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Abstract
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.
... Theoretical framing as justifying (Cai et al., 2019d) J RME Entre los textos analizados, siete fueron capítulos del libro: "Compendium for Early Career Researchers in Mathematics Education" (Compendio para investigadores en el inicio de su carrera en educación matemática, traducción nuestra), cuyos editores son Gabriele Kaiser y Norma Presmeg, y pertenece a la serie "ICME-13 Monographs", publicada en 2019 por Springer. ISSN 1980-4415 DOI: http://dx.doi.org/10.1590/1980 ...
... Según Cai et al. (2019d), una estructura teórica sólida es una parte indispensable de un manuscrito científico, y debe desarrollarse como parte esencial del diseño y la ejecución de la investigación. ...
... Repensar su cuadro teórico como una contribución al campo implica considerarlo como un componente central de la investigación científica, no sólo un paso obligatorio antes de la siguiente fase (Cai et al., 2019d). Esto implica, para estos mismos autores, desarrollar su estructura gradualmente a medida que se desarrolla. ...
Resumen Este artículo pretende ser una guía para investigadores en el campo de la educación matemática, contribuyendo a la buena escritura y a la mejor estructuración de artículos para publicación en revistas especializadas, ya que los autores que construyen un argumento persuasivo y convincente tienen más probabilidades de influir en el público y ganar aceptación dentro de la comunidad investigadora. Para abordar la pregunta de investigación – ¿cómo escribir un artículo sobre educación matemática? – se realizó una revisión no sistemática de la literatura, analizando textos de siete publicaciones que se encuentran entre las diez mejores revistas internacionales de educación matemática. Los resultados ofrecen orientación sobre cómo escribir las secciones principales de un artículo típico- ideal (título, resumen, introducción, revisión de la literatura, marco teórico, metodología, resultados, discusión y conclusión), además de cómo estructurar el artículo en su conjunto.
... In conversations I've had with graduate students just getting started with research (e.g., Tyburski et al., 2022), it's not uncommon for some to express that the theoretical framework they're using "just doesn't feel right." Often, the framework they've crafted satisfies the many roles-both epistemological and ontological-that a theoretical framework should according to the mathematics education literature: identifying what counts as evidence for or against a particular claim, what set of constructs should be attended to, etc. (Cai et al., 2019;Spangler & Williams, 2019). But satisfying these utilitarian purposes is not always enough to quell the unrelenting uncertainty some graduate students feel they ought to resolve before proceeding with their research in a way that feels right to them. ...
... Ensuring a harmony between one's personal worldviews and the (implicit) philosophical assumptions of the theoretical framework they choose to employ is an underdiscussed but important aspect of developing a theoretical framework (Stinson, 2020). There is literature in mathematics education on the roles a theoretical framework should play once it is crafted (e.g., Cai et al., 2019;Spangler & Williams, 2019); however, this literature contains very little guidance for how one might go about creating such a theoretical framework in the first place. In sharing my own story of crafting a theoretical framework that jives with my worldviews, my intention is to add guidance in this domain. ...
... Conversations in our field about the role of theoretical frameworks almost exclusively center on utilitarian epistemological and ontological questions (e.g., Cai et al., 2019;Spangler & Williams, 2019). It is exceedingly rare-outside of perhaps a brief comment about the role of personal choice in theory selection (e.g. ...
In the mathematics education literature, there is plenty written on the roles that theoretical frameworks should play once they are already crafted; however, there is much less guidance on how scholars-especially emerging scholars-might construct a theoretical framework that serves these roles. When guidance is provided, it focuses on issues of epistemology and ontology. In this brief theoretical report, I emphasize the importance of the oft-ignored aesthetic dimension of theorizing. I first argue that aesthetics cannot be separated from our everyday behaviors and choices and therefore our research practice. I then share my experience about how reflecting on my personal aesthetics allowed me to craft a framework that enables me to bring my whole self-worldviews and all-into my research. By sharing my story, I hope to support other emerging scholars in bringing their ways of being, thinking, and feeling into their research.
