Education

A visit to local Math Museum: Using tablets creatively in classroom

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Tablets with their simple interface, portability, speed, affordability and their variety of apps are quickly moving into schools across Europe and a growing number of teachers are experimenting with tablets or are interested in doing so. In the context of monitoring the MOOC “Creative use of Tablets in Schools” provided by the European Schoolnet Academy, the final activity was to create a lesson or a project plan. To design the lesson plan we used a very nice tool called the “Learning Designer” which was developed by the London Institute of Education. According the Scenario student will visit the local Math Museum during Mathematical Week and create Augmented Reality posters for the school. From the implementation of this scenario students will come in contact with the beauty of mathematics, its history and get to know great mathematicians and their works.
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  • 1. Πρακτικά Εργασιών 1ου Διεθνούς Βιωματικού Συνεδρίου Εφαρμοσμένης Διδακτικής, Δράμα, 27-29 Νοεμβρίου 2015 1o Διεθνές Βιωματικό Συνέδριο Εφαρμοσμένης Διδακτικής A visit to local Math Museum: Using tablets creatively in classroom Νικόλαος Μανάρας 1 nikomanara@sch.gr 1 Μαθηματικός 2 ου ΓΕΛ ΑΓ. ΑΘΑΝΑΣΙΟΥ Abstract Tablets with their simple interface, portability, speed, affordability and their variety of apps are quickly moving into schools across Europe and a growing number of teachers are experimenting with tablets or are interested in doing so. In the context of monitoring the MOOC “Creative use of Tablets in Schools” provided by the European Schoolnet Academy, the final activity was to create a lesson or a project plan. To design the lesson plan we used a very nice tool called the “Learning Designer” which was developed by the London Institute of Education. According the Scenario student will visit the local Math Museum during Mathematical Week and create Augmented Reality posters for the school. From the implementation of this scenario students will come in contact with the beauty of mathematics, its history and get to know great mathematicians and their works. Key words: Tablets, Augmented Reality, Aurasma, History of Math. Α. Teaching plan Α1 General features characteristics The general idea is to get students involved with mathematics but not by solving routine exercises. Students will get to know historical moments of mathematics, great mathematicians as well as important theories. The scenario doesn’t begin and finish in the Math museum, the most important thing is the preparation before the visit and after it. Students come into contact with knowledge not with frontal teaching or lecture, but conquer knowledge working in groups and using their creativity to create augmented posters as a guide and analysis to share with the rest of the school. The ICT are present in every phase of the scenario. Choosing the right technology tool each time helps cooperation among students to achieve the final product through their creativity. The project is aimed at 24 high school students (6 groups of 4 students each). The length of time required for implementation of the project in real conditions is 1230 minutes, or about 28 hours of 40 or 45’, that is 14 weeks with two hours a week, so the project will last 3.5 months. Times came so precise with the use of the Leaning Designer. Β. Presentation Β1 Aims From the implementation of this project students will be able to give biography of great mathematician. -Students will be able to identify important theorems. -Students will be able to explain historical context of math works. - Students will have a group discussion discussing a particular math work and will be able to categorize into their correct genres such as definition, request, finding, theorem, proof, conjecture, unsolved problems, etc. -Students will be able to describe particular similarities and differences in math works during centuries and in different civilization. Students will create Posters to be part of an augmented reality exposition at school. The exposition will be called: A visit to local Math Museum. 6 posters will be created. These posters are going to be the physical support to multimedia artifacts created or uploaded by students (videos, PowerPoint presentations, etc.). Aurasma application will be used to link the physical objects in the posters (stamps, photos, drawings, etc.) to the multimedia presentations. Β2 Outcomes Expectations from the implementation of teaching: Knowledge: Learners will discover significant periods of mathematics, will “meet” great mathematicians, their main mathematics results and its applications. Knowledge: Describes math artifacts of great mathematicians.
