Academic journal article Australian Mathematics Teacher

Mathematical Fiction: Its Place in Secondary-School Mathematics Learning

Academic journal article Australian Mathematics Teacher

Mathematical Fiction: Its Place in Secondary-School Mathematics Learning

Article excerpt

When a television series like Numb3rs (Falacci et al., 2005) is considered worthy of discussion at a recent National Council of Teachers of Mathematics (NCTM) conference it is time to take mathematical fiction seriously. Increasingly, film producers and directors are employing mathematicians as film and television consultants--they really want to get the mathematics right, and they are also using universities like Harvard (A Beautiful Mind) and Caltech (Numb3rs) as locations. In the past successful films or television series have led to a significant upsurge in the numbers of students who opt for various majors, including mathematics, at universities (Devlin, 2005).

This article contains a small selection of mathematical fiction chosen with the teaching of mathematics in secondary school in mind. An attempt is made to classify the works and provide a few ideas about how these items may be used by mathematics teachers, sometimes, but not necessarily, in collaboration with science and humanities teachers, to introduce, teach and supplement mathematics learning (for example, in the discussion of mathematical applications) in secondary schools. The selection includes some simple yet effective picture books and some quite sophisticated ones, film, and a television series.

Traditionally, good primary teachers have known of many ways mathematical fiction, mainly picture books, can be employed in the classroom to engage children in mathematical thinking (Padula, 2004). Senior students can learn mathematics from novels, plays, screenplays and film (Padula, in press). Secondary teachers, although aware of many works of science fiction, may not be as aware of the wider genre: mathematical fiction, defined as science in fiction and including science fiction by Kasman (2005).

There are not very many papers published on the subject but Sriraman (2003) claims that literature can be used to teach cross-disciplinary skills by providing a context for critical thinking, for example: the process of making valid inferences, and problem solving, as well as introducing very sophisticated mathematical ideas. The author relates such positive outcomes from using Abbott's (1932) Flatland in a beginning algebra course with 13-14 year-old students.

Sriraman (2004) also found that when the question, "Is mathematics real?" was posed by a student after studying the first five chapters of Flatterland (sequel to Flatland; Stewart, 2001) that (American) ninth graders could even discuss mathematical philosophy at an elementary level. With these chapters they could also explore mathematics problems, further their understanding of dimension and gain a deeper understanding of fractal geometry.

There are at least seven kinds of fiction suitable for the teaching and learning of real mathematics in secondary school.

Mathematical fiction classics

Flatland by A. Square (Abbott, 1884), The Time Machine by H. G. Wells (1895) and What the Tortoise Said to Achilles by Lewis Carroll, 1894 (a humorous tilt at Zeno's paradox; Guedj, 1998) are all examples of literature with mathematics as one of its major themes.

As Stewart remarks in the Preface of his notes on Flatland, the book

   is a charming, slightly pedestrian tale of
   imaginary beings: polygons who live in the
   two-dimensional universe of the Euclidean
   plane. Just below the surface, though, it is a
   biting satire on Victorian values--especially
   as regards women and social status--and
   an accomplished and original piece of scientific
   popularisation about the fourth
   dimension (Abbott & Stewart 2002, p. ix).

Flatland is a guide to the geometry of space-time and relativity, and a clever social commentary (Renz, 2002). Very much tongue-in-cheek, Abbott's book must be among the first mathematical-fiction books by a man with a decidedly feminist perspective. It is a classic that has lasted, because, as Stewart states (Abbott & Stewart, 2002), a twenty-first century reader can identify with "A. …

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