This paper presents the results of a study aimed at diagnosing how newly enrolled mathematics majors reason from a mathematical standpoint when they are required to perform inductive and deductive processes and validate or refute claims of a general nature. The theoretical framework underpinning this research comprises studies and investigations related to mathematical reasoning. The results of this diagnostic reveal that students lack mathematical reasoning skills that would allow them to justify statements of a general nature. In addition, they face difficulties in the development of deductive reasoning, are prone to generalize based on specific cases and lack skills in mathematical argumentation. On the other hand, they lack basic algebra skills such as developing square binomials and factoring. These findings highlight the need to design and implement a didactic proposal that fosters the development of reasoning and argumentation in students.
{"title":"Diagnostic study of mathematical reasoning in novice university students","authors":"Irma Joachin-Arizmendi, Edgardo Locia-Espinoza, Armando Morales-Carballo, Gerardo Reyna-Hernández","doi":"10.29333/iejme/14862","DOIUrl":"https://doi.org/10.29333/iejme/14862","url":null,"abstract":"This paper presents the results of a study aimed at diagnosing how newly enrolled mathematics majors reason from a mathematical standpoint when they are required to perform inductive and deductive processes and validate or refute claims of a general nature. The theoretical framework underpinning this research comprises studies and investigations related to mathematical reasoning. The results of this diagnostic reveal that students lack mathematical reasoning skills that would allow them to justify statements of a general nature. In addition, they face difficulties in the development of deductive reasoning, are prone to generalize based on specific cases and lack skills in mathematical argumentation. On the other hand, they lack basic algebra skills such as developing square binomials and factoring. These findings highlight the need to design and implement a didactic proposal that fosters the development of reasoning and argumentation in students.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141810346","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}
Marina Cotic, Daniel Doz, Matija Jenko, Amalija Žakelj
The evolution of mathematics coincided with advancements in its teaching. The 19th and 20th centuries marked a pedagogical revolution in mathematics education. This paper argues that Bruner’s (1966) model, Gagné’s (1985) taxonomy, innovative teaching methods emphasizing research and problem-solving, and the inclusion of data analysis topics have shaped modern mathematics education. Additionally, the paper explores transformative trends, emphasizing mathematics literacy and the integration of virtual reality (VR) and artificial intelligence (AI) in education. This evolution emphasizes practical, contextually relevant approaches. VR enhances engagement and comprehension of abstract concepts, while AI offers personalized learning experiences, fostering deeper understanding and skill development.
{"title":"Mathematics education: What was it, what is it, and what will it be?","authors":"Marina Cotic, Daniel Doz, Matija Jenko, Amalija Žakelj","doi":"10.29333/iejme/14663","DOIUrl":"https://doi.org/10.29333/iejme/14663","url":null,"abstract":"The evolution of mathematics coincided with advancements in its teaching. The 19th and 20th centuries marked a pedagogical revolution in mathematics education. This paper argues that Bruner’s (1966) model, Gagné’s (1985) taxonomy, innovative teaching methods emphasizing research and problem-solving, and the inclusion of data analysis topics have shaped modern mathematics education. Additionally, the paper explores transformative trends, emphasizing mathematics literacy and the integration of virtual reality (VR) and artificial intelligence (AI) in education. This evolution emphasizes practical, contextually relevant approaches. VR enhances engagement and comprehension of abstract concepts, while AI offers personalized learning experiences, fostering deeper understanding and skill development.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141708414","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 mediated field experience (MFE) mathematics methods course increased both pre-service elementary teachers’ (PSTs) self-efficacy for teaching mathematics and mathematical dispositions. The semester-long MFE with significant, structured teaching experiences was conducted onsite at an elementary school. Quantitative, pre- and post-surveys of mathematics teaching efficacy revealed statistically significant increases over the semester. A qualitative analysis of PSTs as sophomores and seniors further explored and supported this increase in PSTs’ self-efficacy for teaching mathematics. Qualitative data also revealed interesting changes in mathematical dispositions and a shift in PSTs from a self-as-student perspective to a self-as-teacher focus.
