Chapter 7 Physics Teaching and Learning in Informal Settings

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Chapter 7

Physics Teaching and Learning in Informal Settings

Teaching/Learning!Physics:!Integrating!Research!into!Practice!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!915!!

Development of Students´ Interest in Particle Physics as Effect of Participating in a Masterclass

Kerstin Gedigk, Gesche Pospiech TU Dresden, Professur für Didaktik der Physik Abstract The International Hands On Particle Physics Masterclasses are enjoying increasing popularity worldwide every year. In Germany a national program was brought to live in 2010, which offers these appreciated events to whole classes or courses of high school students all over the year. These events were evaluated concerning the issues of students´ interest in particle physics and their perception of the events. How several interest variables interact with each other and the perception of the events is answered by structural equation modelling (section 5.2). The results give information about the events´ effects on the students´ interest development in particle physics, show which event features are important (e.g. the authenticity) and give information about practical approaches to improve the effects of the Masterclasses. Section 5.3 deals with a group of participants which have a high interest in particle physics 6-8 weeks after the participation. The number of these students is remarkable large, with 26% of all participants. The investigation of this group shows that the Masterclass participation has the same positive effect on both sexes and all levels of physics education. Keywords Interest, evaluation study, particle physics research, informal physics teaching and learning, upper secondary education: ages between 15-19

1. Introduction An important concern of physics education is the support of interest in physics issues and phenomena (cf. Berger 2011, p. 99). This interest creates a basis for young people to deal with scientific questions and their social connections, beyond the school education, i.e. “to become lifelong learners and to maintain a sense of wonder about the world around them” (cf. BMBF 2007, p. 159). Another aim of physics education, in addition to the teaching of content, is to offer an insight into modern research processes and questions. These issues enable students to get an adequate picture of nature of science and scientific knowledge gain. All these issues are taken up by events about particle physics for high school students, so called “Particle Physics Masterclasses” offered by the German national program “Netzwerk Teilchenwelt” (English: network particle world). This is a network of 24 German particle physics research institutes and CERN1. In this network high school students, physics teachers and particle physicists, who are involved in the program, are enthusiastic about particle physics. The network offers a wide range of activities for students and teachers whereof the Particle Physics Masterclasses build the basic level. This contribution deals with the evaluation of these events, concerning the supporting effects on students´ interests in physics and particle physics. Some important results of this evaluation study are presented. 2. The Particle Physics Masterclasses The Particle Physics Masterclasses are inspired by the International Hands On Particle Physics Masterclasses, which take place every year in March around the world. With the network's offering of the Particle Physics Masterclasses, high school students can join comparable workshops all over Germany throughout the year and it is possible that whole classes or courses of high school students can participate in such a Masterclass. Every year the network conducts about 120 Masterclasses. They last between 4 to 6 hours and mostly take place in schools with whole classes or courses. The facilitators of these workshops are young particle physicists, typically PhD students who sometimes are assisted by school students or teachers.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1 European Organization for Nuclear Research (near Geneva/ Switzerland)

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Such a Masterclass typically starts with an introductory talk of the young facilitators about the particle physics research, how it is conducted, how scientists work together in an international collaboration, which questions are answered or should be answered by the actual research, why particle accelerators are that huge, how a particle detector like the ATLAS detector2 is working etc. Then the participants get an introduction and exercise how to identify particles by analysing their detector traces. Afterwards the high school students do own measurements with original data from CERN. Thereby they typically work together in pairs to classify about 50 to 100 decay events into different categories. The results of all groups are combined. In a joint discussion, by using statistical methods, they achieve a fundamental result of the recent particle physics research. The overarching aim of the Masterclasses is to give high school students an insight into the modern physics research, especially the particle physics research, in an authentic way. The authenticity includes on one hand making original data from CERN available for high school students and teachers. On the other hand the authenticity should be achieved by the creation of an authentic setting in the Masterclasses. This includes the direct contact with real scientists, the use of a software which is close to the one which is used by the scientists and applying similar methods to interpret and compare their results with the predictions within the standard model of particle physics. A central aim is to support the students´ interest development in particle physics. Individual students should be stimulated to do particle physics in their free time or e.g. to join voluntarily the higher levels of the network program. (cf. Gedigk et al. 2014 p. 397) Students or teachers interested to know more about particle physics than they experienced by attending a Masterclass, can join the higher levels of the network program. For high school students the possible activities in the higher levels are proliferating their experiences with particle physics, participating in workshops or project weeks at CERN or conducting their own research projects. 3. Research questions and theoretical frame The objectives of the evaluation study are twofold: 1. the examination of the effects of the Masterclass participation on the students´ interest development in particle physics, 2. to provide indications how the effect of the Masterclasses could be improved, especially concerning the implementation of the events. The basis of this investigation is formed by the person-object-theory of interest by Krapp: “An interest represents a (…) specific relationship between a person and an object” (Krapp 2002, p.387). Object in this respect “can refer to concrete things, a topic, an abstract idea, or any other content of the cognitively represented life-space” (Krapp 2002, p.387). The interest relationship between the person and the object is characterized by cognitive, “value-related and feeling-related valences” (Krapp 2002, p.388). This means that the person which is highly interested in an object (in best case) feels cognitively activated and “subjectively affected” by the object of interest of and experiences a “relevance for his or her sense of self” (Krapp 2002, p.388). For that reason it is useful to distinguish between cognitive, emotional and value-related components of an interest relationship. The more often and the more intensive a person interacts with the object of interest the more stable the interest relationship becomes. Furthermore, the development of this relationship also depends on the situation or the context in which the person is operating with the object (Krapp 1992, p. 308). Another aspect for developing interest is the learning in an authentic setting (e.g. cf. Kuhn et al. 2010, pp. 6, 10; cf. Euler 2009, pp. 802, 805). Therefore to evaluate the perceived authenticity of the event was an important aspect of the investigation. On the other hand it is difficult to achieve long-term effects on the interest by a one day event (cf. Euler 2009, ). However, as particle physics does only play a small role in the German school curricula, the special interest in this topic is assumed to be influenceable by a Masterclass participation. The interest in physics as a subject and as profession is assumed to be relatively stable, because they were created over several years of physics education. The crucial factors for being engaged to do particle physics beyond the Masterclass are supposed to be the interest in particle physics itself, the (realized) intended actions of interest in particle physics and the interest in participating in the network From this the research question follows:

How does the authentic setting of this one-time event affect students´ interest development in (particle) physics? Concretely the following questions are examined in this article:

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!2 ATLAS in one of the four particle detectors which is used at the Large Hadron Collider at CERN

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• Are students´ interests in physics in general and particle physics in particular fostered by a Masterclass participation?

• Can long-term effects be seen? • Are there differences in the interest development between several participant groups? (e.g.

gender, age, type of school, etc.) • How do different interest and event variables affect each other? Especially which event

properties are related to interest changes and which factors can be identified, that are crucial for a positive perception of the events?

• Is there a group of participants with a high interest in particle physics after the Masterclass? What is characteristic for this group (e.g. age, type of school, gender, …)?

4. The evaluation study To measure the different aspects of interest of the participating high school students an interest questionnaire was developed, tested in a pilot study and then improved. It is based on existing interest questionnaires which were recently used to evaluate out-of-school learning laboratories (e.g. Pawek 2009, Engeln 2004) and was adapted to the specific format and content of the Particle Physics Masterclasses. It contains items with closed answer format with a 5-point Likert scale. For determination of the interest changes the evaluation study follows a pre/ post/ follow-up design. The students filled in the questionnaire at the beginning, at the end of the Masterclass and again after a 6 to 8 week period. The follow-up evaluation enables the investigation of the sustainability of the Masterclasses. Additionally a control group was evaluated with the same instruments and the same procedure, which means that students attending the same school levels were asked, who did not take part in a Masterclass.

Figure 1. Selection of evaluated variables with the assumed stability Figure 1 shows a selection of the evaluated variables. As described in section 3 we distinguish relatively stable and changeable interest variables. It was considered important to ask in the follow-up evaluation for realized "actions of interest" as this was an indicator for the interest of taking part in the higher levels of the network program. For that reason these variables are called target variables. One of the control variables were the "perceived event features". Examples for the items and the internal-consistency coefficients (Cronbach´s alpha) of the variables are presented in Gedigk et al. (2014, p. 404). 5. Selected results of the evaluation study The evaluation study was conducted from October 2011 until May 2012 in 25 Particle Physics Masterclasses with about 500 high school students (“experimental group”). In this article selected crucial results are presented below. More results, for example the comparison between experimental and control group, can be found in Gedigk et al. (2014).

5.1 Description of the sample The experimental group consists of four main groups with different educational background, shown in figure 2. It describes the participants of the evaluated Particle Physics Masterclass (N=195) without those students, who already attended a Masterclass before and without students with incomplete data. Furthermore only


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students attending with their whole class or course were included. Individual students ("selected students") were excluded, because this group shows much higher pre-interests in comparison to the group of whole classes or courses.

Figure 2. Groups of participants in the experimental group

A fifth of the experimental group is female. About 86% of these students state, they did not have the choice whether to participate or not. But 89% declare that they looked forward to the Masterclass. 5.2 The mechanism behind interest development To investigate how different evaluated variables are related, a structural equation model was developed. The model offers an overview how the one-time intervention of participating in a Masterclass affects students´ interest development in particle physics. It was developed on the basis of the interest construct theory (section 3) and chronological considerations. According to the aims of the Masterclasses (see section 4) the most important long-term target variables are the interest in particle physics and (realized) intended actions of interest in particle physics in the follow-up evaluation (marked blue in figure 3). As one of the goals of the evaluation is to get hints for optimization of the Masterclasses (see section 4) in the centre of the model is the focus variable of the perceived event features (marked orange), because this among other things also depends on the implementation of the Masterclasses. The structural equation model was implemented with the statistical software AMOS 22, using maximum likelihood estimation. Key elements of the model are the seven latent variables, which are presented with an elliptical shape in figure 3. Each of them is related to two or three directly measured variables which are represented with rectangular shape. This is based on the assumption that recently measured variables and their correlations can be explained with a non- observable (=latent) background variable. Particularly important are the directed connections between the latent variables, which represent regression paths. These are based on theoretical and chronological considerations (cf. Kline 2012, p. 113).

Figure 3. The mechanism of action between the interest and event variables. Arrows: (directed) regression paths. Variables with elliptical shape: latent (or unobserved) variables. Variables with rectangular shape: measured (or observed) variables, indicators of the according latent variables. Green numbers: estimated standardized regression weights; all of them are significantly different from zero at a 0.001 level. Blue numbers: estimated proportion of the variance of the variable that is accounted for by its predictors.


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The numbers given in the model are estimated values which have the minimal difference to the data w.r.t the maximum likelihood estimation. Blue numbers stand for the estimated proportion of the variance of the according latent variable, “that is accounted for by its predictors” (Arbuckle, p.74). For example, 67% of the variance of the interest in particle physics at the beginning of the Masterclass is explained by the personality traits. The green numbers are estimated standardized regression weights of the according regression path. For example, if the personality traits of two persons are compared, the person with a higher personality trait of one standard deviation is expected to have a higher interest in particle physics at the beginning of the Masterclass by 0.82 standard deviations (i.e. 82 percent of the standard deviation). Furthermore the model gives information about the most important effects and several effect sizes. The model fits the data very well, as several fit indices confirm, shown in table 1. We choose as criteria the most commonly used fit indices (e.g. Pawek 2009, p. 150, Rudolf 2012, pp. 355-358). Concrete formulae for these indices can be found in West et al. (2012, pp. 212 ff).

Table 1. Fit indices for structural equation models. χ²: chi-square statistic; df: number of degrees of freedom; CFI: comparative fit index; RMSEA: Root Mean Square Error of Approximation; SRMR: Standardized Root Mean Square

Residual. Criterions for the indices, cf. West et al (2012, p. 212, 213, 219), ° cf. Rudolf et al (2012, p. 365). Right column shows the values for the model depicted in figure 3.

Fit index

Criterion for good fit

Criterion for acceptable fit

Values for our model

χ²/ df ≤ 2.5° < 5 1.825 CFI ≈ 1 > 0.95 0.955 RMSEA < 0.05 < 0.08 0.065 SRMR < 0.05 < 0.10 0.052

We start the explanation of the model shown in figure 3 from the focus variable (perceived event features). It is assumed to affect the target variables via the intended actions of interest in particle physics at the end of the Masterclass and via the actual interest in the measurement in the follow-up evaluation. On one hand the focus variable of the perceived event features depends on the real event features, which may be influenced by the implementation of the events. On the other hand it also depends on the subjective individual perception. Pursuing this path further backwards the relatively stable personality traits, which represent the interest in physics as subject and profession, in general, act via the special interest in particle physics on the perception of the event. As can be seen in figure 3 the paths via the focus variable of the perceived event features have an influence on the long-term interest development in particle physics. The comparison of the standardized regression weights shows that the influences on the long-term target variables of the perceived event features are in a comparable size (dimension) to the direct effects of the personality traits and the interest in particle physics at the beginning of the Masterclass. But the model shows also that these latter variables affect the perception of the event, so that 40% of the variance of the perceived event features is explained by them. For this reason table 2 shows the standardized total effects of these and the perceived event features on the long-term target variables, which means that direct and indirect effects are added to a total effect. A standardized total effect corresponds to a standardized regression weight. The determined values of the standardized total effects show again that the perceived event features affect the long-term target variables in a comparable effect size to the personality traits and the interest in particle physics at the beginning of the Masterclass.

Table 2. Standardized total effects, columns affect rows

Personality traits (pre)

Interest in particle physics (pre)

Perceived event features (post)

Interest in particle physics (follow-up) .61 .61 .51

(Realized) intended actions of interest in

particle physics (follow-up)

.60 .45 .49


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As these results show the perceived event features have a relatively strong influence on the students´ long-term interest development in particle physics. This is a surprising result, because the Masterclass is an one-time event, which only lasts between 4 to 6 hours. Results from comparable recent studies show that such one-time events do not have a big influence on long-term special interests (e.g. Pawek 2009, p. 151). The following question immediately raises: which factors affect the perception of the event features, besides the personality traits and the interest in particle physics in the pre evaluation? Especially, which objective event properties have an influence? Some answers are given in Gedigk et al. (2014, p. 402): The perception of the event features depends e.g. on the prior knowledge in particle physics, the gender and the type of measurement. In summary, the developed model fits the data very well and it shows that the event variables have a considerable influence on the long-term interest in particle physics of the young participants. It gives information about practical approaches to improve the Masterclasses´ effects and can be used for further investigations of these events.

