Climate conducive to learning is one of criteria of good teaching. Even though current pedagogies argue for contemporary type of instruction, mathematics instruction may still be dominated by traditional type of instruction. The present study examined participant-produced drawings of 250 primary grade students regarding geometry teaching and learning practices. Not only different aspects of traditional type of instruction, such as the teacher standing in front of the classroom and delivering the content while students sit at their desks and passively listen to the teacher with little student-student communication were reported, but also some aspects typical for contemporary type of instruction, such as learning through teacher-student discussions, and the use of teaching materials and tools. Still, the aspects of traditional type of instruction prevailed. The results offer potential opportunities for reconsidering the current teacher education as well as policy that would reflect the teaching practices conducive to contemporary geometry instruction.
{"title":"Depicting classroom social climate: Using drawings to examine primary students’ perceptions of geometry teaching and learning practices","authors":"Ana Kuzle, Dubravka Glasnović Gracin, Ana Krišto","doi":"10.29333/iejme/13743","DOIUrl":"https://doi.org/10.29333/iejme/13743","url":null,"abstract":"Climate conducive to learning is one of criteria of good teaching. Even though current pedagogies argue for contemporary type of instruction, mathematics instruction may still be dominated by traditional type of instruction. The present study examined participant-produced drawings of 250 primary grade students regarding geometry teaching and learning practices. Not only different aspects of traditional type of instruction, such as the teacher standing in front of the classroom and delivering the content while students sit at their desks and passively listen to the teacher with little student-student communication were reported, but also some aspects typical for contemporary type of instruction, such as learning through teacher-student discussions, and the use of teaching materials and tools. Still, the aspects of traditional type of instruction prevailed. The results offer potential opportunities for reconsidering the current teacher education as well as policy that would reflect the teaching practices conducive to contemporary geometry instruction.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135372996","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 this study is to reveal the profiles of pre-service mathematics teachers in terms of learning and studying approaches by cluster-analyzing them on the basis of self-reinforcing and persistence. Learning and studying approaches inventory scale, self-reinforcing and persistence subscales were used to collect the data in the study, which was carried out with a descriptive research design. The participants of the study comprised of 487 pre-service mathematics teachers. According to the results, it was determined that the surface learning approach of the pre-service teachers did not differ according to gender while the strategic learning approach and the deep learning approach differed in favor of males. There was no significant difference in the learning approaches of the participants according to the grade level. According to the cluster analysis, it was revealed that pre-service teachers can be clustered as low motivation, high motivation, high self-reinforcing and high persistence.
{"title":"Examining the differentiation in pre-service mathematics teachers’ learning and studying approaches according to self-reinforcing, and persistence","authors":"Emine Nur Unveren Bilgic, Sahin Danisman","doi":"10.29333/iejme/13712","DOIUrl":"https://doi.org/10.29333/iejme/13712","url":null,"abstract":"The aim of this study is to reveal the profiles of pre-service mathematics teachers in terms of learning and studying approaches by cluster-analyzing them on the basis of self-reinforcing and persistence. Learning and studying approaches inventory scale, self-reinforcing and persistence subscales were used to collect the data in the study, which was carried out with a descriptive research design. The participants of the study comprised of 487 pre-service mathematics teachers. According to the results, it was determined that the surface learning approach of the pre-service teachers did not differ according to gender while the strategic learning approach and the deep learning approach differed in favor of males. There was no significant difference in the learning approaches of the participants according to the grade level. According to the cluster analysis, it was revealed that pre-service teachers can be clustered as low motivation, high motivation, high self-reinforcing and high persistence.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135323376","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 work is the result of a pre-experiment carried out as part of a master’s course, dealing with the study of the parabola through different mathematical views. It aims to recognize possible didactic obstacles in its teaching, based on intuitive manifestations in the resolution of a didactic situation based on GeoGebra software. The methodology adopted was didactic engineering in its four phases, experimented with a teacher in initial training. The observation and data collection provided us with elements for a posteriori analysis and validation of the experiment in which we verified the need to discuss the parabola, articulating its geometric, algebraic, and analytical views.
{"title":"Categories of Intuitive Reasoning in the teaching of parabolas: A structured practice in Didactic Engineering","authors":"Renata Teófilo de Sousa, F. R. Alves, A. P. Aires","doi":"10.29333/iejme/13514","DOIUrl":"https://doi.org/10.29333/iejme/13514","url":null,"abstract":"This work is the result of a pre-experiment carried out as part of a master’s course, dealing with the study of the parabola through different mathematical views. It aims to recognize possible didactic obstacles in its teaching, based on intuitive manifestations in the resolution of a didactic situation based on GeoGebra software. The methodology adopted was didactic engineering in its four phases, experimented with a teacher in initial training. The observation and data collection provided us with elements for a posteriori analysis and validation of the experiment in which we verified the need to discuss the parabola, articulating its geometric, algebraic, and analytical views.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"14 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72730489","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}
In-service teachers must be provided with high-quality professional development (PD) opportunities that not only effectively improves and develops their skills, but also engage, and motivate them to continue growing. In this project, we studied in-service teachers’ perceptions, opinions, and mindset toward the use of mixed-reality simulations (MRS) as a potential tool for PD to advance and enhance their pedagogical knowledge for mathematics. We followed a convergent parallel mixed-method approach with 49 in-service teachers who were exposed to a series of simulations sessions. We found evidence that the use and integration of technologies like MRS as a tool for PD is considered to be an approximation of practice well accepted by the teachers. In addition, the majority of participants perceived the tool as an effective-unique strategy to develop skills related to questioning, eliciting and assessing students.