  • 2. 2 Καινοτόμες Εφαρμογές στη Διδακτική Πράξη Comprehension: Deeper comprehension about different periods of math history, about mathematical thinking through the way great mathematician worked and created. Analysis: Compare (and contrast): Tells the difference between math periods. Psychomotor skills: Makes videos. Evaluation: Reflecting on what to do, telling problems and what is done. Synthesis: Design posters. Analysis: Critique others work. Application: Demonstrates successful use of web tools. Synthesis: Organize information. Analysis: Analyze information about mathematical content and about ICT tools to produce the augmented reality exposition. Β3 Theoretical framework During planning of this project we took into account theories of tutoring mathematics and effective use of ICT in classroom. The theory of Constructivism (with main representatives Piaget, Dienes, Singlair) includes three basic ideas for the learning of mathematics: Students devise personal methods of solving mathematical problems. The learning of mathematics takes place through solving problems. The role of the social group for learning is crucial. With regard to the first idea of construction theory, it has been observed that the students prefer to invent and construct their own ways of solving mathematical problems, in spite of following the instructions of teachers. On the second idea of constructivism, it is a fact that the situations which the trainees find problematic attract much interest. The theory of constructivism gives finally much emphasis on the role and contribution of the social group in the construction of knowledge. The difference of ideas and opinions of team members causing instability, resulting in possible reorganization of prior knowledge and conquest of new within an environment of communication and cooperation. The Socio-cultural approach or theory of personality (Vygotsky). Humans by nature are curious and constantly learning so that knowledge and learning not only acquired within the school environment. The reasons for someone to learn are notable for everyone and are powerful factor learning, so it is necessary to have goals and objectives and learning methodology. The motivation to learn on the one hand related to filling the deepest needs, and on the other to achieve some objectives on the values of a society, we learn in interaction with other people. Important role in this played by the language in which inherent cultural characteristics of the individual. Learning is best achieved when the student becomes responsible for his own personal mental development. Learning that with intellect and emotions involves not only lasts long, but also penetrates virtually everyone by changing him. Effective learning of the mathematical object is a more the most complex processes also to achieve certain preconditions must be met. The main principles which should govern the teaching of Mathematics for effective learning are: The child, in order to learn, first of all has the will and showing interest in learning the subject. The primary role of the teacher is to adjust the object to the needs, interests, aptitudes and abilities of student, in order to motivate to pay attention. Learning is a process of reorganization of prior knowledge and construction of the new. To learn the student is very important that the process to amend the old knowledge be made through experiences related to learning object. Essential component of effective learning is also active student participation. For this reason there must be freedom of thought and expression, good relationship between the child and the teacher, etc. An authority that contributes to effective learning and that every teacher should have in mind is the personal way of learning of every one. The teacher must not impose a model of learning style, but to encourage and strengthen that of each trainee. Also, the individual rate of learning, each student has to be taken into account by the teacher, who in turn must modify and adapt his lesson at the speeds learning of children. About the question of what distinguishes Tablets from devices previously used in schools can partly be answered by looking at what distinguishes mobile technology from other technologies. A UNESCO report (Shuler, Winters et al. 2013) defines mobile learning as learning using mobile technologies such as mobile phones, smartphones, e- readers and Tablets, and argues that these devices offer ‘unparalleled access to communication and information’. The report further argues that the increased affordability and functionality of mobile technology compared to technologies previously used in schools means they can support learning in new ways. Ubiquitous access to technology is recognized by UNESCO as facilitating more personalized learning, benefiting especially children with learning difficulties. Increased affordability of the devices and the option to reduce printing were associated with potential cost savings. In addition to affordability and functionality, an important element in the popularity of mobile devices is their portable nature. This means that the technology can be used outside the classroom, potentially facilitating what has been termed ‘anytime, anywhere learning’ or seamless learning (Sha, Looi et al. 2011; Wong 2012; van 't Hooft 2013). It has been argued that access to a personal device and the portable nature of mobile technology
