UBC Theses and Dissertations
Mathematical flexibility Matthew, Giammarino
Mathematicians, mathematics researchers and educators are now arguing that an essential aim of mathematics education should be to equip students so they can adapt to new mathematical situations and use mathematics to solve authentic problems that arise in day-to-day life. This, mathematical flexibility – defined here as adaptation when dealing with number, magnitude or form – is important to mathematics researchers and educators, but the classroom context may not always promote flexibility. Building across converging lines of cognitive, social-psychological, and neuro-biological research, this study investigated whether mathematical flexibility might be profitably understood as a network of functional components. This study was designed to: 1) investigate the functional components of mathematical flexibility and contrast them with functional components of mathematical competence; and 2) evaluate the effectiveness of a network approach for understanding the relationship between environmental and individual components of mathematical flexibility. Results indicated that flexibility appeared to be associated with network activity which co-activated two or more other networks, while competence appeared to be characterized by a series of network activations which occurred individually and in sequence. Further, results suggested that the case study approach used here to identify network activity could reveal meaningful dynamics in network activity, and these dynamics could be related to flexible or competent performance. Implications for researchers and practitioners are identified in the discussion. However, because this study was constrained by the ways in which flexibility was conceptualized and features of the methodology, limitations and directions for future research are also suggested.
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