5.3 Group with high interest in doing particle physics after participating in a Masterclass The Masterclass participation can be called particularly successful for those participants, who are interested in doing particle physics beyond the Masterclass (cf. aims of the Masterclasses, section 2). For this reason it is investigated, if there is such a group and what characterises this group (cf. research questions, section 3). The evidence for a long-term interest in particle physics are the (realized) intended actions of interest in particle physics in the follow-up evaluation. It plays no role if the students intend to be a part of the network or if they do actions of interest in particle physics in their free time. So on the basis of the questionnaire students were chosen who had a high interest in being a part of the network (upper 20% of the participants) or who realized actions of interest in particle physics (also upper 20%). This resulted in a group of 51 participants of 195 (cf. section 5.1), corresponding to 26%. This group in the following is called “success group”. To characterize this success group χ²-independence tests were used (cf. Bortz, Schuster 2010, pp. 137 ff.) for the investigation of the relation between this success group and gender and between the success group and level of education (grade or school type) (cf. section 5.1). These tests show the independence of the success group on gender (χ²=0.99; p=0.32) as well as on level of education (χ²=3.51; p=0.32). These are remarkable results, implying that practically all students have a similar probability to develop a long-term interest in particle physics. For a further characterization of this success group it was investigated if the success group rate the perceived event features better than the other participants. Table 3 shows the results of the corresponding t-tests with the effect size Cohen´s d. The success group indeed assesses the features better than the others with medium effect sizes (cf. Bortz, Döring 2006, p. 606), whereby the biggest difference occurs regarding to the authenticity. These results confirm the structural equation model shown in figure 3. Table 3. Differences in the perceived event features between the success group and the others. Right column: Cohen´s d as effect size for a significant difference between the means of the groups, t-test for independent samples was used with:

** p<0.01 or *** p<0.001.

Success Group (N=51)

Others (N=141)

Mea

n Standard Deviation

Mean

Standard

Deviation

Cohen´s d

Perceived event features (post)

Challenge and Comprehension

2.71 0.84 2.27 0.83 0.54***

Authenticity 3.04 0.69 2.63 0.65 0.61***

Fit between the event parts

2.67 0.81 2.30 0.83 0.45***


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Another remarkable characteristic of the success group is that there is no significant difference between the intended actions of interest in the post evaluation (M 2.68, SD 0.87) and the realized actions of interest in the follow-up evaluation (M 2.72, SD 0.65). This was tested with a t-test for paired samples (t=0.44; p=0.67). This means that this group realizes its intentions according to the actions of interest in the free time within those 6 to 8 weeks, which exceeds the expectations. To sum up the success group shows that an interest in particle physics can be supported or stabilized for a considerable part of the participants. On the whole it seems that the potential for joining the higher levels of the network is much bigger than the network capacity (cf. Gedigk et al., p. 397). It is a very positive result that the format of the Masterclasses seems to be able to sustain interest independently from gender and class or school form. 6. Conclusions A model was developed showing which variables are important for the interest development of the participants in a particle physics Masterclass. It fits the data very well (table 1) and shows how interest and event variables influence each other (figure 3). On one hand this offers the opportunity to find practical approaches for improving the effect of the events. On the other hand it makes it easier to investigate the effects of Masterclasses again, e.g. when the implementation will be changed systematically. Furthermore the model (and the questionnaire) could be adapted for similar event formats, to investigate the interest development of the participants. It is remarkable that the event variables have a considerable influence on the students´ interest development in particle physics (c.f. table 2). Section 5.3 describes a group of Masterclass´ participants which have a high interest in being a part of the network or in actions of interest in particle physics, 6 to 8 weeks after the Masterclass participation. It is remarkable that this group is independent from gender and class or school form. Furthermore this “success group” is much bigger (26%) than the network capacity for joining the higher levels. So the Masterclasses have a big potential to inspire high school students for doing particle physics. Acknowledgement We thank Michael Kobel for the possibility to evaluate the particle physics Masterclasses of the “Netzwerk Teilchenwelt” and for his support. References Arbuckle, J. L. (2012). IBM SPSS Amos 21 User’s Guide. [online], [cit. 24.11.2014]. Available from: ftp://public.dhe.ibm.com/software/analytics/spss/documentation/amos/21.0/en/Manuals/IBM_SPSS_Amos_Users_Guide.pdf Berger, R. (2011). Interessen im Physikunterricht. In: Wiesner, H., Schecker, H., Hopf, M. (eds.): Physikdidaktik kompakt. Aulis Verlag. (pp. 99-105). BMBF (Ed.) (2007): Zur Entwicklung nationaler Bildungsstandards, Expertise, Bundesministerium für Bildung und Forschung (BMBF), Bonn, Berlin 2007. [online], [cit. 15.12.2014]. Available from: http://www.bmbf.de/pub/zur_entwicklung_nationaler_bildungsstandards.pdf Bortz, J., Döring, N. (2006). Forschungsmethoden und Evaluation. Springer Verlag, Berlin, Heidelberg. Bortz, J., Schuster, C.(2010): Statistik für Human- und Sozialwissenschaftler. Springer Verlag, Berlin, Heidelberg. Engeln, K. (2004): Schülerlabors. Authentische, aktivierende Lernumgebungen als Möglichkeit, Interesse an Naturwissenschaften und Technik zu wecken. Logos-Verlag, Studien zum Physiklernen 36, Berlin. Euler, M. (2009): 25 Schülerlabore: Lernen durch Forschen und Entwickeln. In: Kircher, E., Girwidz, R., Häußler, P. (eds.): Physikdidaktik. Theorie und Praxis. Springer Verlag, Berlin, Heidelberg. (pp. 799-818). Gedigk, K., Kobel, M., Pospiech, G. (2014): Development of interest in particle physics as an effect of school events in an authentic setting. In: Dvorak, L.: ICPE-EPEC 2013 Conference Proceedings. (pp. 396-404). [online.], [cit. 28. 10. 2014]. Available from: http://www.icpe2013.org/uploads/ICPE-EPEC_2013_ConferenceProceedings.pdf


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Krapp, A. (1992): Das Interessenkonstrukt: In: Krapp A., Prenzel M. (eds.): Interesse, Lernen, Leistung. Aschendorff, Münster. (pp. 297-329). Krapp, A. (2002): Structural and dynamic aspects of interest development: theoretical considerations from an ontogenic perpective. In: Boekaerts, M, Boscolo, P.: Learning and Instruction 12, Issue 4. (pp. 383-409). [online], [cit. 23. 10. 2014]. Available from: http://www.sciencedirect.com/science/ article/pii/S0959475201000111 Kline, R.B. (2012): Assumptions in Structural Equation Modeling. In: Hoyle, R. H. (ed.): Handbook of structural equation modeling. (pp. 111-125). Kuhn, J., Müller, A., Müller, W., Vogt, P. (2010): Kontextorientierter Physikunterricht. Konzeptionen, Theorien und Forschung zu Motivation und Lernen. PdN-PhiS, 5(59), pp. 5-20. Pawek, C. (2009): Schülerlabore als interessefördernde außerschulische Lernumgebungen für Schülerinnen und Schüler aus der Mittel- und Oberstufe. Dissertation. Christian-Albrechts-Universität zu Kiel, Kiel. Mathematisch-Naturwissenschaftliche Fakultät. [online], [cit. 10. 06. 2014]. Available from: http://www.dlr.de/schoollab/Portaldata/24/Resources/dokumente/Diss_Pawek.pdf. Rudolf, M., Müller, J. (2012): Multivariate Verfahren. Hogrefe Verlag, Göttingen. West, S. G., Taylor, A. B., Wu, W. (2012): Model Fit and Model Selection in Structural Equation Modelling. In: Hoyle, R. H. (ed.): Handbook of structural equation modeling. (pp. 209-231).! Affiliation and address information Kerstin Gedigk TU Dresden Fachrichtung Physik Didaktik der Physik 01062 Dresden Germany e-mail: [email protected] Gesche Pospiech TU Dresden Fachrichtung Physik Didaktik der Physik 01062 Dresden, Germany e-mail: [email protected]


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“Good Vibrations” - A Workshop on Oscillations and Normal Modes

Sara R. Barbieri1, Marina Carpineti1, Marco Giliberti1, Enrico Rigon2, Marco Stellato1, Marina Tamborini3 1 Physics Department, University of Milan, Italy. 2 Liceo Scientifico "Grassi", Saronno, Italy. 3 Liceo Scientifico “Bottoni”, Milano, Italy.

Abstract We describe some theatrical strategies adopted in a two hour workshop in order to show some meaningful experiments and the underlying useful ideas to describe a secondary school path on oscillations, that develops from harmonic motion to normal modes of oscillations, and makes extensive use of video analysis, data logging, slow motions and applet simulations. Theatre is an extremely useful tool to stimulate motivation starting from positive emotions. That is the reason why the theatrical approach to the presentation of physical themes has been explored by the group “Lo spettacolo della Fisica” [Spettacolodellafisica 2014] of the Physics Department of University of Milano for the last ten years [Carpineti et al. 2011; Carpineti et al. 2006] and has been inserted also in the European FP7 Project TEMI (Teaching Enquiry with Mysteries Incorporated) [Temi 2014] which involves 13 different partners coming from 11 European countries, among which the Italian (Milan) group. According to the TEMI guidelines, this workshop has a written script based on emotionally engaging activities of presenting mysteries to be solved while participants have been involved in nice experiments following the developed path. Keywords Oscillations, theatre, secondary education.

1. Introduction Harmonic oscillations and normal modes are key physical concepts. They are fundamental in quantum physics [Giliberti 2007, Smith 2010], in electromagnetism (especially in treating coupled oscillating circuits and electromagnetic waves), in acoustics and in mechanical systems. The conceptual and practical importance of normal modes emerges also clearly from the fact that every small and sufficiently smooth oscillation of a complex system is given by a linear superposition of its normal modes [Barbieri 2012, Fitzpatrick 2013]. Furthermore, normal modes give also a way of introducing students to the basic concepts of the Fourier Transform in a meaningful way within a phenomenological approach. Moreover, normal modes are important conceptual organizers that allow a unifying approach to many different physics topics, giving students a deeper and also a faster way to face different contexts. Nevertheless, in teaching practice (at least in Italy), only short time is devoted to harmonic motion, rarely coupled oscillators are treated and, in secondary school text-books, normal modes are usually not even present. Potentially high impact curricular innovations, as the one we are proposing here, need to be clearly highlighted to be implemented in schools. As a consequence, a necessary step in this direction implies to give, besides disciplinary topics, also methodological and didactical strategies to put forward. In this regard TEMI offers a didactical approach based on the 5E cycle [Bybee et al 2006, Sherborne et al 2014] to develop understanding of scientific concepts through a guided enquiry process (that is an inquiry process in which the problem is posed by the teacher, but the procedure and the solution are given by the students) that is broken down into the following 5 stages.

• Engage that catches students’ attention using mysteries and leads them in formulating the enquiry question.

• Explore when students try to answer questions by planning experiments and collecting observations and data.

• Explain when students try to make sense of the data, and show their “scientific” ideas to answer enquiry questions.


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• Extend when students try to solve at related different problems using the gained conceptual understanding.

• Evaluate which is the phase of self and teachers assessing students’ understanding and skills.

For what concerns the first, fundamental phase the TEMI project makes use of what we may call mysteries, that is unexpected and unfamiliar phenomena, as a key strategy to raise the attention and to challenge students’ curiosity. One of the most effective way of using mysteries is by means of a theatrical grammar, an aspect of teachers' presentation skills that in TEMI is called “showmanship”. Moreover, if we require that, besides teachers, also students make use of a due theatrical grammar, for instance making a short video or a short show concerning the mystery and its solution, also the other phases of the 5E cycle (from explain to extend phases) can be greatly improved. In this workshop, a theatrical grammar is used to simultaneously achieve some different aims: to describe the general framework of our educational path on oscillations and normal modes (which is intended for students of the 11th and 12th grade, and that has been derived by a PhD designed based research); and to give a concise example of a Milan-TEMI inquiry lab that integrates skills with content, and that is devoted to the continuous professional development of teachers (CPD) towards IBSE, making reference to the model for teaching skills, known as the Gradual Release of Responsibility (GRR) model [Sherborne et al 2014], that is schematically structured in the three stages “I do it”, “We do it” and “You do it”. The workshop contains two complete 5E cycles, the first one on harmonic motion [Giliberti et al 2014] and the second one on normal modes of oscillations. For brevity, in the following we will describe in relative details only the first cycle, while the second one will be only outlined. To better get an idea of what we mean with “theatrical grammar”, we will help from the script, of which we will also give some excerpts (in quotes) when appropriate. 2. 5E cycle on harmonic motion

Engage The purpose is to catch the attention of the public and engage them with simple experiments on oscillation. Realization: A lab-room, filled with experimental devices on oscillations, is shown together with three people dressed like a pack as a stage costume, Fig.1. A kit bag containing material for personal experiments on oscillations is put on each chair. Persons attending the workshop enter the room while the song “Good vibrations” by the Beach Boys is playing.

Figure 1. The stage while people enter the workshop room.

