Mathematical flexibility

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 flexibil...

Full description

Bibliographic Details
Main Author: Matthew, Giammarino
Language:English
Published: University of British Columbia 2010
Online Access:http://hdl.handle.net/2429/28459
id ndltd-UBC-oai-circle.library.ubc.ca-2429-28459
record_format oai_dc
spelling ndltd-UBC-oai-circle.library.ubc.ca-2429-284592018-01-05T17:24:36Z 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. Education, Faculty of Educational and Counselling Psychology, and Special Education (ECPS), Department of Graduate 2010-09-13T14:58:15Z 2010-09-13T14:58:15Z 2010 2010-11 Text Thesis/Dissertation http://hdl.handle.net/2429/28459 eng Attribution-NonCommercial-ShareAlike 3.0 Unported http://creativecommons.org/licenses/by-nc-sa/3.0/ University of British Columbia
collection NDLTD
language English
sources NDLTD
description 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. === Education, Faculty of === Educational and Counselling Psychology, and Special Education (ECPS), Department of === Graduate
author Matthew, Giammarino
spellingShingle Matthew, Giammarino
Mathematical flexibility
author_facet Matthew, Giammarino
author_sort Matthew, Giammarino
title Mathematical flexibility
title_short Mathematical flexibility
title_full Mathematical flexibility
title_fullStr Mathematical flexibility
title_full_unstemmed Mathematical flexibility
title_sort mathematical flexibility
publisher University of British Columbia
publishDate 2010
url http://hdl.handle.net/2429/28459
work_keys_str_mv AT matthewgiammarino mathematicalflexibility
_version_ 1718582625863467008