Ruby L. Lynch-Arroyo, M. Tchoshanov, William Medina-Jerez
Teacher productive disposition is considered as one of the key strands of mathematical proficiency. Teacher disposition and positioning (disposition in action) toward mathematics influence student learning. However, teachers’ productive disposition does not always translate into productive positioning in the mathematics classroom, and vice versa. In this study, we selected teacher dis/position as the unit of analysis to explore the phenomenon of two middle school mathematics teachers’ self-reported affective disposition and observed positioning-by-others. Grounded in positioning theory the relationship between teacher disposition and positioning-by-others was examined utilizing a cross-case analysis. Results of the study indicate that dispositional characteristics such as attitude, self-concept, and nature of mathematics were significantly different between the cases. The study findings also suggest that interconnectedness between teacher core disposition and positional situatedness could potentially contribute to understanding and addressing the complexity of teaching and learning in the mathematics classroom.
{"title":"Math is beautifully intimidating: Analyzing the conflict between teacher affective disposition and observed positioning-by-others","authors":"Ruby L. Lynch-Arroyo, M. Tchoshanov, William Medina-Jerez","doi":"10.29333/iejme/12627","DOIUrl":"https://doi.org/10.29333/iejme/12627","url":null,"abstract":"Teacher productive disposition is considered as one of the key strands of mathematical proficiency. Teacher disposition and positioning (disposition in action) toward mathematics influence student learning. However, teachers’ productive disposition does not always translate into productive positioning in the mathematics classroom, and vice versa. In this study, we selected teacher dis/position as the unit of analysis to explore the phenomenon of two middle school mathematics teachers’ self-reported affective disposition and observed positioning-by-others. Grounded in positioning theory the relationship between teacher disposition and positioning-by-others was examined utilizing a cross-case analysis. Results of the study indicate that dispositional characteristics such as attitude, self-concept, and nature of mathematics were significantly different between the cases. The study findings also suggest that interconnectedness between teacher core disposition and positional situatedness could potentially contribute to understanding and addressing the complexity of teaching and learning in the mathematics classroom.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83051668","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}
I. J. Osakwe, F. Egara, Onyemauche Christopher Inweregbuh, A. C. Nzeadibe, Chinyere N. Emefo
The effect of interaction patterns on JS3 learners’ retention in geometric construction was investigated in Anambra State, Nigeria. The researchers used a quasi-experimental approach with a non-equivalent control group for the pre- and post-test. The population consisted of 1,813 JS3 leaners. The study’s subjects were a group of 155 JS3 learners drawn from two schools. Two JS3 classes in the schools were assigned to the experimental and control groups at random. The geometric construction retention test (GCRT) was used to collect data, and it was validated by three experts. The reliability coefficient of the GCRT was 0.80. The mean and standard deviation of the data were used to report the study’s questions, whereas the hypotheses were tested via analysis of covariance at a 0.05 level of significance. According to the findings, students taught geometric construction utilizing interaction patterns remembered more material than those taught using the expository approach. It also found a statistically significant difference in retention between urban and rural learners, favoring urban learners. The interaction effect of group and location on student retention was not significant. One recommendation of this study is that teachers should use interaction patterns as an instructional method when teaching geometric construction.
