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Measurement Challenges in Mathematics Education Research


Callingham, R, Measurement Challenges in Mathematics Education Research, Handbook of International Research in Mathematics Education, Routledge, LD English and D Kirshner (ed), United Kingdom, pp. 462-480. ISBN 978-0415832045 (2016) [Research Book Chapter]

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Mathematics education research has developed over the last 50 years from its early grounding in psychology into a rich and diverse field of endeavor. At the same time, there is a growing international concern that we are failing the upcoming generations. In many Western countries, fewer school students are undertaking mathematics at high levels. There are calls for improved curricula, better teaching, and structural changes to education systems that will lead to more people wanting to take up mathematics teaching as a career-and a constant refrain of increased accountability. Schoenfeld (2008, p. 513) suggested that the difficulties faced by mathematics education were twofold. Internal to the field, as it expands and takes on new theories and methodologies, is the necessity to "develop and impose the highest standards for its own conduct." To meet external demands for sound and trustworthy information, the methods used should "gather evidence that provides solid warrants for the claims being made." These demands create significant challenges for mathematics education research in designing studies that are rigorous and methodologically sound, and that provide information to practitioners, including policy makers, curriculum and resources developers, teachers, parents, and their students, that meets their very diverse expectations.

At the heart of these issues is the notion of measurement. Regardless of the methodology chosen, are we truly gathering data about the intended construct-whether that be achievement or performance in mathematics, beliefs, and attitudes towards mathematics, "best practice" in classroom teaching, or curriculum materials, for example--or are we in reality addressing some other underlying characteristic or trait? A related but not trivial question concerns the ways in which the research team's perspectives or beliefs privilege particular approaches-to teaching, to research design, or to analyses. Such matters have the potential to distort research outcomes in fundamental ways that go beyond simply having diverse interpretations of the data collected: they reach into the heart of the research itself, affecting the research questions posed, the research design, and data collection and analysis. These challenges for measuring mathematical constructs exist whether the study is qualitative or quantitative, large or small scale, funded or unfunded, mandated or grassroots.

At this point it is necessary to consider what I mean by "measure." An exploration of several online and hardcopy dictionaries reveals two clear meanings of the word as a verb: to determine the quantity of something using an instrument of some form with standard units, and to ascertain the quality of something by making an assessment against some defined standard. Measurement thus encompasses both quantitative and qualitative approaches to research. That is not to say that there are no tensions existing between these two paradigms, but it does suggest that in essence they are the same endeavor, using different approaches to achieve the same end, which is to increase the knowledge base about mathematics education.

Item Details

Item Type:Research Book Chapter
Keywords:mathematics education, Rasch analysis, educational measurement
Research Division:Education
Research Group:Curriculum and pedagogy
Research Field:Mathematics and numeracy curriculum and pedagogy
Objective Division:Education and Training
Objective Group:Other education and training
Objective Field:Other education and training not elsewhere classified
UTAS Author:Callingham, R (Associate Professor Rosemary Callingham)
ID Code:107734
Year Published:2016
Deposited By:Education
Deposited On:2016-03-22
Last Modified:2018-03-29

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