Let G be a graph with a red-blue coloring c of the edges of G . A Ramsey chain in G with respect to c is a sequence G 1 , G 2 , . . . , G k of pairwise edge-disjoint subgraphs of G such that each subgraph G i ( 1 ≤ i ≤ k ) is monochromatic of size i and G i is isomorphic to a subgraph of G i +1 ( 1 ≤ i ≤ k − 1 ). The Ramsey index AR c ( G ) of G with respect to c is the maximum length of a Ramsey chain in G with respect to c . The Ramsey index AR ( G ) of G is the minimum value of AR c ( G ) among all red-blue colorings c of G . A Ramsey chain with respect to c is maximal if it cannot be extended to one of greater length. The lower Ramsey index AR − c ( G ) of G with respect to c is the minimum length of a maximal Ramsey chain in G with respect to c . The lower Ramsey index AR − ( G ) of G is the minimum value of AR − c ( G ) among all red-blue colorings c of G . Ramsey chains and maximal Ramsey chains are investigated for stars, matchings, and cycles. It is shown that (1) for every two integers p and q with 2 ≤ p < q , there exists a graph with a red-blue coloring possessing a maximal Ramsey chain of length p and a maximum Ramsey chain of length q and (2) for every positive integer k , there exists a graph with a red-blue coloring possessing at least k maximal Ramsey chains of distinct lengths with prescribed conditions. A conjecture and additional results are also presented.
设G是一个图，它的边是红蓝色的c。G中关于c的拉姆齐链是一个序列g1, g2，…， G的成对边不相交子图的G k，使得每个子图G i(1≤i≤k)是大小为i的单色，并且G i同构于G i +1(1≤i≤k−1)的子图。G对c的拉姆齐指数AR c (G)是G中拉姆齐链对c的最大长度。G的拉姆齐指数AR (G)是所有G的红蓝颜色c中AR c (G)的最小值。关于c的拉姆齐链是极大的，如果它不能扩展到更长的拉姆齐链。G相对于c的Ramsey下标AR−c (G)是G相对于c的极大Ramsey链的最小长度。G的下拉姆齐指数AR−(G)是G的所有红蓝着色c中AR−c (G)的最小值。研究了Ramsey链和极大Ramsey链的星型、匹配型和环型。证明了(1)对于每两个2≤p < q的整数p和q，存在一个红蓝着色的图，其最大Ramsey链的长度为p，最大Ramsey链的长度为q;(2)对于每一个正整数k，存在一个红蓝着色的图，其具有至少k个不同长度的极大Ramsey链，且具有规定的条件。本文还提出了一个猜想和一些附加结果。
{"title":"Ramsey chains in graphs","authors":"G. Chartrand, Ritabrato Chatterjee, Ping Zhang","doi":"10.47443/ejm.2023.029","DOIUrl":"https://doi.org/10.47443/ejm.2023.029","url":null,"abstract":"Let G be a graph with a red-blue coloring c of the edges of G . A Ramsey chain in G with respect to c is a sequence G 1 , G 2 , . . . , G k of pairwise edge-disjoint subgraphs of G such that each subgraph G i ( 1 ≤ i ≤ k ) is monochromatic of size i and G i is isomorphic to a subgraph of G i +1 ( 1 ≤ i ≤ k − 1 ). The Ramsey index AR c ( G ) of G with respect to c is the maximum length of a Ramsey chain in G with respect to c . The Ramsey index AR ( G ) of G is the minimum value of AR c ( G ) among all red-blue colorings c of G . A Ramsey chain with respect to c is maximal if it cannot be extended to one of greater length. The lower Ramsey index AR − c ( G ) of G with respect to c is the minimum length of a maximal Ramsey chain in G with respect to c . The lower Ramsey index AR − ( G ) of G is the minimum value of AR − c ( G ) among all red-blue colorings c of G . Ramsey chains and maximal Ramsey chains are investigated for stars, matchings, and cycles. It is shown that (1) for every two integers p and q with 2 ≤ p < q , there exists a graph with a red-blue coloring possessing a maximal Ramsey chain of length p and a maximum Ramsey chain of length q and (2) for every positive integer k , there exists a graph with a red-blue coloring possessing at least k maximal Ramsey chains of distinct lengths with prescribed conditions. A conjecture and additional results are also presented.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"8 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82259725","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}
Let G be a simple connected graph with minimum degree δ , second minimum degree δ (cid:48) , and connected domination number γ c ( G ) . It is shown that G has a spanning path whenever γ c ( G ) ≥ n − δ (cid:48) − 1 . This result is best possible for δ (cid:48) < 3 ; that is, if γ c ( G ) ≥ n − δ (cid:48) − 2 and δ (cid:48) < 3 , then G may or may not contain a spanning path. Also, this result settles completely a conjecture posed recently by Chellali and Favaron. In addition, for every choice of δ (cid:48) and δ , an infinite family of non-traceable graphs satisfying δ (cid:48) > δ and γ c ( G ) ≤ n − 2 δ (cid:48) is provided, which shows that if another recent conjecture by Chellali and Favaron is true, then it is best possible in a sense. The obtained results, apart from addressing some stronger versions of conjectures generated by the computer program Graffiti.pc, improve some known results.
