scholarly journals Styles of reasoning for mathematics education

2021 ◽  
Author(s):  
David Kollosche
Keyword(s):  
Education Research ◽  
Mathematics Education ◽  
Mathematical Modelling ◽  
Mathematical Reasoning ◽  
Philosophy Of Mathematics ◽  
Theoretical Framework ◽  
Mathematics Education Research ◽  
Central Concept ◽  
Relativist Account ◽  
Styles Of Reasoning

AbstractAlthough reasoning is a central concept in mathematics education research, the discipline is still in need of a coherent theoretical framework of mathematical reasoning. With respect to epistemological problems in the dominant discourses on proof, mathematical modelling, and post-truth politics in the discipline, and in accordance with trends in the philosophy of mathematics and in mathematics education research in general, it is argued that it is necessary to give a relativist account of mathematical reasoning. Hacking’s framework of styles of reasoning is introduced as a possible solution. This framework distinguished between at least six different styles of reasoning, many of which are closely connected to mathematics, and argues that these frameworks define what we accept as decidable assertions, as justifications for such assertions, and as possible objects of such assertions. The article ends with a discussion of the implications of the framework for chosen fields of mathematics education research, which may motivate more focussed studies in the future.

Review: The Mathematics of Popular Consumption

1996 ◽  
Vol 27 (2) ◽  
pp. 241-243
Author(s):  
Suzanne K. Damarin
Keyword(s):  
Education Research ◽  
Mathematics Education ◽  
Philosophy Of Mathematics ◽  
Mathematics Education Research ◽  
Paradigm Shifts ◽  
Body Of Knowledge ◽  
Mathematics Educators ◽  
Community Of Researchers

Various forms of constructivism have been widely accepted among mathematics educators as describing not only the processes by which individual students learn mathematics, but also the development of mathematic itself as a body of knowledge. Constructivism has led to a revival of research in the philosophy of mathematics as a social-cultural-historical construction (Hersh, 1994) and to paradigm shifts in mathematics education research as we seek to understand the ways mathematics is learned and taught most effectively. Constructivism notwithstanding, however, accepted ideas of what is comprised in mathematics as a body of knowledge have not been significantly altered within the community of researchers and teachers who study. practice, and teach malhematics. the philosophy of mathematics, or mathematics education.

Choosing and Justifying Robust Methods for Educational Research

2019 ◽  
Vol 50 (4) ◽  
pp. 342-348 ◽  
Author(s):  
Jinfa Cai ◽  
Anne Morris ◽  
Charles Hohensee ◽  
Stephen Hwang ◽  
Victoria Robison ◽  
...  
Keyword(s):  
Education Research ◽  
Mathematics Education ◽  
Educational Research ◽  
Theoretical Framework ◽  
Mathematics Education Research ◽  
Robust Methods ◽  
Theoretical Frameworks ◽  
Methodological Choices ◽  
Research Questions ◽  
Selection Of

In our recent editorials (Cai et al., 2019a, 2019b), we discussed the important roles that research questions and theoretical frameworks play in conceptualizing, carrying out, and reporting mathematics education research. In this editorial, we discuss the methodological choices that arise when one has articulated research questions and constructed at least a rudimentary theoretical framework. Just as the researcher must justify the significance of research questions and the appropriateness of the theoretical framework, we argue that the researcher must thoroughly describe and justify the selection of methods. Indeed, the research questions and the theoretical framework should drive the choice of methods (and not the reverse). In other words, a sufficiently well-specified set of research questions and theoretical framework establish the parameters within which the most productive methods will be selected and developed.

scholarly journals Exemplifying a Model-Eliciting Task for Primary School Pupils

2011 ◽  
Vol 1 (1) ◽  
pp. 65-74
Author(s):  
Chan Chun Ming Eric ◽  
Wanty Widjaja ◽  
Ng Kit Ee Dawn
Keyword(s):  
Education Research ◽  
Mathematics Education ◽  
Mathematical Modelling ◽  
Primary School ◽  
Real World ◽  
Primary Schools ◽  
Mathematics Classroom ◽  
Mathematics Education Research ◽  
Primary School Pupils ◽  
Real World Problems

Mathematical modelling is a field that is gaining prominence recently in mathematics education research and has generated interests in schools as well. In Singapore, modelling and applications are included as process components inrevised 2007 curriculum document (MOE, 2007) as keeping to reform efforts. InIndonesia, efforts to place stronger emphasis on connecting school mathematicswith real-world contexts and applications have started in Indonesian primary schools with the Pendidikan Realistik Matematik Indonesia (PMRI) movement a decade ago (Sembiring, Hoogland, Dolk, 2010). Amidst others, modelling activities are gradually introduced in Singapore and Indonesian schools to demonstrate the relevance of school mathematics with real-world problems. However, in order for it to find a place in the mathematics classroom, there is aneed for teacher-practitioners to know what mathematical modelling and what amodelling task is. This paper sets out to exemplify a model-eliciting task that has been designed and used in both a Singapore and Indonesian mathematicsclassroom. Mathematical modelling, the features of a model-eliciting task, and its potential and advice on implementation are discussed.

scholarly journals Future themes of mathematics education research: an international survey before and during the pandemic

2021 ◽  
Vol 107 (1) ◽  
pp. 1-24
Author(s):  
Arthur Bakker ◽  
Jinfa Cai ◽  
Linda Zenger
Keyword(s):  
Education Research ◽  
Mathematics Education ◽  
Teacher Professional Development ◽  
Mathematics Education Research ◽  
International Survey ◽  
Teaching Approaches ◽  
Education Teacher ◽  
Development Technology ◽  
Teacher Professional ◽  
Research In Mathematics Education

AbstractBefore the pandemic (2019), we asked: On what themes should research in mathematics education focus in the coming decade? The 229 responses from 44 countries led to eight themes plus considerations about mathematics education research itself. The themes can be summarized as teaching approaches, goals, relations to practices outside mathematics education, teacher professional development, technology, affect, equity, and assessment. During the pandemic (November 2020), we asked respondents: Has the pandemic changed your view on the themes of mathematics education research for the coming decade? If so, how? Many of the 108 respondents saw the importance of their original themes reinforced (45), specified their initial responses (43), and/or added themes (35) (these categories were not mutually exclusive). Overall, they seemed to agree that the pandemic functions as a magnifying glass on issues that were already known, and several respondents pointed to the need to think ahead on how to organize education when it does not need to be online anymore. We end with a list of research challenges that are informed by the themes and respondents’ reflections on mathematics education research.

scholarly journals Obstacles to Addressing Race and Ethnicity in the Mathematics Education Literature

2012 ◽  
Vol 43 (3) ◽  
pp. 238-252 ◽  
Author(s):  
Amy Noelle Parks ◽  
Mardi Schmeichel
Keyword(s):  
Education Research ◽  
Mathematics Education ◽  
Literature Review ◽  
Race And Ethnicity ◽  
Mathematics Education Research ◽  
Education Literature ◽  
Independent Variables

This Research Commentary builds on a 2-stage literature review to argue that there are 4 obstacles to making a sociopolitical turn in mathematics education that would allow researchers to talk about race and ethnicity in ways that take both identity and power seriously: (a) the marginalization of discussions of race and ethnicity; (b) the reiteration of race and ethnicity as independent variables; (c) absence of race and ethnicity from mathematics education research; and (d) the minimizing of discussions of race and ethnicity, even within equity-oriented work.

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