... 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.
... de grandes corpos de pesquisa (Cai; Hwang, 2019) e pode vir junto/após a revisão da literatura ou, ainda, dentro da seção de metodologia (Herbst et al., 2022). Segundo Cai et al. (2019d), uma forte estrutura teórica é parte indispensável de um manuscrito científico e precisa ser elaborada como uma parte essencial da concepção e execução da pesquisa. ...
... Repensar o seu quadro teórico como uma contribuição para a área implica considerá-lo como um componente central da investigação científica, não apenas uma etapa obrigatória antes da próxima fase (Cai et al., 2019d). Isso implica, para esses mesmos autores, desenvolver sua estrutura gradualmente enquanto avança. ...
Resumo Este artigo tem por objetivo ser um guia para pesquisadores na área de educação matemática, colaborando para uma boa redação e estruturação de artigos para publicação em revistas especializadas, pois autores que constroem um argumento persuasivo e convincente têm maior probabilidade de influenciar o público e de obter aceitação dentro da comunidade de pesquisadores. Para abordar a questão de pesquisa – Como redigir um artigo em educação matemática? –, uma revisão não sistemática da literatura foi conduzida, analisando textos de sete revistas que estão entre as dez melhores revistas internacionais de educação matemática. Os resultados oferecem orientações sobre a redação das principais seções de um artigo típico-ideal – título, resumo, introdução, revisão da literatura, estrutura teórica, metodologia, resultados, discussão e conclusão – bem como a estruturação do artigo como um todo.
... Theoretical frameworks are essential for synthesizing, reorganizing, and providing insights from large research bodies and can come together with/after the literature review or even within the methodology section (Herbst et al., 2022). According to Cai et al. (2019d), a strong theoretical framework is an indispensable part of a scientific manuscript and needs to be developed as an essential part of the design and execution of the research. ...
... Rethinking your theoretical framework as a contribution to the field involves considering it a central component of scientific research, not just a mandatory step before the next phase (Cai et al., 2019d). This implies, for these same authors, developing their structure gradually as they progress. ...
This work is a guide for researchers in the area of mathematics education and aims to contribute to good writing and structuring of journal articles for publication in journals, since authors who construct a persuasive and convincing argument are more likely to influence the readers and gain acceptance within the research community. To address the research question – How to write a good article in mathematics education? –, a non-systematic literature review was conducted, analyzing texts from seven journals that are among the top ten international mathematics education journals. The results offer guidance on writing the main sections of a typical paper – title, abstract, introduction, literature review, theoretical framework, methodology, results, discussions and conclusion – as well as guidance on structuring the article as a whole.
... (e.g., Cai et al., 2019Cai et al., , 2019Cobb, 2007;Mason, 2011) (Mason, 2011;Mason & Waywood, 1996) (Lampert, 1990Schoenfeld, 2008) 5.2 (Su & Bellmann, 2018) Brandom (1994 1 5.3 (Radford, 2021) (e.g., Abtahi, 2022;Chen, 2023;Ernest, 2018Ernest, , 2020 6. ...
... (e.g., Cai et al., 2019Cai et al., , 2019Cobb, 2007;Mason, 2011) (Mason, 2011;Mason & Waywood, 1996) (Lampert, 1990Schoenfeld, 2008) 5.2 (Su & Bellmann, 2018) Brandom (1994 1 5.3 (Radford, 2021) (e.g., Abtahi, 2022;Chen, 2023;Ernest, 2018Ernest, , 2020 6. ...
This paper examines the role of inferentialism in mathematics education research, a complex, transdisciplinary field. We overview constructivism in mathematics education and the emergence of inferentialism, clarifying our perspective of inferentialism in educational research. The focus is on how inferentialism allows researchers to analyze observable learner expressions, overcoming the limitations of constructivism in empirical educational research. We also discussed the implications of educational research for philosophical issues.
