Mathematical Filmlets for Secondary Education Sappl, Thomas; University of Education Weingarten, ([email protected]) Ludwig, Matthias (supervisor); University of Education Weingarten, ([email protected])

Abstract The idea of mathematical filmlets in school is not new, but mobile learning offers now a realistic scenario for the adoption in classes. So there are now the assumption for situated learning in classrooms. In this paper we demonstrate very briefly by the example of modelling how we think that mathematical filmlets can support learning in secondary education. Keywords: mathematical filmlets, mobile learning, modelling

1. Idea of mathematical filmlets The idea of learning mathematical contents among others with the help of the medium film or filmlets has already existed for several years as it was the “vision“ of Litzmann (cf. Litzmann, 1943). In 1982 Metzler did some research on the functions and borders of the mathematical film in lessons. At that time the concept of the tele-lecture arose which made possible the learning by teaching units available on television or video to the student. In consequence of the idea of situated-learning and -cognition the Cognition and Technology Group at Vanderbilt (cf. CTGV, 1997) developed the instructional design of the Anchored Instruction. The most familiar example of the Anchored Instruction are the adventures of Jasper Woodburry. In this series, the leading actor Jasper Woodburry has to solve mathematical problems in the different categories like complex trip planning, statistics and business plan, geometry and algebra. This broadly examined idea (cf. Blumschein, 2004) based on seven design principles indicated a raised transfer achievement. Interestingly this concept has hardly influenced teaching practice in Germany. Also the California Institut of Technology (Tom M. Apostol) developed videos for „basic topics in high school mathematics in ways that cannot be done at the chalkboard or in a textbook“ (cf. www.projectmathematics.com) but just as the Cognition and Technology Group at Vanderbilt they do not produce other films. But for the students at the university are a few films available now: VideoMath for example is a series of videos covering topics form mathematics and its related fields such as computational science, scientific visualisation and mathematical physics (Apostol, T.M., Bourguignon, J.P., Emmer, M., Hege H.-C., Polthier K., 2010) Now due to the concept of mobile learning (cf. Steinberger & Mayr, 2002, Döring & Kleeberg, 2006 and Fischer, Mandl & Todorova 2009) new possibilities for learning in classrooms, for example by mobile handhelds like the iPod-Touch, are given. However a huge number of semiprofessional videoclips with mathematical contents are available on different internetplatforms like “youtube“ to the pupils. Besides, it is important that filmlets can convey different intentions. Referring to Groß (1977) mathematical filmlets can present tasks or problems (cf. Ludwig & Xu, 2010) but also contents of teaching and contexts. The researchwork of Merkt & Schwan (2009) for example demonstrates the general interest of learning with videos. Our research objective is to develop mathematical filmlets for secondary education to foster the comprehension of mathematics. 2. Poll results of math teacher In a requirements analysis 82 math teachers of secondary schools in the region of Weingarten were asked about their attitudes of new media in lessons and the potential of mathematical filmlets. According to the categories of the curriculum the teacher had to answer which were the difficult 1

topics for the students (their estimate) and which were complicated contents for themselves. The idea is to produce mathematical filmlets in topics which seem to be hard for the students and the teacher. The filmlets should be a useful tool for the school and if we can provide different filmlets for different themes, we are convinced that there will be a low barrier to work with filmlets. As a result you can identify three relevant topics: modelling, fraction and number range (related to the categories of the curriculum). We have noticed that there are no significant differences between the teachers´ complicated contents and the students` ones. Besides, there is no significant difference between the two types of secondary school, called middletrack and hightrack. 3. Design and construction of mathematical filmlets Mathematical filmlets can consist of real sequences or of animations or a mixture of both. As far as the didactical idea of these filmlets is concerned it is important that three options are possible: First, at the end of the clip, the student is given a problem/ task (pending questions) and the student should find a strategy to solve this problem. Second, the film presents an explication of an issue, for example „how to use an algorithm“. Third, an overview of the whole topic is shown and demonstrates interfaces with other subjects like physics, economics or sports. According to the use of filmlets in foreign languages we think the time period should be limited to approximately five minutes (cf. Liebelt, 1998) It is also possible to split the filmlet into several short clips: the first one contents only the task while the others give hints for solving the problem. 4. Application in schools For the presentation and adoption of the mathematical filmlets two different types are possible. First, all the students use a laptop or the computer (probably not possible in the classroom) to work with the filmlets. The second alternative is the use of mobile handhelds (e.g. the iPod-Touch or smartphones) in the classroom. It is important that the students have the opportunity to learn individually and of one´s own rate when they watch the film (different mode like play, stop, repeat, forward, …). Besides, the students can use the laptop/pc or the mobile handheld as a multi-tool which combines different tools like a calculator or a functionplotter. Example of a mathematical filmlet: The challenge was to find out how long it will take to empty the Lake Constance related to the waterconsumption by the inhabitants of Stuttgart. This task is typically for modelling in mathematics (in grade 8 of a german middleschool) and we had the intention to demonstrate the cycle of modelling by solving this exercise which was given in the first clip. In the second clip (fig. 1) the students got hints for solving the problem, for example it was necessary to know the volume of the lake. We noted that not all students looked at this film, there were a few students which solved the problem without using any hints.