The workshop started with a slide showing two typical definitions of harmonic motions: a) Harmonic motion is the projection on a diameter of a uniform circular motion. b) An object performs harmonic motions if it is acted upon by a force F = -kx “With definitions such as these, students do not go much further. Our experience with secondary students, and also with graduate students in mathematics, shows that the comprehension of the link between mathematics and physics in the study of oscillations is far from clear if we start this way. The bottom line is that the kinematic definition of harmonic motion a) is not enough to understand the physics implied and the dynamical definition b) is often ineffective. […] In fact, the previous definitions prevents to grasp the


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importance of the harmonic motion as a conceptual organizer that, instead, should emerge from the choice/recognition of particular deep similarities/diversities among different types of periodic motions.” Therefore, the first engaging message is that “We cannot deliver students pre-packed definitions (like those given above) since, in this way we would not give them instruments and concepts to analyse and read the world around them.” To emphasize this message, the three researchers unpack themselves and ask the public to synchronize a pendulum, taken from the kitbag, with the rhythm of a metronome that everyone can hear. What does the period of a pendulum depend on? Of course, attenders had to choose the right length, but in practical it is not quite so simple… And now the guided inquiry engagement comes: many different types of oscillations are also shown, among them a ball oscillating inside a bowl, a mass-spring oscillator, a pendulum, a seesaw on a flat pivot and another one on a round pivot, a bouncing ball, a disk bouncing on an air table, a cycloidal pendulum a Waltenhofen pendulum. Participants are asked to classify the previously seen motions into two or three categories, putting together the motions that, in their opinion, had particular similarities from a mechanical point of view, and then giving us a motivation for their choices. It is interesting to observe that, facing the same task, the majority (~80%) of our secondary school students divided the oscillations according to the form of their trajectories: those having a rectilinear trajectory (such as a mass spring oscillator and a bouncing ball) were put in the same category and those having a curvilinear trajectory (such a pendulum and a ball on a curvilinear track) in another one. The remaining students (~20%), instead, were more impressed by damping and, therefore, put together oscillations having the same “intensity” of damping (such as a bouncing ball and the see-saw on the large flat pivot). These data show the difficulty to look at things from a physical perspective, especially if the purpose is to come to a common agreement of the definition of harmonic motion and to a suitable understanding of it, starting from the typical vision of common sense as regards the oscillations.

Explore An excerpt from the script can well introduce the explore phase. “We are studying mechanics, right? What are the key concepts of mechanics? I’d say: forces and motion, so it seems to me probably meaningful and also fruitful to look at the forces that generate the previous motions.” A very qualitative approach, typical of an exploration phase follows. “First I do it, then we do it all together. Look: this is a mass-spring oscillator: there’s an equilibrium position here… when I pull it downward, the force acting on the mass pushes upwards. And if I push the mass upward the total force acts downwards, towards the equilibrium position”. Once a vertical coordinate is chosen, a qualitative graph of the force vs position can been drawn, Fig.2.

Figure 2. Graphs of the force vs position for a bouncing ball and for some other oscillatory motions.

Audience is asked to make a similar work with all the previously seen oscillations. Now a comment taken from the script is compulsory:


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“It is indeed very difficult for secondary school students to draw graphs like those just seen. But it’s worth to do it. In fact, in our experience, this operation increases students’ general ability in representing and reading graphs. Moreover, as we shall see in few moments, the path we propose, containing that difficult task, allows to recognise the anharmonicity or the harmonicity of a motion at a glance, even without knowing its equation of motion, nor its solution. In other words, without knowing the details of the forces involved [Giliberti et al 2014] that, sometimes, can be quite difficult to determine (as in the case of a ball rolling on a cycloid or in that of a seesaw oscillating on a round pivot). Therefore, making students familiar with the concept of a positional force, the introduction of the potential energy concept is then easier, and it can then conveniently be used in describing oscillations or in dealing with normal modes”

Explain By the previously described guided procedure, one can gain the key observation that some oscillations are driven by a restoring force, which is a force that gives rise to a motion with a stable equilibrium position. Denoting by ξ the curvilinear coordinate, with the zero corresponding to the equilibrium position, the graph of the component of the restoring force along the trajectory, Fξ, vs ξ will lie in the second and in the fourth quadrant. In this case the restoring force can be approximated by its tangent line in the origin, provided the amplitude of oscillation is small enough, Fig.3. So that, a body subjected to a sufficiently regular restoring force, and for small amplitude of oscillation, clearly obeys the equation of motion:

!! = −!", (1) (where k is a positive constant). Eq.(1) can be written as:

! = − !! !, (2)

where a is the acceleration and m is the mass of the oscillating body. Eq.(2) that can be taken as the definition of harmonic motion.

Figure 3. A restoring force and its linearization in the origin. With little efforts, from Eq. (2) all the proprieties of harmonic motions can be obtained. One for all: the isochronism of oscillations. Keeping in mind what we have just done, we are now induced to divide oscillatory motions into two categories: 1) those with harmonic small oscillations, 2) all the others. And by just looking at the qualitative graphs of the component of the force along the trajectory vs the curvilinear coordinate we can also suddenly and easily understand how often the (sufficiently) small oscillations of a body are harmonic. For example: the pendulum, the ball in the bowl, the mass-spring oscillator, all give rise to harmonic oscillations.

Extend The extend phase is proposed towards two different directions. The first one is damping [Giliberti et al 2014], in fact, as said above, besides the trajectories of which we have just taken care, secondary school students were also interested in damping and, therefore, it is worth to consider it in our path. But, for brevity reasons, we do not linger on the damping in this paper. The second direction, that we are going to describe


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here, is how to reach a deeper understanding of harmonicity through a comprehension of what harmonic is not. We would like to dot the i's and cross the t's of our definition of harmonic motion. Preliminarily, it is important to stress that the harmonic motion defined by eq.(2) is not necessarily rectilinear, since ξ is, in general, a curvilinear coordinate. Then, it is also important to emphasize that Fξ is only the component of the total acting force along the direction of motion, since in many cases the intensity of the total resultant force may be different from zero even in the equilibrium position; for instance when the contribution of its centripetal component is important; while, on the contrary Fξ is, still, zero. The path towards the previous definition leads us to say that a one degree of freedom system performs harmonic oscillations in a neighbourhood of an equilibrium point if and only if (a) the equilibrium point ξ=0 is stable; (b) the function Fξ is continuous; (c) the function Fξ is differentiable;

(d) !!!!" 0 ≠ 0.

With these conditions clear in mind, we are now able to realize at a glance the anharmonicity/harmonicity of an oscillation, and also we can understand the link with the mathematical aspects of the problem. Let us see how, with some questions/examples. Q1) Are the oscillations of a disk bouncing back and forth on an air table harmonic or not? The answer is no, because it has not a stable equilibrium point (condition (a) drops). Q2) An interrupted pendulum is a pendulum with a peg between the point of suspension and the equilibrium point, so to change the length of the pendulum for half an oscillation, Fig.4(a).

Figure 4. (a) An interrupted pendulum. (b) Graph of the ξ-component of the restoring force, Fξ, vs ξ. Are the small oscillations of an interrupted pendulum harmonic or not? No, they are not, because the function Fξ(ξ) is not differentiable (condition (c) drops), see Fig. 4(b). It is interesting to observe that the period of the small oscillations of an interrupted pendulum is obviously isochronous, thus providing an example of a motion that is isochronous but not harmonic. Q3) “[This is] a very subtle example: the case when only the condition (d) of our four-point criterion is not satisfied, that is when dFξ(0)/dξ is zero. In this situation, it is easy to demonstrate that, in the neighbourhood of the equilibrium point, the potential energy behaves at least as ξ4 [Giliberti et al 2014]. The small oscillations can, therefore, be realized making a body slide on a track with a y=x4 profile. Let’s try it. You have your own profile in the kitbag. Please take it out and make a ball roll on it and… play with it. Let’s see what happens. Near the equilibrium point, the track is nearly flat and the motion is nearly a uniform motion! Small oscillations are practically impossible to see. Nonetheless, when the amplitude is large enough, we can immediately realize that the motion is not isochronous and, therefore, not even harmonic.” This last observation gives us a simple trick to understand when an oscillation is not harmonic: it suffice to listen to the rhythm it produces. If it is not constant, the oscillation is surely anharmonic.


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Evaluate Both, the self-evaluation (done by students themselves) and the evaluation (done by the teacher) is a systematic procedure that takes place during the whole path and not just at the end. Nonetheless, for clarity reasons, we give here an example of the final evaluation. It is taken from the final results of an evaluation questionnaire on harmonic motion, given to secondary school students during our experimentations in many schools. We consider here only the part concerning students’ skills of classifying oscillations into categories (a more detailed, wide-range analysis is in progress). As already said, while before our path students classified oscillations according to their trajectories (80%) or to the “intensity” of damping (20%); after the path, the percentage of students that used a geometric criterion decreased to 48%, while as much as the 52% of them used the learned anharmonicity/harmonicity criterion to classify. 3. 5E cycle on normal modes of oscillation Another complete 5E cycle has been devoted to normal modes. For the engage phase two very intriguing experiments are shown. a) A wave-pendulum, that consists of a series of pendulums with different lengths so to have decreasing periods. When the pendulums are simultaneously released, they give the impression of a transverse wave that change its shape with time and, eventually, comes back to the initial condition. b) Two coupled pendulums in which the energy is gradually transferred from one pendulum to another. The explore phase starts with the questions: Which are the similarities/diversities of the previous two systems? Is it possible to have a harmonic oscillation, when the oscillators are coupled? To answer this second question we can build systems consisting of two to five physical pendulums coupled by identical springs. These systems are particularly useful: i) to easily introduce some particular (a student said “spectacular”) configurations of motion for the entire system: the normal modes; ii) to recognize that when such a complex system oscillates in one of its normal modes, there is no energy exchange between its single parts (oscillators); iii) to see that every casual motion configuration of the system is a linear superposition of its normal modes. In discussing such systems, we find it particularly useful to use both, sonar data logging techniques and video analysis. In particular, slow motion video of 2 to 5 mass spring oscillator can clearly show the various modes of oscillations and the resulting relations the among frequencies and the relative phases of each oscillator. In the explain phase, some different mathematical explanatory schemas are discussed. Among these, we highlight an algebraic decoupling of the equations of motion of a two mass-spring oscillator system and a simple connection with the Fourier Transform also with the experimental tool of the FFT (Fast Fourier Transform) that can be very useful also in the description of systems with more degrees of freedom. A general conclusion is also reached: in a system with n degrees of freedom, there are always n ways of producing a proper oscillation, such that each oscillator of the system performs harmonic motion. Moreover, a graphic and powerful way of determining the mth mode of n coupled oscillators, in clear analogy with stationary waves on a rod, is given (see Fig.5 for a self-explanatory sketch of the method made by a secondary school student).

Figure 5. A schematic way of representing the 4 modes of oscillation of 4 coupled oscillators

In the extend phase the study of a Shive machine can be undertaken and also a qualitative study of the normal modes of Chladni plates can be done. Moreover, a research for the normal configurations of various more general systems, such as a circular moving track with a heavy ball rolling over while the track can oscillate itself, is of sure help in making the comprehension of normal modes deeper and wider. Even a two degree of freedom non-linear system, the parametric pendulum, that is a vertical mass-spring oscillator with


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the spring frequency that doubles the pendulum-like one [Boscolo et al 2014] is an appropriate conclusive activity of the extend phase. The two normal modes of the parametric pendulum, that are obviously always independent for the linearized condition of very small oscillations, do instead largely interact, when in the resonant condition, with a very intriguing behaviour. In the evaluate phase, a discussion of the results, obtained in classroom experimentations (through written questionnaires and oral interviews) and that brought us to the final version of our path proposed in this workshop, is done. 4. Conclusions The experimental approach here described allows to overcome most of the mathematical difficulties of treating coupled oscillations in secondary school and can also shed light on some conceptual and disciplinary knots. Moreover, the combined use of data logging software and of video-tracking techniques can, in our experience, also enforce the exploration and explanation phase of the adopted 5E cycle and generate great enthusiasm in students. In fact, a student needs only a smartphone to produce a short video that focuses on the mystery to be explained, and he/she is then stimulated in proposing a solution. Students showed us many videos that they realized, even when we didn’t ask them any. “The notion of normal modes is a conceptual organizer. Every time we look around us, we cannot help but seeing a large amount of normal modes all in action. They are in the small ripples of the water in the harbour. They are in motion of the curtain cord. They are in every sound we listen, in every music. They are at the heart of quantum physics: what, but normal modes of vector potential, are the photons? Our universe has chosen the basis of the normal modes so that refracting prisms produce the rainbow. Even the Klein Gordon equation contains a harmonic term. What, if not an expansion in a Fourier series is the Ptolemaic system? So please enjoy the wonder and the mysteries of oscillations keeping in mind how much more beautiful they are when both a poetic and physical perspective are taken into account.” Acknowledgements: This work was partially supported by Project TEMI, FP7-Science-in-Society-2012-1, Grant Agreement N. 321403; the authors thank Claudio Marconi for theatrical direction. References Barbieri S. R., & Giliberti, M., (2012). Laboratorio aperto: Oscillazioni e Onde. Milano: CUSL. Boscolo I, Castelli F, Stellato M & Vercellati S. The parametric spring-mass system, its connection with non-linear optics, and an approach for undergraduate students, arXiv:1402.5318. Bybee, R., Taylor, J. A., Gardner, A., Van Scotter, P., Carlson, J., Westbrook, A., Landes, N. (2006). The BSCS 5E Instructional Model: Origins and Effectiveness. Colorado Springs, CO: BSCS. Carpineti M., Cavallini G., Giliberti M., Ludwig N., Mazza C. & Perini L. (2006). Let's throw light on matter: a physics show for primary school, Nuovo cimento della Società italiana di Fisica B 121(8), 901-911. Carpineti M., Cavinato M., Giliberti M., Ludwig N. and Perini L. (2011). Theatre to motivate the study of physics, JCOM 10(1), 1-10. Falstad (2014). Online simulations retrieved from www.falstad.com/mathphysics.html Fitzpatrick R. (2013). Oscillations and Waves, Boca Raton, Florida. Giliberti M. (2007). Elementi per una didattica della fisica quantistica, CUSL, Milano, Italy. Giliberti M., Stellato M., Barbieri S., Cavinato M. & Tamborini M. (2014). Detecting anharmonicity at a glance, Eur. J. Phys. 35 (6) 065012, doi:10.1088/0143-0807/35/6/065012 Logger Pro software and reference manual (2014). Retrieved from www.vernier.com/products/software/lp/ Sherborne T., Jordan J., Walker J. (2014). TEMI Report D4.2 (2014) http://teachingmysteries.eu/wp-content/uploads/2015/01/D4.2-Pilot-Training-Programme-Feedback.pdf Smith, W. (2010). Waves and Oscillations-a prelude to quantum mechanics. New York: Oxford University Press Spettacolodellafisica (2014). Available at http://spettacolo.fisica.unimi.it TEMI (2014). Available at http://teachingmysteries.eu/en Tracker software and reference manual (gen. 2014). Retrieved from www.cabrillo.edu/~dbrown/tracker


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Affiliation and address information Marco Giliberti UMIL_PERG (University of Milan Physics Education Research Group) Department of Physics University of Milano Viale Celoria, 16 20133 MI Italy e-mail: [email protected]


Chaos Theory and its Manifestations: An Informal Educational Activity to Explain Chaos to Students

Valeria Greco, Salvatore Spagnolo Associazione PALERMOSCIENZA, Palermo, Italy.

