This article aims to analyze the process of the progressive mathematization of the concept of the function by secondary school students through the resolution of a free fall situation. A free-fall mathematical situation was designed and experimented using the Tracker software to obtain movement data. Worksheets and conversations were collected between students and the teacher, and experiments and class discussions were filmed. The analysis consisted of identifying the development from informal strategies associated with the context of the problem to formal procedures. The results show that the process brings meanings to mathematical ideas such as variation, variables, and the relationship between variables, allows coordination and transition between representations and contributes to the learning of functions as a representation of the variation of physical phenomena.
{"title":"Progressive mathematics of functions in secondary school students using a free-fall activity","authors":"Rosa Isela González-Polo, Apolo Castaneda","doi":"10.29333/iejme/14108","DOIUrl":"https://doi.org/10.29333/iejme/14108","url":null,"abstract":"This article aims to analyze the process of the progressive mathematization of the concept of the function by secondary school students through the resolution of a free fall situation. A free-fall mathematical situation was designed and experimented using the Tracker software to obtain movement data. Worksheets and conversations were collected between students and the teacher, and experiments and class discussions were filmed. The analysis consisted of identifying the development from informal strategies associated with the context of the problem to formal procedures. The results show that the process brings meanings to mathematical ideas such as variation, variables, and the relationship between variables, allows coordination and transition between representations and contributes to the learning of functions as a representation of the variation of physical phenomena.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"31 48","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139382626","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}
Armando Morales-Carballo, Miguel Díaz Cárdenas, Angie Damián Mojica
This article presents a theoretical-didactic perspective on the formation and development of concepts concerning mathematical objects as a result of research on didactic difficulties in dealing with concepts in school. The theoretical foundation that supports the research is based on the contributions of the materialist approach to the theory of knowledge. Specifically, an interpretation of its application in the teaching of mathematics is under investigation, specifically in the process of formation and development of concepts in the field of Euclidean geometry. However, the elements that are derived are essential for the treatment of concepts in any sub-branch of mathematics. The analysis of this process and the factors that influence the development show some fundamental elements to consider in the research activity in the field of mathematics education.
{"title":"Formation and development of mathematical concepts: Elements for research and teaching","authors":"Armando Morales-Carballo, Miguel Díaz Cárdenas, Angie Damián Mojica","doi":"10.29333/iejme/14023","DOIUrl":"https://doi.org/10.29333/iejme/14023","url":null,"abstract":"This article presents a theoretical-didactic perspective on the formation and development of concepts concerning mathematical objects as a result of research on didactic difficulties in dealing with concepts in school. The theoretical foundation that supports the research is based on the contributions of the materialist approach to the theory of knowledge. Specifically, an interpretation of its application in the teaching of mathematics is under investigation, specifically in the process of formation and development of concepts in the field of Euclidean geometry. However, the elements that are derived are essential for the treatment of concepts in any sub-branch of mathematics. The analysis of this process and the factors that influence the development show some fundamental elements to consider in the research activity in the field of mathematics education.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"34 20","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139127071","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}
M. Bratkovich, Jane Harvey, Katherine M. Hellmann, Kimberly A. Cooper
This study examines language demands in undergraduate university mathematics classes with a view to better preparing and supporting international and other culturally and linguistically diverse (CLD) students in the United States universities. We observed and analyzed the language demands of 13 entry-level mathematics classes across two large universities. Findings showed that mathematics instruction required extensive and varied listening skills requiring students to listen to long and uninterrupted stretches of sometimes fast paced speech. Technical vocabulary contributed to the language demands, but instructors used both academic and colloquial varieties of language in instruction, interweaving mathematical nouns with phrasal verbs to explain mathematical processes. We suggest a greater focus on development of academic listening skills in English language classes as well as potential collaboration with mathematics campus resources and faculty for additional student support for preparing CLD students for potential future discourse practices.