{"title":"Interaction patterns: An approach for enhancing students’ retention in geometric construction","authors":"I. J. Osakwe, F. Egara, Onyemauche Christopher Inweregbuh, A. C. Nzeadibe, Chinyere N. Emefo","doi":"10.29333/iejme/12596","DOIUrl":"https://doi.org/10.29333/iejme/12596","url":null,"abstract":"The effect of interaction patterns on JS3 learners’ retention in geometric construction was investigated in Anambra State, Nigeria. The researchers used a quasi-experimental approach with a non-equivalent control group for the pre- and post-test. The population consisted of 1,813 JS3 leaners. The study’s subjects were a group of 155 JS3 learners drawn from two schools. Two JS3 classes in the schools were assigned to the experimental and control groups at random. The geometric construction retention test (GCRT) was used to collect data, and it was validated by three experts. The reliability coefficient of the GCRT was 0.80. The mean and standard deviation of the data were used to report the study’s questions, whereas the hypotheses were tested via analysis of covariance at a 0.05 level of significance. According to the findings, students taught geometric construction utilizing interaction patterns remembered more material than those taught using the expository approach. It also found a statistically significant difference in retention between urban and rural learners, favoring urban learners. The interaction effect of group and location on student retention was not significant. One recommendation of this study is that teachers should use interaction patterns as an instructional method when teaching geometric construction.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"7 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87890425","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}
Turkey experiences distance education at the master’s and doctorate degrees for the first time. This study aims to reveal the essence of the distance education experiences of mathematics teachers who continue their postgraduate education with distance education due to the COVID-19 pandemic. This study was carried out using the phenomenological research design with six mathematics teachers who continue their postgraduate education at a state university in the Central Anatolia Region in the 2019-2020 academic year. Of the participants selected by the criterion sampling, three were master’s degree students and three were doctoral degree students. Research data were collected using semi-structured interview forms designed in line with expert opinions. The interviews were conducted online via video call on the WhatsApp application due to the COVID-19 pandemic. The experiences of the participants were identified with the phenomenon of “solo pantomime”. Participants had positive experiences such as easy access, possibility of review, improvement in technological pedagogical content knowledge, and negative experiences such as communication and connection problems, the irregularity in the schedule, inadequacy of the lesson hours, and focusing problems regarding synchronized distance education. Distance graduate education is also considered quite suitable for mathematics education courses, but insufficient for mathematics field courses. It is also understood that some participants had plans to make radical changes in their thesis topics. Participants avoid long-term experimental studies or studies that can be conducted with a large sample, and they tend towards studies that can be carried out with document analysis or small groups and had problems with their supervisors.
{"title":"The solo pantomime in the pandemic: Distance postgraduate education in the department of mathematics education during COVID-19","authors":"Naci Kucukgencay, B. Peker","doi":"10.29333/iejme/12716","DOIUrl":"https://doi.org/10.29333/iejme/12716","url":null,"abstract":"Turkey experiences distance education at the master’s and doctorate degrees for the first time. This study aims to reveal the essence of the distance education experiences of mathematics teachers who continue their postgraduate education with distance education due to the COVID-19 pandemic. This study was carried out using the phenomenological research design with six mathematics teachers who continue their postgraduate education at a state university in the Central Anatolia Region in the 2019-2020 academic year. Of the participants selected by the criterion sampling, three were master’s degree students and three were doctoral degree students. Research data were collected using semi-structured interview forms designed in line with expert opinions. The interviews were conducted online via video call on the WhatsApp application due to the COVID-19 pandemic. The experiences of the participants were identified with the phenomenon of “solo pantomime”. Participants had positive experiences such as easy access, possibility of review, improvement in technological pedagogical content knowledge, and negative experiences such as communication and connection problems, the irregularity in the schedule, inadequacy of the lesson hours, and focusing problems regarding synchronized distance education. Distance graduate education is also considered quite suitable for mathematics education courses, but insufficient for mathematics field courses. It is also understood that some participants had plans to make radical changes in their thesis topics. Participants avoid long-term experimental studies or studies that can be conducted with a large sample, and they tend towards studies that can be carried out with document analysis or small groups and had problems with their supervisors.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"30 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78494651","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}
Ayanaw Yigletu Asfaw, Kassa Michael Weldeyesus, M. Ayele
Three mathematics teacher educators who were assigned to teach fundamental concepts of algebra course in a teacher education college, as well as their prospective elementary mathematics teachers who took the course, took part in a job-embedded, context-specific, and content-based comprehensive professional development (PD) program on assessment for learning (AfL). Three teacher educators and 129 prospective elementary mathematics teachers from three teacher education colleges took part in the study. The findings demonstrated that prospective elementary mathematics teachers in the intervention group significantly outperformed prospective teachers in both of the comparative groups in their post-test scores in algebra. Furthermore, it was found out that after the intervention, there was no statistically significant mean difference among achiever levels in the treatment group on post-test scores, despite a statistically significant mean difference among achiever levels in their pre-test scores. This research adds to our knowledge of the impact of comprehensive, job-embedded, context-specific, and content-based PD on prospective teachers’ achievements in algebra in elementary school mathematics teacher education. Implications of implementing AfL as well as recommendations for further research are highlighted.
