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Graph2Go in M-Learning

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pbehar

1. The document describes a pilot study that used the mobile application Graph2Go to teach mathematics concepts related to functions and graphs. 2. A pedagogical model was developed for using Graph2Go in a face-to-face setting that was based on social-historical learning theory and emphasized cooperative work and teacher/peer mediation. 3. The pilot study involved 12 college students using Graph2Go on their mobile devices to complete activities on quadratic and sine functions. Analysis found that students easily learned to use the application and saw benefits of visualizing graphs, but also limitations.

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Key Competencies of the Knowledge Society - (KCLS 2010) Use of Graph2Go in M-Learning: a View from the Pedagogical Model Silvia Batista1, 2, Patricia Behar2, Liliana Passerino2 1 Instituto Federal Fluminense Campus Campos-Centro, Rio de Janeiro, Brazil. 2 Postgraduate Program in Computer Science in Education - Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil. {silviac@iff.edu.br, patricia.behar@ufrgs.br, liliana@cinted.ufrgs.br}
Summary 1. Introduction 2. Pedagogical Models 3. M-Learning and Mathematics: Educational Modalities 4. Pilot study using Graph2Go: building a pedagogical model 5. Pilot study: analysis of results 6. Final Considerations References 2
1. Introduction Popularization of mobile devices and wireless Internet access networks. Changes in social practices and to how information is produced and accessed. Mobile Communication Society M-learning Field that comprehends wireless technologies and mobile computing to enable learning to occur at any time and place, maximizing the students freedom. 3
1. Introduction Studies have associated m-learning with Mathematics several advantages Dynamic visualization and investigation of mathematical facts; Different forms of approaching concepts (for example, through videos, working on visual approaches); Autonomy in the study of mathematical themes; Learning in real situations. 4
1. Introduction Applications for mobile devices have been developed, specifically for Mathematics. Among these applications is Graph2Go (http://www.math4mobile.com/). Such applications are essential, but it is also necessary to organize forms of applying them in varied educational modalities (face to face, blended and distance learning). Development and analysis of pedagogical models for this purpose are important. Such models allow organizing pedagogical practices. This work presents a pedagogical model built and applied in a face to face pilot study, using Graph2Go in an m- learning experiment with college students. 5
2. Pedagogical Models A model is a shared mental representation of a set of relations defining a phenomenon, aiming at a better understanding of it. Pedagogical model A system of theoretical premises that represent, explain and guide the way the curriculum is approached and that is consolidated in the pedagogical practices and in the interactions professor-student-object of knowledge . 6
2. Pedagogical Models Fig. 1. Structure of a pedagogical model. Source: Behar - p. 25 - adapted with permission from the author. 7
2. Pedagogical Models Development of pedagogical models Confluence of aspects related to content and organizational, methodological and technological elements Pedagogical actions with more defined purposes More adequate use of resources, more coherence with the real context and reduction in unpredictable situations. 8
3. M L - earning and Mathematics: Educational Modalities M-learning application in several educational modalities. Fig. 2. M-learning: educational modalities In figure 2, two-way arrows between m-learning and educational modalities indicate there is benefit in both senses. 9
3. M L - earning and Mathematics: Educational Modalities It is important that studies include all three modalities, aiming to analyze the importance of m-learning for the teaching and learning process of Mathematics. Fig. 3. M-learning in mathematical learning: educational modalities 10
4. Pilot study using Graph2Go: building a pedagogical model Graph2Go free application (for non-commercial purposes), specific for cell phones, developed by Michal Yerushalmy and Arik Weizman - project Math4Mobile (http://www.math4mobile.com/); Connections between graphic and algebraic representation for a Fig. 4. Graph2Go - given set of functions through Maths4Mobile Project dynamic changes. 11
4. Pilot study using Graph2Go: building a pedagogical model Objective: developing and analyzing a pedagogical model involving use of mobile devices at a face to face experiment. Fig. 5. Pedagogical model pilot study using Graph2Go 12
4. Pilot study using Graph2Go: building a pedagogical model Social-Historical Theory In this theory, mediation includes use of instruments and signs within the social context, and the combination of use for such resources allows development of superior psychological processes; In addition to instruments and signs, the role of a human mediator, encouraging reflections through assistance, is also essential for student autonomy and knowledge appropriation. 13