Abstract In spite of being present in many topics of classical physics and in everyday life, the chaos theory is not present in the Italian school curricula and textbooks. Chaotic dynamics are, in fact, involved in phenomena easily accessible to everyone or in events experienced by most people in their lives (the dripping of a faucet which keeps people awoken in the night, meteorology, traffic, population growth), but they don’t know it and what chaos really is. Some people think that chaos is synonymous of mess – like in teenagers’ rooms – or at best that it has a relationship with the unpredictable but they are not able to explain how or why. In this paper we propose a series of experiences related to the chaos theory. In particular, we will present three activities based on the Sinai billiard, a double pendulum and on a simple convection example. It is well known from the literature that these physical systems can have chaotic dynamics under certain particular conditions. These systems have the advantage that involve objects or everyday phenomena with which all people have or have had something to do; on the other hand, these systems allow some simple visualizations of the concept to be conveyed. These experiences are developed to be managed in an informal setting, so that they can be implemented quite simply in schools or in science centers. Keywords Informal education, nonlinear system, chaos, double pendulum, Sinai billiard, convection.

1. Introduction The most important feature of chaos theory is that the descriptive models developed have a strong dependence on the initial conditions, just as the phenomena which aims to describe. The mathematical models of this field are complicated and typically are based on tools or on a cultural background hardly possessed by people. Nonetheless, it is possible to find physical systems whose chaotic evolution is easily viewable through computer simulations or through experiences specially designed. A good starting-point to introduce the theory is beginning from the laboratory that everyday life is. Of course, a significant learning is characterized by the fact that the new concepts or ideas to learn is connected and put into relation with the ones already possessed by each person. So, the new ideas assume a meaning for everyone because people can increase and sometimes restructure their previous knowledge with new concepts. On the other hand, the transmission of scientific knowledge must use new ways to communicate closer to the citizens and especially young people. Also, it is necessary to recognize the need to create a cultural environment suitable to the development of science and characterized by the fall of barriers between science and society. For years, the association PALERMOSCIENZA promotes the growth of scientific communication of young people and citizens outside usual formal structures. In particular, the Association works with students with the idea that the informal educational activities aim to the development of concepts and to the key processes rather than to contents. We believe interaction and confrontation are indeed elements leading – if constantly and correctly attended for – to individual and collective growth of people in general and students in particular. So, we start from experiments and go on interacting with students in different ways, analyzing an everyday fact or phenomenon to come to understand abstraction. Through this process a significant learning is promoted. 2. Methodology


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Significant learning is characterized by the fact that the new material to be learned is connected and correlated with the concepts and skills already possessed by the student. Therefore, new knowledge doesn’t remain isolated, but it will be well connected with the previous cognitive structure of the student. The challenge we face as PALERMOSCIENZA members, is to create an efficient and valid environment where formal and informal learning converge making significant learning achievable. In opposition to formal learning (that is official, curriculum-fixed, scheduled, pedagogically designed with organized learning paths, controlled and often evaluated), informal learning is unofficial, serving a concrete purpose, unstructured, often uncontrolled and tacit. People learn science not only when at the end of a cognitive process master a theory, solve an equation or are able to do practical work in laboratory (typical results of formal learning). Also, learning science means to be able to build and manage interpretative schemes where to place and to interpret scientific phenomena observed every day. So it is important not only to know the concepts, but also to build, to use and to analyse models, to understand a phenomenon and to transform it between different representations. This process actualizes itself when the people communicate, argue, ask questions etc. and let to acquire not only knowledge but, above all, competences. In order to achieve this result, we build situations where experiences and tools from formal and informal learning can be settled in new contexts. So, this environment could stimulate both the investigative attitude and fun inherent to scientific activities. From a methodological point of view, we borrow strategies from open inquiry based learning education adapted to the informal learning environment where our experiences take place. So, we put people in a position to tackle questions, issues and controversies from real world, with the aim to solve problems or create solutions in collaboration. Usually, we pose a problem or a case-study or we represent an experience and we ask to people, through an engagement, to design a solution. So people are involved in the construction of knowledge through active involvement. In contrast to the formal techniques of teaching and to formal learning processes, inuiry allows deep understanding in people in addition to the acquisition of knowledge and skills. Moreover, typically people has preconceptions about the world. In this sense, the cognitive process stimulated by inquiry tends to eliminate misconceptions present before the deep understanding of the phenomenon. So, the main goal of inquiry method is not only to transfer scientific knowledge, facts, definitions, and concepts, but rather stimulates people to enhance their ability of reasoning. Moreover this method makes people independent learners capable of identifying main questions and to find relevant answers by a gradually acquisition and expansion of a body of scientific knowledge and abilities. 3. Educational Experiences As we have just mentioned, a good starting point to introduce the theory is beginning from the laboratory that everyday life is or from a funny activity like a sport. We proposed three different items to introduce the topic both to a group of students and to the workshop participants. The laboratory for students is organized to last three hours, the workshop two. Laboratory Items

The first item was a Sinai table because a pool table is an object of common use among young (and not only) people that gives the opportunity to convey scientific concepts through everyday life experiences shared most likely by all the students. With the introduction of a circular element placed in the middle of the table, under certain conditions a little change of the ball starting point can cause chaotic behaviour and so it’s impossible to predict its path. Our intention was to involve students in the design of this object. So we asked to the students of Vincenzo Ragusa e Otama Kiyorama High School to build the pool table.

They built a table lighter and smaller than an ordinary one but they respected the ratio of a standard Italian pool table (ratio between sides 1:2). The surface of the table was composed by rigid solid wood covered by game table cloth and cushions were of vulcanized rubber without cloth. We spread talcum on the cushions


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so that the balls rebounded five or six times before stopping. The students built a wood disc to place in the middle of the table to introduce chaotic elements. We know the table isn’t perfect because there is more friction than a real pool table and the Fermat’s Principle isn’t respected perfectly. However for us it was more important the engage of students than to have a perfect object.

A second experience was based on the use of a double pendulum because it allows to locate within the context of deterministic classical physics a system that appropriately modified manifests chaotic behaviour. Such a system is particularly useful to understand what is the role played by the initial conditions in the dynamics of a physical system and to break the idea that chaos is present only in many-body systems. In this case we asked a craftsman to build it. He used ordinary material like wood for the support of the pendulum and polycarbonate plastic for the arms. We used ball bearings to reduce friction to an absolute minimum between the arms. We use wooden table and bar to build the support for the pendulum. The last item was an equipment for experiences on fluid

convection easily available in a school laboratory. Such an experience allows to present the context in which the theory of chaos is traditionally introduced looking at thermodynamics and meteorology (E.N. Lorenz, butterfly effect etc.)

We used a big plastic box for water and two smaller ones for ice and hot water. We placed the boxes as shown in the picture and used two eyedroppers to drop colours in the water in the big box.

Experiences vs students We proposed the experiences to a group of fifteen students of the last year of an Italian high school. Starting with the idea that, in informal contexts, theory should emerge from laboratory activities, we used simple questions to present the objects without explaining how they worked to register students’ reaction. We will not present here detailed statistical analysis of the responses, subject of a forthcoming publication, but here we want to report our activities and to point out the most interesting answers. We introduced chaos laboratory starting from the question “What’s chaos?”. An interesting answer was “It is something you cannot explain with a first grade equation”, that showed how it is normal for a student linking linearity to a first grade equation. The first example we introduced strengthened this idea because we chose a spring with a mass. In fact, this is a linear system and a little difference in the initial condition produces a small shift from the final position which would be obtained in the absence of perturbation. The second example was about the meteorology, in which systems depend on many variables. For students it is clearly a chaotic system and they gave us as an example many bouncing balls on the floor. We explained it is perfectly possible to have a system with many interacting objects which does not show a chaotic behaviour (for example, a rigid body represented as the continuous version of a large number of atoms strictly connected among them). Starting from the idea that multi-variables systems could manifest chaos, we chose to introduce the double pendulum. They assembled it (the arms, the bolts and the nuts were on the table) fixing the long arm in the middle to have a symmetric and supposed stable situation. After some attempts, they realized that in order to have a evident chaotic behaviour, the best solution was to fix the arm using the first hole like in the picture.


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They tried to predict the motion according to what they observed but after some oscillations they noted that it was impossible. We teased them with a question: “Is there a connection between order and chaos?”. Their answer was “NO!” because they linked order with predictable events. In order to contest this idea, we stimulated the students to use the equipment for convection. At first they kept thinking that it is mess to create chaotic motion. After a careful observation of the pigment motion in the water they learnt that without an organization of the water molecules the chaotic motion wouldn’t exist.

We concluded our activity with the Sinai table to realize why it is impossible to predict the evolution of a chaotic motion. We drew two paths on the table and we invited the students to play first without the disc on the middle and then with it. In the second case, they did many attempts to follow the paths unsuccessfully. In fact, they observed that, in the presence the disc in the middle, if the ball

hits the disc first, a very small change in the initial conditions “snowballed” and after just two rebounds the ball was clearly off the path. If the ball hits the table sides without to hit the disc, they didn’t observe the effect (the balls can rebound only five or six times on our table). At the end of the experiences, we have delivered to the students the following logbook 1. What have I studied? 2. Which materials have I used? 3. How did I do? (I'll have to be very detailed) 4. What did it happen? What have I got? 5. Why did it happen? Did I get the expected results? 6. Have I conducted the experience alone or in a group? What did I do? What did the others do? 7. Which part or moment did I like most? 8. What would I change? 9. Do I think that there is a connection with the life I live every day? In what? in order to understand if our goals had been achieved. We triggered a brainstorming in order to capture possible evolution in the students understanding of the phenomena linked to the enveloped activities. For example, some students had found a possible source of chaos in the motion of the solar system planets when the interaction between all the planets and not only with the Sun is considered. Other students recognized the analogy between some images present in a slide we showed them during our presentation and a Lorenz attractor they saw during a visit to a science center. Also, other students linked the chaos (with particular attention to the dependence from initial time conditions) to the problem of the cars traffic in the morning when they go to school. The reaction of students supported us on the efficacy of the path we have chosen because they linked the chaos theory with the concepts of non-linearity and linearity in physical systems and found other trackable examples in everyday life. The experience with this class stimulated us to organize a well structured laboratory on physical systems manifesting non-linear and linear behaviour depending on initial conditions. In our opinion, the basic concepts communicated through these experiences with students are observation, statistical uncertainties description and schematisation (models, prediction, interpretation), laws and theories from a physical point of view; from a mathematical point of view, instead, they are numbers, relations, functions (representations) and data (analysis and forecasting). Finally, a topic like chaos has the advantage to have many connections with biology, chemistry and philosophy and to promote the development of many interdisciplinary activities. Experiences vs workshop participants We presented our idea on introducing nonlinear system starting from linear system at GIREP-MPTL 2014 International Conference. We chose the workshop modality to involve the participants in interactive and critic way. In the first part of the workshop we reported what are the didactic programs of Italian school and why we chose the items proposed. We continued presenting the activity done with students and exposing our idea on extending the educational experiences to laboratories spread in more time. In the second part, we involved the participants in the activity through the items. We recieved some suggestions in order to improve


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and to enrich the laboratory. For example, in the perspective to extend the laboratory timetable including both the building of the items and the activities related to them, the possible challenges suggested by the workshop participants and expressed under form of engagement for students, are:

• Pull table: “How to reduce the friction of the ball with the table? And with the banks? How to hold the central body?”

• Double pendulum: “How to reduce the friction between the moving parts of the pendulum? How to highlight trajectories?”

• Convection: “How the convective motion of the fluid can be observed as detailed as possible?“ • Other possible engagements are: • Pool table: “Try to throw a ball more than once in the same way” • Double pendulum: “Try to let go the pendulum several times making it trace the same trajectory” • Convection: “What effect temperature can have on convective motions? Do they depend heavily on

temperature?” Through this process, the students are involved in the resolution of problems rising from the building of items making them responsible for their learning. We think that this is resonant with the possibility to promote their competences and their significant learning. 4. Conclusions In conclusion, in this paper we have shown three physical experiences whose dynamics, under certain conditions, are nonlinear. The experiments presented here are suitable to be used in a context of informal learning We have engaged students in these experiences successfully and report it to workshop participants who suggested us how to improve our activities with interesting challenges. Our idea is to include these items in a laboratory spread in more time where we would start from linear systems as for example oscillations of simple pendulum or coupled pendulums or fluid dynamics under laminar regime. References Dolin, J., Evans, R., Quistgaard, N. (2009) “Teaching and Learning Scientific Literacy and Citizenship in Partnership with Schools and Science Museums” Department of Science Education, University of Copenhagen, in http://www.museoscienza.org/setac/resources.asp Work Package 3 Report: Guide for developing ESTABLISH, Teaching and Learning Units Shinbrot T., Grebogi C., Wisdom J., Yorke J. A., Chaos in a double pendulum, American Journal of Physics 60, 491 (1992) Ottimo J. The mixing of fluids, Scientific American, 260, 56-67 (1989) Crutchfield J. P., Packard N. H., Farmer, J. D., Shaw, R. S. Chaos, Scientific American 255, 46-57 (1986) Affiliation and address information Valeria Greco Associazione PALERMOSCIENZA, c.o. Consorzio ARCA Viale delle Scienze, ed.16 90128 Palermo, PA, Italy e-mail: [email protected] Salvatore Spagnolo Associazione PALERMOSCIENZA, c.o. Consorzio ARCA Viale delle Scienze, ed.16 90128 Palermo, PA, Italy e-mail: [email protected]


Multimedia Software “Archimedes and his Work: a Deepening Path in the Arkimedeion Museum of Siracusa.