... 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. ...
... Based on the aim of each publication, different theoretical and conceptual frameworks have been used. In line with Cai et al. (2019a), the terms theoretical framework and conceptual framework have been used interchangeably, encompassing assumptions, theories, hypotheses, and claims guiding the studies in this thesis. ...
From an inclusive perspective in mathematics education, the aim of this
Ph.D. thesis is to gain profound knowledge of didactical and relational
aspects of mathematics teaching concerning students’ participation in
mathematics education. The overarching research questions delve into
methodological and theoretical aspects that enable the study of enacted
mathematical and relational knowing of teachers, as well as how
mathematical and relational knowing supports inclusion in mathematics for
students. Three studies were conducted. The first study investigated the
possibilities of various data collection methods to document mathematics
teachers’ reflections on mathematical and relational knowing in
mathematics education. The second study aimed to gain theoretical and
empirical insights into teachers’ mathematical and relational knowing, as
well as into students’ participation in mathematics. The third study
examined earlier research regarding how co-teaching organized
mathematics education can contribute to inclusion. These three studies
generated four publications that answered the overarching research
questions. The methodological and theoretical findings emphasize the
complexity involved in exploring inclusive mathematics education.
Understanding mathematical and relational knowing of teachers requires a
broad conceptual framework that considers how these forms of knowing
come into play when teaching. The coordinated conceptual frameworks used
have core elements connected to the situated nature of inclusive
mathematics education. These frameworks are based on contextual factors
that focus on how and when teaching materials, mathematical examples and
connections are used. They also consider the particular teacher-student
interactions that occur in the moments of teaching. Hence, from a special
didactic perspective, it is essential to emphasize not only the ‘what, ‘how,’
and ‘why’, but also the ‘when’ question, considering both mathematical and
relational knowing in the context of inclusion in mathematics. Furthermore,
findings show that if students are to be didactically included, meaning they
participate in mathematics within the community of classroom mathematics,
it appears important for teachers to enact mathematical and relational
knowing simultaneously, whether distributed between one or two teachers
in a co-teaching setting. Moreover, co-teaching does not automatically lead
to didactical inclusion. However, if all students’ learning is the point of
departure and the teachers, together or individually, enact mathematical and
relational knowing, this can contribute to didactical inclusion.
... The Diagnostic Job Survey instrument depends on a particular hypothesis about what occupation configuration means for work inspiration and gives a goal proportion of occupation aspects individual mental states coming about because of these aspects, representatives' emotional responses to work and settings. Work and individual development require strength (characterized as the singular's status to answer an enhanced work) (Cai et al., 2019;Lesener et al., 2019). The components of occupation qualities are essential. ...
Employee productivity is crucial since it forms the basis and guide for every firm. However, the nature and formality of the work organization play a significant role in determining job characteristics, and although they have an impact on other workplace circumstances, changing job characteristics has inherent restrictions. The purpose of this study is to examine the structural relations among job characteristics, organizational citizenship behavior, self-efficacy related employee performance. The samples of this study consist of 351 representatives utilizing a straightforward irregular inspecting procedure and information from respondents utilizing research instruments utilizing on the web surveys. The exploration technique utilized in this study is Structural Equation Modelling examination and information investigation instruments utilizing SmartPLS 3.3.3. Analysis and interpretation of the data indicate that; self-efficacy have a relationship with employee performance, job characteristics have a relationship with employee performance, organizational citizenship behavior have a relationship with employee performance. The implementation of job characteristics, organizational citizenship behavior, and self-efficacy will greatly impact and make a positive contribution to the hotel activities in improving the performance of its employees.