4. Pilot study using Graph2Go: building a pedagogical model Organizational aspects The target audience: 12 college students at Instituto Federal Fluminense (Rio de Janeiro, Brazil): - 8 students of Control and Industrial Automation Engineering (1st semester); - 4 undergraduate students in Mathematics (2nd semester). Content: graphic changes of functions. November 2009: 4 hours. 14
4. Pilot study using Graph2Go: building a pedagogical model Content Booklet of activities - three sections: i) general information on Graph2Go and instructions of use; ii) activities to study changes in graphs of quadratic functions through changes in coefficients; iii) similar study to that performed with quadratic functions, but involving the sine function. Available at: <http://www.es.cefetcampos.br/softmat/projeto_TIC/ati vidades.html>. 15
4. Pilot study using Graph2Go: building a pedagogical model Methodological aspects To encourage cooperative work, pair activities were proposed; Interaction between individuals, according to the social-historical theory, plays an essential role in human development; Digital technologies are mediating tools. In which context Graph2Go is inserted. 16
4. Pilot study using Graph2Go: building a pedagogical model Technological aspects Mobile devices: cell phones; Transfer of the application into the students cell phone was performed via Bluetooth using a laptop equipped with such technology; Direct transfer of the application, from the Internet to cell phones, would be more practical, but it was avoided due to connection and download costs (the application itself is free). 17
4. Pilot study using Graph2Go: building a pedagogical model Strategies First, the application was transferred. At that time, there were a few problems. After the initial stage, nine out of twelve students had the application in their cell phones. However, since the work was performed in pairs, development of activities was not impaired by this problem. The first section of the booklet, which explained Graph2Go features, was discussed with the students; Activities related to graphic changes were performed, after the importance of such theme to learn integral calculus had been highlighted; 18
5. Pilot study: analysis of results There were no comments or actions that showed difficulties in using the application, and understanding of the issue was achieved. To ensure a deeper qualitative analysis of the experiment, a questionnaire was organized. None of the participants had used an application for cell phone in the study of an educational theme (not restricted to Mathematics). even so 75% of the participants reported being easy to learn the Graph2Go resources, and the remaining considered it as very easy. 19
5. Pilot study: analysis of results One of the questions was about the advantages and disadvantages of using Graph2Go. Advantages: Disadvantages: -visualization and movement; - limitation of options of -easy to understand and use; functions; -practicability and mobility; - impossibility to draw -being free; graphs of different functions on the same screen; -graphs for the derivative and integral function (with -language (the application is possibility of changing the in English, with which not all integration constant). students were familiar); -size of graphs. 20
5. Pilot study: analysis of results With regard to use of applications for cell phones for mathematical learning, 67% of the participants considered it very important and the remaining classified it as important. Classmates collaboration during activities using Graph2Go was considered as very important by 58% of the participants, while the others considered it as important. In general, interaction between students was stressed as being significant to discuss proposed concepts and to better understand them. 21
5. Pilot study: analysis of results Teachers role as a mediator during activities using Graph2Go was classified as very important by 75% of the participants; for 17%, it was important, and for one participant (8%) it was little important. The participants stressed that, although the application was easy to understand and use and activities were clear, the teachers work of making students think about the concepts was essential. The justification of the student who classified it as little important is as follows: Little important because it is possible to understand the application without the teachers help, although extremely important to help with the mathematical thought (Participant 4). 22
6. Final Considerations In Mathematics, digital technologies create possibilities, allowing simulations, visualizations, experiments, hypothesis generation, among other actions. M-learning adds extra possibilities, such as practicability, mobility, reaching a higher number of people, learning in real contexts, among others. In this sense, use of mobile devices, specific applications or even general resources, such as text messages, photographs, videos, among others, can favor the process of Mathematics teaching and learning, making it more accessible and closer to the students reality. 23
6. Final Considerations The pilot study showed that: i) the difference between available devices and resources in cell phones is a setback for their use with educational purposes; ii) Internet-related costs are another factor making use of mobile devices difficult; iii) the participants skill to deal with cell phone keys is quite favorable; iv) practicability of cell phone use (very similar to how a calculator is used, being available when needed) is a very interesting aspect in educational terms; v) it is important that pedagogical models take into account the role of teacher and classmate mediation in the learning process. 24

