#3: Bharath Sriraman
Handbook of the Mathematics of the Arts and Sciences
Bharath Sriraman, University of Montana- Missoula
Abstract: This Handbook aims to become a definitive source with chapters that show the origins, unification, and points of similarity between different disciplines and mathematics. The seven sections in this book explore: Mathematics and Architecture; Mathematics, Biology and Dynamical Systems; Mathematics, Humanities and the Language Arts; Mathematics, Art and Aesthetics; Mathematics, History and Philosophy; Mathematics in Society; and New Directions. Science and Art are used as umbrella terms to encompass the physical, natural and geological sciences, as well as the visual and performing arts.
Keywords: Mathematics and Architecture; Mathematics and Dynamical Systems; Mathematics and Humanities; Mathematics, Art and Aesthetics; Mathematics, History and Philosophy
AMS Subject Classification: 00
#2: Bharath Sriraman
On Measures of Measurement and Mismeasurement: A commentary on Planning and Assessment
Bharath Sriraman, University of Montana - Missoula
Abstract: In this commentary the six Canadian chapters on planning and assessment in mathematics are critiqued. Some common strands are discussed on what entails a measurable item in mathematics assessments at the secondary school level. Implications are made for teachers.
Keywords: Learning; Teaching; Mathematical Memory; Testing; Rubrics; Assessment
AMS Subject Classification: 097D60
#1: Bharath Sriraman, Per Haavold
Reconciling the Realist/Anti Realist Dichotomy in the Philosophy of Mathematics
University of Montana
University of Tromso, Norway
In the philosophy of mathematics, the realist vs. anti-realist debate continues today with differing positions on the status of mathematical objects. For realists, objects sit in “Plato’s heaven”, immovable, objective, eternal, and we contemplate them, whereas anti-realists (or Constructionists) are the opposite, and emphasize epistemology over ontology, saying that we construct mathematical objects. There are numerous results in mathematics which can be arrived at both from a realist and an anti-realist viewpoint. In other words, they can be contemplated (proved) via methods deemed unsuitable by anti-realists- or simply arrived at it through methods (or construction) as the anti-realist would say. In this chapter, we argue that realism and anti-realism can be seen as two sides of the same coin, or different ways of knowing the same thing, and therefore the so called dichotomy between these positions is reconcilable for particular mathematical objects.
Keywords: Intuitionism - Constructionism - Realism - Platonism - Anti-realism - Brouwer - Constructive mathematics - Philosophy of mathematics
AMS Subject Classification: 03A, 03F