设G为具有最小度δ、第二次最小度δ (cid:48)和连通支配数γ c (G)的简单连通图。结果表明，当γ c (G)≥n−δ (cid:48)−1时，G具有生成路径。当δ (cid:48) < 3;即，如果γ c (G)≥n−δ (cid:48)−2且δ (cid:48) < 3，则G可能包含也可能不包含生成路径。此外，这一结果完全解决了最近由Chellali和Favaron提出的一个猜想。此外，对于δ (cid:48)和δ的每一个选择，都给出了满足δ (cid:48) > δ和γ c (G)≤n−2 δ (cid:48)的无限族非可迹图，这表明如果Chellali和Favaron最近的另一个猜想成立，那么它在某种意义上是最可能的。获得的结果，除了解决了计算机程序涂鸦产生的一些更强版本的猜想之外。Pc，改进一些已知的结果。
{"title":"Connected domination number and traceable graphs","authors":"Phillip Mafuta","doi":"10.47443/ejm.2023.027","DOIUrl":"https://doi.org/10.47443/ejm.2023.027","url":null,"abstract":"Let G be a simple connected graph with minimum degree δ , second minimum degree δ (cid:48) , and connected domination number γ c ( G ) . It is shown that G has a spanning path whenever γ c ( G ) ≥ n − δ (cid:48) − 1 . This result is best possible for δ (cid:48) < 3 ; that is, if γ c ( G ) ≥ n − δ (cid:48) − 2 and δ (cid:48) < 3 , then G may or may not contain a spanning path. Also, this result settles completely a conjecture posed recently by Chellali and Favaron. In addition, for every choice of δ (cid:48) and δ , an infinite family of non-traceable graphs satisfying δ (cid:48) > δ and γ c ( G ) ≤ n − 2 δ (cid:48) is provided, which shows that if another recent conjecture by Chellali and Favaron is true, then it is best possible in a sense. The obtained results, apart from addressing some stronger versions of conjectures generated by the computer program Graffiti.pc, improve some known results.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"66 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80835074","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 article gives several properties of a new type of submodules, namely weakly ( m, n ) -semiprime submodules where m and n are positive integers satisfying m > n . The primary objectives of the present article are to characterize weakly ( m, n ) - semiprime submodules and to provide a new characterization of the von Neumann regular modules in terms of weakly ( m, n ) -semiprime submodules.
{"title":"Weakly (m,n)–semiprime submodules","authors":"Mohammed Issoual","doi":"10.47443/ejm.2023.017","DOIUrl":"https://doi.org/10.47443/ejm.2023.017","url":null,"abstract":"This article gives several properties of a new type of submodules, namely weakly ( m, n ) -semiprime submodules where m and n are positive integers satisfying m > n . The primary objectives of the present article are to characterize weakly ( m, n ) - semiprime submodules and to provide a new characterization of the von Neumann regular modules in terms of weakly ( m, n ) -semiprime submodules.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"03 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86269088","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 investigates the extent to which student and task-related characteristics are associated with different types of note-taking and analyzes how task success depends on these elements. For this purpose, a sample of n=866 students (age: mean=13.99) completing two reality-based tasks as part of a paper and pencil test are considered. The results demonstrate that the note-taking type differs significantly between the two parallel constructed tasks. For example, language skills (r=.26), interest in mathematics (r=.13), and the socio-economic statuses (r=.12) are observed to be significantly correlated to greater note-taking frequency. Based on linear regression (dependent variable: successful task solution), 34% of the variance is attributed to note-taking and other student characteristics. The most relevant predictor for a successful task solution (β=.36) is notes containing an elaboration of the given task information.