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Graph2Go in M-Learning

  • 1. Key Competencies of the Knowledge Society - (KCLS 2010) Use of Graph2Go in M-Learning: a View from the Pedagogical Model Silvia Batista1, 2, Patricia Behar2, Liliana Passerino2 1 Instituto Federal Fluminense Campus Campos-Centro, Rio de Janeiro, Brazil. 2 Postgraduate Program in Computer Science in Education - Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil. {silviac@iff.edu.br, patricia.behar@ufrgs.br, liliana@cinted.ufrgs.br}
  • 2. Summary 1. Introduction 2. Pedagogical Models 3. M-Learning and Mathematics: Educational Modalities 4. Pilot study using Graph2Go: building a pedagogical model 5. Pilot study: analysis of results 6. Final Considerations References 2
  • 3. 1. Introduction Popularization of mobile devices and wireless Internet access networks. Changes in social practices and to how information is produced and accessed. Mobile Communication Society M-learning Field that comprehends wireless technologies and mobile computing to enable learning to occur at any time and place, maximizing the students freedom. 3
  • 4. 1. Introduction Studies have associated m-learning with Mathematics several advantages Dynamic visualization and investigation of mathematical facts; Different forms of approaching concepts (for example, through videos, working on visual approaches); Autonomy in the study of mathematical themes; Learning in real situations. 4
  • 5. 1. Introduction Applications for mobile devices have been developed, specifically for Mathematics. Among these applications is Graph2Go (http://www.math4mobile.com/). Such applications are essential, but it is also necessary to organize forms of applying them in varied educational modalities (face to face, blended and distance learning). Development and analysis of pedagogical models for this purpose are important. Such models allow organizing pedagogical practices. This work presents a pedagogical model built and applied in a face to face pilot study, using Graph2Go in an m- learning experiment with college students. 5
  • 6. 2. Pedagogical Models A model is a shared mental representation of a set of relations defining a phenomenon, aiming at a better understanding of it. Pedagogical model A system of theoretical premises that represent, explain and guide the way the curriculum is approached and that is consolidated in the pedagogical practices and in the interactions professor-student-object of knowledge . 6
  • 7. 2. Pedagogical Models Fig. 1. Structure of a pedagogical model. Source: Behar - p. 25 - adapted with permission from the author. 7
  • 8. 2. Pedagogical Models Development of pedagogical models Confluence of aspects related to content and organizational, methodological and technological elements Pedagogical actions with more defined purposes More adequate use of resources, more coherence with the real context and reduction in unpredictable situations. 8
  • 9. 3. M L - earning and Mathematics: Educational Modalities M-learning application in several educational modalities. Fig. 2. M-learning: educational modalities In figure 2, two-way arrows between m-learning and educational modalities indicate there is benefit in both senses. 9
  • 10. 3. M L - earning and Mathematics: Educational Modalities It is important that studies include all three modalities, aiming to analyze the importance of m-learning for the teaching and learning process of Mathematics. Fig. 3. M-learning in mathematical learning: educational modalities 10
  • 11. 4. Pilot study using Graph2Go: building a pedagogical model Graph2Go free application (for non-commercial purposes), specific for cell phones, developed by Michal Yerushalmy and Arik Weizman - project Math4Mobile (http://www.math4mobile.com/); Connections between graphic and algebraic representation for a Fig. 4. Graph2Go - given set of functions through Maths4Mobile Project dynamic changes. 11
  • 12. 4. Pilot study using Graph2Go: building a pedagogical model Objective: developing and analyzing a pedagogical model involving use of mobile devices at a face to face experiment. Fig. 5. Pedagogical model pilot study using Graph2Go 12
  • 13. 4. Pilot study using Graph2Go: building a pedagogical model Social-Historical Theory In this theory, mediation includes use of instruments and signs within the social context, and the combination of use for such resources allows development of superior psychological processes; In addition to instruments and signs, the role of a human mediator, encouraging reflections through assistance, is also essential for student autonomy and knowledge appropriation. 13
  • 14. 4. Pilot study using Graph2Go: building a pedagogical model Organizational aspects The target audience: 12 college students at Instituto Federal Fluminense (Rio de Janeiro, Brazil): - 8 students of Control and Industrial Automation Engineering (1st semester); - 4 undergraduate students in Mathematics (2nd semester). Content: graphic changes of functions. November 2009: 4 hours. 14
