
06514357
j
2016a.00313
Sollervall, H{\aa}kan
Stadler, Erika
Validating affordances as an instrument for design and a priori analysis of didactical situations in mathematics.
Int. J. Math. Teach. Learn. 2015, 23 p., electronic only (2015).
2015
Centre for Innovation in Mathematics Teaching (CIMT) at Plymouth University, Plymouth; Mathematics Education Department at College of Ny\'{\i}regyh\'aza, Ny\'{\i}regyh\'aza
EN
D40
G60
D20
teaching methods
mathematical concepts
trigonometry
affordances
didactical situations
designbased research
validity
http://www.cimt.plymouth.ac.uk/journal/sollervall.pdf
Summary: The aim of the presented case study is to investigate how coherent analytical instruments may guide the a priori and a posteriori analyses of a didactical situation. In the a priori analysis we draw on the notion of affordances, as artefactmediated opportunities for action, to construct hypothetical trajectories of goaloriented actions that have not yet been initiated by an actor. These hypothetical action trajectories guide the design of a didactical situation, involving trigonometry in triangles and on the unit circle, for the specific purpose of illuminating how students in Swedish upper secondary school handle conceptually challenging tasks without making use of calculators. The a posteriori analysis puts corresponding focus on the actions that students have actually engaged in with respect to the available artefacts. We conclude that affordances, when embedded in the presented methodological framework, may be considered as a scientifically valid instrument for designing and evaluating didactical situations in mathematics.