{"title":"Language demands in undergraduate mathematics courses","authors":"M. Bratkovich, Jane Harvey, Katherine M. Hellmann, Kimberly A. Cooper","doi":"10.29333/iejme/13904","DOIUrl":"https://doi.org/10.29333/iejme/13904","url":null,"abstract":"This study examines language demands in undergraduate university mathematics classes with a view to better preparing and supporting international and other culturally and linguistically diverse (CLD) students in the United States universities. We observed and analyzed the language demands of 13 entry-level mathematics classes across two large universities. Findings showed that mathematics instruction required extensive and varied listening skills requiring students to listen to long and uninterrupted stretches of sometimes fast paced speech. Technical vocabulary contributed to the language demands, but instructors used both academic and colloquial varieties of language in instruction, interweaving mathematical nouns with phrasal verbs to explain mathematical processes. We suggest a greater focus on development of academic listening skills in English language classes as well as potential collaboration with mathematics campus resources and faculty for additional student support for preparing CLD students for potential future discourse practices.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"35 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139129834","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}
Riyan Hidayat, Tay Ying Qi, Putri Nur’afrina Binti Tajul Ariffin, Mohamad Hafizullah Bin Mohd Hadzri, Lin Mei Chin, Jacqueline Lee Xuan Ning, Nurihan Nasir
In contemporary education, game-based learning (GBL) has become a captivating instructional method applied across various academic subjects, including mathematics. The utilization of online GBL in mathematics education constitutes a segment of the activities that mathematics educators can employ during their lessons to teach students and enhance their educational progress. The primary goal of this study was to examine recent research endeavors involving the use of online GBL in mathematics education for Generation Z cohort. To achieve this objective, a systematic review (SR) was carried out to investigate the types of online games employed, analyze previous research methodologies, and explore the educational contexts relevant to mathematics education that align with the needs of Generation Z. An SR process was conducted to gather relevant articles from three databases, namely Science Direct, Scopus, and Springer. Full-text articles were meticulously assessed based on predetermined eligibility criteria. The review revealed many online games suitable for mathematics education, including Augmented Reality, Digital Inquiry Game, E-Rebuild, Math-Island Game, NanoRoboMath, Quizizz, and Wuzzit Trouble. The incorporation of online games in mathematics education offers numerous advantages.
{"title":"Online game-based learning in mathematics education among Generation Z: A systematic review","authors":"Riyan Hidayat, Tay Ying Qi, Putri Nur’afrina Binti Tajul Ariffin, Mohamad Hafizullah Bin Mohd Hadzri, Lin Mei Chin, Jacqueline Lee Xuan Ning, Nurihan Nasir","doi":"10.29333/iejme/14024","DOIUrl":"https://doi.org/10.29333/iejme/14024","url":null,"abstract":"In contemporary education, game-based learning (GBL) has become a captivating instructional method applied across various academic subjects, including mathematics. The utilization of online GBL in mathematics education constitutes a segment of the activities that mathematics educators can employ during their lessons to teach students and enhance their educational progress. The primary goal of this study was to examine recent research endeavors involving the use of online GBL in mathematics education for Generation Z cohort. To achieve this objective, a systematic review (SR) was carried out to investigate the types of online games employed, analyze previous research methodologies, and explore the educational contexts relevant to mathematics education that align with the needs of Generation Z. An SR process was conducted to gather relevant articles from three databases, namely Science Direct, Scopus, and Springer. Full-text articles were meticulously assessed based on predetermined eligibility criteria. The review revealed many online games suitable for mathematics education, including Augmented Reality, Digital Inquiry Game, E-Rebuild, Math-Island Game, NanoRoboMath, Quizizz, and Wuzzit Trouble. The incorporation of online games in mathematics education offers numerous advantages.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"10 7","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139129335","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 presents a case study and ideas to flip classical dialogic learning method. Some possibilities of using ChatGPT to stimulate the active role of the student in the dialogic teaching method are shown. Data from observations of students training to be teachers of mathematics and informatics in their work with artificial intelligence (AI) are presented. A model for the application of the flipped dialogue in the education of students is proposed. An example of dialogue is given. The study concludes that that the main advantages of using flipped dialog learning with AI are easy access to the platforms, the lack of stress and stimulating the research qualities of students when searching for specific information or stimulating the system to make mistakes. The ability to ask the right leading questions and to detect the gaps of the “interlocutor” are important competencies applicable in dealing with life’s problems.
{"title":"Flipped dialogic learning method with ChatGPT: A case study","authors":"Nataliya Hristova Pavlova","doi":"10.29333/iejme/14025","DOIUrl":"https://doi.org/10.29333/iejme/14025","url":null,"abstract":"This article presents a case study and ideas to flip classical dialogic learning method. Some possibilities of using ChatGPT to stimulate the active role of the student in the dialogic teaching method are shown. Data from observations of students training to be teachers of mathematics and informatics in their work with artificial intelligence (AI) are presented. A model for the application of the flipped dialogue in the education of students is proposed. An example of dialogue is given. The study concludes that that the main advantages of using flipped dialog learning with AI are easy access to the platforms, the lack of stress and stimulating the research qualities of students when searching for specific information or stimulating the system to make mistakes. The ability to ask the right leading questions and to detect the gaps of the “interlocutor” are important competencies applicable in dealing with life’s problems.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":" 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139391699","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}
Understanding the concepts related to real function is essential in learning mathematics. To determine how students understand these concepts, it is necessary to have an appropriate measurement tool. In this paper, we have created a web application using 32 items from conceptual understanding of real functions (CURF) item bank. We conducted a psychometric analysis using Rasch model on 207 first-year students. The analysis showed that CURF is a dependable and valid instrument for measuring students’ CURF. The test is uni-dimensional; all items are consistent with the construct and have excellent item fit statistics. The results indicate that the items are independent of each other and unbiased towards the gender and high school background of the students.
