education: Juan José Navarro’s Translation of Paul Hoste for the Academia de Guardias Marinas

From its origins in 1540 to its final expulsion in 1767, the far-flung Jesuit network of schools and scholars influenced the development of scientific and mathematical pedagogy in the Spanish Empire. The most important of these schools was the Colegio Imperial of Madrid where young noblemen and members of the Spanish court learned mathematics. Therefore, when Juan José Navarro, an early eighteenth-century Spanish naval officer and reformer, began to teach at the newly founded Academia de Guardias Marinas, he translated French Jesuit Paul Hoste’s L’Art des armées navales into a Spanish manuscript to serve as the basis of a curriculum on contemporary naval tactics. Navarro’s efforts highlight the continuity between the Jesuit science and mathematics of the seventeenth century and the emerging scientific institutions of the Spanish Enlightenment.

Implementing the Professional Standards for Teaching Mathematics: Supporting the Development of Mathematical Pedagogy

In the Professional Standards for Teaching Mathematics (NCTM 1991), the National Council of Teachers of Mathematics has explicated what a teacher needs to know and be able to do to teach mathematics in the spirit of reform. Teachers' current knowledge of mathematics and mathematics pedagogy may not be adequate to meet the new instructional goals. Toward this end, the Professional Teaching Standards document includes six standards that are intended to guide the preparation, support, and career development of teachers. This article focuses on one of these standards—Standard 4: Knowing Mathematical Pedagogy—which is integral to the effective teaching of mathematics.

Implementing the “Professional Standards for Teaching Mathematics”: Rethinking How We Teach: Learning Mathematical Pedagogy

A human child is at the most learning age of the most learning species that has yet evolved on this planet” (Skemp 1987, p. 101). So begins Skemp's essay titled “A New Model oflntelligence.” Skemp goes on to point out that the extent to which the learner's potential will be realized is largely dependent on the individual's teachers. In Skemp's view, teachlng is any kind of action that influences the learning process. This “learning process” is not directly observed but, warns Skemp (1987), “a person who intervenes without an adequate mental image of what is going on inside is as likely to do harm as good” (p. 101).