Pub Date : 2021-12-02DOI: 10.1080/10986065.2021.2012737
Martin A. Simon, Daniela Della Volpe, Arundhati Velamur
ABSTRACT Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely respected hypotheses that explain cardinality-principle development as building on young learners’ ability to subitize small numbers. These hypotheses consider subitizing to be the basis of cardinality-principle development. We argue that there is a qualitative and significant difference between subitizing and the cardinality principle and that the explanation provided are insufficient to account for a change of this magnitude. We then propose a conjecture intended to better explain this change. The conjecture describes counting as the medium for a series of reflective abstractions leading to the cardinality principle.
{"title":"Construction of the cardinality principle through counting: critique and conjecture","authors":"Martin A. Simon, Daniela Della Volpe, Arundhati Velamur","doi":"10.1080/10986065.2021.2012737","DOIUrl":"https://doi.org/10.1080/10986065.2021.2012737","url":null,"abstract":"ABSTRACT Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely respected hypotheses that explain cardinality-principle development as building on young learners’ ability to subitize small numbers. These hypotheses consider subitizing to be the basis of cardinality-principle development. We argue that there is a qualitative and significant difference between subitizing and the cardinality principle and that the explanation provided are insufficient to account for a change of this magnitude. We then propose a conjecture intended to better explain this change. The conjecture describes counting as the medium for a series of reflective abstractions leading to the cardinality principle.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"465 - 480"},"PeriodicalIF":1.6,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43417554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-16DOI: 10.1080/10986065.2021.1983691
A. Shvarts, Gitte van Helden
ABSTRACT Educational technologies develop quickly. Which functions of face-to-face education can be substituted by technology for distance learning? One of the risks of online education is the lack of embodied interactions. We investigate what embodied interactive technologies might offer for teaching trigonometry when learning at a distance. In a multiple case study, we analyze the potential of embodied action-based design for fostering conceptual understanding of a sine graph. It appears that independent learning with tablet-based activities leads to acquiring new sensory-motor coordinations. Some students include these new embodied experiences into mathematical discourse and trigonometry problem solving themselves, while others still need some support from a teacher. However, distantly acquired embodied experiences can be easily recalled in a few days after learning and serve well as a substrate for further conceptualization and problem-solving. The results speak for a clear contribution that embodied design might provide for grounding conceptual understanding in distance learning. However, we expect embodied design to be particularly helpful in a blended learning format.
{"title":"Embodied learning at a distance: from sensory-motor experience to constructing and understanding a sine graph","authors":"A. Shvarts, Gitte van Helden","doi":"10.1080/10986065.2021.1983691","DOIUrl":"https://doi.org/10.1080/10986065.2021.1983691","url":null,"abstract":"ABSTRACT Educational technologies develop quickly. Which functions of face-to-face education can be substituted by technology for distance learning? One of the risks of online education is the lack of embodied interactions. We investigate what embodied interactive technologies might offer for teaching trigonometry when learning at a distance. In a multiple case study, we analyze the potential of embodied action-based design for fostering conceptual understanding of a sine graph. It appears that independent learning with tablet-based activities leads to acquiring new sensory-motor coordinations. Some students include these new embodied experiences into mathematical discourse and trigonometry problem solving themselves, while others still need some support from a teacher. However, distantly acquired embodied experiences can be easily recalled in a few days after learning and serve well as a substrate for further conceptualization and problem-solving. The results speak for a clear contribution that embodied design might provide for grounding conceptual understanding in distance learning. However, we expect embodied design to be particularly helpful in a blended learning format.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"409 - 437"},"PeriodicalIF":1.6,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43236675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-24DOI: 10.1080/10986065.2021.1993034
J. Mason
{"title":"Learning mathematics as occasioned by disturbance","authors":"J. Mason","doi":"10.1080/10986065.2021.1993034","DOIUrl":"https://doi.org/10.1080/10986065.2021.1993034","url":null,"abstract":"","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"487 - 488"},"PeriodicalIF":1.6,"publicationDate":"2021-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42556873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-17DOI: 10.1080/10986065.2021.1990744
N. Webb, M. Franke, N. Johnson, Marsha Ing, Joy Zimmerman
ABSTRACT Educators, researchers, and policy makers recognize that student participation in classroom mathematics conversations, especially explaining one’s own thinking and engaging with others’ ideas, can promote students’ mathematics learning. However, precisely how participating in these ways supports learning has not often been examined in detail. Using in-depth analyses of videotaped whole-class discussions, small-group collaborative work, and private partner conversations in two third-grade mathematics classrooms on six occasions over a five- month period, we show advances that students made in their mathematical thinking or mathematical work in the context of explaining their thinking and/or engaging with others’ ideas. The detailed analyses focus on students who had previously scored low on standardized tests of mathematics proficiency. The results show how students not considered to have extensive mathematics knowledge can forge new connections between mathematical ideas and representations, and extend their problem-solving strategies in ways that are directly related to their participation.