{"title":"Measuring students’ conceptual understanding of real functions: A Rasch model analysis","authors":"Anela Hrnjičić, Adis Alihodžić","doi":"10.29333/iejme/13942","DOIUrl":"https://doi.org/10.29333/iejme/13942","url":null,"abstract":"Understanding the concepts related to real function is essential in learning mathematics. To determine how students understand these concepts, it is necessary to have an appropriate measurement tool. In this paper, we have created a web application using 32 items from conceptual understanding of real functions (CURF) item bank. We conducted a psychometric analysis using Rasch model on 207 first-year students. The analysis showed that CURF is a dependable and valid instrument for measuring students’ CURF. The test is uni-dimensional; all items are consistent with the construct and have excellent item fit statistics. The results indicate that the items are independent of each other and unbiased towards the gender and high school background of the students.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"40 5","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139129435","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 this article, the goal is to describe students’ mathematical reasoning in the context of different settings of problem-solving tasks. The core of the tasks are real objects, which are presented to the students with the help of photos, a 3D model or in the environment itself. With reference to the experiential learning theory and relations to problem-solving and modelling, theoretical potentials for mathematical reasoning emerge. In a qualitative study with 19 secondary school students these are empirically tested. The evaluation of the video recordings of the students’ solution processes are coded with the help of qualitative content analysis, among others with references to problem-solving and linguistic categories of conclusive speech acts. The results show that mathematical reasoning can be observed especially in the work with photos and that the work with real objects generally evokes reasoning activities in the area of planning and exploration of strategies.
{"title":"Real objects as a reason for mathematical reasoning – A comparison of different task settings","authors":"Simone Jablonski","doi":"10.29333/iejme/13859","DOIUrl":"https://doi.org/10.29333/iejme/13859","url":null,"abstract":"In this article, the goal is to describe students’ mathematical reasoning in the context of different settings of problem-solving tasks. The core of the tasks are real objects, which are presented to the students with the help of photos, a 3D model or in the environment itself. With reference to the experiential learning theory and relations to problem-solving and modelling, theoretical potentials for mathematical reasoning emerge. In a qualitative study with 19 secondary school students these are empirically tested. The evaluation of the video recordings of the students’ solution processes are coded with the help of qualitative content analysis, among others with references to problem-solving and linguistic categories of conclusive speech acts. The results show that mathematical reasoning can be observed especially in the work with photos and that the work with real objects generally evokes reasoning activities in the area of planning and exploration of strategies.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"117 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135725215","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}
Declining enrollments in teacher preparation programs across the United States signal a critical need for institutions of higher education to consider innovative recruitment initiatives. This pilot study investigates a novel approach to recruiting undergraduates into a teacher preparation program. Nine participants, mostly first-year college students, engaged in a year-long experiential learning program. The program provided participants with an early teaching experience in a classroom-like setting by engaging them in the collaborative development, planning, and teaching of mathematics in a summer camp for high school students. Data were collected throughout the year on their: planned major, attitudes towards mathematics and mathematics education, mathematics teaching self-efficacy, and perceptions of the program. Results showed the program was successful at improving attitudes, increasing self-efficacy, and stimulating reflection on a potential career as a mathematics teacher. Participants also shared positive impressions of the experience. Implications for research and future practice are discussed.
