Digital learning resources are commonly employed to support learning in out-of-class contexts, either as a complement to the learning in formal classrooms or as an alternative that can be used by learners to pursue personal learning goals. This study identified a significant gap in the literature concerning children's use of digital technology to support STEM (science and mathematics in particular) learning outside of the classroom. To develop a framework for further research in this area, this study adopted a multiple case study design using semi-structured interviews and observations as data collection methods. Following a sociocultural framework, this research primarily confirmed existing work regarding the identification of motivational factors and concluded that the user interface (UI), all-in-one features of digital technology, simulation and alternative learning experience were factors that influenced the learning motivation of secondary schoolage learners when learning science and mathematics with digital technology in out-of-class contexts.
{"title":"An Investigation into Secondary School- age Learners’ Out -of-class (Community and Home-based Settings) STEM Learning Experience with Digital Technology","authors":"Xinyue Li","doi":"10.1564/tme_v30.3.4","DOIUrl":"https://doi.org/10.1564/tme_v30.3.4","url":null,"abstract":"Digital learning resources are commonly employed to support learning in out-of-class contexts, either as a complement to the learning in formal classrooms or as an alternative that can be used by learners to pursue personal learning goals. This study identified a significant gap in the literature concerning children's use of digital technology to support STEM (science and mathematics in particular) learning outside of the classroom. To develop a framework for further research in this area, this study adopted a multiple case study design using semi-structured interviews and observations as data collection methods. Following a sociocultural framework, this research primarily confirmed existing work regarding the identification of motivational factors and concluded that the user interface (UI), all-in-one features of digital technology, simulation and alternative learning experience were factors that influenced the learning motivation of secondary schoolage learners when learning science and mathematics with digital technology in out-of-class contexts.","PeriodicalId":433766,"journal":{"name":"The International Journal for Technology in Mathematics Education","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135691236","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}
Music provides an excellent setting for students to explore trigonometric functions in a setting which is independent of their utility in resolving triangles. In this paper, we present several investigations using trigonometric functions to model musical phenomena. From a mathematical technology point of view, most examples require only function graphing and can be explored using a modern interactive graphing application. One example, however, is an excellent application of trigonometric simplification, for which a Computer Algebra System is a useful tool. A final application is suitable for calculus students and provides an exercise in integration by parts. This can be done by hand, or with the aid of an algebra system.
{"title":"Trigonometric Functions and the Sensations of Tone","authors":"Philip Todd, Danny Aley","doi":"10.1564/tme_v30.3.6","DOIUrl":"https://doi.org/10.1564/tme_v30.3.6","url":null,"abstract":"Music provides an excellent setting for students to explore trigonometric functions in a setting which is independent of their utility in resolving triangles. In this paper, we present several investigations using trigonometric functions to model musical phenomena. From a mathematical technology point of view, most examples require only function graphing and can be explored using a modern interactive graphing application. One example, however, is an excellent application of trigonometric simplification, for which a Computer Algebra System is a useful tool. A final application is suitable for calculus students and provides an exercise in integration by parts. This can be done by hand, or with the aid of an algebra system.","PeriodicalId":433766,"journal":{"name":"The International Journal for Technology in Mathematics Education","volume":"376 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690960","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 ability to solve geometric construction problems is justly regarded as an essential component of mathematical culture. The dynamic, general nature of objects provided by dynamic geometry systems allows the development of intuitive methods for solving construction problems. The core mathematical concept underlying this approach is the loci method, in which the main element of the required object forms as the intersection of two loci, each one obtained by purposely ignoring part of the conditions of the problem. With GeoGebra, the relevant locus may be visualized and detected in trace mode. Using dynamic geometry this way for problem solving replaces the single object by the infinite locus and is similar to the introduction of variables for solving equations in school algebra. This paper presents some examples of how this approach may be realized along with the results of a small-scale experiment with pre-service mathematics teachers.