{"title":"Learning through explaining and engaging with others’ mathematical ideas","authors":"N. Webb, M. Franke, N. Johnson, Marsha Ing, Joy Zimmerman","doi":"10.1080/10986065.2021.1990744","DOIUrl":"https://doi.org/10.1080/10986065.2021.1990744","url":null,"abstract":"ABSTRACT Educators, researchers, and policy makers recognize that student participation in classroom mathematics conversations, especially explaining one’s own thinking and engaging with others’ ideas, can promote students’ mathematics learning. However, precisely how participating in these ways supports learning has not often been examined in detail. Using in-depth analyses of videotaped whole-class discussions, small-group collaborative work, and private partner conversations in two third-grade mathematics classrooms on six occasions over a five- month period, we show advances that students made in their mathematical thinking or mathematical work in the context of explaining their thinking and/or engaging with others’ ideas. The detailed analyses focus on students who had previously scored low on standardized tests of mathematics proficiency. The results show how students not considered to have extensive mathematics knowledge can forge new connections between mathematical ideas and representations, and extend their problem-solving strategies in ways that are directly related to their participation.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"438 - 464"},"PeriodicalIF":1.6,"publicationDate":"2021-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47065433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-29DOI: 10.1080/10986065.2021.1984070
Michael N. Fried
The premise of dialectical materialism is, we recall: ‘It is not men’s consciousness that determines their existence, but, on the contrary, their social existence that determines their consciousnes...
{"title":"Radford’s theory of objectification: a cultural-historical theory of learning, knowing, and becoming","authors":"Michael N. Fried","doi":"10.1080/10986065.2021.1984070","DOIUrl":"https://doi.org/10.1080/10986065.2021.1984070","url":null,"abstract":"The premise of dialectical materialism is, we recall: ‘It is not men’s consciousness that determines their existence, but, on the contrary, their social existence that determines their consciousnes...","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"481 - 486"},"PeriodicalIF":1.6,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45311432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-29DOI: 10.1080/10986065.2021.1982666
Jessica F. Shumway, Lise E. Welch, Joseph S. Kozlowski, Jody Clarke-Midura, Victor R. Lee
ABSRACT The purpose of this study was to explore how kindergarten students (aged 5–6 years) engaged with mathematics as they learned programming with robot coding toys. We video-recorded 16 teaching sessions of kindergarten students’ (N = 36) mathematical and programming activities. Students worked in small groups (4–5 students) with robot coding toys on the floor in their classrooms, solving tasks that involved programming these toys to move to various locations on a grid. Drawing on a semiotic mediation perspective, we analyzed video data to identify the mathematics concepts and skills students demonstrated and the overlapping mathematics-programming knowledge exhibited by the students during these programming tasks. We found that kindergarten children used spatial, measurement, and number knowledge, and the design of the tasks, affordances of the robots, and types of programming knowledge influenced how the students engaged with mathematics. The paper concludes with a discussion about the intersections of mathematics and programming knowledge in early childhood, and how programming robot toys elicited opportunities for students to engage with mathematics in dynamic and interconnected ways, thus creating an entry point to reassert mathematics beyond the traditional school content and curriculum.
{"title":"Kindergarten students’ mathematics knowledge at work: the mathematics for programming robot toys","authors":"Jessica F. Shumway, Lise E. Welch, Joseph S. Kozlowski, Jody Clarke-Midura, Victor R. Lee","doi":"10.1080/10986065.2021.1982666","DOIUrl":"https://doi.org/10.1080/10986065.2021.1982666","url":null,"abstract":"ABSRACT The purpose of this study was to explore how kindergarten students (aged 5–6 years) engaged with mathematics as they learned programming with robot coding toys. We video-recorded 16 teaching sessions of kindergarten students’ (N = 36) mathematical and programming activities. Students worked in small groups (4–5 students) with robot coding toys on the floor in their classrooms, solving tasks that involved programming these toys to move to various locations on a grid. Drawing on a semiotic mediation perspective, we analyzed video data to identify the mathematics concepts and skills students demonstrated and the overlapping mathematics-programming knowledge exhibited by the students during these programming tasks. We found that kindergarten children used spatial, measurement, and number knowledge, and the design of the tasks, affordances of the robots, and types of programming knowledge influenced how the students engaged with mathematics. The paper concludes with a discussion about the intersections of mathematics and programming knowledge in early childhood, and how programming robot toys elicited opportunities for students to engage with mathematics in dynamic and interconnected ways, thus creating an entry point to reassert mathematics beyond the traditional school content and curriculum.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"380 - 408"},"PeriodicalIF":1.6,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46148624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-22DOI: 10.1080/10986065.2021.1977086
Jonathan Thomas, David M. Dueber, Molly H. Fisher, C. Jong, E. Schack
ABSTRACT Teacher noticing and related variants have ascended in prominence among the mathematics education research community. While the component processes of such noticing (e.g., attending, interpreting and deciding) have been cast as interrelated, capturing the relationships amongst the components has been more elusive. We focused on the component processes of teacher noticing with particular attention given to interrelatedness. Specifically, we were interested in how and the extent to which the component processes of professional noticing (attending, interpreting, deciding) are thematically connected when preservice elementary teachers are engaged in an assessment approximating professional noticing. We refer to this thematic linkage in this paper as coherence. Our findings suggest a complex interplay between the creation and continuation of themes when enacting professional noticing, and the quality of such noticing.