... Partiendo de los conceptos de saber y labor conjunta, ubicados en el núcleo de la conceptualización del aprendizaje que propone la Teoría de la Objetivación, ha sido posible plantear una manera de entender cómo los profesores de matemáticas ponen en movimiento saberes profesionales acerca de la resolución, análisis y diseño de tareas investigativas de geometría dinámica, cuando se involucran en determinadas actividades de formación continua. Como lo sugieren Cai et al. (2019), el artículo ha permitido mostrar cómo sus autores se basan en estas ideas centrales, y las combinan con otras aportaciones de estudios sobre la formación de profesores de matemáticas, para producir un marco teórico que se muestra potente tanto para la interpretación del fenómeno del aprendizaje docente en contextos formativos particulares, como para la justificación de las decisiones y acciones necesarias para avanzar en la investigación que ha motivado este trabajo. ...
A pesquisa tem como objeto de estudo os saberes profissionais que são mobilizados na formação continuada de professores que ensinam matemática, orientados à resolução, à análise e à elaboração de tarefas investigativas de geometria dinâmica (TIGD) para o ensino de geometria na Educação Básica. Este estudo orientou-se pela pergunta de pesquisa: como um grupo de professores que ensinam matemática, em um contexto de formação continuada, mobilizam saberes vinculados à resolução, à análise e à elaboração de TIGD para o ensino de geometria na Educação Básica? Para respondê-la, estabeleceu-se o objetivo de pesquisa analisar a forma em que um grupo de professores que ensinam matemática, em um contexto de formação continuada, mobilizam saberes vinculados à resolução, à análise e à elaboração de TIGD para o ensino de geometria na Educação Básica. A dissertação, em formato multipaper, está estruturada em três partes. A primeira parte contempla a introdução, em que são descritos aspectos como a trajetória acadêmica e profissional do autor, a pergunta diretriz e seu processo de construção, a relevância, os objetivos e o contexto de estudo, assim como os procedimentos metodológicos delimitados para responder a pergunta de pesquisa. Na segunda parte apresentam-se três capítulos que correspondem aos artigos. No capítulo I descreve-se a revisão de literatura realizada para conhecer o estado de conhecimento do objeto de estudo. Foi desenvolvida uma metassíntese, que consistiu na análise e no confronto de 21 artigos científicos obtidos após um processo de busca em três bases de dados. No capítulo II debruça-se no marco teórico utilizado para analisar os dados empíricos da pesquisa. Para a constituição do marco foram utilizados os conceitos de saber e labor conjunto fornecidos pela Teoria da Objetivação (TO), e adaptados ao contexto da formação continuada de professores que ensinam matemática, orientado à resolução, à análise e à elaboração de TIGD para o ensino de geometria. No capítulo III descreve-se a pesquisa empírica. Para tal, empregou-se um procedimento metodológico que permitiu identificar e examinar sete eventos críticos que forneceram informação sobre como os saberes de interesse da pesquisa foram mobilizados por dez professores que ensinam matemática em situação de formação continuada, enquanto interagiam entre si e com o formador para resolver um conjunto de tarefas. Por fim, a terceira e última parte da dissertação está dedicada a algumas reflexões finais, realizando um olhar retrospectivo do desenvolvimento da pesquisa e apontando possíveis pesquisas futuras.
... divulgação dos resultados de uma investigação seja fundamentada e comunicada de forma a explicitar coerência entre a questão norteadora, a justificativa, as hipóteses dos prováveis resultados do estudo e o método (CAI et al., 2019). ...
Na busca de maior aprofundamento da compreensão da Teoria da Atividade, o objetivo do presente artigo é apresentar como essa teoria tem orientado as pesquisas que investigam o ensino de conteúdos acadêmicos em contexto escolar inclusivo. Os trabalhos selecionados, para compor nosso referencial bibliográfico, revelam a Teoria da Atividade como um referencial teórico e metodológico, orientador para a coleta e tratamento dos dados e para a fundamentação dos conhecimentos produzidos a partir dos resultados das investigações. Concluímos que a Teoria da Atividade ainda é pouco explorada em trabalhos que se ocupam em investigar o ensino de conteúdos acadêmicos no contexto escolar inclusivo, apesar de fornecer elementos que permitem responder a questões que emergem deste cenário de grandes desafios para a comunidade científica.