  • 3. 3 Καινοτόμες Εφαρμογές στη Διδακτική Πράξη allow learners to build links between school and everyday life, bridge formal and informal learning contexts, and transcend the limitations of their immediate environment (Seipold and Pachler 2011; Wong 2012; Shuler, Winters et al. 2013) Mobile technology is believed to facilitate access to personalized learning content (Sha, Looi et al. 2011; Shuler, Winters et al. 2013). Along with the ability to learn outside traditional classroom settings, this is argued to support independent learning and the development of metacognitive skills or ‘learning to learn’ skills in young learners (Sha, Looi et al. 2011; Kearney, Schuck et al. 2012; Wong 2012). Wong argues that access to mobile technology allows students to design their own learning contexts in terms of when, where and how they feel they learn best, and learning thereby becomes increasingly self-directed. Kearney, Schuck et al. (2012) reviewed over 30 case studies of mobile technology use in education and found personalization to be one of three main benefits, alongside collaboration and authenticity. Although the authors do not highlight one-to-one access, it appears that this is important to achieve the degree of independence described by this pedagogical framework. Personalization is, according to Kearney, Schuck et al. (2012), a result both of being able to adapt learning content and activities to suit the individual learner’s needs, and of the sense of agency and independence the student feels from being able to customize his or her own learning. Authenticity in this context means that the learning can be contextualized in ways that make the lessons relevant to the student, and it is therefore linked with this personalized approach to learning. Thanks to the ease of accessing emails and messaging applications using mobile devices, researchers have noted improved communication between teachers and students as well as increased opportunities for feedback and continual assessment (Shuler, Winters et al. 2013). According to Snell and Snell-Siddle (2013), enhanced mobile communication and feedback can lead to greater student motivation and greater understanding of the learning process. West (2013) similarly argues that ongoing digital assessment can give students opportunities to reflect on their learning progress and therefore support greater student autonomy. Collaboration is highlighted by Kearney, Schuck et al. (2012) as the third main benefit of mobile learning in addition to personalization and authenticity. Collaboration is defined as the ability to engage in discussions about learning which are supported by technology, as well as the ability to transfer and collaborate on content. This degree of collaboration is facilitated by a personalized approach to learning where all students have access to mobile technology. According to van’t Hooft (2013), mobile devices support collaborative learning thanks to their high mobility (i.e. they are small enough to be carried in one hand) and their small form factor (in other words, they are unobtrusive and do not interfere with face-to-face interaction). Van’t Hooft further points to the accessibility of mobile devices (ease of use and ability to turn on instantly), the ability to create, access and display information in multiple modalities (text, video, audio, graphics) and the ability to communicate and share information; these are cited as other facilities of mobile technology that support collaboration between students and between students and teachers. One of the arguments for adopting mobile learning is that young people have access to and use mobile technology seamlessly in their individual lives, and that they will increasingly expect to have access to instant communication and personalized content in school (West 2013). Others, however, have warned against introducing mobile technology ‘just’ because students will expect it (Kinash, Brand et al. 2012). It has also been argued that students’ perceptions of using mobile technology will differ greatly and that teachers must incorporate mobile technology alongside other methods of teaching in order to reach all students (Snell and Snell-Siddle 2013). Van’t Hooft (2013) argues that pressures on educational institutions to allow the same kind of access to technology will continue to increase, and sees it as logical that teachers and students take advantage of mobile devices. He also argues, however, that integrating mobile technology requires making changes to education in order for mobile learning to be ‘meaningful, effective and safe’ (van't Hooft 2013). Digital tools have the ability to enhance these educational technologies of the self. But we need to make sure that these tools are also aligned with learning outcomes which prioritize human dignity rather than haste, consumption, and algorithmic metrics (Jordan Shapiro 2014). Β4-5 Teaching Techniques – Evaluation, Teaching-Learning activities Introduction Produce 45 minutes 24 students Tutor is available Teacher creates Project wiki. Teacher’s instructions, videos, photos, rubrics, tools and all media files presented on the project wiki. The project wiki link is shared in school website. Students use these wikis for their collaboration, sharing and communication. Edmodo account is created and used for project management, communication and sharing the work done on project wiki with other communities. After the teams are formed, project groups are created. Also, parent accounts are created to share anything about the project. Teacher collaborates with ICT teacher to design the scenario. Read Watch Listen 30 minutes 24 students Tutor is available