{"title":"The effect of assessment for learning on prospective teachers’ learning of algebra through a professional development program","authors":"Ayanaw Yigletu Asfaw, Kassa Michael Weldeyesus, M. Ayele","doi":"10.29333/iejme/12587","DOIUrl":"https://doi.org/10.29333/iejme/12587","url":null,"abstract":"Three mathematics teacher educators who were assigned to teach fundamental concepts of algebra course in a teacher education college, as well as their prospective elementary mathematics teachers who took the course, took part in a job-embedded, context-specific, and content-based comprehensive professional development (PD) program on assessment for learning (AfL). Three teacher educators and 129 prospective elementary mathematics teachers from three teacher education colleges took part in the study. The findings demonstrated that prospective elementary mathematics teachers in the intervention group significantly outperformed prospective teachers in both of the comparative groups in their post-test scores in algebra. Furthermore, it was found out that after the intervention, there was no statistically significant mean difference among achiever levels in the treatment group on post-test scores, despite a statistically significant mean difference among achiever levels in their pre-test scores. This research adds to our knowledge of the impact of comprehensive, job-embedded, context-specific, and content-based PD on prospective teachers’ achievements in algebra in elementary school mathematics teacher education. Implications of implementing AfL as well as recommendations for further research are highlighted.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"25 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90386405","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 atom-bond sum-connectivity ( ABS ) index is a recently introduced variant of three earlier much studied graph-based molecular descriptors: connectivity (Randi´c), atom-bond connectivity, and sum-connectivity indices. In this paper, the graphs with minimum, second-minimum, maximum, and second-maximum values of the ABS index are determined over the class of connected unicyclic graphs with a fixed order. Possible chemical applications of the ABS index are also investigated on particular sets of chemical graphs
{"title":"Atom-Bond Sum-Connectivity Index of Unicyclic Graphs and Some Applications","authors":"Akbar Ali, Ivan Gutman, Izudin Redˇzepovi´c","doi":"10.47443/ejm.2022.039","DOIUrl":"https://doi.org/10.47443/ejm.2022.039","url":null,"abstract":"The atom-bond sum-connectivity ( ABS ) index is a recently introduced variant of three earlier much studied graph-based molecular descriptors: connectivity (Randi´c), atom-bond connectivity, and sum-connectivity indices. In this paper, the graphs with minimum, second-minimum, maximum, and second-maximum values of the ABS index are determined over the class of connected unicyclic graphs with a fixed order. Possible chemical applications of the ABS index are also investigated on particular sets of chemical graphs","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"14 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91014386","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}
S. Rexhepi, Saranda Kamberi, Ismet Latifi, E. Iseni
In this paper, we have tried to clearly explain the meaning of fractions and operations with fractions. Also, we have tried to illustrate with some examples how to apply the rules of operations with fractional numbers, giving different practical techniques through different figures, visualization methods, and concretizing problems. The paper presents with examples of the most common mistakes made by students, giving suggestions for their avoidance, as well as through a questionnaire, which considered the survey of 60 students of grade 6 of school, “Elena Gjika” City Prishtina, Kosovo, with the help of the statistical test we have concluded that practical techniques such as figures, visualizations, and video lessons have a close dependence on the meaning and operation of fractions.