... The COP of the ASHP of the hybrid DX-SAHP water heater is the ratio of the thermal energy gained by stored water due to the ASHP unit to the electrical energy consumed during the vapor compression refrigeration cycle and is given by Equation (1) [66]. ...
This paper focused on the performance monitoring and modeling of a 6.0 kW, 2000 L hybrid direct expansion solar assisted heat pump (DX-SAHP) water heater used for the production of hot water in a university students’ accommodation with 123 females. The data of total electrical energy consumed, volume of hot water consumed, ambient temperature, relative humidity, and solar irradiance were obtained from the data acquisition systems and analyzed in conjunction with the energy factor (EF) of the system. A multiple linear regression model was developed to predict the EF. The EF of the hybrid DX-SAHP water heater was determined from the summation of the coefficient of performance (COP) of the heat pump unit and the solar fraction (SF) of the solar collectors. The operations of the hybrid energy system were analyzed based on three phases (first phase from 00:00–08:00, second phase from 08:30–18:30, and third phase from 19:00–23:30) over 24 h for the entire monitoring period. The average EF of the hybrid energy system per day during the second phase of operation was 4.38, while the SF and COP were 0.697 and 3.683, respectively. The developed multiple linear regression model for the hybrid DX-SAHP water heater accurately predicted the determined EF.
... Considering your theoretical framework as a contribution to the field means you should treat it as a central part of scientific inquiry, not just as a required step that must be completed before moving to the next phase. To be useful, the theoretical framework should be constructed as a critical part of conceptualizing and carrying out the research (Cai et al., 2019c). This also means you should write out your framework as you are developing it. ...
... Considering your theoretical framework as a contribution to the field means you should treat it as a central part of scientific inquiry, not just as a required step that must be completed before moving to the next phase. To be useful, the theoretical framework should be constructed as a critical part of conceptualizing and carrying out the research (Cai et al., 2019c). This also means you should write out your framework as you are developing it. ...
Theoretical frameworks can be confounding. They are supposed to be very important, but it is not always clear what they are or why you need them. Using ideas from Chaps. 1 and 2 , we describe them as local theories that are custom-designed for your study. Although they might use parts of larger well-known theories, they are created by individual researchers for particular studies. They are developed through the cyclic process of creating more precise and meaningful hypotheses. Building directly on constructs from the previous chapters, you can think of theoretical frameworks as equivalent to the most compelling, complete rationales you can develop for the predictions you make. Theoretical frameworks are important because they do lots of work for you. They incorporate the literature into your rationale, they explain why your study matters, they suggest how you can best test your predictions, and they help you interpret what you find. Your theoretical framework creates an essential coherence for your study and for the paper you are writing to report the study.
... Those studies that have investigated learning with games have employed broad constructs, such as International Journal of Education in Mathematics, Science, and Technology (IJEMST) 273 affect, motivation, and other factors and that if games are used for learning, then a cognitive aspect must be considered (e.g., Garris et al., 2002;Plass et al., 2015). However, given the specificity of theorizing expected within the field of mathematics education (Cai et al., 2019;Leatham, 2019;Spangler & Williams, 2019), extant frameworks about cognition with games from other disciplines (e.g., Garris, et al., 2002) have been too broad to be useful to advance scholarly or practical understanding of game-based mathematics learning. Thus, an innovation of this study was to ensure that theoretical perspectives draw from research specific to mathematics learning. ...