{"title":"The effects of a mediated field experience methods course on pre-service elementary mathematics teachers’ beliefs","authors":"Valorie L. Zonnefeld, Luralyn M. Helming","doi":"10.29333/iejme/14729","DOIUrl":"https://doi.org/10.29333/iejme/14729","url":null,"abstract":"A mediated field experience (MFE) mathematics methods course increased both pre-service elementary teachers’ (PSTs) self-efficacy for teaching mathematics and mathematical dispositions. The semester-long MFE with significant, structured teaching experiences was conducted onsite at an elementary school. Quantitative, pre- and post-surveys of mathematics teaching efficacy revealed statistically significant increases over the semester. A qualitative analysis of PSTs as sophomores and seniors further explored and supported this increase in PSTs’ self-efficacy for teaching mathematics. Qualitative data also revealed interesting changes in mathematical dispositions and a shift in PSTs from a self-as-student perspective to a self-as-teacher focus.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141706382","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 analyze the graphical comprehension of 5th and 6th grade students in multigrade rural primary education in Chile. The theoretical framework considers levels of reading and semiotic levels in statistical graphs. A qualitative methodology of descriptive level is followed, using content analysis method for the responses given to a questionnaire by 22 students from five multigrade rural schools. The results show that, overall, students do not encounter difficulties in answering questions at level 1 reading (literal reading), but difficulties gradually increase as the reading level increases. Regarding semiotic levels, difficulties arise in constructing graphs using data distribution (semiotic level 3) and completing a graph with two data distributions (semiotic level 4).
{"title":"Understanding statistical graphs of students attending multigrade rural schools in Chile","authors":"Matías Bustamante-Valdés, Danilo Díaz-Levicoy","doi":"10.29333/iejme/14743","DOIUrl":"https://doi.org/10.29333/iejme/14743","url":null,"abstract":"This study aims to analyze the graphical comprehension of 5th and 6th grade students in multigrade rural primary education in Chile. The theoretical framework considers levels of reading and semiotic levels in statistical graphs. A qualitative methodology of descriptive level is followed, using content analysis method for the responses given to a questionnaire by 22 students from five multigrade rural schools. The results show that, overall, students do not encounter difficulties in answering questions at level 1 reading (literal reading), but difficulties gradually increase as the reading level increases. Regarding semiotic levels, difficulties arise in constructing graphs using data distribution (semiotic level 3) and completing a graph with two data distributions (semiotic level 4).","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141707905","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}
We conducted a descriptive study among first-year engineering students at the Anton de Kom University of Suriname. We analyzed students’ errors regarding necessary prior knowledge in a calculus A exam. We found that the stage of the solution in which prior knowledge is required impacts the importance of prior knowledge. We also found that many errors concerned basic algebra and trigonometry concepts and skills. We concluded that even though the required prior knowledge concerns basic algebra and trigonometry, the stage of the solution in which prior knowledge is needed is of great importance.
我们对苏里南安东-德-科姆大学工程系一年级学生进行了一项描述性研究。我们分析了学生在微积分 A 考试中关于必要先验知识的错误。我们发现，需要先验知识的解题阶段会影响先验知识的重要性。我们还发现，许多错误涉及基本的代数和三角概念和技能。我们的结论是，尽管所需的先验知识涉及基础代数和三角学，但需要先验知识的解题阶段非常重要。
{"title":"Prior knowledge of a calculus course: The impact of prior knowledge on students’ errors","authors":"Regina Mahadewsing, Diana Getrouw, S. M. Calor","doi":"10.29333/iejme/14765","DOIUrl":"https://doi.org/10.29333/iejme/14765","url":null,"abstract":"We conducted a descriptive study among first-year engineering students at the Anton de Kom University of Suriname. We analyzed students’ errors regarding necessary prior knowledge in a calculus A exam. We found that the stage of the solution in which prior knowledge is required impacts the importance of prior knowledge. We also found that many errors concerned basic algebra and trigonometry concepts and skills. We concluded that even though the required prior knowledge concerns basic algebra and trigonometry, the stage of the solution in which prior knowledge is needed is of great importance.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141692531","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 literature review examines the use of photography in educational research and in education, to learn how photography could be better used in teaching and learning mathematics and mathematics education research. The authors analyzed 125 publications published between 1975 and 2023 to identify different research methods and teaching solutions that utilize photography. Within educational research two main approaches that are often used combined were photo-elicitation (photographs are used in an interview as a stimulus) and photovoice (taking photographs is a way the participant communicates their perspective). Mathematics education research could also combine these methods, for example in identity research. Our findings regarding teaching show that photographs have an important role in connecting mathematics to the real world and for visualizing mathematics. The best way to engage students is when they take photographs of themselves as a starting point to mathematical activity. Based on this review we identify future exploratory directions and various research gaps.