{"title":"Innovating with in-service mathematics teachers’ professional development: The intersection among mixed-reality simulations, approximation-of-practice, and technology-acceptance","authors":"Jair J. Aguilar, Seokmin Kang","doi":"10.29333/iejme/13628","DOIUrl":"https://doi.org/10.29333/iejme/13628","url":null,"abstract":"In-service teachers must be provided with high-quality professional development (PD) opportunities that not only effectively improves and develops their skills, but also engage, and motivate them to continue growing. In this project, we studied in-service teachers’ perceptions, opinions, and mindset toward the use of mixed-reality simulations (MRS) as a potential tool for PD to advance and enhance their pedagogical knowledge for mathematics. We followed a convergent parallel mixed-method approach with 49 in-service teachers who were exposed to a series of simulations sessions. We found evidence that the use and integration of technologies like MRS as a tool for PD is considered to be an approximation of practice well accepted by the teachers. In addition, the majority of participants perceived the tool as an effective-unique strategy to develop skills related to questioning, eliciting and assessing students.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"589 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74715795","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 aims to present a first approximation of the conceptual field of measures of central tendency (MCT), grounded in the theory of conceptual fields. We propose six situations according to type of variable, data presentation (raw or grouped) and amount of data. We revisit specific situations for the mean and exemplify several possibilities for introducing these measures. This is a theoretical reflection and a systematization of the knowledge produced in the area with a view to aiding it teaching in Brazilian basic education (PreK-12). We argue that from the early school years, students should collect data, use concrete and manipulable material, analyze the types of variable and context of data, transform them into different representations and based on the visual observation of data distribution, intuit the location of MCT to then calculate them.
{"title":"The conceptual field of measures of central tendency: A first approximation","authors":"I. Cazorla, Miriam Cardoso Utsumi, Sandra Magina","doi":"10.29333/iejme/13571","DOIUrl":"https://doi.org/10.29333/iejme/13571","url":null,"abstract":"This article aims to present a first approximation of the conceptual field of measures of central tendency (MCT), grounded in the theory of conceptual fields. We propose six situations according to type of variable, data presentation (raw or grouped) and amount of data. We revisit specific situations for the mean and exemplify several possibilities for introducing these measures. This is a theoretical reflection and a systematization of the knowledge produced in the area with a view to aiding it teaching in Brazilian basic education (PreK-12). We argue that from the early school years, students should collect data, use concrete and manipulable material, analyze the types of variable and context of data, transform them into different representations and based on the visual observation of data distribution, intuit the location of MCT to then calculate them.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"23 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89058154","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 paper reports on an exploratory study about probabilistic intuition in learning mathematics for decision-making. The analysis was carried out on a group of high school students in relation to their probabilistic intuition in problem-solving, after performing playful learning activities on a simulation platform specifically designed for this study. The analysis used a mixed qualitative-quantitative method. The results showed that the simulation activities facilitated the students’ probabilistic intuition and boosted their performance in solving problems, particularly avoiding decisions based on previous results (when unnecessary) and identifying situations, where binomial distribution can be used.
{"title":"A study on mathematics students’ probabilistic intuition for decision-making in high school","authors":"Alejandro Ramírez-Contreras, Leopoldo Zúñiga-Silva, Ezequiel Ojeda-Gómez","doi":"10.29333/iejme/13586","DOIUrl":"https://doi.org/10.29333/iejme/13586","url":null,"abstract":"This paper reports on an exploratory study about probabilistic intuition in learning mathematics for decision-making. The analysis was carried out on a group of high school students in relation to their probabilistic intuition in problem-solving, after performing playful learning activities on a simulation platform specifically designed for this study. The analysis used a mixed qualitative-quantitative method. The results showed that the simulation activities facilitated the students’ probabilistic intuition and boosted their performance in solving problems, particularly avoiding decisions based on previous results (when unnecessary) and identifying situations, where binomial distribution can be used.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"359 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76420904","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}
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":"40 1","pages":"0"},"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":"290 1","pages":"0"},"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}
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":"62 1","pages":"0"},"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}
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":"42 1","pages":"0"},"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}
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