{"title":"Professional noticing coherence: exploring relationships between component processes","authors":"Jonathan Thomas, David M. Dueber, Molly H. Fisher, C. Jong, E. Schack","doi":"10.1080/10986065.2021.1977086","DOIUrl":"https://doi.org/10.1080/10986065.2021.1977086","url":null,"abstract":"ABSTRACT Teacher noticing and related variants have ascended in prominence among the mathematics education research community. While the component processes of such noticing (e.g., attending, interpreting and deciding) have been cast as interrelated, capturing the relationships amongst the components has been more elusive. We focused on the component processes of teacher noticing with particular attention given to interrelatedness. Specifically, we were interested in how and the extent to which the component processes of professional noticing (attending, interpreting, deciding) are thematically connected when preservice elementary teachers are engaged in an assessment approximating professional noticing. We refer to this thematic linkage in this paper as coherence. Our findings suggest a complex interplay between the creation and continuation of themes when enacting professional noticing, and the quality of such noticing.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"361 - 379"},"PeriodicalIF":1.6,"publicationDate":"2021-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49152391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-25DOI: 10.1080/10986065.2021.1940432
Ofer Marmur, B. Koichu
ABSTRACT This paper explores student emotion and learning experiences fostered by lecturing-style instruction in Real-Analysis problem-centered lessons. We focus on two lessons that were taught by two reputable instructors and involved challenging, mathematically-related problems the students did not understand. Nonetheless, one lesson evoked negative emotional reactions, while the other positive emotional reactions – a phenomenon we aimed at explaining. The main data comprise the filmed lessons and subsequent stimulated-recall interviews with nine students. The analysis draws on conceptual tools from three perspectives: mathematical discourse, variation theory, and a recently developed construct of key memorable events (KMEs) that offers an affective-cognitive lens for investigating the interrelation between teaching and learning. The findings indicate that the positively-perceived lesson contained instances of what we call heuristic-didactic discourse: a meta-level discourse that presents heuristics monitored from an expert’s perspective, yet derived from a student’s perspective. Implications for research and practice are drawn.
{"title":"Between expert and student perspectives: on the intersection of affect and heuristic-didactic discourse in the undergraduate classroom","authors":"Ofer Marmur, B. Koichu","doi":"10.1080/10986065.2021.1940432","DOIUrl":"https://doi.org/10.1080/10986065.2021.1940432","url":null,"abstract":"ABSTRACT This paper explores student emotion and learning experiences fostered by lecturing-style instruction in Real-Analysis problem-centered lessons. We focus on two lessons that were taught by two reputable instructors and involved challenging, mathematically-related problems the students did not understand. Nonetheless, one lesson evoked negative emotional reactions, while the other positive emotional reactions – a phenomenon we aimed at explaining. The main data comprise the filmed lessons and subsequent stimulated-recall interviews with nine students. The analysis draws on conceptual tools from three perspectives: mathematical discourse, variation theory, and a recently developed construct of key memorable events (KMEs) that offers an affective-cognitive lens for investigating the interrelation between teaching and learning. The findings indicate that the positively-perceived lesson contained instances of what we call heuristic-didactic discourse: a meta-level discourse that presents heuristics monitored from an expert’s perspective, yet derived from a student’s perspective. Implications for research and practice are drawn.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"115 - 144"},"PeriodicalIF":1.6,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46965499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-14DOI: 10.1080/10986065.2021.1966713
Hyunyi Jung, Marta T. Magiera
ABSTRACT This paper contributes to accumulating the knowledge base about prospective elementary school teachers’ (PTs’) understanding of socio-critical modeling by exploring how PTs make connections to features of mathematical modeling and social justice while posing mathematical problems and reflecting on their problem-posing. We present a conceptual framework for posing problems that connect social justice issues with the features of mathematical modeling. Drawing on the analysis of 36 individual modeling problems generated by the PTs and 36 written reflections PTs completed throughout their problem-posing activity, we illustrate various ways in which PTs connect the multi-faceted features of mathematical modeling (i.e., realistic context, model development, and shareable process) and social justice (i.e., micro – and macro – level). The PT-posed problems were categorized as (a) modeling problems presenting micro – and macro-level social justice issues (27%), (b) modeling problems presenting micro-level social justice issues (22%), (c) contextualized mathematical problems presenting micro – and macro-level social justice issues (25%), and (d) contextualized mathematical problems presenting micro-level social justice issues (17%). Our work describing the complexity of posing social justice-oriented mathematical modeling (SJMM) problems and articulating decisions PTs make while posing SJMM problems set directions for future efforts and research in teacher preparation.
