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Natalie E. Selinski, Chris Rasmussen, Megan Wawro and Michelle Zandieh

The central goals of most introductory linear algebra courses are to develop students' proficiency with matrix techniques, to promote their understanding of key concepts, and to increase their ability to make connections between concepts. In this article, we present an innovative method using adjacency matrices to analyze students' interpretation of and connections between concepts. Three cases provide examples that illustrate the usefulness of this approach for comparing differences in the structure of the connections, as exhibited in what we refer to as dense, sparse, and hub adjacency matrices. We also make use of mathematical constructs from digraph theory, such as walks and being strongly connected, to indicate possible chains of connections and flexibility in making connections within and between concepts. We posit that this method is useful for characterizing student connections in other content areas and grade levels.

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Jens Holger Lorenz

The social aspect is playing an expanding role in instructional research. The participants in instruction (teacher and students) are no longer seen as objects of research that react to stimuli (the students' verbal remarks on the one hand; the teachers' questions and the curriculum on the other), but they are seen as interpreting subjects of the teaching-learning process under a new paradigm (the epistemological subject-model in the human sciences, and particularly in psychology; see Groeben, 1975). A comprehensive macrotheory of the instructional process seen as having interacting individuals is not yet established, due equally to the complexity of the content and the lack of adequate research methods.

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Margaret A. Eisenhart

Although in theory ethnography has been put forward as a powerful naturalistic methodology, in practice it has rarely been used by educational researchers because of differences in assumptions, goals, and primary research questions. From my perspective as an educational anthropologist, I describe the research tradition of ethnography—its underlying assumptions, its heritage in holistic cultural anthropology, its goals and research questions, and the organization of its research methods. Throughout, I compare elements of this ethnographic tradition with more common educational research practices. In the final section, I discuss the advantages of improved communication for future research in both mathematics education and educational anthropology.

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Jinfa Cai

issues, such as the political climate, funding, policy, and advances in research methods and technology. The reflections will appear in chronological order throughout 2020. We are pleased to present James Wilson’s inaugural reflection in this issue

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Jeremy Kilpatrick

( Kilpatrick, 1992b ), but it was apparently much more extensive. Nonetheless, it is certainly fair to say that the assortment of research methods used today in studies reported in JRME is much more diverse than it was when I was editor (see Presmeg

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Frank K. Lester Jr.

issues of the journal published from 1989 through 1996, 2 I identified four integrated themes that characterized those years: the Standards movement, growing demands to conduct “what works” research, a shift in the nature of research methods, and

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Edward A. Silver

the dawn of the 21st century, there was a warm embrace of qualitative research methods and a multiplicity of theoretical frames and research paradigms. Thus, though many shared the concerns of practitioners and policy makers about the need to enhance

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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer, James Hiebert and Arthur Bakker

small) studies that move incrementally toward more comprehensive and precise answers. We conjecture that many research methods commonly used to generate descriptive and evaluative data in educational settings will be useful for conducting research on

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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer, James Hiebert and Arthur Bakker

kinds of designs and analyses could reveal the kinds of lesson-level knowledge that can be preserved and shared? What research methods can tease out the conditions that influence the knowledge teachers develop while teaching (e.g., during planning

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Bilge Yurekli, Mary Kay Stein, Richard Correnti and Zahid Kisa

. Hoffman , L. , & Rovine , M. J. ( 2007 ). Multilevel models for the experimental psychologist: Foundations and illustrative examples. Behavior Research Methods , 39 ( 1 ), 101 – 117 . doi: 10.3758/BF03192848 16. Lobato