{"title":"Impact of a mathematics early teaching experience for undergraduates: A teacher preparation recruitment strategy","authors":"Jessica A. de la Cruz, Samantha E. Goldman","doi":"10.29333/iejme/13860","DOIUrl":"https://doi.org/10.29333/iejme/13860","url":null,"abstract":"Declining enrollments in teacher preparation programs across the United States signal a critical need for institutions of higher education to consider innovative recruitment initiatives. This pilot study investigates a novel approach to recruiting undergraduates into a teacher preparation program. Nine participants, mostly first-year college students, engaged in a year-long experiential learning program. The program provided participants with an early teaching experience in a classroom-like setting by engaging them in the collaborative development, planning, and teaching of mathematics in a summer camp for high school students. Data were collected throughout the year on their: planned major, attitudes towards mathematics and mathematics education, mathematics teaching self-efficacy, and perceptions of the program. Results showed the program was successful at improving attitudes, increasing self-efficacy, and stimulating reflection on a potential career as a mathematics teacher. Participants also shared positive impressions of the experience. Implications for research and future practice are discussed.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"117 15","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135725383","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 the changes in students’ mental constructions of function transformation based on the designed activities, classroom discussions, exercises (ACE) teaching cycle in the light of the action, process, object, schema (APOS) theoretical framework. The study was conducted by seven volunteer students who were enrolled in mathematics teacher education program. The data consisted of video records of the designed teaching sessions, students’ worksheets and the researcher’s field notes. The results indicated that ACE teaching cycle was effective in developing students’ mental constructions of function transformation through sequential activities. Even though all the students initially did not reveal evidence for sufficient theoretical or practical knowledge on function transformation, which was evidence of their action level, through the process, it became evident that all the students provided evidence regarding at least their process level of function transformations. Some of the students also showed evidence related to their object levels of function transformations.
{"title":"Changes in students’ mental constructions of function transformations through the APOS framework","authors":"Melike Yiğit Koyunkaya, Burcak Boz-Yaman","doi":"10.29333/iejme/13515","DOIUrl":"https://doi.org/10.29333/iejme/13515","url":null,"abstract":"This study aims to examine the changes in students’ mental constructions of function transformation based on the designed activities, classroom discussions, exercises (ACE) teaching cycle in the light of the action, process, object, schema (APOS) theoretical framework. The study was conducted by seven volunteer students who were enrolled in mathematics teacher education program. The data consisted of video records of the designed teaching sessions, students’ worksheets and the researcher’s field notes. The results indicated that ACE teaching cycle was effective in developing students’ mental constructions of function transformation through sequential activities. Even though all the students initially did not reveal evidence for sufficient theoretical or practical knowledge on function transformation, which was evidence of their action level, through the process, it became evident that all the students provided evidence regarding at least their process level of function transformations. Some of the students also showed evidence related to their object levels of function transformations.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"98 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86060580","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 study focused on development and validation of the mathematics persistence scale (MPS) for measuring secondary school students’ persistence in learning mathematics. The study employed a descriptive survey design. Three research questions guided the study. The population of the study comprised 13,516 students distributed in 59 public secondary schools in Nsukka Education Zone, Enugu State, Nigeria. A multi-stage sampling procedure was used in selecting a sample size of 1,378 secondary school mathematics students used for the study. In the development of MPS, 85 items were first constructed and subjected to face validity. After face validation, eight items were deleted in line with the recommendations and suggestions of the validators. The remaining 77 items were further subjected to exploratory factor analysis using statistical package for the social science version 25. 28 factorial pure items, that loaded into four salient factors (persistence in classroom mathematics exercise, persistence in mathematics take home assignments, persistence in a group mathematics tasks, and persistence in mathematics examination) emerged from the analysis. Confirmatory factor analysis of four factors using lavaan and semPlot packages indicated a harmony between four factor model and the data. The internal consistency coefficients of four factors ranges from 0.78 to 0.92.
{"title":"Development and validation of mathematics persistence scale for secondary school students","authors":"Sunday Ogbu, Felicia Chinyere Ugwu","doi":"10.29333/iejme/13742","DOIUrl":"https://doi.org/10.29333/iejme/13742","url":null,"abstract":"The study focused on development and validation of the mathematics persistence scale (MPS) for measuring secondary school students’ persistence in learning mathematics. The study employed a descriptive survey design. Three research questions guided the study. The population of the study comprised 13,516 students distributed in 59 public secondary schools in Nsukka Education Zone, Enugu State, Nigeria. A multi-stage sampling procedure was used in selecting a sample size of 1,378 secondary school mathematics students used for the study. In the development of MPS, 85 items were first constructed and subjected to face validity. After face validation, eight items were deleted in line with the recommendations and suggestions of the validators. The remaining 77 items were further subjected to exploratory factor analysis using statistical package for the social science version 25. 28 factorial pure items, that loaded into four salient factors (persistence in classroom mathematics exercise, persistence in mathematics take home assignments, persistence in a group mathematics tasks, and persistence in mathematics examination) emerged from the analysis. Confirmatory factor analysis of four factors using lavaan and semPlot packages indicated a harmony between four factor model and the data. The internal consistency coefficients of four factors ranges from 0.78 to 0.92.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"151 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":"135373216","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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