Many studies on professionalization research deal with the question of how teachers actually learn or how teacher change occurs. In this context, Clarke and Hollingsworth (2002) describe a model for capturing teacher change in different domains (external, personal, domain of practice and domain of consequence) and how changes in one domain can affect other domains over time. The present article suggests the notion of resonance for analyzing teachers’ professionalization processes in order to better understand the reasons for teacher change on a micro level in their complexity. The idea was to supplement the model by the dimension of teachers’ professional conditions, to capture and describe the phenomenon that an active process of engagement with the professional development (PD) content is set in motion. We consider teachers’ resonance to be a condition for a successful professionalization process. Insights from two different research projects from Germany and Norway demonstrate the scope of the notion of resonance. Consequences for facilitators and the design of further PD programs are discussed.
{"title":"Specifying and identifying signs of ‘resonance’ in teachers’ professionalization processes as a condition for teacher change","authors":"Carina Büscher, M. Andresen","doi":"10.29333/iejme/13307","DOIUrl":"https://doi.org/10.29333/iejme/13307","url":null,"abstract":"Many studies on professionalization research deal with the question of how teachers actually learn or how teacher change occurs. In this context, Clarke and Hollingsworth (2002) describe a model for capturing teacher change in different domains (external, personal, domain of practice and domain of consequence) and how changes in one domain can affect other domains over time. The present article suggests the notion of resonance for analyzing teachers’ professionalization processes in order to better understand the reasons for teacher change on a micro level in their complexity. The idea was to supplement the model by the dimension of teachers’ professional conditions, to capture and describe the phenomenon that an active process of engagement with the professional development (PD) content is set in motion. We consider teachers’ resonance to be a condition for a successful professionalization process. Insights from two different research projects from Germany and Norway demonstrate the scope of the notion of resonance. Consequences for facilitators and the design of further PD programs are discussed.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75643935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The role of executive function training in supporting child development has been increasingly studied. Executive function is largely related to the prefrontal cortex. The anterior portion of the prefrontal cortex, which is area 10 on the Brodmann map, is essential for the emergence of higher-order executive functions. Accumulating evidence indicates that mental abacus training, which is closely related to mathematics education, activates the prefrontal cortex. Based on these findings, it can be hypothesized that the mental abacus is valuable for training more advanced functions. Therefore, this study analyzed the activation of children’s brains with a focus on the frontal pole (Brodmann area 10). The results illustrated that mental abacus task more strongly activated the brain than piano task, the marshmallow test, or letter–number sequencing tasks. Thus, it was suggested that the mental abacus is valuable for training higher-level executive functions (i.e., frontal pole).
{"title":"Mental abacus training affects high-level executive functions: Comparison of activation of the frontal pole","authors":"Nobuki Watanabe","doi":"10.29333/iejme/13220","DOIUrl":"https://doi.org/10.29333/iejme/13220","url":null,"abstract":"The role of executive function training in supporting child development has been increasingly studied. Executive function is largely related to the prefrontal cortex. The anterior portion of the prefrontal cortex, which is area 10 on the Brodmann map, is essential for the emergence of higher-order executive functions. Accumulating evidence indicates that mental abacus training, which is closely related to mathematics education, activates the prefrontal cortex. Based on these findings, it can be hypothesized that the mental abacus is valuable for training more advanced functions. Therefore, this study analyzed the activation of children’s brains with a focus on the frontal pole (Brodmann area 10). The results illustrated that mental abacus task more strongly activated the brain than piano task, the marshmallow test, or letter–number sequencing tasks. Thus, it was suggested that the mental abacus is valuable for training higher-level executive functions (i.e., frontal pole).","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90082800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is important to note that the development of pre-service teachers’ noticing abilities does not happen spontaneously; hence, assistance programs are crucial. This qualitative study aimed to examine pre-service teachers’ noticing of student thinking within the context of lesson study. Three pre-service teachers conducted three lesson study cycles. Lesson plans, voice and video recordings of lesson study meetings and implementations, observations, field notes, and reflective writings are used as data collection techniques. The findings indicated that the pre-service teachers’ early levels of noticing were constrained. Their noticing levels increased as the lesson study progressed. Hence, the improvement of pre-service teachers’ noticing abilities can be assisted by lesson study. Activities such as planning, reflection and implementation helped pre-service teachers develop their noticing levels. To enhance the development of noticing skills, it can be proposed that lesson study should be integrated into teacher training programs.