{"title":"The Intuitive Way to Solve Construction Problems in the Dynamic Geometry Environment","authors":"Ilya Sinitsky","doi":"10.1564/tme_v30.3.2","DOIUrl":"https://doi.org/10.1564/tme_v30.3.2","url":null,"abstract":"The ability to solve geometric construction problems is justly regarded as an essential component of mathematical culture. The dynamic, general nature of objects provided by dynamic geometry systems allows the development of intuitive methods for solving construction problems. The core mathematical concept underlying this approach is the loci method, in which the main element of the required object forms as the intersection of two loci, each one obtained by purposely ignoring part of the conditions of the problem. With GeoGebra, the relevant locus may be visualized and detected in trace mode. Using dynamic geometry this way for problem solving replaces the single object by the infinite locus and is similar to the introduction of variables for solving equations in school algebra. This paper presents some examples of how this approach may be realized along with the results of a small-scale experiment with pre-service mathematics teachers.","PeriodicalId":433766,"journal":{"name":"The International Journal for Technology in Mathematics Education","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135691237","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}
Fadhlan Muchlas Abrori, Zsolt Lavicza, Mathias Tejera, Branko Anđić
Integrating biology and mathematics can potentially solve problems associated with students' inability to solve quantitative biology problems. To face this issue, we embarked on a project to develop biological and mathematical content-based comics for elementary school students. It would assist them in gaining early comfort with transdisciplinary work. However, we need experts’ perceptions to see if our comics are feasible. This exploratory interview research attempted to understand how experts perceive mathematical representation in biology comics. The three experts involved in the interview were a biology teacher, a mathematics lecturer, and a comics enthusiast. This study's empirical data were collected using semi-structured interviews and analyzed using thematic analysis. The research uncovered three major themes: 1) comic content, 2) graph type, and 3) graph modification. Experts have a positive opinion of our comics. We highlight the experts’ feedback for some revision, such as adding additional information, expanding the storyline, and modifying the graph through Concrete-Pictorial-Abstract approach.
{"title":"Experts‵ Perception on the Usage of Mathematical Representations in Biology Comics","authors":"Fadhlan Muchlas Abrori, Zsolt Lavicza, Mathias Tejera, Branko Anđić","doi":"10.1564/tme_v30.3.8","DOIUrl":"https://doi.org/10.1564/tme_v30.3.8","url":null,"abstract":"Integrating biology and mathematics can potentially solve problems associated with students' inability to solve quantitative biology problems. To face this issue, we embarked on a project to develop biological and mathematical content-based comics for elementary school students. It would assist them in gaining early comfort with transdisciplinary work. However, we need experts’ perceptions to see if our comics are feasible. This exploratory interview research attempted to understand how experts perceive mathematical representation in biology comics. The three experts involved in the interview were a biology teacher, a mathematics lecturer, and a comics enthusiast. This study's empirical data were collected using semi-structured interviews and analyzed using thematic analysis. The research uncovered three major themes: 1) comic content, 2) graph type, and 3) graph modification. Experts have a positive opinion of our comics. We highlight the experts’ feedback for some revision, such as adding additional information, expanding the storyline, and modifying the graph through Concrete-Pictorial-Abstract approach.","PeriodicalId":433766,"journal":{"name":"The International Journal for Technology in Mathematics Education","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135691230","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}
On the one hand, mathematical software is ubiquitous in mathematics education. On the other hand, word problems are an important part of the curriculum, and they often require modelling skills. This is especially true with optimisation and extrema problems proposed to high school and undergraduate students. We propose two activities around extrema problems, modelling with Dynamic Geometry Software (DGS). The exploration relies on the synchronised representations offered by the DGS. We discuss the different registers of representations used, their synchronisation and the limitations of the models versus the concrete occurrence.
{"title":"Using DGS in Investigating Synchronised Registers of Representations of Extrema Problems","authors":"Guillermo Bautista Jr, Mathias Tejera, Thierry Dana-Picard, Zsolt Lavicza","doi":"10.1564/tme_v30.3.7","DOIUrl":"https://doi.org/10.1564/tme_v30.3.7","url":null,"abstract":"On the one hand, mathematical software is ubiquitous in mathematics education. On the other hand, word problems are an important part of the curriculum, and they often require modelling skills. This is especially true with optimisation and extrema problems proposed to high school and undergraduate students. We propose two activities around extrema problems, modelling with Dynamic Geometry Software (DGS). The exploration relies on the synchronised representations offered by the DGS. We discuss the different registers of representations used, their synchronisation and the limitations of the models versus the concrete occurrence.","PeriodicalId":433766,"journal":{"name":"The International Journal for Technology in Mathematics Education","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135691234","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 aims to investigate the construction of the area of rectangle with GeoGebra and how students can formulate it. It focuses on describing the cognitive process involved in constructing this concept and how technology mediates such a process. The research was conducted in a classroom with 5th grade students in a secondary school and was designed qualitatively as a case study. A readiness test was prepared to determine the preliminary knowledge of the students about the concept of area. The teaching process was carried out with the activities based on GeoGebra. Considering the test results, researcher observations, and teacher views, five voluntary participants were selected, and we had three interviews with each of them. The obtained data from the teaching process and interviews were analyzed according to APOS theoretical framework. The results of the research demonstrate that one of the participants could not conceptualize the area as an object as the number of unit squares that cover the area without any space, while two of the participants could not conceptualize the formula of area of rectangle as an object. The students generally had difficulty in encapsulating the concept of the area and its formula. Area conservation and unit concept are important for conceptualizing the concept of area by realizing the covering feature of it, and understanding the dimension relationship is significantly effective in conceptualizing its formula.