Games are often used to foster student engagement and motivation to learn content, such as mathematics. Although digital games dominate game-based learning research, the table games commonly used in classrooms warrant investigation. Especially for mathematics learning, prior research has not taken into account content-specific frameworks. Integer arithmetic (i.e., calculations with negative numbers) is a difficult topic that is crucial for later mathematics. Thus, this study synthesized multiple theoretical perspectives to understand students’ experiences playing games during an integer unit. A mixed methods design study was conducted to answer the primary question: How was student experience (motivation to learn and engagement) related to game features? Student perspectives about the three integer games they played and observations of student engagement during gameplay were analyzed using perspectives from game design and the Cognitive Demand framework for mathematical tasks. Overall, students positively perceived playing games, however, individuals’ motivation and engagement varied in relation to game features. Students provided valuable insights for research and practice as to which game features were engaging or motivating and why. Speed-based synchronous games that exclusively used skill, rather than a chance-skill balance induced stress and decreased motivation for many students. Thus, a critical implication was to first do no harm by selecting or designing classroom games that have features of turn-taking and chance. We suggest recommendations for mathematics learning and provide the STEM Classroom Games Features Framework to benefit research and practice of any STEM content area.
... Partiendo de los conceptos de saber y labor conjunta, ubicados en el núcleo de la conceptualización del aprendizaje que propone la TO ha sido posible plantear una manera de entender cómo profesores de matemáticas en servicio ponen en movimiento saberes TED profesionales en actividades orientadas hacia la resolución, el análisis y el diseño de TIGD para la enseñanza de las matemáticas, cuando participan en procesos de formación docente en geometría. Como lo sugieren Cai et al. (2019), el artículo ha permitido mostrar cómo sus autores se basan en estas ideas centrales y las combinan con otras aportaciones de estudios sobre la formación de profesores de matemáticas, para producir un marco teórico que se muestra útil tanto para interpretar el fenómeno del aprendizaje docente en contextos formativos particulares, como para justificar las decisiones y acciones necesarias para avanzar en la investigación que ha motivado este trabajo. ...
Desarrollar las capacidades del profesor para gestionar curricularmente las tareas matemáticas que propone en el aula es un objetivo de la formación docente que ha cobrado gran relevancia en los últimos años. Inmerso en esta temática, el presente artículo de reflexión plantea una manera de entender cómo profesores de matemáticas movilizan saberes acerca de la resolución, el análisis y el diseño de tareas investigativas de geometría dinámica (TIGD) para la enseñanza de las matemáticas durante el desarrollo de actividades de formación continua. Para lograr este objetivo, se definen los conceptos de saber y labor conjunta según la teoría de la objetivación y se destacan sus principales características. Posteriormente, se adaptan estos conceptos al contexto de actividades de resolución, análisis y diseño de TIGD en la formación continua de profesores de matemáticas, para conceptualizar a continuación tres tipos de labor conjunta (resolución, análisis y diseño) y tres saberes profesionales susceptibles de movilización en ese contexto formativo. Para cada uno de estos saberes, se describen las acciones y reflexiones específicas que pueden caracterizar a cada tipo de labor conjunta desplegada por los profesores durante la formación. Finalmente, se concluye que la aproximación teórica aquí expuesta no es un producto acabado, sino una reflexión crítica de partida que podrá ser refinada eventualmente al analizar procesos formativos específicos en geometría, orientados hacia la resolución, el análisis y el diseño de TIGD para la enseñanza de las matemáticas en la educación básica.
... Haciendo énfasis en la vertiente disciplinaria, ha sido posible identificar y describir el saber docente que se pone de manifiesto durante la resolución de tareas de construcción euclidianas con GeoGebra, teniendo como referencia algunos problemas de construcción con regla y compás en los Elementos de Euclides que han tenido cierta trascendencia histórica (Iglesias y Ortiz, 2018). Estos dos aspectos del artículo (las ideas de aprendizaje como objetivación y SACEG como un saber docente) constituyen parte fundamental del entramado de supuestos y afirmaciones teóricas que han permitido a los autores tomar decisiones particulares en cuanto a la actividad formativa y su implementación, otorgando a su diseño un lugar privilegiado en el desarrollo de la investigación doctoral (Cai et al., 2019). ...