{"title":"Pre-service mathematics teachers’ learning to notice student statistical thinking in the context of lesson study","authors":"Nadide Yilmaz, Iffet Elif Yetkin Ozdemir","doi":"10.29333/iejme/13398","DOIUrl":"https://doi.org/10.29333/iejme/13398","url":null,"abstract":"It is important to note that the development of pre-service teachers’ noticing abilities does not happen spontaneously; hence, assistance programs are crucial. This qualitative study aimed to examine pre-service teachers’ noticing of student thinking within the context of lesson study. Three pre-service teachers conducted three lesson study cycles. Lesson plans, voice and video recordings of lesson study meetings and implementations, observations, field notes, and reflective writings are used as data collection techniques. The findings indicated that the pre-service teachers’ early levels of noticing were constrained. Their noticing levels increased as the lesson study progressed. Hence, the improvement of pre-service teachers’ noticing abilities can be assisted by lesson study. Activities such as planning, reflection and implementation helped pre-service teachers develop their noticing levels. To enhance the development of noticing skills, it can be proposed that lesson study should be integrated into teacher training programs.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72489387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study aims to examine how being involved in an argumentation process relates to the formal proof process in geometry. Prospective mathematics teachers were involved in an argumentation process while producing conjectures before engaging in formal proof of the recently produced conjectures. To collect data, four geometry-proof tasks that involve two sections were employed. The first section of the tasks demands the production of conjectures, which stands for the term argumentation. The second section asks for the formal proof of one of the recently produced conjectures. Based on the data analysis, the affordances of being involved in argumentation before engaging in the formal proof process were listed as positive affective occasions, arrangement of knowledge related to the content of the task, visual aspect, and the veracity of the statement. Negative affective occasions and confusion related to the difference between conjecturing and proving were coded as constraints of being involved in argumentation before formal proof.
{"title":"How argumentation relates to formal proof process in geometry","authors":"Esra Demiray, Mine Işıksal-Bostan, Elif Saygı","doi":"10.29333/iejme/13214","DOIUrl":"https://doi.org/10.29333/iejme/13214","url":null,"abstract":"This study aims to examine how being involved in an argumentation process relates to the formal proof process in geometry. Prospective mathematics teachers were involved in an argumentation process while producing conjectures before engaging in formal proof of the recently produced conjectures. To collect data, four geometry-proof tasks that involve two sections were employed. The first section of the tasks demands the production of conjectures, which stands for the term argumentation. The second section asks for the formal proof of one of the recently produced conjectures. Based on the data analysis, the affordances of being involved in argumentation before engaging in the formal proof process were listed as positive affective occasions, arrangement of knowledge related to the content of the task, visual aspect, and the veracity of the statement. Negative affective occasions and confusion related to the difference between conjecturing and proving were coded as constraints of being involved in argumentation before formal proof.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91322173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lisa Skultety, E. Saclarides, Neet Priya Bajwa, Karie Brown, Adam Poetzel, J. Gerardo
We, six elementary mathematics teacher educators (MTEs), noticed that many of our elementary pre-service teachers (EPSTs) were limited by their views of mathematics, typically as the result of their prior experiences with learning mathematics. Much of the research around such limiting views focuses primarily on negative experiences or treats such views as associated with individual factors (e.g., self-efficacy, mathematics anxiety, and views about problem solving). Using a (re)humanizing mathematics perspective, we sought to identify these limiting views of mathematics in a more holistic approach, considering the complexity of views that EPSTs hold. In this article, we introduce a framework, developed through collaborative self-study methodology, to give shared language to the types of mathematical wounds EPSTs may have. Utilizing this framework, MTEs can support EPSTs’ mathematical healing by enacting intentional instructional practices. We provide three general approaches to frame these intentional practices as well as reflection questions to support other MTEs in reconsidering their own courses and how they may take EPSTs’ mathematical wounds and healing into account.
