Beauty Functionality Power to express succinctly Power to generalise Abstraction Geometric Numeric Infinity Logic Statistical Limits Simplicity Complexity A language Algebraic Infinitessimals Graphs Power to explain Proof Probability Calculus Structures
Pring Carr and Kemmis Lincoln and Guba How does mathematics education fit within here? Davis & Hersch
What are your epistemological and ontological positions?
What kinds of ethical issues are likely to be involved?
What kinds of knowledge? What IS? Do you seek objectivity? What kinds of interpretations are likely to be involved and how do you expect to deal with them? What questions of bias might arise? Do you expect to address human issues and values, and if so what is your stance on these?
‘ the study of a social situation with a view to improving the quality of action within it’. It aims to feed practical judgement in concrete situations, and the validity of the ‘theories’ or hypotheses it generates depends not so much on ‘scientific’ tests of truth, as on the usefulness in helping people to act more intelligently and skillfully …. In action research ‘theories’ are not validated independently and then applied to practice. They are validated through practice’ (1991, p. 69).
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