Resumen El trabajo describe los elementos constituyentes de una actividad formativa diseñada para promover aprendizaje sobre las construcciones euclidianas con GeoGebra por futuros profesores de matemáticas. Comenzamos fijando posición respecto al aprendizaje de dicho saber, partiendo de la concepción histórico-cultural de aprendizaje como procesos de objetivación. Luego conceptualizamos el saber sobre las construcciones euclidianas con GeoGebra como un saber docente que se nutre desde lo disciplinario. Los elementos de la actividad incluyen el motivo, objetivo y metas de la formación, así como las tareas y su modo de implementación. Finalizamos con algunas consideraciones sobre la puesta en escena de la propuesta.
Palabras clave: Procesos de objetivación; Saberes docentes; Tareas de construcción; Formación inicial docente.
Mathematics teacher leadership is promising, yet complex work, and research interest in this form of leadership is on the rise. This systematic review takes stock of the current research landscape on mathematics teacher leadership, specifically mathematics specialists as teacher leaders (MSTLs), and approaches the questions: (1) What are the historical publication trends for MSTLs? and (2) What are the various methods, research questions, and framing used in research design for MSTLs? For this review, we use a subset of articles focused on in-service MSTLs that are part of a larger systematic review that includes constructs such as coaching, mathematics specialists (MS), and other forms of leading teachers. Findings provide evidence that research on MSTLs is certainly on the rise, with nearly 90% of the MSTL research originating in the last decade and published within mainly general education journals. Furthermore, the majority of MSTL studies were qualitative in nature, answered research questions centered on leader interactions with others and leader reactions to professional development programs, and used various theories and constructs to ground the work. Overall, this study extends what is known about the research surrounding MSTLs, illuminates the complexities of this work, and discusses future directions for the field. K E Y W O R D S mathematics education, professional development, teacher education, teachers and teaching
Heavy metal pollution of the environment is a global issue that has an impact on all types of natural life. Arsenic (As) and Cadmium (Cd), along with other heavy metals, permeate our environment and have a number of negative impacts. As and Cd are harmful compounds that are currently prevalent everywhere as a result of water pollution, temperature rise, and climate change in aquatic ecosystems. Using bacteria and algae to remove, decompose, or render harmless contaminants and harmful chemicals (As and Cd) in aquatic systems is currently gaining more attention. the use of bioremediation to remove heavy metals from aquatic environments. Heavy metal pollution of the environment is a global issue that has an impact on all types of natural life. Arsenic (As) and Cadmium (Cd), along with other heavy metals, permeate our environment and have a number of negative impacts. As and Cd are harmful compounds that are currently prevalent everywhere as a result of water pollution, temperature rise, and climate change in aquatic ecosystems. Using bacteria and algae to remove, decompose, or render harmless contaminants and harmful chemicals (As and Cd) in aquatic systems is currently gaining more attention. the use of bioremediation to remove heavy metals from aquatic environments.
In this piece, we share our experiences as we navigate the whiteness of academia. Each of us has taken different pathways to get where we are today as gears within the academic machine. We wrote dangerously to aid our processes of unlearning and (re)learning to disrupt mechanisms of this cruel (white) apparatus. As counterstories do, we hope to be able to help others reflect and determine ways to act against an institution promoting assimilation and erasure of historically and contemporarily excluded populations. Our counterstory centers around the memories of a mathematics education doctoral student, Lily. Her story is presented in a back-and-forth between time periods and gives the reader an opportunity to have their own unique experience with the reading. Instead of a discussion and conclusion, we provide the reader the opportunity to stop or listen to our discussion, available online.
This chapter discusses the nature of the Danish mathematical competencies framework (also known as the KOM framework) as a framework for specifying what it means to successfully learn and master mathematics, and how it differs in nature from other mathematics education constructs and frameworks that set out to do similar things. To do so, we first address the questions “what is a theoretical framework—and a theory—in the field of mathematics education research?” and “how can the KOM framework be placed in this landscape?”. We discuss the KOM framework’s potentials for engaging in connections with other theoretical constructs. We do so through three rich examples of areas within mathematics education that hold important potentials for such connections. The chapter ends with a discussion focusing on the lessons that can be learnt regarding connection with, and potential networking of, various theories with the KOM framework. We suggest that the adequate kind of connection in relation to this framework is best captured by the notion of ‘mutual fertilisation’.