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Fig. 1: First hint for solving the problem (second clip) Shortly after finding the solution, the students looked at the 6th filmlet (filmlets no. 3-5 gave only hints) to see retroactivly the circle of modelling (fig. 2) The intention was a demonstration how you could transform a real-world problem into a mathematical term, found a solution and completed the cycle by interpreting the result in the real-world context.

Fig. 2: Cycle of modelling (6th clip) The results of the students were very impressive: nearly all students got a right solution. According to the test of motivation and interest with the scales of SRQ-A (Müller, Hanfstingl & Andreitz, 2007) and the items of „interest and pleasure of the subject mathematics“ (cf. PISA 2003, WallnerPaschon & Schwantner, 2004) all students were questioned by a pre- and a posttest because we wanted to verify if the use of mathematical filmlets has an effect for the motivation and the interest in mathematics. Due to the unique adoption of mathematical filmlets it´s difficult to refer findings. But in this class the vast majority of the students think their own motivation increases by working with filmlets. The observance of the lesson supported this notice, there was nearly no noise in the classroom or other troubles, the students seemed to be concentrated. 3

5. Perspective In the near future we will produce more storyboards and filmlets according to the results of the requirements analysis. On the other hand it is a very important aim to construct a testdesign which operationalises our hypothesis: is it possible to develop mathematical filmlets for secondary education to foster the comprehension of mathematics.

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6. Literatur Apostol, T.M., Bourguignon, J.P., Emmer, M., Hege H.-C., Polthier K. (2010) VideoMath. Berlin: Springer Blumschein, P. (2004). Eine Metaanalyse zur Effektivität des multimedialen Lernens am Beispiel der Anchored Instruction. Verfügbar unter: http://www.freidok.uni-freiburg.de/volltexte/1546 Cognition and Technology Group at Vanderbilt (1997). The Jasper project: Lessons in curriculum, instruction, assessement and professional development. Mahwah: Erlbaum Döring, N. & Kleeberg, N. (2006). Mobiles Lernen in der Schule. Unterrichtswissenschaft – Zeitschrift für Lernforschung. 34, 70-91 Fischer, F., Mandl, H. & Todorova, A. (2009). Lehren und Lernen mit neuen Medien. In Tippelt, R. & Schmidt, B. (Hrsg.). Handbuch Bildungsforschung. Wiesbaden: VS-Verlag Groß, E. (1977). Erziehungswissenschaftlicher Unterricht. Didaktische Perspektiven für die Praxis. Academia Verlag Liebelt, W. (1998). Der Film zu John Steinbecks of mice and men im Englischunterricht. Hildesheim, Niedersächsisches Landesinstitut für Fortbildung und Weiterbildung im Schlwesen und Medienpädagogik (NLI) Litzmann, W. (1943). Lebendige Mathematik. Breslau. Ferdinand Hirt Ludwig, M. & Binyan, Xu (2010). A Comparative Study of Modelling Competencies Among Chineses and German Students. In Journal für Mathematik-Didaktik (JMD), Volume 31, Springer: Berlin/ Heidelberg Merkt, M., & Schwan, S. (2009). Wissenserwerb mit interaktiven Unterrichtsfilmen im Fach Geschichte. geschichtsdidaktik empirisch 09. Basel. Merkt, M., & Schwan, S. (2009). Die Nutzung interaktiver Videos im Schulunterricht: Lernstrategien und Wissenserwerb. 12. Fachtagung Pädagogische Psychologie der Deutschen Gesellschaft für Psychologie (DGPs). Saarbrücken Metzler, W. (1982). Was leisten mathematische Filme? Aufgaben und Grenzen des mathematischen Films im Unterricht. In Kautschitisch, H & Metzler, W. (Hrsg.), Visualisierung in der Mathematik. Band 6 (S.79-94). Stuttgart: B.G. Teubner Müller, F.H., Hanfstingl, B. & Andreitz, I. (2007). Skalen zur motivationalen Regulation beim Lernen von Schülerinnen und Schülern: Adaptierte und ergänzte Version des Academic SelfRegulation Questionnaire (SRQ-A) nach Ryan & Conell. Wissenschaftliche Beiträge aus dem Institut für Unterrichts- und Schulentwicklung. Klagenfurt: Alpen-Adria-Univeristät Steinberger, C. & Mayr, H.C. (2002). Computergestütztes mobiles Lernen. (196-216) In. D. Hartmann (Hrsg.). Geschäftsprozesse mit Mobile Computing. Brauschweig: Vieweg Wallner-Paschon, C. & Schwantner, U. (2004). Mathematik-Kompetenz und individuelle, familiäre sowie schulische Bedingungen. In G. Haider & C. Reiter (Hrsg.). PISA 2003. Internationaler Vergleich von Schülerleistungen. Graz: Leykam 5