Various features have been found hidden in the Pascal triangle. In this paper, some very well-known properties of the Pascal triangle will be presented, as well as the properties related to different extensions of the triangle, namely the Pascal pyramid. Given that in the textbooks of the tenth grade, respectively in the school, where we realised the research but also in general in other schools, the importance of the Pascal triangle is not at the right level, then in this paper it has been shown very well that many different exercises in mathematics. The purpose of this paper is to look at the difference and importance of explaining mathematical units against units that students do not have knowledge of, namely the explanation of Pascal’s triangle in the efficiency of solutions to various mathematical exercises. This research is mainly based on descriptive and quantitative method, while research instruments are two tests. From the study of Pascal’s triangle, many solutions of problems in mathematics emerged through this triangle, starting from the binomial formula, the extension of the binomial formula, and the combinatorics as well as the probability. So the students realized that Pascal’s triangle enables the solution of all these exercises in an easier and more understandable way and this also came from the results of two tests. Also, the students were open and motivated for the idea of using Pascal’s triangle for other exercises but what now remains for them to find other possible solutions to the exercises through Pascal’s triangle.
{"title":"Efficiency of understanding some mathematical problems by means of Pascal’s triangle","authors":"Arta Aliu, Shpetim Rexhepi, Egzona Iseni","doi":"10.29333/iejme/13713","DOIUrl":"https://doi.org/10.29333/iejme/13713","url":null,"abstract":"Various features have been found hidden in the Pascal triangle. In this paper, some very well-known properties of the Pascal triangle will be presented, as well as the properties related to different extensions of the triangle, namely the Pascal pyramid. Given that in the textbooks of the tenth grade, respectively in the school, where we realised the research but also in general in other schools, the importance of the Pascal triangle is not at the right level, then in this paper it has been shown very well that many different exercises in mathematics. The purpose of this paper is to look at the difference and importance of explaining mathematical units against units that students do not have knowledge of, namely the explanation of Pascal’s triangle in the efficiency of solutions to various mathematical exercises. This research is mainly based on descriptive and quantitative method, while research instruments are two tests. From the study of Pascal’s triangle, many solutions of problems in mathematics emerged through this triangle, starting from the binomial formula, the extension of the binomial formula, and the combinatorics as well as the probability. So the students realized that Pascal’s triangle enables the solution of all these exercises in an easier and more understandable way and this also came from the results of two tests. Also, the students were open and motivated for the idea of using Pascal’s triangle for other exercises but what now remains for them to find other possible solutions to the exercises through Pascal’s triangle.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135323374","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 qualitative case study of four middle school and secondary school mathematics teachers examines how teachers’ reflective practice supported their selection of strategies that align with the needs of current mathematics education according to the 10 dimensions of mathematics education. The findings suggest that teachers’ reflection practice, through collaboration with other teachers and creating a positive safe environment within their classroom for students’ feedback, impacts their design of classroom practices. They prioritize planning and preparing for the dimensions that are being discussed in the meetings with other teachers. Another major finding is that high level reflective teachers’ attitudes toward teaching mathematics is consistent with the needs of current mathematics education. Lastly, meeting individual needs of students is the dimension that all teachers in this study, regardless of their level of reflection, were struggling to reflect on and plan for. Overall, each teacher reported reflective practices that appeared to align with the attitudes and practices for teaching mathematics survey.
{"title":"Developing reflective practice among teachers of mathematics","authors":"Sima Aghakhani, Rachael A. Lewitzky, Asia Majeed","doi":"10.29333/iejme/13715","DOIUrl":"https://doi.org/10.29333/iejme/13715","url":null,"abstract":"This qualitative case study of four middle school and secondary school mathematics teachers examines how teachers’ reflective practice supported their selection of strategies that align with the needs of current mathematics education according to the 10 dimensions of mathematics education. The findings suggest that teachers’ reflection practice, through collaboration with other teachers and creating a positive safe environment within their classroom for students’ feedback, impacts their design of classroom practices. They prioritize planning and preparing for the dimensions that are being discussed in the meetings with other teachers. Another major finding is that high level reflective teachers’ attitudes toward teaching mathematics is consistent with the needs of current mathematics education. Lastly, meeting individual needs of students is the dimension that all teachers in this study, regardless of their level of reflection, were struggling to reflect on and plan for. Overall, each teacher reported reflective practices that appeared to align with the attitudes and practices for teaching mathematics survey.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136079921","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 at highlighting the relationship between mastery learning models and academic performance in mathematics, moderated by the number of hours allotted to studying mathematics. There are 305 first to eighth-grade students who learn at Nae A. Ghica Middle School in Romania. Students in sixth, seventh, and eighth grades (n=101) were selected to participate in this research because they study both algebra and geometry. We have used purposive sampling to control certain variables, i.e., mastery learning strategies and academic performance. The data were analyzed in Jamovi (2022). The level of performance was measured according to the progress students made. Data analysis revealed that the moderation effect of the time each student allocated to studying mathematics individually is not statistically significant in the relationship between the mastery learning model and academic performance in mathematics. This study was conducted on a small number of students, so it is recommended to be expanded on a larger scale.
