qualitative research methods in mathematics education

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Approaches to qualitative research in mathematics education.

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Angelika Bikner-Ahsbahs, Christine Knipping, and Norma Presmeg, editors

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Over the last twenty years, qualitative research has fought hard to earn legitimacy as opposed to the critical eyes of the positivist approach. Slowly these have emerged as complementary paradigms of scientific inquiry. It is still not uncommon, however, for colleagues and students to ridicule qualitative research methods as being loose, unscientific, or illegitimate. Approaches to Qualitative Research in Mathematics Education: Examples of Methodology and Methods is a clever gift for the skeptics who believe that pursuing truth is only possible through traditional empirical research.

In the book are 19 total chapters that cover the theories and methodologies of qualitative inquiry for research in mathematics education. Each chapter includes an abstract, keywords, sections and references. Together they cohesively showcase the variety of theories and methods within the broad framework of qualitative research and focus on connecting theories and research methods along with rich research examples. The theories and methods covered in the book include grounded theory, ideal type construction, theory of argumentation, the Vygotskian semiotic approach, networking of theories, mixed methods, multilevel analysis, qualitative content analysis, triangulation, and design-based research.

The book is too thick to be read in several days, but this is not a bad thing. Still, I doubt that the book can serve as an effective text for undergraduate students. Given the academic and technical nature of this book, it will better serve doctoral students in mathematics education, particularly students interested in examples of theoretical framework, design, and methods for qualitative study; as well as mathematics education researchers interested in gaining a current snapshot of advanced qualitative methodologies in the field.

It should be noted that each chapter stands alone: the chapters are neither interconnected nor presented in sequence. So readers may search for theories or methods in the subject index and read their chapters of interest. The author index is useful as well. For example, I was interested in how students develop abstract knowledge in the mathematics classroom. I searched the subject index and found an entry for abstractions, which led me to Chapter 8, titled “The Nested Epistemic Actions Model for Abstraction in Context.” The abstract for the chapter stated, “abstraction in context is a theoretical framework for studying students; processes of constructing abstract mathematical knowledge as it occurs in a context that includes specific mathematical, curricular and social components as well as a particular learning environment (p.185).” I was hooked and kept reading. The chapter provided an outline of the theoretical framework of Abstraction in Context, background information on the methodology, and a detailed account of how the theory and methodology supported one another in research design along with findings and analysis.

The work of the contributors inspires researchers in the field of mathematics education to replicate the studies and, more importantly, creates opportunities to further reflect on the ways theories inform qualitative research designs and methods. Whether the editors meant to achieve this or not, one thing is clear from reading the collective scholarly work: the book offers endless possibilities for our field to pursue truth beyond statistical significance in the phenomena of teaching and learning mathematics.

Woong Lim ( [email protected] ) is an Assistant Professor of Mathematics Education at University of New Mexico. His research interests include interrelations between language and mathematics, content knowledge for teaching, and social justice issues in mathematics education.

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Approaches to qualitative research in mathematics education : examples of methodology and methods