{"title":"Taking notes as a strategy for solving reality-based tasks in mathematics","authors":"Lisa-Marie Wienecke, D. Leiss, T. Ehmke","doi":"10.29333/iejme/13312","DOIUrl":"https://doi.org/10.29333/iejme/13312","url":null,"abstract":"This study investigates the extent to which student and task-related characteristics are associated with different types of note-taking and analyzes how task success depends on these elements. For this purpose, a sample of n=866 students (age: mean=13.99) completing two reality-based tasks as part of a paper and pencil test are considered. The results demonstrate that the note-taking type differs significantly between the two parallel constructed tasks. For example, language skills (r=.26), interest in mathematics (r=.13), and the socio-economic statuses (r=.12) are observed to be significantly correlated to greater note-taking frequency. Based on linear regression (dependent variable: successful task solution), 34% of the variance is attributed to note-taking and other student characteristics. The most relevant predictor for a successful task solution (β=.36) is notes containing an elaboration of the given task information.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"65 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80932083","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}
J. Hartman, Sarah Hart, Eric Alan Nelson, P. Kirschner
To learn mathematics, historically students had no choice but to memorize fundamental facts and apply memorized algorithms. Since 1995 in the US, all states have adopted standards to govern K-12 mathematics instruction, and in most, standards have de-emphasized memorization and emphasized reasoning based on concepts. This change assumed the brain could reason in mathematics without relying on memorized knowledge. Scientists who study the brain have recently verified this assumption was mistaken. Due to stringent limitations in working memory (where the brain solves problems), mathematical problem-solving of any complexity requires applying well-memorized facts and procedures. A decade after the implementation of standards in most states, US young adults ranked last in testing in mathematics among 22 nations. Changes are proposed to state K-12 standards, which recent scientific research suggests would substantially improve student mathematics achievement.
{"title":"Designing mathematics standards in agreement with science","authors":"J. Hartman, Sarah Hart, Eric Alan Nelson, P. Kirschner","doi":"10.29333/iejme/13179","DOIUrl":"https://doi.org/10.29333/iejme/13179","url":null,"abstract":"To learn mathematics, historically students had no choice but to memorize fundamental facts and apply memorized algorithms. Since 1995 in the US, all states have adopted standards to govern K-12 mathematics instruction, and in most, standards have de-emphasized memorization and emphasized reasoning based on concepts. This change assumed the brain could reason in mathematics without relying on memorized knowledge. Scientists who study the brain have recently verified this assumption was mistaken. Due to stringent limitations in working memory (where the brain solves problems), mathematical problem-solving of any complexity requires applying well-memorized facts and procedures. A decade after the implementation of standards in most states, US young adults ranked last in testing in mathematics among 22 nations. Changes are proposed to state K-12 standards, which recent scientific research suggests would substantially improve student mathematics achievement.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"29 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74560358","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}
Cristian Nava Guzmán, M. S. G. García González, Mario Sánchez Aguilar
This research explores the link between achievement emotions and covariational reasoning, a type of mathematical reasoning involving two variables. The study employs a case study approach, focusing on a high school calculus student named Valeria, and develops a theoretical framework based on the control-value theory and levels of covariational reasoning. The results reveal that Valeria’s ability to coordinate variables and her perceived importance of solving mathematical problems influence her experience of achievement emotions, including enjoyment and frustration. The case study enables the creation of a hypothetical model that explains how students feel achievement emotions when tackling mathematical tasks that require covariational reasoning. The study highlights the significance of comprehending the interplay between emotions and mathematical reasoning to cultivate advanced cognitive and emotional abilities. This research is essential in bridging the gap between emotions and mathematical reasoning, a topic that has been previously overlooked in research on the affective domain.
{"title":"Connections between achievement emotions and covariational reasoning: The case of Valeria","authors":"Cristian Nava Guzmán, M. S. G. García González, Mario Sánchez Aguilar","doi":"10.29333/iejme/13180","DOIUrl":"https://doi.org/10.29333/iejme/13180","url":null,"abstract":"This research explores the link between achievement emotions and covariational reasoning, a type of mathematical reasoning involving two variables. The study employs a case study approach, focusing on a high school calculus student named Valeria, and develops a theoretical framework based on the control-value theory and levels of covariational reasoning. The results reveal that Valeria’s ability to coordinate variables and her perceived importance of solving mathematical problems influence her experience of achievement emotions, including enjoyment and frustration. The case study enables the creation of a hypothetical model that explains how students feel achievement emotions when tackling mathematical tasks that require covariational reasoning. The study highlights the significance of comprehending the interplay between emotions and mathematical reasoning to cultivate advanced cognitive and emotional abilities. This research is essential in bridging the gap between emotions and mathematical reasoning, a topic that has been previously overlooked in research on the affective domain.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"14 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91231466","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}
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":"3 1","pages":""},"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":"6 1","pages":""},"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":"19 23-25","pages":""},"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":"1 1","pages":""},"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}
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