We report findings from an investigation of one teacher's instruction as he guided students through the proofs of 21 theorems in a Grade 8 Honors Geometry course. We describe a routine involving four distinct phases, including Setting up the Proof and Concluding the Proof. Results from an end-of-course proof test are also presented to attest to the effectiveness of the teacher's approach. By engaging with descriptions of the theorem-proving routine, one can learn about different strategies that may support students to learn to prove theorems, such as asking students to put forth claims in the form of conjectures or other statements that they believe are true and seeking justifications for these claims as well as sanctioning a theorem once proven.
The original version of this article unfortunately contains correction.
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 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.
This is an opinion piece on the subject of whether or not ‘theoretical’ and ‘conceptual’ frameworks are conceptual synonyms, or they refer to different constructs. Although, generally, a lot of literature uses these
two terms interchangeably – suggesting that they are conceptually equivalent, the researcher argues that these are two different constructs – both by definition and as actualised during the research process. Thus, in this paper, the researcher starts by developing his argument by examining the role of theory in research, and then draws a distinction between areas of research that typically follow deductive versus inductive approaches, with regard to both the review of literature and data collection. The researcher then subsequently argues that whereas a deductive approach to literature review typically makes use of theories and theoretical frameworks, the inductive approach tends to lead to the development of a conceptual framework – which may take the form of a (conceptua l) model. Examples depicting this distinction are advanced.
The theoretical framework is one of the most important aspects in the research process yet is often misunderstood by doctoral candidates as they prepare their dissertation research study. The importance of theory-driven thinking and acting is emphasized in relation to the selection of a topic, the development of research questions, the conceptualization of the literature review, the design approach, and the analysis plan for the dissertation study. Using a metaphor of the ‘blueprint’ of a house, this article explains the application of a theoretical framework in a dissertation. Steps for how to select and integrate a theoretical framework to structure all aspects of the research process are described, with an example of how to thread theory throughout the dissertation.
The purpose of this book is to collect, organize and disseminate collective wisdom with respect to designing, conducting, and publishing quality research in mathematics education. This wisdom will be gleaned from among those who, over the past several decades, have been instrumental in guiding the field in the pursuit of excellence in mathematics education research—insightful editors, educative reviewers, prolific writers, and caring mentors. Each chapter is written to the novice researcher with the intent of aiding them in avoiding common pitfalls, navigating difficult intellectual terrain, and understanding that they are not alone in experiencing rejection, frustration, confusion, and doubt. This book differs from existing literature in the sense that it is written about the enterprise of designing, conducting and publishing research in mathematics education as opposed to being reports of the results of such work. It also differs in the sense that it is written with the intent to mentor the rising generation as opposed to capture the state of the field (as would happen in a handbook, for example). It is written for the express purpose of helping the field work collectively to aid in the often isolated enterprise of mentoring new researchers. The primary audience is a potentially wide one: graduate students, novice researchers, graduate faculty, advisors, and mentors – or anyone seeking to improve their own abilities to design, conduct, and publish quality research in mathematics education.
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.
Using grounded theory as an example, this paper examines three methodological questions that are generally applicable to all qualitative methods. How should the usual scientific canons be reinterpreted for qualitative research? How should researchers report the procedures and canons used in their research? What evaluative criteria should be used in judging the research products? We propose that the criteria should be adapted to fit the procedures of the method. We demonstrate how this can be done for grounded theory and suggest criteria for evaluating studies following this approach. We argue that other qualitative researchers might be similarly specific about their procedures and evaluative criteria.
Conceptual frameworks for research circa 1991: Ideas from a cultural anthropologist; implications for mathematics education researchers
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On the theoretical, conceptual, and philosophical foundations for research in mathematics education
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