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• Part 1: Grounded theory methodology.
• Chapter 1: Anne R. Teppo. Grounded Theory Methods.
• Chapter 2: Maike Vollstedt. To see the wood for the trees: The development of theory from empirical interview data using grounded theory.-
• Part 2: Approaches to reconstructing argumentation.
• Chapter 3: Gotz Krummheuer. Methods for reconstructing processes of argumentation and Chaptericipation in primary mathematics classroom interaction.
• Chapter 4: Christine Knipping and David Reid. Reconstructing argumentation structures: A perspective on proving processes in secondary mathematics classroom interactions.-
• Part 3: Ideal type construction.
• Chapter 5: Angelika Bikner-Ahsbahs. Empirically grounded building of ideal types. A methodical principle of constructing theory in the interpretive research in mathematics education.
• Chapter 6: Angelika Bikner-Ahsbahs. How ideal type construction can be achieved: An example.-
• Part 4: Semiotic research.
• Chapter 7: Luis Radford and Cristina Sabena. The question of method in a Vygotskian semiotic approach.-
• Part 5: A theory on abstraction and its methodology.
• Chapter 8: Tommy Dreyfus, Rina Hershkowitz and Baruch Schwarz. The nested epistemic actions model for Abstraction in Context: Theory as methodological tool and methodological tool as theory.-
• Part 6: Networking of theories.
• Chapter 9: Ivy Kidron and Angelika Bikner-Ahsbahs. Advancing research by means of the networking of theories.
• Chapter 10: Angelika Bikner-Ahsbahs and Ivy Kidron. A cross-methodology for the networking of theories: The general epistemic need (GEN) as a new concept at the boundary of two theories.-
• Part 7: Multi-level-analysis.
• Chapter 11: Geoffrey B. Saxe, Kenton de Kirby, Marie Le, Yasmin Sitabkhan, Bona Kang. Understanding learning across lessons in classroom communities: A multi-leveled analytic approach.-
• Part 8: Mixed Methods.
• Chapter 12: Udo Kelle and Nils Buchholtz. The combination of qualitative and quantitative research methods in mathematics education-A "Mixed Methods" study on the development of the professional knowledge of teachers.-
• Part 9: Qualitative Content Analysis.
• Chapter 13: Philipp Mayring. Qualitative Content Analysis: Theoretical background and procedures.
• Chapter 14: Bjorn Schwarz. A study on professional competence of future teacher students as an example of a study using Qualitative Content Analysis.-
• Part 10: Triangulation and cultural studies.
• Chapter 15: Ida Ah Chee Mok and David J. Clarke. The contemporary importance of triangulation in a post-positivist world: Examples from the Learner's Perspective Study.-
• Part 11: Design research as a research methodology.
• Chapter 16: Arthur Bakker and Dolly van Eerde. An introduction to design-based research with an example from statistics education.
• Chapter 17: Michele Artigue. Perspectives on design research: The case of didactical engineering.
• Chapter 18: Erin Henrick, Paul Cobb and Kara Jackson. Educational design research to support system-wide instructional improvement.
• Part 12: Looking back.
• Chapter 19: Angelika Bikner-Ahsbahs, Christine Knipping and Norma Presmeg. Appendix.- References.- Index of keywords.
• (source: Nielsen Book Data)

Qualitative Approaches in Mathematics Education Research: Challenges and Possible Solutions

2013, Education Journal

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With the development of qualitative methodologies, interviewing has become one of the main tools in mathematics education research. As the first step in analyzing interviewing in mathematics education we focus here on the stage of planning, specifically, on designing the interview questions. We attempt to outline several features of interview questions and understand what guides researchers in choosing the interview questions. Our observations and conclusions are based on examining research in mathematics education that uses interviews as a data-collection tool and on interviews with practicing researchers reflecting on their practice.

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Mathematics is important for a person to live a better life. It has a special position in the educational curriculum. However, it is well known that most students find mathematics challenging. This study examined the high school student's struggles and challenges in learning Mathematics. The Interpretative Phenomenological Analysis (IPA) anchored from the Modified Van Kaam Approach popularized by Moustakas was utilized in this study to come up with meaningful data on the struggles and challenges of the high school students in learning Mathematics. The subject of this research was chosen using a purposive sampling technique and the participants are all qualified according to the study's inclusion criteria. 10 high school students of Bartolome and Manuela Pañares Memorial National High School participated in the interview. Analyzing the causes is crucial before taking additional steps to enhance students' Math learning. Through an open-ended survey questionnaire, students were questioned about potential causes of their learning challenges. The researchers generated four themes from the gathered data, and these are the following: The Crux of the Matter, Stumbling Block, Get to Grips With, and Significantly Essential Matter. These themes were formulated based on the students' shared experiences in learning Mathematics. The study included cognitive, affective, and contextual factors that determine the struggles and challenges in learning Mathematics. The challenges that students have in learning mathematics include having trouble recalling information from previous classes, forgetting information easily, and having trouble understanding mathematical ideas. It has been observed that students who find mathematics to be extremely difficult tend to give up more easily than those who find the subject simple. The results also showed that teachers must understand the value of making classroom mathematics engaging so that the students will put effort in learning the subject. The result is presented in the context of the students' perspectives and learning methods.

