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Abstract
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.
... Because I could not imagine how I would implement the think-pair-share strategy in a virtual classroom, or how I would hand out quotes to different students in real time online, I had to decide on another way to introduce my students to what it means to conduct research in mathematics education. The first decision I made was to upload to the course website four different papers [32][33][34][35] and assign each student one paper to read and summarize. Thus, the first lesson was asynchronized. ...
... On the one hand, there are not many opportunities in this course for students to articulate what they know; thus, the original lesson has merit. On the other hand, I am not sure when the opportunity would arise for students to read the four, in my opinion, important papers written by Cai et al. [32][33][34][35]. Perhaps in the future, I would begin in the same way as I did in the original lesson and end the course with the four editorial papers, as a summary for the course. ...
... Michal has not taught the same course again since the pandemic. However, the resources that she adopted during that year, including the four papers authored by Cai et al. [32][33][34][35], have become part of her repertoire, especially as she mentors graduate students in mathematics education who are writing a thesis. While Michal read those papers when they were first published and always thought about integrating them into her teaching, it took the discussion of these papers with students during the pandemic to realize that these papers can help students conceptualize what it means to conduct (good) research in mathematics education. ...
A time of crisis is a time of uncertainty, when many decisions need to be made. This study combines self-reflection, along with community inquiry, as three mathematics teacher educators recount a lesson that they taught in the past and how it was changed due to the COVID-19 crisis. Decisions were analyzed in terms of goals, orientations, and resources. The findings showed that the key issue was the immediate requirement to change one’s regular routine. For some, resources were replaced. For others, dominant orientations receded to the background, and new goals were set. A final reflection conducted after returning to the classroom revealed how challenges during the crisis led to change and the adoption of new goals both during and after the crisis, clarifying our values and leading to the use of additional resources today.
... With respect to coherence, Cai, Morris, et al. (2019c) described how the conceptual framework provides a connecting thread that ties together all of the parts of a research report into a coherent whole. With respect to claims, Cai, Morris, et al. (2019a) discussed 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 conceptual framework, they argue that the researcher must thoroughly justify the selection of methods. ...
... Which claims to highlight is both an art and a science in the sense that the highlighted claims need to demonstrate the significance of the contribution. Based on our experience processing a number of manuscripts for both JRME and MTE, a common error we see with claims and evidence that are not connected is the making of presumed claims that do not have the support of the data (Cai, Morris, et al., 2019a). We recommend three strategies for connecting claims with the evidence. ...
Communicating research insights is challenging and is often work that is underestimated. In this chapter, readers are invited to take the stance of writing as communicating with reviewers. After sharing how reviewers are assigned to manuscripts, the authors (experienced journal editors) discuss three of the common issues reviewers usually raise when recommending that manuscripts not be accepted for publication—coherence, claims, and contribution. They also share strategies that prospective authors can use to anticipate and address these issues when preparing and revising their manuscripts.
... yo misma tomé sus referencias para documentar la redacción de esta editorial y también las utilicé como guía para buscar en nuestra disciplina discusiones cercanas. Encontré un capítulo interesante de Sandra Crespo y Jinfa Cai (2019) donde proponen la escritura como una comunicación con los revisores, poniendo atención en los criterios de coherencia, fundamentación de las afirmaciones y la contribución de la investigación, siendo estos los que más resaltan en las evaluaciones de los revisores; también de Sandra Crespo (2016), como editora de la Mathematics Teacher Educator, encontré una interesante editorial donde habla de la retroalimentación de la revisión como proceso formativo, para repensar la forma en que leemos y damos retroalimentación a los manuscritos de nuestros pares; y, finalmente, la serie de editoriales del Journal for Research in Mathematics Education en 2019, sobre la escritura científica tomando en cuenta los procesos de revisión por pares que se han vivido en la revista en un lapso considerable (Cai et al, 2019a(Cai et al, , 2019b(Cai et al, , 2019c(Cai et al, , 2019d. En ninguno encontré un debate en torno a la revisión por pares en sí misma y sobre las dinámicas de sus modelos, así como del impacto de estos en la investigación y sus procesos de comunicación; pero claramente resultan importantes como punto de partida para caminar hacia la revisión por pares como un diálogo para aprender y crecer en colectivo. ...
... While the Journal for Research in Mathematics Education has been making moves through its editorial pages to "firm up" what counts as mathematics education research (e.g. Cai et al., 2019), it is especially important that the Journal of Urban Mathematics Education make moves through this section and throughout its pages to re-affirm its commitment to different ways of doing science in mathematics education. Doing so is not a criticism of traditional ways of doing science per se but rather an acknowledgement of a widening of the boundaries for mathematics education researchers to radically reconfigure the field with and for students, teachers, and humanity more broadly. ...