{"title":"Making sense of elementary pre-service teachers’ mathematical wounds: A proposed framework for practice","authors":"Lisa Skultety, E. Saclarides, Neet Priya Bajwa, Karie Brown, Adam Poetzel, J. Gerardo","doi":"10.29333/iejme/13170","DOIUrl":"https://doi.org/10.29333/iejme/13170","url":null,"abstract":"We, six elementary mathematics teacher educators (MTEs), noticed that many of our elementary pre-service teachers (EPSTs) were limited by their views of mathematics, typically as the result of their prior experiences with learning mathematics. Much of the research around such limiting views focuses primarily on negative experiences or treats such views as associated with individual factors (e.g., self-efficacy, mathematics anxiety, and views about problem solving). Using a (re)humanizing mathematics perspective, we sought to identify these limiting views of mathematics in a more holistic approach, considering the complexity of views that EPSTs hold. In this article, we introduce a framework, developed through collaborative self-study methodology, to give shared language to the types of mathematical wounds EPSTs may have. Utilizing this framework, MTEs can support EPSTs’ mathematical healing by enacting intentional instructional practices. We provide three general approaches to frame these intentional practices as well as reflection questions to support other MTEs in reconsidering their own courses and how they may take EPSTs’ mathematical wounds and healing into account.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78340211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nagham Mohammad, Mihai Nica, K. M. Levere, Rachel Okner
Out-of-class activities play a crucial role in student learning. However, student opinions on the design of these activities are rarely measured across several different classes. The purpose of this study is to understand students’ preferences and attitudes towards new “Engaged Mathematics Labs” in which professors and teaching assistants assisted students in completing an assignment during lab time. We analyze both qualitative and quantitative survey responses from ~200 first year students participating in “Engaged Mathematics Labs” across two different levels of mathematics classes at a large Canadian public university. Results indicate that students enjoy being able to work in groups regardless of major or gender. Moreover, students learned to effectively use resources available in the course to solve questions that deepen their understanding of course concepts. Understanding the student preferences from this study can help form the design of future learning activities and future pedagogical studies.
{"title":"Promoting engagement via engaged mathematics labs and supportive learning","authors":"Nagham Mohammad, Mihai Nica, K. M. Levere, Rachel Okner","doi":"10.29333/iejme/12960","DOIUrl":"https://doi.org/10.29333/iejme/12960","url":null,"abstract":"Out-of-class activities play a crucial role in student learning. However, student opinions on the design of these activities are rarely measured across several different classes. The purpose of this study is to understand students’ preferences and attitudes towards new “Engaged Mathematics Labs” in which professors and teaching assistants assisted students in completing an assignment during lab time. We analyze both qualitative and quantitative survey responses from ~200 first year students participating in “Engaged Mathematics Labs” across two different levels of mathematics classes at a large Canadian public university. Results indicate that students enjoy being able to work in groups regardless of major or gender. Moreover, students learned to effectively use resources available in the course to solve questions that deepen their understanding of course concepts. Understanding the student preferences from this study can help form the design of future learning activities and future pedagogical studies.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74713392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of the study is to determine the extent to which the root values were included in the middle school mathematics textbooks that were recommended in the 2018 middle school mathematics curriculum by Ministry of National Education (MoNE). In this study, mathematics textbooks were assumed to be an important material in terms of development of students’ intention to use root values. The data were collected from ten mathematics textbooks, including two fifth grade, three sixth grade, two seventh grade, and three eighth grades, recommended by MoNE for use in middle schools in the 2019-2020 academic year. A basic qualitative research design was used in the study. To analyze the data a content analysis process was implemented. As a result, it was found that while the values of friendship, self-control, responsibility, patriotism, and benevolence were used in the textbooks in detail and with their first meanings, there was not enough content about the values of justice, honesty, respect, and love and these values were being used differently from their first meanings. It is recommended that the content involving root values should be distributed more homogeneously to the grade levels and values should be used with their first meaning in mathematics textbooks. In addition, there should be more specific information in mathematics textbooks about how to integrate root values into a mathematics classroom.
{"title":"Examination of middle school mathematics textbooks in terms of values","authors":"Tuğba Horzum, Esra Yildiz","doi":"10.29333/iejme/12908","DOIUrl":"https://doi.org/10.29333/iejme/12908","url":null,"abstract":"The aim of the study is to determine the extent to which the root values were included in the middle school mathematics textbooks that were recommended in the 2018 middle school mathematics curriculum by Ministry of National Education (MoNE). In this study, mathematics textbooks were assumed to be an important material in terms of development of students’ intention to use root values. The data were collected from ten mathematics textbooks, including two fifth grade, three sixth grade, two seventh grade, and three eighth grades, recommended by MoNE for use in middle schools in the 2019-2020 academic year. A basic qualitative research design was used in the study. To analyze the data a content analysis process was implemented. As a result, it was found that while the values of friendship, self-control, responsibility, patriotism, and benevolence were used in the textbooks in detail and with their first meanings, there was not enough content about the values of justice, honesty, respect, and love and these values were being used differently from their first meanings. It is recommended that the content involving root values should be distributed more homogeneously to the grade levels and values should be used with their first meaning in mathematics textbooks. In addition, there should be more specific information in mathematics textbooks about how to integrate root values into a mathematics classroom.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74531181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
José Gerardo Piña-Aguirre, Rosa María Farfán Márquez
With the objective of identifying intrinsic forms of mathematical production in complex analysis (CA), this study presents an analysis of the mathematical activity of five original works that contributed to the development of Cauchy’s integral theorem. The analysis of the mathematical activity was carried out through the identification of the types of expressions used and the way they were used by the historical subjects when communicating their results, to subsequently identify transversal elements of knowledge production. The analysis was refined by the notion of confrontation, which depicts the development of mathematical knowledge through the idea of building knowledge against previous knowledge. As a result of the study we established epistemological hypothesis, which are conceived as conjectures that reveal ways in which mathematical knowledge was generated in CA.