Silvia Merlino1, Marco Bianucci1, Carlo Mantovani1, Roberto Fieschi2 1 ISMAR-CNR, Forte Santa Teresa, Pozzuolo di Lerici, La Spezia, Italy 2 Department of Physics, University of Parma, Viale delle Scienze 7/A, 43020 Parma, Italy Abstract!The distinctive feature of the Arkimedeion, the modern interactive Museum located in Siracusa, Sicily (Italy) - which includes an exhibition of twenty-four interactive exhibits as well as a planetarium, is the "hands-on" approach, characteristic of modern international science centres, strictly based on interactivity between visitors and the proposed exhibits, for an active participation and a full intellectual involvement "minds on." (Bianucci et al. 2011a). Moreover, multimedia support material is especially designed to allow visitors to get a self explaining tour of the museum: general information about exhibits, historical news, mathematical demonstrations, and sources review are supplied by means of video and audiovisual interactive material, very rich in pictures, diagrams and animations, structured in different deepening levels. The multimedia software also provides visual examples, interactive models and virtual objects manipulation in a simple and very powerful way. Such material has been designed and implemented by a CNR team of physicists with expertise in science communication, in collaboration with some of the major Archimedes’ experts around the word, especially from like Baltimora University, USA, and Pisa University, Italy. A special attention is given to interactive educational games. Keywords Scientific museum, science communication, teaching/learning strategies, educational games

1. Introduction Mathematics and Physics are often abstract disciplines; thus we face some difficulties both in learning and teaching them. For that it turns really helpful to take advantage of the modern multimedia technologies (Fieschi et al. 2003, Bussei et al. 2007), including hardware exhibits, that are really effective to explain concepts through visual examples, models, real objects manipulation. Moreover new multimedia tools and modern exhibits allow us to try unexploited new teaching strategies. The “Arkimedeion” is an Interactive Science and Technology Museum dedicated to the many-sided genius Archimedes (287 B.C. – 212 B.C.) and to his work, and it is located in Siracusa, Italy (Bianucci et al. 2011b). A series of interactive exhibits, movies and multimedia software on touch screen kiosks, guide visitors into the middle of Archimedes’ historical period and into the heart of his scientific work, making them discover and appreciate his great contribution to Science, and in particular to his work on mathematics and physics. The principle that inspired the authors, beyond rigorousness and accuracy, was the need for a good educational and accessible approach. The museum contents and in particular the multimedia tools are structured in different levels of complexity, allowing multiple levels of approach by visitors, depending on their background. We attempted to expose part of the Archimedes’ original documents in an easy-to-understand way with the help of modern tools in order to facilitate the understanding of complex mathematical demonstrations. For this purpose, a special role is devoted to the mathematical and physical interactive games, considered as educational spaces of play-learning (Merlino at al. 2003), and based on the many scientific discoveries and demonstrations of Archimedes (Arkimedeion’s interactive laboratory and the Stomakion tool). Archimedes was, in fact, also one of the earliest known brain-teaser enthusiasts, among which we mention: the Archimedes' cattle problem (or the problema bovinum); the investigation about the number of grains of sand that the universe could contain, opportunity to introduce a system of counting based on the myriad that anticipated our numeral positional system and the exponential notation; the Stomachion, a dissection puzzle made of 14 pieces originally forming a square, presented in the Museum both as exhibit and educational videogame.


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We are aware that the playful moments stimulate the ability to abstract (Bondioli 2002, Gee 2007), and provides an opportunity of de-contextualization compared to schoolwork, (Green and MacNeese 2007, Green and MacNeese 2011), activating then personal learning processes (Michelini et.al 2008); in this way the game can become an important opportunity for learning (Bateson 2002, Gee 2003) 2. Scientific path, exhibits and structure of multimedia After an introductory presentation, focused on the discovery of the Palimpsest and on the importance of this event (including interviews with famous historians and researchers), visitors follow a scientific path organized in four macro-areas: Machines for Society, Equilibrium, Mathematics and Planetarium. Each area is equipped with several touch-screen kiosks showing the multimedia contents related to this area. Multimedia are structured with different levels of detail and are based on animation of graphical and textual elements helping to develop and illustrate concepts often abstract and not very intuitive. Each macro-area is organized in few themes. In fig.1 and 2 we only show some examples, as the theme Give me the place to stand, in the equilibrium macro-area. !

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Figure 1. Using a large lever the visitor can raise, with a little effort, a person sitting in the building that reproduces the shape of the Earth; in this way we realize the famous Archimedes’ quote: “Give me the place to stand and I shall move the Earth”

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Figure 2. A sequence of two screenshots from the theme “Give me the place to stand”: it illustrates the visual approach to mathematical demonstrations through animations related to the exhibit in fig.1

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Figure 3. Another theme is the “geometry of position: the plane curves and the solids of revolution”. One of the exhibits is composed by a big cone of Plexiglas and by a structure mounted on the wall

(see Fig. 3). The structure holds up four steerable laser projectors that generate plans of light. Every time one plane intersects the cone it produces a conic section. It is possible to show four different conic sections at the same time: ellipse, circle, parabola and hyperbola. Here the draft (on the left)

and the exhibit (on the right).!!

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Figure 4. Screenshots of the animation used to visualize conic sections in an amusing and intuitive way. The multimedia support of the theme “geometry of position: the plane curves and the solids of revolution” deepens the concept of conic section and its importance in the history of Greek mathematics. It also discusses the various methods used to obtain the four plane figures (ellipse, circle, parabola and hyperbole) and the connections with the physical phenomena, such as orbits of planets and asteroids.


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!3. The Arkimedeion Virtual Laboratory. The Archimedes’ Lab is an educational computer game intended for people of all ages and backgrounds. It’s inspired by other famous games like the Incredible Machine computer game series (Jeff Tunnell - PushButton Labs), and many other 2D platform-like computer games where the player must arrange a given collection of objects in a needlessly complex fashion so as to perform some simple task. In our case the task is to allow a ball moving in a vertical board to reach a given target. The ball is affected by gravity, there are many obstacles disseminated on the board, and there are a lot of tools that can be used to avoid/destroy the obstacles and to route the ball along the right path.! Archimedes’ Lab is designed, like most of the computer games, with an increasing level of difficulty. Moreover, being an educational game, it is also calibrated to allow users to gradually improve their knowledge, in this case about the physical principles and results related to the Archimedes work. In fact, the interacting objects on the game’s stage are strictly linked with the Archimedes opera, as they are levers, parabolic mirrors, solids of revolution, catapults, etc., and they behave following physical laws, although in a simplified way because represented in a 2D cartoon-style world. It means, for instance, that the player can balance a lever attaching different solids of revolution to the edge of the lever, however this must be done according to the proportions between such solids’ volume, as found by Archimedes. In general all the objects must be combined and placed in the correct position in the stage so that, when the player starts the simulation, they can allow the ball to reach the target. In the most advanced levels additional elements are added, e.g. the levers can be located underwater, involving in such way also the Archimedes’ principle about buoyancy. The design of the Lab was mainly focused on developing a game easy to use, entertaining, and at the same time able to force the player to manipulate and apply concepts related to the work of Archimedes. Application of the physical concepts described in the game and in the museum, and immediate feedback in the result of the game, make players to understand connections of the theory with the real world. By learning from their mistakes, players improve their ability to solve game situations. Moreover, in each level the path leading the ball to the goal is not unique, so that the tools to use, and the actions to be performed, are not bounded: the player moves in a playing environment with many degrees of freedom. This fact gives the chance to solve the same game level using different strategies, more or less efficient, contributing to a personalized learning of concepts. The Virtual Lab can also work as a game levels editor, promoting the user from a simple player to a game’s level designer, i.e. giving the possibility to realize a customized versions of the game. This editing mode not only stimulates and reinforces the learning of concepts related to the Archimedes’ work, but also encourage personal manipulation of concepts, fantasy, improvement on game strategy and consequently on problem solving ability. !


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Figure 5. Screenshots of the virtual Lab. This Lab is designed as a modern app, with a good playability and with an original cartoon-style “drag and drop” GUI (graphical user interface). On the left we can see the menu where it is possible to enter the “Level Editor” mode. 4. Teaching and learning use of Archimedes’ lab and related pedagogical Archimedes’ Lab has been designed in order to improve the science museum visiting experience, but it also represents an useful educational tool for teaching and learning physics:

- in a museum context, it can be used both as a recreational game without educational purposes, and for consolidating or assessing the learning of concepts related to the Archimedes’ work. Obviously, in the latter case it is desirable to browse through the entire Archimedes’ multimedia before trying this game.

- as teaching/learning tool, it can be used in the classroom to introduce or deepen knowledge in the field of physics, such as the balance of forces, the laws of motion and gravity, buoyancy, and also the principles of geometrical optics.

The question of how knowledge acquired during the game can be transferred into the real world reveals the Achilles’ heel of digital gaming. We think that in our case the main limitation is the simplification of the simulation: needless to say, physical laws used in the game are approximation of the real ones (for example, friction is not included in the simulation). !


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Figure 6. Screenshots of the virtual Lab. Using in a proper way some mirrors to focus sound waves (left) or light waves (right), and catapults, the player should find the way to build a path for the ball to reach the goal.!

Simplifications and schematic representations of reality could also lead the player to miss the link between the game solving strategy and the concepts about Archimedes’ work we would like him to learn through the game. In other words, a student could become very able in solving the game levels, but then he could still find difficulties in solving simple problems of statics in the classroom. !

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Figure 7.Other screenshots of the virtual Lab where the player can place, move and set mirrors and catapults to build the right path for the ball.!


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The pedagogical question here is to determine in which real context players can apply what they have learnt and which aspects can be transferred directly from the game. A process of de-contextualization is required, in order to create correlation between learning accomplishments in play and those in the real-life context. Once players/students have been made aware of the relevant content and their learning accomplishments, a link between the virtual and the real domain must be created. Here is where the importance of the teacher’s role is, when games are used – something that is underestimated to this day –. The learners require constructive support to identify and consider, in the settings of the game, any aspect relevant to their learning process. External impetus is therefore needed to direct attention to the potential of the games and to what has been learnt in them (Thai et al. 2009). This is a meta perspective that teachers can and should adopt in order to foster the educational potential of games. If teachers are able to create a link between the virtual and the real context, their action may make a transfer possible. This educational role demands that teachers be interested and willing to engage with educational games (Klopfer et al. 2009). Being aware of this, using games like the virtual Lab as didactic tools, can be well worthwhile, becoming a new learning challenge for teachers. !

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Figure 8. Here the player should use some knowledge regarding the laws of the lever and the ratio between the volumes of different solids of revolution.!!5. Stomachion game: the exhibit and the computer game Every game begins with a challenge that motivates the players to put their knowledge and skills to the test. The challenge of the game allows players to fail in an enjoyable way while encouraging them to learn and improve. The players find out whether their abilities are sufficient to meet the requirements. Their own progress in the game gives them the reassurance of having achieved and learnt something. In this sense, the game “Stomachion”, represent a mathematical challenge. Stomachion was an ancient game widespread in Greece and Rome (Napolitani 2001), and basically consists on a 14-piece dissection puzzle where the pieces are polygons that can be reassembled to form different


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shapes (geometrical shapes but also animals, trees, etc.). But the biggest challenge is to arrange them in different ways to form a square. The game is attributed to Archimedes, as one of its most complete descriptions was found in the Archimedes’ Palimpsest! 1 . A research published by Dr. Reviel Netz of Stanford University and his co-workers (Netz et al. 2004) argued that actually Archimedes was attempting to determine in how many ways the pieces could be assembled into the shape of a square. Therefore the puzzle could represent an early problem in combinatory, even if the ancient authors exclude the use of combinatorial analysis in the Archimedes’ treatise (Napolitani 2001). An interesting point is that Archimedes was able to calculate the area of each polygon of the Stomachion.

The exhibit In the Arkimedeion Museum, Stomachion is proposed both as interactive computer game and as interactive exhibit; this last is a big 14-piece dissection puzzle made of wood. Visitors can manipulate pieces and place them on a table to form classical shapes. These represent the first and simple level of the game, and it is particularly useful for young students. In fact, here children can test their ability to solve puzzles, and understand some important geometrical properties of polygons. For mathematics enthusiasts and more expert in mathematics, it is possible to go a little more in deep, analyzing the case of the square and trying to form it with different arrangements 2. In any case, to help visitors not familiar with the game, a touch-screen monitor installed on the exhibit shows instructions and suggestions on request, as a “tutorial”.

Figure 9.The Stomachion exhibit. This wood game is especially studied to result appealing for children and young students. The first level approach is easy and, at the same time, instructive, and can be used to discover some important geometrical properties of polygons.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1 The foremost document containing the work of Archimedes is the Archimedes Palimpsest, discovered in 1906 in Constantinople (Istanbul) by the Danish professor Johan LudvigHeiberg . The palimpsest is now stored at the Walters Art Museum in Baltimore, Maryland, where it has been subjected to a range of modern tests including the use of ultraviolet and x-ray light to read the overwritten. 2 Actually, the most interesting aspect of the Stomachion – the real “mathematical challenge” - is to determine in how many ways the pieces can be

assembled to form a square. This brainteaser was solved first on 2003 by Bill Cutler. He demonstrated, with the aid of a computer, that there are 536 possible independent arrangements. It means that solutions obtained by rotation and/or reflection of another given solution are not considered in this number.