{"title":"Connecting mathematical modeling and social justice through problem posing","authors":"Hyunyi Jung, Marta T. Magiera","doi":"10.1080/10986065.2021.1966713","DOIUrl":"https://doi.org/10.1080/10986065.2021.1966713","url":null,"abstract":"ABSTRACT This paper contributes to accumulating the knowledge base about prospective elementary school teachers’ (PTs’) understanding of socio-critical modeling by exploring how PTs make connections to features of mathematical modeling and social justice while posing mathematical problems and reflecting on their problem-posing. We present a conceptual framework for posing problems that connect social justice issues with the features of mathematical modeling. Drawing on the analysis of 36 individual modeling problems generated by the PTs and 36 written reflections PTs completed throughout their problem-posing activity, we illustrate various ways in which PTs connect the multi-faceted features of mathematical modeling (i.e., realistic context, model development, and shareable process) and social justice (i.e., micro – and macro – level). The PT-posed problems were categorized as (a) modeling problems presenting micro – and macro-level social justice issues (27%), (b) modeling problems presenting micro-level social justice issues (22%), (c) contextualized mathematical problems presenting micro – and macro-level social justice issues (25%), and (d) contextualized mathematical problems presenting micro-level social justice issues (17%). Our work describing the complexity of posing social justice-oriented mathematical modeling (SJMM) problems and articulating decisions PTs make while posing SJMM problems set directions for future efforts and research in teacher preparation.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"232 - 251"},"PeriodicalIF":1.6,"publicationDate":"2021-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44117548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-26DOI: 10.1080/10986065.2021.1943608
E. Parr
ABSTRACT The purpose of this study is to investigate how students interpret expressions from calculus statements in the graphical register. To this end, I conducted 150-minute clinical interviews with 13 undergraduate mathematics students who had completed at least one calculus course. In the interviews, students evaluated six calculus statements for various real-valued functions depicted in graphs in the Cartesian plane. From my analysis of these interviews, I found four distinct interpretations of expressions in the graphical register that students used in this study while evaluating the statements using the graphs. I describe the characteristics of these four interpretations, which I refer to as (1) nominal, (2) ordinal, (3) cardinal, and (4) magnitude. For some students, the use of these interpretations supported their graphical reasoning and correct evaluations of the statements. For other students, the use of some interpretations rather than others presented obstacles to their graphical understanding of the expressions in the statement. For instance, seven of the students never used a magnitude interpretation (interpreting an expression as a distance in the graph), even when working with difference expressions. I discuss implications of these findings for teaching with graphs across levels and directions for future research.
{"title":"Undergraduate students’ interpretations of expressions from calculus statements within the graphical register","authors":"E. Parr","doi":"10.1080/10986065.2021.1943608","DOIUrl":"https://doi.org/10.1080/10986065.2021.1943608","url":null,"abstract":"ABSTRACT The purpose of this study is to investigate how students interpret expressions from calculus statements in the graphical register. To this end, I conducted 150-minute clinical interviews with 13 undergraduate mathematics students who had completed at least one calculus course. In the interviews, students evaluated six calculus statements for various real-valued functions depicted in graphs in the Cartesian plane. From my analysis of these interviews, I found four distinct interpretations of expressions in the graphical register that students used in this study while evaluating the statements using the graphs. I describe the characteristics of these four interpretations, which I refer to as (1) nominal, (2) ordinal, (3) cardinal, and (4) magnitude. For some students, the use of these interpretations supported their graphical reasoning and correct evaluations of the statements. For other students, the use of some interpretations rather than others presented obstacles to their graphical understanding of the expressions in the statement. For instance, seven of the students never used a magnitude interpretation (interpreting an expression as a distance in the graph), even when working with difference expressions. I discuss implications of these findings for teaching with graphs across levels and directions for future research.","PeriodicalId":46800,"journal":{"name":"Mathematical Thinking and Learning","volume":"25 1","pages":"177 - 207"},"PeriodicalIF":1.6,"publicationDate":"2021-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10986065.2021.1943608","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42985735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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