{"title":"What enabled the production of mathematical knowledge in complex analysis?","authors":"José Gerardo Piña-Aguirre, Rosa María Farfán Márquez","doi":"10.29333/iejme/12996","DOIUrl":"https://doi.org/10.29333/iejme/12996","url":null,"abstract":"With the objective of identifying intrinsic forms of mathematical production in complex analysis (CA), this study presents an analysis of the mathematical activity of five original works that contributed to the development of Cauchy’s integral theorem. The analysis of the mathematical activity was carried out through the identification of the types of expressions used and the way they were used by the historical subjects when communicating their results, to subsequently identify transversal elements of knowledge production. The analysis was refined by the notion of confrontation, which depicts the development of mathematical knowledge through the idea of building knowledge against previous knowledge. As a result of the study we established epistemological hypothesis, which are conceived as conjectures that reveal ways in which mathematical knowledge was generated in CA.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89146798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Angelina G. González Peralta, Mario Sánchez Aguilar
Educational research has reported different benefits related to the use of practice tests. In the case of the teaching and learning of mathematics, evidence has been found that the use of practice tests is associated with an improved performance in standardized tests. However, it is less known about the emotions that students experience during such practice tests. This paper reports on a study on the use of practice test in mathematics instruction at the undergraduate level, which focuses on exploring students’ emotions during a practice test for linear algebra. 78 students answered a questionnaire one day after having participated in an oral practice test on linear algebra. The results suggest that before the practice test nervousness was predominant among students, but this emotion decreases as the activity progresses.
{"title":"Undergraduate students’ emotions around a linear algebra oral practice test","authors":"Angelina G. González Peralta, Mario Sánchez Aguilar","doi":"10.29333/iejme/13007","DOIUrl":"https://doi.org/10.29333/iejme/13007","url":null,"abstract":"Educational research has reported different benefits related to the use of practice tests. In the case of the teaching and learning of mathematics, evidence has been found that the use of practice tests is associated with an improved performance in standardized tests. However, it is less known about the emotions that students experience during such practice tests. This paper reports on a study on the use of practice test in mathematics instruction at the undergraduate level, which focuses on exploring students’ emotions during a practice test for linear algebra. 78 students answered a questionnaire one day after having participated in an oral practice test on linear algebra. The results suggest that before the practice test nervousness was predominant among students, but this emotion decreases as the activity progresses.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87345672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A review of studies analyzing the statistical knowledge of primary schoolchildren (6-12 years old) is carried out. Based on a review in JCR/SSCI, Scopus, Eric, Google Scholar, Science Direct, World Scientific, Springer, and Wiley Online library, 18 articles (2003-2021) have been identified and analyzed based on two objectives: (i) to identify the different study approaches and (ii) to analyze the elements of statistical knowledge. The results show that almost half of the investigations were carried out based on one of the following approaches: the Toulmin approach (TM), the statistical mathematical working space (SMWS), the structure of observed learning outcomes (SOLO) taxonomy and Curcio’s graph reading levels (CGRL). It is concluded that CGRL is the most common approach and statistical graphs are the most analyzed statistical objects.
{"title":"Statistical knowledge of primary schoolchildren: An overview of study approaches","authors":"Daniel Londoño, Ángel Alsina","doi":"10.29333/iejme/12984","DOIUrl":"https://doi.org/10.29333/iejme/12984","url":null,"abstract":"A review of studies analyzing the statistical knowledge of primary schoolchildren (6-12 years old) is carried out. Based on a review in JCR/SSCI, Scopus, Eric, Google Scholar, Science Direct, World Scientific, Springer, and Wiley Online library, 18 articles (2003-2021) have been identified and analyzed based on two objectives: (i) to identify the different study approaches and (ii) to analyze the elements of statistical knowledge. The results show that almost half of the investigations were carried out based on one of the following approaches: the Toulmin approach (TM), the statistical mathematical working space (SMWS), the structure of observed learning outcomes (SOLO) taxonomy and Curcio’s graph reading levels (CGRL). It is concluded that CGRL is the most common approach and statistical graphs are the most analyzed statistical objects.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73316931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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