{"title":"Concept Formation Processes of Area and its Formula with GeoGebra: Case of Rectangle","authors":"Fatma Agacdiken, Rezan Yilmaz","doi":"10.1564/tme_v30.3.10","DOIUrl":"https://doi.org/10.1564/tme_v30.3.10","url":null,"abstract":"This research aims to investigate the construction of the area of rectangle with GeoGebra and how students can formulate it. It focuses on describing the cognitive process involved in constructing this concept and how technology mediates such a process. The research was conducted in a classroom with 5th grade students in a secondary school and was designed qualitatively as a case study. A readiness test was prepared to determine the preliminary knowledge of the students about the concept of area. The teaching process was carried out with the activities based on GeoGebra. Considering the test results, researcher observations, and teacher views, five voluntary participants were selected, and we had three interviews with each of them. The obtained data from the teaching process and interviews were analyzed according to APOS theoretical framework. The results of the research demonstrate that one of the participants could not conceptualize the area as an object as the number of unit squares that cover the area without any space, while two of the participants could not conceptualize the formula of area of rectangle as an object. The students generally had difficulty in encapsulating the concept of the area and its formula. Area conservation and unit concept are important for conceptualizing the concept of area by realizing the covering feature of it, and understanding the dimension relationship is significantly effective in conceptualizing its formula.","PeriodicalId":433766,"journal":{"name":"The International Journal for Technology in Mathematics Education","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135691229","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 research, we investigated whether the use of GeoGebra Augmented Reality (AR) can foster students in conceptualising a mathematical object by manipulating its different semiotic representations. We designed and implemented, with thirty university mathematics students, a teaching sequence on paraboloids using GeoGebra AR supported by GeoGebra 3D with the aim of fostering students??? work with different semiotic representations. All the activities carried out during the teaching case study were video-recorded, transcribed, and analysed according to Duval???s Theory. Results show how GeoGebra AR facilitated students in the manipulation of different semiotic representations of paraboloids involved by highlighting the cognitive activities of treatments and conversions which emerge while conceptualising the mathematical object at stake.
{"title":"GeoGebra Augmented Reality to Facilitate the Manipulation of Different Semiotic Representations of Paraboloids","authors":"Mario Lepore, Federica Mennuni","doi":"10.1564/tme_v30.3.3","DOIUrl":"https://doi.org/10.1564/tme_v30.3.3","url":null,"abstract":"In this research, we investigated whether the use of GeoGebra Augmented Reality (AR) can foster students in conceptualising a mathematical object by manipulating its different semiotic representations. We designed and implemented, with thirty university mathematics students, a teaching sequence on paraboloids using GeoGebra AR supported by GeoGebra 3D with the aim of fostering students??? work with different semiotic representations. All the activities carried out during the teaching case study were video-recorded, transcribed, and analysed according to Duval???s Theory. Results show how GeoGebra AR facilitated students in the manipulation of different semiotic representations of paraboloids involved by highlighting the cognitive activities of treatments and conversions which emerge while conceptualising the mathematical object at stake.","PeriodicalId":433766,"journal":{"name":"The International Journal for Technology in Mathematics Education","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135691231","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}
Rosamaria Crisci, Umberto Dello Iacono, Eva Ferrara Dentice
In this paper, we describe an educational activity involving the use of a digital artifact, implemented in a visual programming environment, for mediating the learning of axial symmetry in primary school through algorithmics and computer programming. The educational activity was designed with the aim of bringing out increasingly “advanced” utilization schemes and solving strategies by students. We use an instrumental approach for analyzing how the systematic and intentional choice of technological artifacts and tools, i.e. the instrumental orchestration, guided instrumental genesis by the students. The analysis of the case study of Arianna seems to show how her evolution of utilization schemes is related both to the emergence of increasingly time and effort efficient strategies and to a growing understanding of the functionality of the visual programming environment.