  • 4. 4 Καινοτόμες Εφαρμογές στη Διδακτική Πράξη Inspiring Teacher gives students the design brief. School director visits the classroom and asks students to design a poster for school students to inform about the math museum. It will address basic elements of math to help in knowledge and analysis the history of math. They are grouped with TeamUP tool. Links of student group wiki's are added to the project wiki by teacher after the session. REFLECT –Each group of students uses ReFlex to record their reflection. Reflections can be done at home. Read Watch Listen 25 minutes 24 students Tutor is available Teacher familiarizes students with the math museum. Students watch videos of math museum with history of math and about great mathematicians. All the media’s and information’s are embedded on the main project wiki. They plan to visit math museum. Read Watch Listen 80 minutes 24 students Tutor is available Augmented Reality app Aurasma, Popplet, Canva, Padlet, Edmodo are introduced to the students in the class. They watch tutorials how to use these tools. They are embedded on project wiki for the students to learn from them in their own pace at home. All the instructions presented on the project wiki. Students can get any help using Edmodo any time. Practice 80 minutes 4 students Tutor is available They make a poster of the group using Canva and printed. They are allowed to make their self-Aura with their photo introducing themselves. They record their video introducing themselves and use as overlay. Their posters are also uploaded on their wiki. Discuss 45 minutes 4 students Tutor is not available Teacher will provide to each group some indications of what are the contents of each poster: Your group will create a Poster to be exposed in the school about History of Math. The poster must have (at least) these five components: 1. who are we? (You may create a video to present your group to the school) 2. The period of investigation (You may create a video or share some digital content that presents the period: 1st Period: Greek Mathematics, 2nd period: Arab’s & India’s Mathematics, 3rd period: Middle Ages & Renaissance, 4th period: 17th- 18th century, 5th period: 19th – 20th century, 6th period: 21st century) 3. Biography of at least three great mathematicians of that period and why did you choose them. (You may create a video or share some digital content) For example: Pythagoras, Fibonacci, Newton, Euler, Gauss, Hilbert, and Perelman 4. Significant Theorem’s or substantial work of them (You can find some information about them in the internet or you can simply consult your library books. You can create a video explaining them. Use GeoGebra software to present a theorem (http://www.geogebra.org/cms/pt_BR/), record your geometric construction using screen recorder software (like ZD Soft screen recorder). Then you can use the Movie Maker to produce your video and to put your explanation in it (using for instance windows sound recorder)). 5. How can we use these theorems to solve real- life problems or pure mathematical problems? (You can search in the internet for possible applications of these theorems but it can be very helpful if you could explain how to solve some problems of your own text book.) Good Luck! In their groups students have to read it and to discuss ideas about their future work. Collaborate 45 minutes 4 students Tutor is not available Each group will use Popplet in this stage to generate ideas and to start planning their posters. It will be important that students discuss task division in the groups, making substantial decisions about the content, the process and the products. Discuss minutes 1 students Tutor is not available REFLECT –Each group of students uses ReFlex to record their reflection. Reflections can be done at home. Math and ICT teacher decide on the design scenario. Reflections throughout the activities are mainly about: What did you do? What will you do? What are the problems? Dream Collaborate 60 minutes 4 students Tutor is available Teacher asks groups “why is mathematically important the period your team is investigating?”, "how to categorize, analyze and describe math artifacts". Then they investigate it with online tools and discuss. They send post it notes of their ideas to Padlet on the Smart Board or Projector. Teacher expectation is: 1. Give short description of the math period. 2. Give short biographies of mathematicians of that period. 3. Explain the context of math in the mathematician's life and work 4. Explain historical and geographical context of math artifacts 5.Categorize into their correct genres such as definition, request, finding, theorem, proof, conjecture, unsolved problems, etc. 6. Describe particular similarities and differences in math works during centuries and in different civilization. Investigate 60 minutes 4 students Tutor is available
  • 5. 5 Καινοτόμες Εφαρμογές στη Διδακτική Πράξη They brainstorm and use mind mapping Popplet to organize all their ide
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