{"title":"The potential of photography for mathematics education and research–A literature review","authors":"S. Oksanen, Markku S. Hannula, Anu Laine","doi":"10.29333/iejme/14613","DOIUrl":"https://doi.org/10.29333/iejme/14613","url":null,"abstract":"This literature review examines the use of photography in educational research and in education, to learn how photography could be better used in teaching and learning mathematics and mathematics education research. The authors analyzed 125 publications published between 1975 and 2023 to identify different research methods and teaching solutions that utilize photography. Within educational research two main approaches that are often used combined were photo-elicitation (photographs are used in an interview as a stimulus) and photovoice (taking photographs is a way the participant communicates their perspective). Mathematics education research could also combine these methods, for example in identity research. Our findings regarding teaching show that photographs have an important role in connecting mathematics to the real world and for visualizing mathematics. The best way to engage students is when they take photographs of themselves as a starting point to mathematical activity. Based on this review we identify future exploratory directions and various research gaps.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141697252","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}
Classroom assessment is essential for tracking students’ progress and improving teaching and learning in the classroom. However, the lack of clear documentation to guide teachers in assessing student mastery often hinders effective communication between teachers and stakeholders about the students’ progress. This study aimed to develop and test the digital classroom assessment document (CA-Do) for form one mathematics to improve classroom assessment practices. Design research and development method, based on ADDIE model, was used to create the digital CA-Do, and 55 mathematics teachers from 55 schools were sampled using stratified sampling. The data collected was then analyzed using SPSS version 27. The digital CA-Do received a satisfactory expert validity score of content validity index (1.00), and found all four tested sub-constructs (i.e., usefulness, ease of use, ease of learning, and satisfaction of use) to be of high level. There were significant differences in teachers’ knowledge post-familiarization with the digital CA-Do. The study concludes that the digital CA-Do can aid teachers in recording the intervention and impact of teaching and learning information and consistently assessing pupils’ mastery level. This research provides guidance to educators on how to modify their classroom assessment strategies to enhance teaching outcomes and classroom assessment methods, particularly formative assessment.
{"title":"Development and effectiveness of digital classroom assessment document for form one mathematics in secondary school","authors":"Nurihan Nasir, M. Adnan, Murugan Rajoo, Anis Oweeda Ismail, Riyan Hidayat","doi":"10.29333/iejme/14766","DOIUrl":"https://doi.org/10.29333/iejme/14766","url":null,"abstract":"Classroom assessment is essential for tracking students’ progress and improving teaching and learning in the classroom. However, the lack of clear documentation to guide teachers in assessing student mastery often hinders effective communication between teachers and stakeholders about the students’ progress. This study aimed to develop and test the digital classroom assessment document (CA-Do) for form one mathematics to improve classroom assessment practices. Design research and development method, based on ADDIE model, was used to create the digital CA-Do, and 55 mathematics teachers from 55 schools were sampled using stratified sampling. The data collected was then analyzed using SPSS version 27. The digital CA-Do received a satisfactory expert validity score of content validity index (1.00), and found all four tested sub-constructs (i.e., usefulness, ease of use, ease of learning, and satisfaction of use) to be of high level. There were significant differences in teachers’ knowledge post-familiarization with the digital CA-Do. The study concludes that the digital CA-Do can aid teachers in recording the intervention and impact of teaching and learning information and consistently assessing pupils’ mastery level. This research provides guidance to educators on how to modify their classroom assessment strategies to enhance teaching outcomes and classroom assessment methods, particularly formative assessment.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141698438","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 is based on the analysis of the relationship between early education, mathematical skills, and student achievement in Bosnia & Herzegovina, using data from the trends in international mathematics and science study (TIMSS) 2019. The study involves 5,628 fourth-grade students whose average age was 10.1 years. The research specifically focuses on factors such as the age of students at the beginning of schooling, attendance at preschool institutions, and their mathematical skills before starting school. Through the application of SPSS analysis, insights into the statistical relationships and trends between these factors are provided, emphasizing the importance of early educational experiences to improve the quality of education in Bosnia & Herzegovina. The analysis results show that the length of stay in preschool institutions, attendance in preschool programs, and the early acquisition of mathematical skills (counting skills, recognition of numeral representations, numeral writing, simple addition, and subtraction) impact later mathematical achievements of students.