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Figure 10. The “tutorial” assists visitors in the use of the wood exhibit “Stomachion”. On the right, one of the different shapes that can be realized using the all pieces. On the left, one of the 536 dispositions of pieces to form a square.

The computer game In Stomachion brain-teaser there are 536 possible independent ways to arrange polygons to form a square, and it could be interesting to see all of them, or better to give the possibility to find them interactively. For this purpose an interactive computer game has been developed. It can identify and enumerate each solution of the puzzle, and, when a solution is found, a counter shows the number of the remaining arrangements. Another important feature of the game is the capability to check partial arrangements and to show which polygon is in the right place and which is not and, on request, to provide suggestions on the following piece and its correct position. A scoring system is under development. We consider it a very important part of the game, as it pushes users to avoid asking for help and suggestions, therefore to think better and faster, and finally to improve the understanding of many mathematical and geometrical issues. The game is developed with Adobe Flash technology. This fact ensures compatibility with many platforms and devices and allows its distribution online to entertain and engage gamers all over the world, increasing the Archimedes’ worldwide reputation. Archimedes is, undoubtedly, one of the greatest mathematical geniuses ever. It must be realized, however, that the distinction between the different categories of scientists, based on the current classification of scientific disciplines, is not applicable to ancient scientists like Archimedes. Thus, when we say that Archimedes was a great mathematician, this is because today we include in mathematics much of his work. But such precinct is actually too limiting as Archimedes applied his formal and logical deductive methodologies both to quite abstract mathematical issues and to problems we today consider belonging to the field of physics, such as the laws of the lever, the buoyancy, the study of the equilibrium of the bodies (statics). The countless contributions he gave to the development of what we now call the physical sciences are based on mathematical considerations, often geometric (algebra had not been formalized yet). The original opera of Archimedes is hard to understand for modern readers because of formalism, language, key “primitive” assumptions and the logical construction used to expose its results. They are objectively a tremendous obstacle for reading and understanding the work of this great genius. That's why we believe that our work of "adaptation", using a modern formalism and a multimedia interactive presentation, can be really effective in introducing the user (museum visitor or student) to Archimedes and in disseminating the results of the work of this great scientist, unfortunately well known most of the time for the famous Archimedes' principle of buoyancy, and not for the many other contributions he gave to the modern science.


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Figure 11.Screenshots from the Stomachion computer game.

Acknowledgment Infmedia Company, the Italian software house that developed multimedia software in cooperation with the Informando team of CNR; Luca Busi Video recording studio “Zero-frame” for the introductory video. Weisstein, Eric W. "Stomachion." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Stomachion.html

References Bateson G. (2002). Mind and Nature. A Necessary Unity, Hampton Press and Institute for Intercultural Studies, Cresskill - NJ. Bianucci, M., Fieschi, R., Mantovani, C., and Merlino, S. (2011a) “Promoting and teaching “hard” science in an amusing way: the “Domus Archimedea” approach to Greek mathematics”, (ICBL 2011), Antigua Guatemala, 2-4 Novembre 2011. Published by Kassel University Press (2011). ISBN of Collection: 978-3-89958-556-8 Bianucci M., Fieschi R. and Merlino S (2011b). The Museum of Archimedes, The key to the thinking of Archimedes, Ed Itinera Thesauron, pp 6. Bondioli A. (2002). Il tempo nella quotidianità infantile, Edizioni Junior, Bergamo Bussei P., Bianucci M., Fieschi R., Gambarelli L., Mantovani C., Merlino S. (2007). "WESPA, a multilingual European Project for teaching Energy and Semiconductors concepts using interactive approaches”, Journal of Materials Educations, 29 (3-4), 233. Cutler,B. (2003). The Loculus of Archimedes, solved, Ed Pegg Jr. Fieschi R., Bianucci M. and Merlino S., (2003). Teaching and popularising physics by multimedia instruments: INFM experiences AND ACTIONS. Proceeding of GIREP (Gruppo Internazionale di Ricerca sull’Insegnamento della Fisica): “Quality development in teacher education and training”, Udine, 1-6 Settembre 2003; Gee J.P. (2003). What video games have to teach us about learning and literacy. New Yourk: Palgrave.


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Gee J.P. (2007 ). Video games, learning and “content”. Harward Interactive Media Review, 1(1), 24-29 Green, M. E and McNeese, M.N. (2007). Using edutainment software to enhance online learning, International Journal on E-Learning, 6(1), 5-16 Green, M.E. and McNeese M.N (2011). Using digital games and virtual environmentes to ehnance learning. pp 79-105. In: Learning to play. Exploring the Future of Education with Video games, Ed. Myint Swe Khine Collana “New literacies and digital epistemologies, V 53), ISSN 1523-9543, Peter Lang Publishing, Inc., New York. 2011 Klopfer, E., Osterweil, S., Groff, J., and Haas, J. (2009). The instructional power of digital games social networking: simulation and how teachers can leverage them. , from The Educatioanl Arcade, http://www.educationalarcade.org/., Merlino S., Roberto Fieschi R., Bianucci M. and Davies B. “EPS becomes partner in exciting European education project”; Europhysics New 33/2 2002, March/April. Michelini M., Santi L.., Stefanel A., Mossenta A., Viola R.., Colombo M. (2008). Educazione informale e giochi nelle ricerche sull’apprendimeno. http://www.fisica.uniud.it/URDF/articoli/ftp/2008/2008-32.pdf Morelli G. (2009). Lo stomachion di Archimede nelle testimonianze antiche, Bollettino di storia delle scienze matematiche 14 (2). Napolitani P.D., (2001)."Archimede", Collana “I grandi della scienza”, Le Scienze, Italia, Netz F., Acerbi F. and Wilson N., (2004). Towards a Reconstruction of Archimedes’ Stomachion, Sciamus, 5, pp.67-99. Thai, A., Lowenstein, D., Ching, D., Rejeski, D. (2009). Game changer: Investing in digital play to advance childre’s learning and health. New Youk:The Joan Ganza Cooney Center at Sersame Workshop !! Affiliation and address information Silvia Merlino ISMAR-CNR, U.O.S. La Spezia, Forte Santa Teresa, Pozzuolo di Lerici, 19038 La Spezia.SP, Italy e-mail: [email protected]


Physics Competitions for Learners of Primary Schools in Slovenia

Barbara Rovšek1, Robert Repnik2 1 Faculty of Education, University of Ljubljana, Slovenia, and DMFA Slovenije. 2 Faculty of Natural Sciences and Mathematics,University of Maribor, Slovenia.

Abstract We are going to present our experiences with physics competitions for young learners in Slovene primary schools. We will describe our 3-level organizational format of competitions. At the last, national level, competitors have to solve theoretical and experimental problems. We will give reasons for having and keeping the experimental part at the last level; we will show examples of results and comment achievements of learners at experimental vs. theoretical part and show also frequency of physics topics, having a role in experimental problems in competition. An example of experimental problem at competition will be given. Keywords Physics competitions, experimental problems, IBSL

1. Brief history and format of physics competitions Physics became a primary school subject in Slovenia even before the major educational reform in 1958, when obligatory 8-years (in 1996 changed to obligatory 9-years) primary school was introduced. Learners of ages 13 and 14 are taught physics in the last two grades (8th and 9th) of primary school since then. The same holds for chemistry and biology, as the other two science discipline subjects. More than 95% of primary schools in Slovenia are public schools and are obliged to follow the same curriculum. In 1981 the first national competition in physics for learners of primary schools took place and in the school year 2013/2014 Slovene Association of Mathematicians, Physicists and Astronomers (DMFA Slovenije, in ref.), with substantial help from Universities of Ljubljana and Maribor and also teachers from all participating primary schools organized 34. competition already. Only mathematics competitions have longer tradition among all competitions in school subjects in Slovenia. Since its beginning the format of the competition gradually evolved and in the present it is a three-level competition, starting with the first, school level, followed by the second, regional, and completed by the last, national level. In the last decade approximately stable one quarter of generation participates in the physics competition, which amounts to approximately 9000 learners participating altogether each year. Competitors literally come from almost all Slovene primary schools. Competition being completely voluntary for learners we consider this proportion of learners showing enough interest for physics to put some additional efforts and invest some spare time into preparations, satisfactory. We understand it is a result of united efforts not only of the learners themselves, but also of their teachers, acting as their mentors and also as more or less voluntary organizers of school and regional stages of the competition, and finally, members of national competition committee, who are the authors of physics problems on all three levels of the competition. The number of competitors at the 2nd, regional stage is around 1700, which means that every fifth participant of the school level competition enters the next level. We have 300 competitors at the last, national level: from 30 competitors at the school level one of them enters the last level. Questions and problems for all levels of competition are developed by the same team; national competition committee, more or less voluntary group of 5-7 enthusiastic members. Solutions and marking schemes are produced by the same team. The school level competition is organized in all primary schools at the same time by physics teachers, teaching at those schools. According to the given marking scheme the teachers themselves evaluate the papers of their pupils and also submit their results to the internet server. In few weeks the next, regional level of competition is organized (in the last few years in 17 regions) in corresponding number of voluntary primary schools. Again teachers gather to mark the papers of competitors and submit their results. The last level of competition is organized at Faculty of Education in Ljubljana (for central Slovenia), at Faculty of Natural Sciences and Mathematics in Maribor (for eastern parts), and at one primary school (for western parts).


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2. Questions and problems at physics competitions Problems, which are to be solved at the first two levels of competition, are theoretical. There are some multiple choice questions (around 5) and few open problems (2 or 3). In accordance with the nature of physics, being experimental science discipline, the last stage of the competition consists of two parts: theoretical and experimental. Each part lasts for 90 minutes (changed to 80 minutes in the last year). Physics competitions are, expressing appreciation for experimental part, rather unique among other existing science (and mathematics) competitions. Before the last school year competitors had to solve two shorter and simpler experimental problems and from the last school year they were changed for one, more complex experiment. Due to this organizational change also the rationale of experimental problems changed a little, taking into account the new timing and to ensure the optimal (normal) distribution of performance in solving the problems. We think it is important to keep the experimental part of the competition for several reasons. One was mentioned above; physics is also experimental discipline. It is good to have a balance between theory and experiment also in competition, to demonstrate they are both important. Experiments can also have motivational potential for many pupils, who like to experiment. At last, with theory and experiment each competitor has a possibility to express his or her stronger side; some are more theoreticians, others are better skilled experimentalists. We have a balance again. The evidence is shown in Table 1, where as an example, a distribution of 299 competitors at the national level of competition in 2013/2014 according to their results in theoretical vs. experimental part is presented. We have divided competitors twice into 5 success categories: into 5 success categories from Th-1 to Th-5 for results from theoretical problems and 5 success categories from Ex-1 to Ex-5 for results of experimental problem. In every category we have approximately the same number of competitors (1/5 of all, who have achieved approximately the same result and are therefore in the same category). In groups Th-1 (Ex-1) there are those with the lowest results in theoretical (experimental) part and in groups Th-5 (Ex-5) there are those with the best results in theoretical (experimental) part. Among all 299 participant 109 were awarded. How the awarded competitors are distributed in success categories is presented in Table 1 with numbers in parenthesis.

Table 1. Cross table is showing distribution of all 299 competitors at the national level into different theoretical (Th) and experimental (Ex) success categories, for the school year 2013/2014.

From Table 1 we see that there are pupils who posses universal abilities and skills and do well at theoretical and experimental problems. But there are also some, who performed experiments very well and were rather weak at theoretical part, or just the opposite, but are still good enough on the average and therefore earn the award. For example, those 5 in the cross-section of categories Th-2 and Ex-5 or those 3 + 2 in cross-section of Th-5 and Ex-1 and Ex-2. There are also some virtual anomalies present in the table, which originate from the cross-sections of categories at their edges. 3. Topics at experimental problems Syllabus for physics competitions to a large extent corresponds to the physics core curriculum, obligatory for all. Even if the curriculum does not prescribe how the topics should be taught in sequence, there are topics, which are traditionally taught during the lessons in the beginning of the school year, and other topics


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naturally follow. National level of competition takes place in the spring, near the end (but not at the end) of the school year. By that time all but the last topics are taught. Traditionally, the last content in the last grade of primary school is magnetism. Therefore we never have had an experimental problem in magnetism. Table 2 shows which topics and how often they appeared in experimental problems at national level of competition in the last 22 years. There were 86 experimental problems altogether. In the last column of the table there are some supports or obstacles mentioned, which influence the frequency of using certain topic at experimental problem.

Table 2. Topics, which appear in experimental problems at national level of physics competition in the last 22 years, the frequency N of their appearing and possible reasons, influencing the frequency.

Topic N Pros and contras

Density, hydrostatic pressure, buoyancy

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• Important topics (with plenty of time allocated for them in curriculum),

• many variations possible (what and how to measure),

• simple, not expensive equipment, • can be performed in a short time.

Electric circuits 22

• Important topics, • many variations possible, • can be performed in a short time.

Simple measurements, kinematics

7 • Spatially demanding, • difficult to perform sitting behind a desk.

Light (geometrical optics) 6 • Darkness in the classroom/lab,

• disturbing light sources of others. Forces (also Hook’s law)

10

• Quite popular, but have exhausted many variations.

Newton’s 2nd law of motion 5 • Spatially demanding,

• difficult to perform sitting behind a desk.

Work and energy 7 • Spatially demanding, • difficult to perform sitting behind a desk.