This book by-passes both psychology and sociology to present an original social theory centered on seeing mathematical learning by everyone as an intrinsic dimension of how mathematics develops as a field in support of human activity. Here, mathematics is defined by how we collectively talk about it. Drawing on psychoanalytic theory, the student is seen as participating in the renewal of mathematics through their contributions to our collective gaze on mathematics as the field responds to ever new demands. As such learning takes a critical stance on the standard initiations into current practices often promoted by formal education. In the field of mathematics education, researchers have moved from psychology where individual students were seen as following natural paths of development through existing mathematical knowledge, to socio-cultural models predicated on students being initiated into the human world and understood through the reflective gazes this world has of itself, such as those found in comparisons of student learning in different countries. This book addresses the domain, purpose and functioning of contemporary research in mathematics education and is an original contribution to this theme. The book is aimed at a mathematics education research audience. It continues a dialogue with existing publications, seen widely as a cutting edge and will also be of interest to students and practitioners in the fields of qualitative research, social theory and psychology. New book- Tony Brown A contemporary theory of mathematics education research https://www.springer.com/gp/book/9783030550998#aboutBook A preface providing an action-packed overview is freely downloadable as a pdf: https://link.springer.com/book/10.1007%2F978-3-030-55100-1

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This paper draws on two studies, one conducted by each author, where procedures for gaining insights into people’s beliefs about mathematics and learning were developed or adapted for use by the researcher. In this paper we discuss the use in each study of variations of the procedure called Pupil Perceptions of Effective Learning Environments in Mathematics (PPELEM). The paper demonstrates the flexibility of PPELEM as a data collection tool and shows that, even with a large age difference of respondents, the procedure can be used as a prompt for both adults and primary school children and provides insights into beliefs.

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The Oxford Encyclopedia of Qualitative Research Methods in Education

The  Oxford  Encyclopedia of Qualitative Research Methods in Education  provides a diverse overview of the wide variety of qualitative approaches to studying education, including ethnography, interviews, narrative, and case studies. These methods facilitate detailed description, interpretation, and critique that, in education, enable an understanding of how different forms of learning take place, how relationships are implicated in learning, and how contexts enhance and/or impede learning. Articles in the Encyclopedia variously discuss the history of qualitative research methodology, the theoretical underpinnings of qualitative methods, and interdisciplinary applications of qualitative methods, as well as emerging topics that are particularly helpful for scholars, students, and practitioners alike. All of the articles appear online as part of the Oxford Research Encyclopedia of Education .

Editor in Chief

George Noblit , University of North Carolina at Chapel Hill

Associate Editors

Dennis Beach, University of Gothenburg

Belmira Bueno, University of São Paulo

Letitia Fickel, University of Canterbury

Wanda Pillow, University of Utah

Meenakshi Thapan, University of Delhi

Printed from Oxford Research Encyclopedias, Education. Under the terms of the licence agreement, an individual user may print out a single article for personal use (for details see Privacy Policy and Legal Notice).

date: 27 March 2024

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Qualitative Approaches in Mathematics Education Research: Challenges and Possible Solutions

Sashi Sharma

Department of Mathematics, Science and Technology Education, Faculty of Education,The university of Waikato, Hamilton, New Zealand

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Despite being relatively new in mathematics education research, qualitative researchapproaches need special attention as attempts are being made to enhance the credibility and trustworthiness of this approach. It is important that researchers are aware of the limitations associated with these methods so that measures are put in place to try and minimize the effects of these limitations Philosophical roots and key features of this paradigm are outlined. Qualitative methods such as the interview approach in research literature as a data gathering tool are considered next. Challenges faced by qualitative researchers in terms of reliability, validity and generability are considered. Examples are provided to illustrate methodological problems and solutions related to qualitative methods.