The Field Disruptions and Field Connections section of the Journal of Urban Mathematics Education (JUME) seeks manuscripts that bring to light innovative, underutilized, or marginalized theories and methods that show potential for radical reconfiguration in (urban) mathematics education research. In this introductory and invitational editorial to the section, I provide illustrations of field disruptions through the use of poststructural and agential realist theories in mathematics education research. The purpose in doing so is to highlight how past disruptions have caused shifts in what counts as mathematical knowledge and who can be seen as mathematical. I also point to examples of field connections that demonstrate the importance of innovation and creativity in not only what we research but also in the ways we research in urban mathematics education. Because new and newly considered theories and methods can and have shifted the field of mathematics education research, an intellectual space to share and explore these innovative contributions to the field is being created within JUME. Specifically, the section seeks submissions that bring forward theories, methods, and concepts that the author argues have potential to disrupt the structures that support systemic racism and other forms of exclusion in mathematics teaching and learning. In addition, as section editor, I welcome alternative texts, poetry, and research texts and data that may not fit or have been systematically excluded in more traditional disciplined spaces but speak to important issues in urban mathematics education.
... Choosing an appropriate research methodology depends on the research questions asked and the theoretical framework adopted. Furthermore, as Cai et al. (2019) emphasised, authors need to justify the research methods chosen. ...
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In this brief commentary, I first overview the strengths and weaknesses of qualitative research in education and also briefly consider mixed methods. I then offer a few suggestions for reporting on particular methodological components and the results of qualitative research. I do not address the reporting on other significant components such as the literature review and theoretical framework, given that these aspects are generic to both qualitative and quantitative research. The points I make are brief and are by no means exhaustive. Nevertheless, it is hoped that they offer some guidance for authors in education who adopt primarily qualitative methods.
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... Choosing an appropriate research methodology depends on the research questions asked and the theoretical framework adopted. Furthermore, as Cai et al. (2019) emphasised, authors need to justify the research methods chosen. ...
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The early detection of children with special needs is very important for educators, as they require special handling in the learning process so that they can develop optimally. The first important level for early detection is the early childhood education level. Early childhood teachers become agents who play a major role of early detection. Problems that occur due to late diagnosis of children with special needs often lead to learning and behavioural problems. If not handled properly, these disturbances will continue to the next level of further education. Knowledge of various types of disorders and early intervention in children with special needs must be the responsibility of early childhood education teachers to reduce the negative effects of any disruption that may occur. In order to assist teachers in early detection, this paper presents a study related to various developmental disorders that occur in children with special needs and the skills, techniques and steps that are needed for early detection.
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... Consecuencia de esta coyuntura se conforma un marco conceptual ad hoc para abordar nuestro objeto de estudio, este fundamento conceptual expone y justifica argumentos, razones e hipótesis que guiaron nuestra forma de pensar dentro de la investigación (Cai, et al., 2019), dado que es necesario "[…] apropiarnos de cualquier teoría y perspectiva disponible en nuestra búsqueda de respuestas a nuestras preguntas de investigación" (Lester, 2005, p. 460), resaltando y sustentando las decisiones metodológicas que nos llevaron a dichas apropiaciones y las relaciones que pueden haber entre ellas. Para nuestro ejemplo particular se declara la importancia de estudiar esos razonamientos espaciales que acompañan la actividad geométrica que se pretende analizar, por ello se documenta una estructura que refiere a los conceptos asociados a este tipo de razonamiento, que serán observables con el método que se expondrá en este capítulo para un posterior análisis de datos. ...
The unanimous consensus that recognizes geometry as fundamental in the student’s formation contrasts with its almost complete absence from school programs, especially Space Geometry. A clear example are the conics, the genesis of these geometric notions is based on Plane and Space Geometry, but given its curricular position in the school, priority has been given to algebraic treatments —in part— lacking in meaning. This phenomenon of algebraization of conics limited the problem and served to value studies on the geometric construction of conics with special interest in its genesis: the solid conic construction.
The shortage of studies in Mathematics Education in this regard determined the approach of a documentary research, specifically a historical-epistemological study of an original text related to the construction of the conic section. In order to front facing the object of study, a conceptual framework was configured, first, by the Socio-epistemological Theory (ST) whose methodological frame guides the study of original texts enclosed in a historical-epistemological analysis or historization, and second, by a vision on the Spatial Reasoning consistent with the theoretical principles and allowing the extraction of spatial processes from an original text.