{"title":"A Computer Programming-Based Digital Artifact to Introduce Axial Symmetry in Primary School: An Instrumental Approach","authors":"Rosamaria Crisci, Umberto Dello Iacono, Eva Ferrara Dentice","doi":"10.1564/tme_v30.3.1","DOIUrl":"https://doi.org/10.1564/tme_v30.3.1","url":null,"abstract":"In this paper, we describe an educational activity involving the use of a digital artifact, implemented in a visual programming environment, for mediating the learning of axial symmetry in primary school through algorithmics and computer programming. The educational activity was designed with the aim of bringing out increasingly “advanced” utilization schemes and solving strategies by students. We use an instrumental approach for analyzing how the systematic and intentional choice of technological artifacts and tools, i.e. the instrumental orchestration, guided instrumental genesis by the students. The analysis of the case study of Arianna seems to show how her evolution of utilization schemes is related both to the emergence of increasingly time and effort efficient strategies and to a growing understanding of the functionality of the visual programming environment.","PeriodicalId":433766,"journal":{"name":"The International Journal for Technology in Mathematics Education","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690961","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}
Pham Sy Nam, Ngoc-Giang Nguyen, Hoa Anh Tuong, Ben Haas, Zsolt Lavicza, Yves Kreis
Problem-based learning puts students in situations that suggest problems without providing instructions and available knowledge. Therefore, when using problem-based learning, students need to be flexible, self-disciplined, active and self-occupied with knowledge and turn the knowledge the teacher intends to impart into their knowledge. For locus problems, learners often make mistakes in predicting results. GeoGebra software has been brought into teaching and has been a great help for students in the process of detecting and correcting mistakes in locus problems. Our article will analyze the views on problem-based learning and the scientific basis and provide a teaching process to detect and correct mistakes in locus problems with the help of GeoGebra software. In addition, we designed a teaching example that explicitly illustrates the above process. We found that students were more interested and excited.
{"title":"Problem-Based Learning about Error Detection and Correction in Locus Problems with the Aid of GeoGebra Software","authors":"Pham Sy Nam, Ngoc-Giang Nguyen, Hoa Anh Tuong, Ben Haas, Zsolt Lavicza, Yves Kreis","doi":"10.1564/tme_v30.3.9","DOIUrl":"https://doi.org/10.1564/tme_v30.3.9","url":null,"abstract":"Problem-based learning puts students in situations that suggest problems without providing instructions and available knowledge. Therefore, when using problem-based learning, students need to be flexible, self-disciplined, active and self-occupied with knowledge and turn the knowledge the teacher intends to impart into their knowledge. For locus problems, learners often make mistakes in predicting results. GeoGebra software has been brought into teaching and has been a great help for students in the process of detecting and correcting mistakes in locus problems. Our article will analyze the views on problem-based learning and the scientific basis and provide a teaching process to detect and correct mistakes in locus problems with the help of GeoGebra software. In addition, we designed a teaching example that explicitly illustrates the above process. We found that students were more interested and excited.","PeriodicalId":433766,"journal":{"name":"The International Journal for Technology in Mathematics Education","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135691232","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}
Learning with understanding is essential to enabling students to solve problems that they will inevitably face in the future. Students will be more successful, if they are engaged in thought-provoking activities that encourage them to grow in their mathematical understanding and identity. With this study we intended to understand how the application of exploratory tasks for teaching and learning mathematics in primary school, using the Poly-Universe tool, promotes a comprehensive learning of mathematics. We concluded that the activities involving the Poli-Universe, a tool to teach mathematics are motivating, as the students' interest and motivation during this study was notorious. The use of objects with such attractive characteristics, that appeal to visualisation, permitted the exploration of different figures and its characteristics and the comprehension of some geometric concepts. As well as positive interaction and collaboration of the students, the discussion and the development of their geometric reasoning were remarkable.
{"title":"Comprehensive Learning in Mathematics: The Contribution of the Poly-Universe Tool","authors":"Luís Sousa, Vanda Santos, Dina Tavares","doi":"10.1564/tme_v30.3.5","DOIUrl":"https://doi.org/10.1564/tme_v30.3.5","url":null,"abstract":"Learning with understanding is essential to enabling students to solve problems that they will inevitably face in the future. Students will be more successful, if they are engaged in thought-provoking activities that encourage them to grow in their mathematical understanding and identity. With this study we intended to understand how the application of exploratory tasks for teaching and learning mathematics in primary school, using the Poly-Universe tool, promotes a comprehensive learning of mathematics. We concluded that the activities involving the Poli-Universe, a tool to teach mathematics are motivating, as the students' interest and motivation during this study was notorious. The use of objects with such attractive characteristics, that appeal to visualisation, permitted the exploration of different figures and its characteristics and the comprehension of some geometric concepts. As well as positive interaction and collaboration of the students, the discussion and the development of their geometric reasoning were remarkable.","PeriodicalId":433766,"journal":{"name":"The International Journal for Technology in Mathematics Education","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690959","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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