Heat and internal energy 2 (g) Difficult to arrange equipment,

(h) time consuming. Some topics are evergreens; they appeared at competitions literally every year. On the other hand, there are few topics coming rarely to the schedule, for variety of reasons some of which are mentioned in the last column of Table 2. The most obvious are time and space limitations. There is another important theme never used in experimental problem in competition, but supported by curriculum: astronomy. We have approximately 300 competitors in the experimental part; we did not think of appropriate astronomical experimental problem yet which could be solved by so many learners at the same time with spatial, time and other organizational limitations put upon us. As was already mentioned, in the last run of competition we have reformed the format of competition; two shorter experimental problems were substituted by one longer problem. There are few reasons for introducing one extensive experiment in 80 minutes instead of two more simple experiments in 2-times 45 minutes. We are able to introduce more complex experimental problem, which would be impossible to perform in 45 minutes. Partially new topic can be introduced with some explanation in the beginning. Also, some tasks can be easier; on lower taxonomy level, and there is still time for more advanced tasks at the end. At last but not least, there is enough time to repeat some part of experiment, if needed. We think of the experimental problem given at competition as an example of guided IBSL problem. Learners need to carefully read the instructions, possess basic skills to perform simple measurements, be familiar with presentations of results of measurements, and be able to analyze, synthesize and use their findings in new examples. In each experimental problem there can be parts where reasoning goes from general to specific or/and from specific to general. We somehow managed to include tasks at different taxonomy levels


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(Anderson and Krathwohl) already in the short 45-minutes experimental problems, as shown with an example in Appendix, and the aim is even more easily achieved with 80-minutes experimental problems. We conclude this short presentation of our practice and experiences with an example of results, showing how successful competitors have been at performing and solving the 45-minutes experimental problems in national level of competition in the school year 2010/2011. There were four different experiments given, two to 8th graders (E1-8 and E2-8; one of them is given in Appendix) and two to 9th graders (E1-9 and E2-9). Total number of points for each problem was 10. A distribution of competitors according to the total number of points they have earned at particular experimental problem is shown in Figure 1 and averages of their points in Table 3.

Figure 1. Distribution of competitors (133 in 8th grade and 151 in 9th grade) according to the total number of points (out of maximum 10) they have earned at each experimental problem (E1 and E2) at competition in the school year 2010/2011.

Table 3. Average points obtained at experimental problems in competition in the school year 2010/2011.

Experimental problem Average points

E1 – 8 4.96 ± 2.14 E2 – 8 4.95 ± 2.28 E1 – 9 6.60 ± 2.02 E2 – 9 6.60 ± 1.97

One can grasp immediately that 9th graders were more successful at performing their experiments, due mostly to not completely balanced difficulties of problems. Obtaining such distributions of points with appropriate resolution at the high end also at theoretical problems we were completely able to identify the winners, with acceptable – very small – measurement error. We can be pretty much certain that the prizes went into the right hands. 4. Conclusions We have presented the contemporary format of physics competitions for learners of primary schools in Slovenia. In spite of long tradition we never consider the format as final; on the contrary, we moderately experiment with the format itself and search for possible improvements or adaptations to new circumstances (for example, changing curriculum). However we consider some attributes of competition as firm and constant; among these the most important are the 3-level system of competition and inclusion of experimental part in the last level of competition. We have arguments to stay steady about these issues.

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

35

40

E1 - 8E2 - 8E1 - 9E2 - 9

Total number of points at experimental problems

Num

ber o

f com

petit

ors


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References Anderson, L. W. and Krathwohl, D. R., et al. (Eds.) (2001). A Taxonomy for Learning, Teaching, and Assessing: A Revision of Bloom’s Taxonomy of Educational Objectives. Allyn & Bacon. Boston, MA (Pearson Education Group). Association of Mathematicians, Physicists and astronomers of Slovenia, web page of primary school physics competitions committee, http://www.dmfa.si/fiz_OS/index.html Affiliation and address information Barbara Rovšek Faculty of Education, University of Ljubljana Kardeljeva ploščad 16 1000 Ljubljana, Slovenia e-mail: [email protected]


A Singing Wine Glass as an Instrument for Teaching Acoustics.

José Antonio Zárate Colín, Marisol, Rodríguez Arcos, Karina Ramos Musalem, Estela Margarita Puente Leos, Marcos Ley Koo Facultad de Ciencias, Universidad Nacional Autónoma de México.

Abstract In this paper, we present the work done by a group of three undergraduate students majoring in physics during their leisure time, in order to study the singing wine glass phenomenon. Here we describes the tests performed to identify variables, and their measurement, that where used in the experimental analysis. Although this is a simple experiment, considering it for teaching sound waves can be a very illustrative experience. Keywords Laboratory activities. Informal physics teaching and learning. Wine glasses singing. Sound waves.

1. Teaching method proposal Throughout its history, physics has been based on experimental research. Thus, experimental physics education is essential for a complete training of students majoring in physics, regardless of their theoretical or as experimental interest. Unfortunately, in México, most of the experimental physics courses at all educational levels, follow very strict traditional formats, where the students initiative is of no concern; just guided by the teacher, students construct their knowledge mechanically. Most of the times, courses have the tendency to make students follow a series of instructions, as a recipe, which include the list of material and equipment, the procedure, step by step, and even the results and conclusions that should be obtained, as the goal of the experiment; so that students lost interest, as well as the opportunity to develop capabilities and abilities, which are essential for their professional lives, provided by a good experimental training. This kind of method can limit the vision that students have on the experimental practice, leading students to think that experimentation plays a minor role in science and prefer to become a theoretical physicist. A rigid and restrictive experimental course can mean a barrier to develop skills such as: critical thinking, problem solution orientation, hypothesis formulation, etc. Having theses ideas in mind, we launch an effort, looking for alternative methods of experimental teaching in the Physics department of the Facultad de Ciencias of the Universidad Nacional Autónoma de México, and this proposal comes up. The method here proposed is not strictly based in one pedagogical theory but it has ideas of the constructivism learning theory which is based on observation and analysis Students construct their own understanding and knowledge of phenomenon, through experiencing and taking into account those experiences. If they encounter something new, they have to check against it with previous ideas and experiences, maybe changing what they believe, or maybe discarding the new information as irrelevant. In any case, they actively build their own knowledge, to do this, they must ask questions, explore and evaluate what they know. Always guided by the teacher, students construct their knowledge actively rather than just mechanically acquiring knowledge from the teacher or the textbook. We considered also some proposal of interactive methods of teaching (Etkina et al). The method can be summarized in the following steps:

• reproduction of a system, a phenomenon already known, or propose a project on which students want to focus their attention;

• observation and reflection set out hypothesis that explain what is observed in the phenomenon being studied;

• design one or more experiments to test the proposed hypothesis; • observation and reflection, once more, to confirm hypothesis; • recognition of important variables to the experiment and suggestion on how to quantify them;


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• analyze the results; and • draw up a model, which allows prediction of results under conditions different to those under which

the experiment has been conducted. • If necessary, to reconsider hypothesis and carry out complementary activities.

2. Experiments carried out and results This work is an example of the type of experiments designed and carried out by a group of three undergraduate students (José Antonio Zárate Colín, Marisol, Rodríguez Arcos and Karina Ramos Musalem), as students of physics of the Facultad de Ciencias of the Universidad Nacional Autónoma de México, The project arisen from a final project for an experimental course of third semester course (Collective Phenomena) of the Physics Curriculum of the Facultad de Ciencias of the Universidad Nacional Autónoma de México. Students had to choose the project and the only condition was to choose a phenomenon, which aroused their interest and comprised the topics (thermodynamics, fluid mechanics and waves) studied in the course during the semester. After a bibliography search, they read some papers and choose (Chen, Rossing), the singing wine glass phenomenon. For this project they carry out the experiment presented here as the two first stages (dependence of the resonance frequency on the wine glass shape and dependence of the resonance frequency on volume of liquid inside a wine glass). For these stages they worked during a month in the laboratory class time. After finishing the semester they were so interested on the subject that they asked the teachers to continue with experimentation during their leisure time, for almost one year. They work in a laboratory, which is not used for classes. Vibration and waves are classical topics in all physics curricula. One of the more usual lecture demonstration is to make a wine glass sing by rubbing its rim with a wet finger. Young people are very familiar with the phenomenon and many street musicians can even be found giving concerts with wineglasses containing water, but most of the students only observe and they never analyze and quantify. In this work, we present the results of the study of the phenomenon well known of a “Singing Wine Glass”; on which the group of students focused their attention. A wine glass can be simple and complex at the same time: to produce sound is easy but to understand the phenomenon and quantify it is different matter. As a topic for physics courses can be not only an amusing event but also a very useful instrument of learning and can become an excellent way towards experimentation. The student’s work was done during the time they fulfilled their course requirements for the B.Sc. degree, and it comprising different stages, in which some goals were reached via different experiments the students carried out, and follow the method proposed. Most of the time they worked alone but their teachers Marcos Ley Koo and Estela Margarita Puente Leos always supervised them. The study was divided into four main stages:

Dependence of the resonance frequency on the wine glass shape. Students wondered about the variables on which depends the frequency of sound produced while rubbing the rim of a wine glass. The first hypothesis was that the wine glass resonance frequency depends on shape and the volume of liquid inside of it. So they observed and they carried out hypotheses that explain what they observed. Firstly, in order to analyze the dependence on shape they use four different shape wine glasses (figure 1): a champagne glass, a Burgundis glass, a cocktail glass and a red wine glass.

Figure 1. Different shape wine glasses (from left to right): champagne glass, Burgundis glass, cocktail glass and red wine glass


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With the help of a laptop, a microphone, and the digital audio editing software Goldwave the sound produce while rubbing with a wet finger the rim of each shape of the wine glasses was recorded, analyzed and the natural vibration frequency for each shape obtained. The results obtained allowed to conclude that the frequency depends on the shape. Resonance frequency is greater when its shape is closer to that of a cylinder and smaller when is more spherical.

Dependence of the resonance frequency on volume of liquid inside a wine glass. The wine glasses were filled with different amounts of water to obtain a relation between the volume and the frequency for each type of wine glass when its rim is rubbed. Again with a microphone, a laptop, and the software Goldwave the natural vibration frequency was obtained. The results showed (figure 2) that frequency decreases as liquid filling volume increases, and this behavior is independent of glass shape. No matter which shape is, frequency depends no linearly on volume of liquid inside. As sound obtained while rubbing the rim of the glass, depend on the resonant cavity and when the amount of liquid changes the resonant cavity changes, frequency changes. This would be able to be confirmed using glasses of same form but of different size.

Figure 2. Dependence of frequency on volume of liquid inside a wine glass

Dependence of the resonance frequency on the kind of liquid inside. After finishing the experiment, students continued to design more experiments to test the formulated new hypothesis. So, they asked themselves what would happen if instead of water they used another liquid: Frequency changes?. On which characteristic of the liquid depends? Once more, they observed and though about, in order to confirm the hypothesis. Wine glasses were filled with different liquids; the characteristics studied were density, viscosity and compressibility. With this goal in mind, students carried out three experiments so they could study the dependence of the resonance frequency of the glass wine with respect to different properties of the liquid that it contains. Again, with a microphone and a laptop, the vibration frequency was measured for different kinds of liquids. To observe the effect of changing density, students worked with one wine glass filled with 200 ml of liquid. They use a mixture water-alcohol, and the proportion of water and alcohol was changed, from 10 ml to 200 ml of alcohol, the total volume was always 200 ml. With this process, liquid density was less than water. In a similar way, they work with a mixture of corn syrup and water, so liquid density increased. With Goldwave software, students while rubbed the rim of the wine glass, recorded during 30 s in order to obtain frequency. Frequency does not change meaningfully within the density range evaluated. So, students concluded that frequency does not depend on density, but this cannot affirm for densities ranges out of those of experiment.


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In order to observe if frequency depends on viscosity, students use liquids of different viscosities: corn syrup, auto motor oil (SAE 40), glycerin, ketchup, peanut butter, liquid chocolate, condensed milk, salad dressing, y shampoo. Frequency was measure for 200 ml of each liquid. Viscosity was obtained with a Brookfield DV-II viscometer. Data shows that frequency depends of viscosity, but, with the amount of data obtained, it was not possible to predict its behavior. To evaluate the hypothesis that frequency depends on isothermal compressibility, students did not measure the compressibility but they qualitative changed it. They use a wine glass of 450 ml of capacity and a mixture of water and gelatin. More gelatin less compressibility. With 300 ml of mixture inside, they waited to thicken and measure frequency while rubbing the rim of the wine glass. From data, frequency decreases with increased compressibility

Energy needed to break a wine glass. During the experiments, students questioned if the frequency value obtained with the software was the right one, due to the non-controlled way of making the wine glass to vibrate. They used their finger to rub the rim of the wine glass, so they suppose that if the frequency obtained was the fundamental frequency of the wine glass, then they could make it to vibrate until reach the resonance and the wine glass would break. The obtained a mean frequency of 650 Hz. They propose the following method: the fundamental frequency for different wine glasses without liquid inside was found knowing the resonance frequency of the wine glasses, with the help of a signal generator, a speaker and an amplifier, the wineglasses were excited at their resonance frequency until they were broken. Electric power supplied to the speaker, as well as the time needed to break the wine glass were measured in order to quantify the energy needed to rupture.

Figure 3. Experimental set up use to vibrate wine glass until reach the resonance and breakup. A high definition and a high speed cameras were used to record the standing waves formed in the rim of the wineglasses. The resulting photographs and videos were analyzed with a Tracker video analysis and modeling software and it was possible to obtain quantitative results.


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Figure 4. Time needed to break the wine glass vs electric power supplied to the speaker

From data obtained, after a log-log plot, it was possible to quantify the energy needed to break the wine glass, arriving to the equation:

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P = 10bt a (1)

where t is the Time needed to break the wine glass and P is the electric power supplied to the speaker, and,

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a = (−5.7 ± 0.6) and

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b = (7.6 ±1.6) (2)

From here we have, from the electric power supplied to the speaker, as

€

P =dEdt

, integrating, we obtain for

the energy (E) need to break the wine glass:

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E =10b

a +1t a +1 (3)

Students continued to have questions: from the relation between the time needed to break the wine glass and electric power supplied to the speaker, they found a value for the electrical energy used to break the wine glass, but was this energy the same of the acoustical energy transferred to the wine glass during the process?. So, finally, with the help of a decibel meter they obtained the relation between the sound pressure obtained from the speaker and electric power supplied to it. Frequency was fixed at 650 Hz, the mean resonance frequency of the wine glasses.


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Figure 5. Sound intensity obtained from the speaker vs electric power supplied to the speaker.