The method chosen and strengthened —standardized by the ST— detailed: the text Conics of Apollonius of Perga selection as a primary source of data, the approaches to the mathematics of the past and the consolidation of analysis units. Historization was composed of a contextual analysis that culminates with the stratification of the context of meaning: this condensed and filtered the socio-cultural events that influenced the social construction of the conics, which in turn are portrayed in the textual analysis framed in the pragmatic reconstruction of mathematical activity, where each proposition or unit of analysis was reproduced in search of actions and activities among them spatial processes.
As main results it is highlighted that the spatial processes have a role, besides communicative, epistemological in the construction and constitution of the conics as mathematic knowledge, in addition the epistemological hypothesis stands out rotation, section and application of areas like the practices that accompany and precede the geometric object. Finally, the meaning of conics in the epistemology of their genesis is perceived through use of the common section.
... On the other end of the continuum is an approach that focuses on quickly gathering small amounts of data to test very local, targeted hypotheses about instruction and learning opportunities-in other words, just enough data to tell whether something is working. The goal of this alternative approach to data collection is to inform the continuous, iterative development of a gradually accumulating set of small improvements in instruction (Cai et al., 2018d(Cai et al., , 2019(Cai et al., , 2019a. Because classroom time is a highly limited resource, such data collection will require what Improvement Science researchers have called "practical measures": measures to inform improvement that can be embedded in the regular work of teaching and learning (Bryk et al., 2015). ...
Significant research in science and mathematics education should advance the field’s knowledge and understanding of the teaching and learning of science and mathematics. How, then, should the significance of a research question in science and mathematics education be assessed? And, when disseminating the findings of research, how should the significance of the research questions be communicated? In this study, we analyzed peer reviews to answer these questions. Our analysis revealed the main issues peer reviewers identify about research questions and the ways they are communicated during the dissemination of research. The findings provide insights for new and experienced researchers about communicating the significance of research questions, and they also illustrate how reviewer comments in peer-reviewed journals can provide a window into the field’s frontiers.
Although often asked tactfully, a frequent question posed to authors by JRME reviewers is “So what?” Through this simple and well-known question, reviewers are asking: What difference do your findings make? How do your results advance the field? “So what?” is the most basic of questions, often perceived by novice researchers as the most difficult question to answer. Indeed, addressing the “so what” question continues to challenge even experienced researchers. All researchers wrestle with articulating a convincing argument about the importance of their own work. When we try to shape this argument, it can be easy to fall into the trap of making claims about the implications of our findings that reach beyond the data.
In our May editorial (Cai et al., 2018a), we explored how collaborations among teacher-researcher partnerships could harness emerging technological resources to address the problem of isolation in the work of teachers and researchers. In particular, we described a professional knowledge base (Cai et al., 2018b) and a mechanism by which that knowledge base could be continuously populated, updated with data and resources that are useful to teachers and researchers, and shared among partnerships thereby enabling them to work on the same instructional problems. In this editorial, we shift our focus to discuss how data on students' thinking and classroom experiences could be leveraged within such a system to improve instructional practice. We will explore how the knowledge base could serve as a tool to (a) gather, process, and analyze data from individual students; (b) increase our understanding of the effects of students' mathematical learning experiences; and (c) help teacher-researcher partnerships understand and improve students' learning.
In our March editorial (Cai et al., 2019), we discussed the nature of significant research questions in mathematics education. We asserted that the choice of a suitable theoretical framework is critical to establishing the significance of a research question. In this editorial, we continue our series on high-quality research in mathematics education by elaborating on how a well-constructed theoretical framework strengthens a research study and the reporting of research for publication. In particular, we describe how the theoretical framework provides a connecting thread that ties together all of the parts of a research report into a coherent whole. Specifically, the theoretical framework should help (a) make the case for the purpose of a study and shape the literature review; (b) justify the study design and methods; and (c) focus and guide the reporting, interpretation, and discussion of results and their implications.
In 2002, the National Research Council (NRC) released Scientific Research in Education , a report that proposed six principles to serve as guidelines for all scientific inquiry in education. The first of these principles was to “pose significant questions that can be investigated empirically” (p. 3). The report argued that the significance of a question could be established on a foundation of existing theoretical, methodological, and empirical work. However, it is not always clear what counts as a significant question in educational research or where such questions come from. Moreover, our analysis of the reviews for manuscripts submitted to JRME ¹ suggests that some practical, specific guidance could help researchers develop a significant question or make the case for the significance of a research question when preparing reports of research for publication.
We concluded our November editorial (Cai et al., 2018b) with a promise to consider research paradigms that could bring us closer to the new world we have envisioned where research is intertwined with practice. We will call the paradigms we have in mind research pathways to avoid the range of complicated connotations often applied to the term paradigm . By research pathways in education, we mean the collection of assumptions that define the purposes of educational research, the principles that differentiate research from other educational activities, and the guidelines for how research should be conducted.