本研究旨在探讨掌握学习模式与数学学习成绩之间的关系，并以学习数学的学时数为调节因子。有305名一至八年级学生在Nae A. gica中学学习。在罗马尼亚。六年级，七年级和八年级的学生(n=101)被选中参加这项研究，因为他们学习代数和几何。我们使用有目的的抽样来控制某些变量，即掌握学习策略和学习成绩。这些数据在Jamovi(2022年)进行了分析。成绩水平是根据学生取得的进步来衡量的。数据分析显示，在掌握学习模式与数学学业成绩的关系中，每个学生分配给单独学习数学的时间的调节作用不具有统计学意义。这个研究是在少数学生中进行的，所以建议扩大规模。
{"title":"The relationship between mastery learning models and academic achievement in mathematics","authors":"Cristina Vlădescu","doi":"10.29333/iejme/13705","DOIUrl":"https://doi.org/10.29333/iejme/13705","url":null,"abstract":"This study aims at highlighting the relationship between mastery learning models and academic performance in mathematics, moderated by the number of hours allotted to studying mathematics. There are 305 first to eighth-grade students who learn at <i>Nae A. Ghica Middle School</i> in Romania. Students in sixth, seventh, and eighth grades (n=101) were selected to participate in this research because they study both algebra and geometry. We have used purposive sampling to control certain variables, i.e., mastery learning strategies and academic performance. The data were analyzed in Jamovi (2022). The level of performance was measured according to the progress students made. Data analysis revealed that the moderation effect of the time each student allocated to studying mathematics individually is not statistically significant in the relationship between the mastery learning model and academic performance in mathematics. This study was conducted on a small number of students, so it is recommended to be expanded on a larger scale.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135274892","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}
Despite the research regarding the importance of peer review and feedback in pre-service special education teachers, there exists a gap in teaching complex mathematical concepts such as fractional operations. This study sought to address this gap by investigating how pre-service teachers can effectively appraise and revise peer-generated teaching transcripts focusing on fraction operations and compare their feedback with those of experienced educators. The research sought to understand how this integrated approach can contribute to improving the instruction of pre-service special education teachers in the field of mathematics education. A modified version of Crespo’s (2018) generating, appraising, and revising of representations was utilized to analyze the video content. Comparisons of the reviews showed that pre-service teachers may not have the content knowledge or experience to provide in-depth feedback to support learning as experienced educators. The article concludes with findings and recommendations for teacher educators who utilize anonymous peer review in teacher preparation for special educators.
{"title":"Pre-service special education teachers’ learning through recorded mini-lessons and peer review","authors":"Lindsay Vance, Joanne Caniglia, Michelle Meadows","doi":"10.29333/iejme/13714","DOIUrl":"https://doi.org/10.29333/iejme/13714","url":null,"abstract":"Despite the research regarding the importance of peer review and feedback in pre-service special education teachers, there exists a gap in teaching complex mathematical concepts such as fractional operations. This study sought to address this gap by investigating how pre-service teachers can effectively appraise and revise peer-generated teaching transcripts focusing on fraction operations and compare their feedback with those of experienced educators. The research sought to understand how this integrated approach can contribute to improving the instruction of pre-service special education teachers in the field of mathematics education. A modified version of Crespo’s (2018) generating, appraising, and revising of representations was utilized to analyze the video content. Comparisons of the reviews showed that pre-service teachers may not have the content knowledge or experience to provide in-depth feedback to support learning as experienced educators. The article concludes with findings and recommendations for teacher educators who utilize anonymous peer review in teacher preparation for special educators.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135323375","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 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":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":"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":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":"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":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":"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}
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