From figure 5, relation between sound intensity (Ia) obtained from the speaker and electrical power supplied to the speaker (Pe) is a logarithmic relation:

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I a = 14.3 log(Pe ) +121.0 (4)

In acoustics (Kisnley et al, Heller), sound pressures and intensities are usually described using logarithmic scales known as sound levels. This is because most of sound pressures and intensities vary from 10-12 to 10 W/m2. Logarithmic are consistent with the humans sensing of the relative loudness of two sounds by the ratios of their intensities. The decibel (dB) scale is used in acoustics as a unit of sound levels, Sound intensity is defined as the sound power per unit area. The intensity level (IL) of a sound is defined by

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IL = 10 log10II 0

"

# $ $

%

& ' ' (5)

where I0 is the reference intensity, which is the standard threshold of hearing intensity, IL is expressed in decibels referenced to Io 10−12 watt/m2. Since audible sound consists of pressure waves, one of the ways to quantify the sound is to state the amount of pressure variation relative to atmospheric pressure caused by the sound. Because of the great sensitivity of human hearing, the threshold of hearing corresponds to a pressure variation less than a billionth of atmospheric pressure. As the intensity and effective pressure of progressive plane and spherical waves is related by I=p2/ρ0c, then the sound pressure level (SPL) can be expressed as the effective sound pressure of a sound p relative to a reference value p0.

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SPL = 20 log10pp0

"

# $ $

%

& ' ' (6)

SPL is measured in dB referenced to p0=20 micropascals in air. This reference pressure in air is set at the typical threshold of perception of an average human.


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Sound power level (SWL) or acoustic power level is a logarithmic measure of sound intensity in comparison to a reference level of 10−12 watt (1 pW).

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SWL = 10 log10PaP0

"

# $

%

& ' (7)

Sound Power Levels and Sound Pressure Levels are expressed in decibels, but they are not the same decibels. The decibel is only used to compress a wide range of absolute values into a manageable range. It is not an absolute unit, but is a ratio. Without a reference level, it means nothing. The sound power level indicates the total acoustic energy that a machine, or piece of equipment, radiates to its environment. The sound pressure level is a measure for the effect of the energy of an acoustic source (or a collection of sources) and depends on the distance to the source(s) and acoustic properties of the surroundings of the source

From equation (4), and taking into account equations (5) and (7), for the sound power Pa, we have:

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Pa = 14.3 log(Pe ) +121.0

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= 10 log10PP0

"

# $

%

& '

€

10121.0 Pe14.3

€

=PP0

"

# $ $

%

& ' '

10

Then,

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P = 1012.1 Pe1.4P0 = 100.1 Pe

1.4

as, P0 is 10−12 watt, we have a relation between the sound power P obtained from the speaker and electrical power supplied to the speaker (Pe). Students wonder about more questions about the singing wine glass phenomenon, but they must continue with other projects and new experiments.

Conclusion

• The method used for experimental teaching motivated students to continue making experiments even outside classroom and beyond the original course.

• Students learned to apply acquired knowledge, from different areas of physics, to propose an experiment and carried it in different stages, in order to analyze the phenomenon they were interested on.

• Students could confirm or reject the hypothesis they suggest at different stages of the experiment.

• Students learned to perform critical analysis, which improved their ability to solve technical as well as conceptual problems.

References Chen Yoh-Yuh. (2005). Why does Water Change the Pitch of a Singing Wineglass that Way it does?. American Journal of Physics. 73. 2-6. Etkina Eugenia, Planinsi Gorazd, Vollmer Michael. (2013). A Simple Optics Experiment to Engage in Scientifics Inquiry. American Journal Physics. 81. 2-9. Kinsler, Laurence E., Frey, Austin R., Coppers, Alan, B. and Sanders, James V. (2000) Fundamental of acoustics. 4th edition. John Wiley and Sons, Inc. USA Heller, Erick J. (2013).. Why You Hear What You Hear. Princeton University. USA.


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Rossing, Thomas D. (1990). Wine Glasses, Bell mode, and Lord Rayleigh. The Physics Teacher. 28. 2-5. Affiliation and address information José Antonio Zárate Colín, Marisol, Rodríguez Arcos, Karina Ramos Musalem, Estela Margarita Puente Leos and Marcos Ley Koo Laboratorio de Acústica, Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, 04510, México, D.F., México e-mail:antonioyakuza @gmail.com e-mail: [email protected] e-mail: [email protected] Appendix: An example of 45-minutes experimental problem for 8th graders in 2010/2011 (E1-8): Density of inhomogeneous matter We present an example of experimental problem, which was to be solved individually in 45 minutes. For each task the number of points for correct answer is given in brackets and the cognitive level of the task according to revised Bloom's taxonomy is given in square brackets. Equipment: a measuring cylinder 100 ml, a balance, a measuring cup, beans, grits. During this experiment you measure how density of the bean and grits mixture depends on the mass fraction of grits. You should measure volumes as precisely as you can.

Measure densities of beans and grits. Write down the results. (2 points) [Bloom taxonomy: apply]

Put 40 ml of beans into the measuring cylinder. With a measuring cup gradually add cups of grits into the cylinder. At each step measure the mass m and volume V of the mixture. Add 10 cups altogether. Write the results of your measurements in the table. (2 points) [understand, apply]

N of cups 0 1 2 3 4 5 6 7 8 9 10

M [g] V [ml]

Plot a graph showing density of the mixture ρm depending on the mass mz of grits in it.

(4 points) [apply]


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Predict how the plot will continue if you add more cups of grits. Plot your prediction with dashed line.

(1 point) [analyze] How many (kilo)grams of grits would you have to mix into 1 kg of beans to get the most dense mixture?

(1 point) [create]


Informal Teaching of Physics at a Hungarian Science Center

Péter Mészáros ELTE Budapest and Mobilis Science Center Győr, Hungary Abstract Nowadays, students do not like learning physics at school; however, for the development of economy, experts with sufficient scientific knowledge are required. Therefore, the greatest challenge is to develop a enthusiasm for science in students. At the Mobilis Science Center physics is taught by informal teaching methods in the fields of transportation and engineering. These demonstrated main topics are the following: The most influenced age range by the stereotypes of adults are the the primary school students. Parents and teachers should be motivated to reform their approach. This project also supports the vocational guidance of students. Schools’ financial and human resources are limited; as a result, methodological assistance should be provided to them. Schools do not possess the appropriate tools for talent scouting and fostering. To cultivate this, new methods are needed to be developed in cooperation with the schools. Public education, higher education and economy frame together is a system; therefore, the connection between the components should be strengthened. This is realised in special themed events with the use of custom-developed tools. Keywords science center, informal teaching, vocational orientation, methodological assistance, experiments

1. Mobilis Science Center and the vocational orientation Physics can be learnt not only inside the school walls. Long-lasting knowledge, deeper understanding, and creative practice skills could be obtained in a non-formal, adventurous, and inspiring atmosphere through the demonstration of complex problems and innovative teaching methods. The best places of informal education are the world wide popular science centers. One of these centers is the Mobilis Science Center located in Győr, Hungary with its unique transportation theme in Europe. ‘Learning by doing’ is the center’s motto, which means that informal teaching methods like the dissemination of knowledge and learning through discovery and experiment are put into practice.

Figure 1. Experiments with liquid nitrogen

The activities at a science center motivate and help students, teachers, and parents. Through the quite narrow window of transportation, people can get closer to various applications and better understand the basic theories of natural science and engineering. Meanwhile, the participants of industry, primary and tertiary education become fused into an integrating process, which activates them, improves their creative thinking and provides a surface for cooperation.


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Figure 2. How does it works? The visitors can learn about how to operate a vehicle One of the most important goals of science centers is to introduce the values of natural sciences in pair with changing the approach of visitors and to promote positive attitude towards the fields of science. This should be started in the early ages of childhood. It is easy to arouse kids’ interest; however, it is much harder to keep the long-term attention of teenagers’. The primary target group of Mobilis Science Center is teenagers between the age of 13 and 16, but the center is able to entertain and inform people between 6 and 100. Parents can join themed experiment shows and try out interactive exhibits which have a significant role in approach forming. Most of the games have several, equally good solution, so they are prominent in knowledge widening. Parents’ way of thinking and their attitudes provide the basis of children’s career choice. Accordingly, we highly promote family visits, when parents can play and learn with their children. We strongly believe in narrowing the gap between generations and to exchange their experience.

Figure 3. Vocational orientation through playing

One of the biggest problems in Hungary is that youngsters have lost their interest in technical professions and disciplines. In Győr, the vehicle industry (Audi and its partners) offers great career possibilities for young people. As a result, our programs are aimed to guide children to these directions, since a lot of training is needed to become an expert in this field. Elementary school students are oriented towards high school education, in order to choose from the many trainings Győr offers them in its technical secondary schools. On another level, high schools’ graduate students are oriented towards technical and science Universities. Mobilis has a great location as it is in the neighbourhood of one of the biggest technical universities in Hungary called Széchenyi István University. The programmes in a Science Center try to cover a wide range of subjects, in order to satisfy public interests. Some of the special events Mobilis took part in: European Mobility Week, old-timer cars reconfigured to be electric ones, exhibition of military techniques, Mini Science Picnic, Night of the Researchers, Night of the Museums, projects in co-operation with the Széchenyi University. With its numerous interactive devices Mobilis exhibits the traffic’s many aspects like engineering, logistics, technology, science, history, aesthetics and sociology. On our project days experimentations and competitions are organised where university students, local and regional companies can present their latest developments (e.g. alternative-powered vehicles, solar bicycle charger, computer applications: virtual reality, 3D design). Events like these project days also give opportunity to visit the laboratories of Széchenyi István University (e.g. Audi-lab, other technologies).


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Figure 4. High School visitors at Audi-lab

In jUNIor University, professors give lectures about their research on various areas to secondary school students. We organize roadshows in schools together with automotive companies. On our vocational guidance roadshow organized with Széchenyi István University, 6 engineering courses are promoted for high school students. 2 custom-developed exhibits per majors are represented and experiments are held with probe able tools. 2. Methodological assistance and talent development Science centers are the link between informal training and school education. Science centers provide supplementary education, they are based on the curriculum and teaching methods of traditional subjects such as physics and chemistry. A science center could never replace classic school education, it only expands it. Methodological assistance and additional opportunities are given to teachers and schools. Teacher’s fear has to be dispelled: their task and their talented students will not be stolen from them; in fact, multiple possibilities of motivation, valuable information and ideas will be given to them in addition. Searching and mentoring talented students is also one of the most important goal of a science center. We were mentoring a high school student at an international innovation competition (he designed a vehicle made by superconductor). From June to August summer camps are organized where children learn how to research and do various natural scientific experiments. There are tenders for university students to create more experimental tools. Children between 8 and 13 can take part in talent study groups in cooperation with their own schools (study groups based on tablet PC, „Young Physicist” groups). Mini Science Picnic is also one of our organizations, where talented high school students together with their teachers present experiments all day long. This event is also an experiment developing competition.

Figure 5. 30 High School groups made experiments in Mobilis at the event Mini Science Picnic

Another contest is AttrActive Science, which consists of a general natural scientific and technological quiz, a scientific presentation and a short experiment show. With the sustainable transport in focus, we have an E-gokart study group, too. The team competition called The TechTogether is designed for Hungarian university students, where groups’ logical, engineering and designing skills are tested. The Junior version of TechTogether is organized to support vocational guidance for high school students across the country. At Mobilis, on demand, students are prepared for the high-level physics school leaving exam in another study group. Moreover, there is a Lego robot study group available for children between 8 and 12.


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Figure 6. Talented students with his vehicle made by superconductor

Project days’ themes and applied methodologies vary on a large scale. Mobilis can simultaneously occupy 80-120 students. They can be involved in competitive tasks, visit lectures presented by guest performers on natural science issues, take part in quizzes, try out and make experimental devices and probe special, occasionally available activities (e.g. test and learn the mechanism of vehicles run by solar cells, natural gas or electricity).

Figure 7. Solar- and pneumobils developed by students of Széchenyi István University

Besides our own competitions, Mobilis provides a venue for regional, national and custom-developed contests, as well. There is also an opportunity to join special classes, which are held in 6 different topics in the domain of physics and chemistry. For teachers’ request, unique themes can be created in basic or special physics subjects. There are conferences for high school teachers and university lecturers about how to improve their talented students’ knowledge, organize study groups and about physics teaching. In cooperation with Széchenyi István University, a science communication subject is developed. The local science teacher training on higher education level is also fostered. Special, own developed tools, experiments Part of the big interactive exhibits (6 out of 74) are based on my own ideas. On the air-cushion table we presented the aquaplaning phenomenon in a TV show, which introduced the physical aspects of Formula 1. This TV series consisted of 8+4 episodes and I was responsible for providing the background support for its professional content. All the hands-on-experiments are self made/original design. Some of them also won awards, such as the fire tornado, which has got four variations. Besides the regular experimental demonstrations in the Mobilis Center, experiments can be seen on our interactive online surface and we also present them on outside festivals. Our toolbar is improved in cooperation with companies (e.g. Lenz-cannon). For the thermal experiments we use an infrared camera. At the tinkering workshops those who take part can take home their self made products. The experiments present the physics and chemical side of the vehicles and transport.

Figure 8. Water explosions with liquid nitrogen at external events


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Visitors’ interest in physics and their motivation to lean more can be enhanced by making experiments and measurements personally and by showing them innovative devices and spectacular phenomenon. It was proved that the motivation of teachers and students can be increased by systematically organized visits to the Science Center. The increasing number of periodic visitors, co-operations with schools and industrial partners shows that transportation is an excellent topic to motivate. Although lot of exhibits and lectures are placed in the Center, to meet with the Hungarian educational and pedagogical requirements, more industrial or governmental support is needed. With these sources, it would be possible to purchase new experimental devices or to organize more special themed roadshows.

Figure 9. The self developed fire tornado Affiliation and address information Péter Mészáros PhD student – professional and methodological leader ELTE Budapest – Mobilis Science Center Győr, Hungary Vásárhelyi Str. 66. 9026 Győr, Hungary e-mail: [email protected]

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Chapter 7 Physics Teaching and Learning in Informal Settings