{"title":"The impact of early childhood education and mathematical abilities on student achievement: Analysis of TIMSS 2019","authors":"Naida Bikić, Nevzudin Buzađija, Anela Hrnjičić","doi":"10.29333/iejme/14599","DOIUrl":"https://doi.org/10.29333/iejme/14599","url":null,"abstract":"This paper is based on the analysis of the relationship between early education, mathematical skills, and student achievement in Bosnia & Herzegovina, using data from the trends in international mathematics and science study (TIMSS) 2019. The study involves 5,628 fourth-grade students whose average age was 10.1 years. The research specifically focuses on factors such as the age of students at the beginning of schooling, attendance at preschool institutions, and their mathematical skills before starting school. Through the application of SPSS analysis, insights into the statistical relationships and trends between these factors are provided, emphasizing the importance of early educational experiences to improve the quality of education in Bosnia & Herzegovina. The analysis results show that the length of stay in preschool institutions, attendance in preschool programs, and the early acquisition of mathematical skills (counting skills, recognition of numeral representations, numeral writing, simple addition, and subtraction) impact later mathematical achievements of students.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141711490","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 research paper explores the integration of ChatGPT as a tool for interactive learning of numerical methods in a differential equations (DEs) course. DE course is crucial for engineering students to model real-world phenomena. However, many DE courses focus only on analytical solutions and neglect important numerical solutions. To overcome this gap, an active learning approach was adopted, where students were asked to select a real-life phenomenon in their field of interest, find an appropriate model to describe it using DEs, and subsequently solve DE numerically using various numerical methods. The authors allowed students to use ChatGPT to generate codes and learn how to adapt them to their personalized learning needs. The findings derived from the students’ survey responses demonstrated that ChatGPT significantly enhanced their interests and improved their coding skills. Students reported increased engagement and excitement in their learning journey with the integration of ChatGPT. By sharing this experience, we aim to inspire other educators to explore the potential of innovative technologies and instructional methods to enhance their own courses.
{"title":"Enhancing students’ learning experience in mathematics class through ChatGPT","authors":"Rim Gouia-Zarrad, Cindy Gunn","doi":"10.29333/iejme/14614","DOIUrl":"https://doi.org/10.29333/iejme/14614","url":null,"abstract":"This research paper explores the integration of ChatGPT as a tool for interactive learning of numerical methods in a differential equations (DEs) course. DE course is crucial for engineering students to model real-world phenomena. However, many DE courses focus only on analytical solutions and neglect important numerical solutions. To overcome this gap, an active learning approach was adopted, where students were asked to select a real-life phenomenon in their field of interest, find an appropriate model to describe it using DEs, and subsequently solve DE numerically using various numerical methods. The authors allowed students to use ChatGPT to generate codes and learn how to adapt them to their personalized learning needs. The findings derived from the students’ survey responses demonstrated that ChatGPT significantly enhanced their interests and improved their coding skills. Students reported increased engagement and excitement in their learning journey with the integration of ChatGPT. By sharing this experience, we aim to inspire other educators to explore the potential of innovative technologies and instructional methods to enhance their own courses.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141700275","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 evaluates the Mythematix prototype, an innovative adaptive e-learning system designed specifically to enhance secondary school students’ understanding and proficiency in mathematics. Utilizing a mixed-methods approach, it combines qualitative and quantitative research methodologies to thoroughly assess students’ perceptions and experiences with the Mythematix prototype. The study involved a group of 30 students participating in a comprehensive usability survey, which included a range of Likert scale questions alongside an open-ended response. This survey was designed to evaluate the usability of the prototype, pinpointing its strengths and weaknesses from the students’ perspectives. The analysis of the survey results provided detailed insights into the most and least effective aspects of the prototype. Overall, the study contributes valuable insights into the effectiveness of adaptive e-learning platforms in enhancing and enriching students’ learning experiences in mathematics, and it lays the groundwork for future research in this evolving educational field.
{"title":"Insights on usability testing: The effectiveness of an adaptive e-learning system for secondary school mathematics","authors":"Liz Aliza Awang, F. Yusop, Mahmoud Danaee","doi":"10.29333/iejme/14621","DOIUrl":"https://doi.org/10.29333/iejme/14621","url":null,"abstract":"The study evaluates the Mythematix prototype, an innovative adaptive e-learning system designed specifically to enhance secondary school students’ understanding and proficiency in mathematics. Utilizing a mixed-methods approach, it combines qualitative and quantitative research methodologies to thoroughly assess students’ perceptions and experiences with the Mythematix prototype. The study involved a group of 30 students participating in a comprehensive usability survey, which included a range of Likert scale questions alongside an open-ended response. This survey was designed to evaluate the usability of the prototype, pinpointing its strengths and weaknesses from the students’ perspectives. The analysis of the survey results provided detailed insights into the most and least effective aspects of the prototype. Overall, the study contributes valuable insights into the effectiveness of adaptive e-learning platforms in enhancing and enriching students’ learning experiences in mathematics, and it lays the groundwork for future research in this evolving educational field.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141696755","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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