{"title":"The influence of practical illustrations on the meaning and operation of fractions in sixth grade students, Kosovo-curricula","authors":"S. Rexhepi, Saranda Kamberi, Ismet Latifi, E. Iseni","doi":"10.29333/iejme/12517","DOIUrl":"https://doi.org/10.29333/iejme/12517","url":null,"abstract":"In this paper, we have tried to clearly explain the meaning of fractions and operations with fractions. Also, we have tried to illustrate with some examples how to apply the rules of operations with fractional numbers, giving different practical techniques through different figures, visualization methods, and concretizing problems. The paper presents with examples of the most common mistakes made by students, giving suggestions for their avoidance, as well as through a questionnaire, which considered the survey of 60 students of grade 6 of school, “Elena Gjika” City Prishtina, Kosovo, with the help of the statistical test we have concluded that practical techniques such as figures, visualizations, and video lessons have a close dependence on the meaning and operation of fractions.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"228 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89030926","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 subset R of a product set X×Y is called a relation on X to Y . A relation U on the power set P (X) to Y is called a super relation on X to Y . The relation R can be identified, to some extent, with the set-valued function φR defined by φR (x) = R (x) = { y ∈ Y : (x, y) ∈ R } for all x ∈ X, and the union-preserving super relation R . defined by R (A) = R [A ] = ⋃ a∈A R (a) for all A ⊆ X. By using the relation R , we also define two super relations lbR and clR on Y to X such that lbR (B) = { x ∈ X : {x}×B ⊆ R } and clR (B) = { x ∈ X : R (x) ∩ B 6= ∅ } for all B ⊆ X . By using complement and inverse relations, we prove that lbR = cl c Rc and clR (B) = R−1 [B ] . We also consider the dual super relations ubR = lbR−1 and intR = cl c R ◦ CY . If U is a super relation on X to Y and V is a super relation on Y to X, then having in mind Galois connections and residuated mappings, we say that U is V –normal if, for all A ⊆ X and B ⊆ Y , we have U (A) ⊆ B if and only if A ⊆ V (B) . Thus, if U is V –normal, then by defining Φ = V ◦ U and following Pataki’s ideas, we see that U is Φ–regular in the sense that, for all A1 , A2 ⊆ X, we have U (A1) ⊆ U (A2) if and only if A1 ⊆ Φ (A2) . In this paper, by considering a relator (family of relations) R on X to Y , we investigate normality properties of the more general super relations lbR = ⋃ R∈R lbR and clR = ⋂ R∈R clR , and their duals ubR = lbR−1 and intR = cl c R ◦ CY . However, as some applicable results of the paper, we only prove that if R is a relation on X to Y , then the following assertions hold : (1) clR−1 is intR – normal, or equivalently clR is intR−1 – normal ; (2) ub c R is lbR ◦ CY – normal, or equivalently lb c R is ubR ◦ CX – normal ; (3) R is a function of X to Y if and only if clR−1 is clR – normal, or equivalently intR is intR−1 – normal . The closure-interior and the upper-lower-bound Galois connections, established in assertions (1) and (2), are applied in the calculus of relations and the completion of posets, respectively. Some of the implications in assertion (3) require that Y 6= ∅ .
乘积集X×Y的子集R称为X到Y的关系。幂集P (X)到Y上的关系U称为X到Y上的超关系。关系R在一定程度上可以用φR (x) = R (x) = {y∈y: (x, y)∈R}定义的集值函数φR和保并超关系R来标识。由R (A) = R [A] = ` ` A∈A R (A)定义，对于所有A的X，我们还利用关系R在Y到X上定义了两个超关系lbR和clR，使得对于所有B的X, lbR (B) = {X∈X: {X}×B任任R}， clR (B) = {X∈X: R (X)∩B 6=∅}。利用补和逆关系，证明了lbR = cl c Rc和clR (B) = R−1 [B]。我们还考虑了对偶超关系ubR = lbR−1和intR = cl c R◦CY。如果U是X到Y上的超关系，V是Y到X上的超关系，那么考虑到伽罗瓦连接和剩余映射，我们说U是V -正规的，当且仅当，对于所有的a, X和B，我们有U (a)，它是B。因此，如果U为V -法线，则通过定义Φ = V◦U并遵循Pataki的思想，我们可以看到U为Φ-regular，即对于所有A1、A2的任一个X，当且仅当A1≥Φ (A2)时，我们有U (A1)≥U (A2)。本文通过考虑X到Y上的一个关系族R，研究了更一般的超关系lbR =∈R lbR和clR = R∈R clR及其对偶ubR = lbR−1和intR = cl c R◦CY的正态性性质。然而，作为本文的一些适用结果，我们只证明了如果R是X到Y上的关系，则下列断言成立:(1)clR−1是intR -正规的，或者等价地clR是intR−1 -正规的;(2) b c R为lbR◦CY -正常，或b c R为ubR◦CX -正常;(3) R是X到Y的函数当且仅当clR−1是clR -正规的，或者等价地，intR是intR−1 -正规的。在断言(1)和断言(2)中建立的闭包内连接和上界下界伽罗瓦连接分别应用于关系演算和偏序集补全。断言(3)中的某些含意要求y6 =∅。