Research Methods, Qualitative Research, Data Collection, Quality Criteria, Limitations, Possible Solutions

Sashi Sharma. (2013). Qualitative Approaches in Mathematics Education Research: Challenges and Possible Solutions. Education Journal , 2 (2), 50-57. https://doi.org/10.11648/j.edu.20130202.14

Sashi Sharma. Qualitative Approaches in Mathematics Education Research: Challenges and Possible Solutions. Educ. J. 2013 , 2 (2), 50-57. doi: 10.11648/j.edu.20130202.14

Sashi Sharma. Qualitative Approaches in Mathematics Education Research: Challenges and Possible Solutions. Educ J . 2013;2(2):50-57. doi: 10.11648/j.edu.20130202.14

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Interventions and diversity, equity, and inclusion: Two current directions in research on the teaching and learning of calculus

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• Published: 25 March 2024

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• Tenchita Alzaga Elizondo 2 &
• Sean Larsen   ORCID: orcid.org/0000-0002-6179-3783 1  

Calculus continues to be an important topic of discussion among mathematics education researchers given how it often acts as a gatekeeper for students in STEM. In their extensive 2017 review of calculus literature, Larsen and colleagues identified two main areas of applied research that had largely been neglected: research related (1) to efforts to improve calculus teaching and learning and (2) to equity and social justice. In this review we investigate how scholars have answered this call by reviewing recent literature related to these two themes. First we identified some promising intervention studies that investigated changes at the course level (e.g., calculus courses intended for engineering students) and at the level of specific calculus topics (e.g. using digital tools to help students understand the Fundamental Theorem). Second, we identified several studies on diversity, equity, and inclusion. We found that some studies in this collection still approached this research through traditional methods (e.g., so called achievement gaps) but we also identified promising new directions for research in which scholars utilize critical theories and provide counter-narratives that highlight the strengths of calculus students from historically marginalized groups. We conclude our review by discussing future directions we hope to see in the field that we argue will strengthen current work.

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*Arnold, E. G., Burroughs, E. A., & Deshler, J. M. (2020). Investigating classroom implementation of research-based interventions for reducing stereotype threat in calculus. International Journal of Research & Method in Education, 43 (1), 67–77. https://doi.org/10.1080/1743727X.2019.1575352

*Bakri, S. R. A., Liew, C. Y., Chen, C. K., Tuh, M. H., & Ling, S. C. (2021). Bridging the gap between the derivatives and graph sketching in calculus: An innovative game-based learning approach. Asian Journal of University Education, 16 (4), 121–136.

**Battey, D., Amman, K., Leyva, L. A., Hyland, N., & McMichael, E. W. (2022). Racialized and gendered labor in students’ responses to precalculus and calculus instruction. Journal for Research in Mathematics Education, 53 (2), 94–113. https://doi.org/10.5951/jresematheduc-2020-0170 . This study investigated the type of labor, and associated coping mechanisms, women, Black, and Latino/a calculus students described in response to instructional events they perceive as racialized or gendered. Results indicated that students engaged in both cognitive and emotional labor in response to these events and mitigated their participation in class in order to cope with that labor. The authors described implications of the students’ coping mechanisms.

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**Bos, R., Doorman, M., & Piroi, M. (2020). Emergent models in a reinvention activity for learning the slope of a curve. The Journal of Mathematical Behavior, 59 , 100773. https://doi.org/10.1016/j.jmathb.2020.100773 . This paper reports on an instructional design study that is supported by the theory of Realistic Mathematics Education and focused on the concept of slope of a curve. Within an a-didactical context students begin the process of reinventing the concept and the authors analyzed their mathematical activity to connect it to various approaches identified in their a priori analysis. They identified a number of informal approaches that could be productively developed during a subsequent institutionalization phase directed by a teacher.

Bressoud, D. M., Carlson, M. P., Mesa, V., & Rasmussen, C. (2013). The calculus student: insights from the Mathematical Association of America national study. International Journal of Mathematical Education in Science and Technology , 44 (5), 685–698.

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Cetina-Vázquez, M., Cabañas-Sánchez, G., & Sosa-Moguel, L. (2019). Collective mathematical progress in an introductory calculus course during the treatment of the quadratic function. International Journal of Education in Mathematics, Science and Technology, 7 (2), 155–169.

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Alzaga Elizondo, T., Larsen, S. Interventions and diversity, equity, and inclusion: Two current directions in research on the teaching and learning of calculus. ZDM Mathematics Education (2024). https://doi.org/10.1007/s11858-024-01553-3

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