  • 15. 4. Pilot study using Graph2Go: building a pedagogical model Content Booklet of activities - three sections: i) general information on Graph2Go and instructions of use; ii) activities to study changes in graphs of quadratic functions through changes in coefficients; iii) similar study to that performed with quadratic functions, but involving the sine function. Available at: <http://www.es.cefetcampos.br/softmat/projeto_TIC/ati vidades.html>. 15
  • 16. 4. Pilot study using Graph2Go: building a pedagogical model Methodological aspects To encourage cooperative work, pair activities were proposed; Interaction between individuals, according to the social-historical theory, plays an essential role in human development; Digital technologies are mediating tools. In which context Graph2Go is inserted. 16
  • 17. 4. Pilot study using Graph2Go: building a pedagogical model Technological aspects Mobile devices: cell phones; Transfer of the application into the students cell phone was performed via Bluetooth using a laptop equipped with such technology; Direct transfer of the application, from the Internet to cell phones, would be more practical, but it was avoided due to connection and download costs (the application itself is free). 17
  • 18. 4. Pilot study using Graph2Go: building a pedagogical model Strategies First, the application was transferred. At that time, there were a few problems. After the initial stage, nine out of twelve students had the application in their cell phones. However, since the work was performed in pairs, development of activities was not impaired by this problem. The first section of the booklet, which explained Graph2Go features, was discussed with the students; Activities related to graphic changes were performed, after the importance of such theme to learn integral calculus had been highlighted; 18
  • 19. 5. Pilot study: analysis of results There were no comments or actions that showed difficulties in using the application, and understanding of the issue was achieved. To ensure a deeper qualitative analysis of the experiment, a questionnaire was organized. None of the participants had used an application for cell phone in the study of an educational theme (not restricted to Mathematics). even so 75% of the participants reported being easy to learn the Graph2Go resources, and the remaining considered it as very easy. 19
  • 20. 5. Pilot study: analysis of results One of the questions was about the advantages and disadvantages of using Graph2Go. Advantages: Disadvantages: -visualization and movement; - limitation of options of -easy to understand and use; functions; -practicability and mobility; - impossibility to draw -being free; graphs of different functions on the same screen; -graphs for the derivative and integral function (with -language (the application is possibility of changing the in English, with which not all integration constant). students were familiar); -size of graphs. 20
  • 21. 5. Pilot study: analysis of results With regard to use of applications for cell phones for mathematical learning, 67% of the participants considered it very important and the remaining classified it as important. Classmates collaboration during activities using Graph2Go was considered as very important by 58% of the participants, while the others considered it as important. In general, interaction between students was stressed as being significant to discuss proposed concepts and to better understand them. 21
  • 22. 5. Pilot study: analysis of results Teachers role as a mediator during activities using Graph2Go was classified as very important by 75% of the participants; for 17%, it was important, and for one participant (8%) it was little important. The participants stressed that, although the application was easy to understand and use and activities were clear, the teachers work of making students think about the concepts was essential. The justification of the student who classified it as little important is as follows: Little important because it is possible to understand the application without the teachers help, although extremely important to help with the mathematical thought (Participant 4). 22
  • 23. 6. Final Considerations In Mathematics, digital technologies create possibilities, allowing simulations, visualizations, experiments, hypothesis generation, among other actions. M-learning adds extra possibilities, such as practicability, mobility, reaching a higher number of people, learning in real contexts, among others. In this sense, use of mobile devices, specific applications or even general resources, such as text messages, photographs, videos, among others, can favor the process of Mathematics teaching and learning, making it more accessible and closer to the students reality. 23
  • 24. 6. Final Considerations The pilot study showed that: i) the difference between available devices and resources in cell phones is a setback for their use with educational purposes; ii) Internet-related costs are another factor making use of mobile devices difficult; iii) the participants skill to deal with cell phone keys is quite favorable; iv) practicability of cell phone use (very similar to how a calculator is used, being available when needed) is a very interesting aspect in educational terms; v) it is important that pedagogical models take into account the role of teacher and classmate mediation in the learning process. 24