{"title":"Galois and Pataki Connections for Ordinary Functions and Super Relations","authors":"Santanu Acharjee, M. Rassias, Á. Száz","doi":"10.47443/ejm.2022.017","DOIUrl":"https://doi.org/10.47443/ejm.2022.017","url":null,"abstract":"A subset R of a product set X×Y is called a relation on X to Y . A relation U on the power set P (X) to Y is called a super relation on X to Y . The relation R can be identified, to some extent, with the set-valued function φR defined by φR (x) = R (x) = { y ∈ Y : (x, y) ∈ R } for all x ∈ X, and the union-preserving super relation R . defined by R (A) = R [A ] = ⋃ a∈A R (a) for all A ⊆ X. By using the relation R , we also define two super relations lbR and clR on Y to X such that lbR (B) = { x ∈ X : {x}×B ⊆ R } and clR (B) = { x ∈ X : R (x) ∩ B 6= ∅ } for all B ⊆ X . By using complement and inverse relations, we prove that lbR = cl c Rc and clR (B) = R−1 [B ] . We also consider the dual super relations ubR = lbR−1 and intR = cl c R ◦ CY . If U is a super relation on X to Y and V is a super relation on Y to X, then having in mind Galois connections and residuated mappings, we say that U is V –normal if, for all A ⊆ X and B ⊆ Y , we have U (A) ⊆ B if and only if A ⊆ V (B) . Thus, if U is V –normal, then by defining Φ = V ◦ U and following Pataki’s ideas, we see that U is Φ–regular in the sense that, for all A1 , A2 ⊆ X, we have U (A1) ⊆ U (A2) if and only if A1 ⊆ Φ (A2) . In this paper, by considering a relator (family of relations) R on X to Y , we investigate normality properties of the more general super relations lbR = ⋃ R∈R lbR and clR = ⋂ R∈R clR , and their duals ubR = lbR−1 and intR = cl c R ◦ CY . However, as some applicable results of the paper, we only prove that if R is a relation on X to Y , then the following assertions hold : (1) clR−1 is intR – normal, or equivalently clR is intR−1 – normal ; (2) ub c R is lbR ◦ CY – normal, or equivalently lb c R is ubR ◦ CX – normal ; (3) R is a function of X to Y if and only if clR−1 is clR – normal, or equivalently intR is intR−1 – normal . The closure-interior and the upper-lower-bound Galois connections, established in assertions (1) and (2), are applied in the calculus of relations and the completion of posets, respectively. Some of the implications in assertion (3) require that Y 6= ∅ .","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"29 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87061791","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}
{"title":"Misconceptions and resulting errors displayed by in service teachers in the learning of linear independence","authors":"L. Mutambara, S. Bansilal","doi":"10.29333/iejme/12483","DOIUrl":"https://doi.org/10.29333/iejme/12483","url":null,"abstract":"","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"6 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73289406","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}
{"title":"Comparison of the learning outcomes in online and in-class environments in the divisibility lessons","authors":"Dina Kamber Hamzić, Daniela Zubović, Lamija Šćeta","doi":"10.29333/iejme/12473","DOIUrl":"https://doi.org/10.29333/iejme/12473","url":null,"abstract":"","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"8 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87815886","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}
{"title":"The didactical phenomenology in learning the circle equation","authors":"Clement Ayarebilla Ali","doi":"10.29333/iejme/12472","DOIUrl":"https://doi.org/10.29333/iejme/12472","url":null,"abstract":"ABSTRACT","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"46 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73761655","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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