EURASIA Journal of Mathematics, Science and Technology Education
Volume 13, Issue 6 (June 2017), pp. 20052038
DOI: 10.12973/eurasia.2017.01211a
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Research Article
Published online on May 09, 2017
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Kmeans Clustering to Study How Student Reasoning Lines Can Be Modified by a Learning Activity Based on Feynman’s Unifying Approach
Onofrio Rosario Battaglia, Benedetto Di Paola, Claudio Fazio
Research in Science Education has shown that often students need to learn how to identify differences and similarities between descriptive and explicative models.
The development and use of explicative skills in the field of thermal science has always been a difficult objective to reach. A way to develop analogical reasoning is to use in Science Education unifying conceptual frameworks.
In this paper we describe a 20hour workshop focused on Feynman’s Unifying Approach and the twolevel system. We measure its efficacy in helping undergraduate chemical engineering students explain phenomena by applying an explanatory model. Contexts involve systems for which a process is activated by thermally overcoming a welldefined potential barrier. A questionnaire containing six openended questions was administered to the students before instruction. A second one, similar but focused on different physical content was administered after instruction. Responses were analysed using kmeans Cluster Analysis and students’ inferred lines of reasoning about the analysed phenomena were studied. We conclude that students reasoning lines seem to have clearly evolved to explicative ones and it is reasonable to think that the Feynman Unifying Approach has favoured this change.
Keywords: Boltzmann Factor, evaluation, quantitative data analysis in education, kmeans clustering, thermallyactivated phenomena
 Aubusson, P. J., Harrison, A. G., & Ritchie, S. M. (2006). Metaphor and analogy: Serious thought in science education. In P. J. Aubusson, A. G. Harrison, & S. M. Ritchie (Eds.), Metaphor and analogy in science education (pp. 1–10). Dordrecht, the Netherlands: Springer.
 Aubusson, P. J. Treagust, D. & Harrison, A. G. (2009). Learning and teaching science with analogies and metaphors. In S. M. Ritchie (Ed.), The world of science education: Handbook of research in Australasia (pp. 199–216). Rotterdam, the Netherlands: Sense Publishers.
 Bao, L. and Redish, E.F. (2006). Model Analysis: Representing and Assessing the Dynamics of Student Learning. Phys. Rev. ST Phys. Educ. Res, 2, 010103
 Battaglia, O. R., Bonura, A., & SperandeoMineo, R. M. (2009). A pedagogical approach to the Boltzmann factor through experiments and simulations. Eur. J. Phys., 30, 1025.
 Battaglia, O. R., Guastella, I., & Fazio, C. (2010). The Boltzmann probability as a unifying approach to different phenomena. Am. J. Phys., 78, 1331.
 Battaglia, O. R., & Di Paola, B. (2015). A quantitative method to analyse an open answer questionnaire: a case study about the Boltzmann Factor. Il Nuovo Cimento, 38C(3), id 87.
 Battaglia, O. R., Di Paola, B., & Fazio, C. (2016). A New Approach to Investigate Students’ Behavior by Using Cluster Analysis as an Unsupervised Methodology in the Field of Education. Applied Mathematics, 7, 16491673.
 Boltzmann, L. (1909). Bermerkungen über einige Probleme der mechanische Wärmetheorie, Wiener Berichte, 75, 62–100 in L. Boltzmann Wissenschaftliche Abhandlungen Vol. II, ed F. Hasenöhrl, (Leipzig Barth, 1909, reissued New York Chelsea, 1969, paper 39)
 Black, D., & Solomon, J. (1987). Can Pupils Use Taught Analogies for Electric Current? School science review, 69(247), 24954.
 Boltzmann, L. (1909). Über die beziehung dem zweiten Haubtsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung respektive den Sätzen über das Wärmegleichgewicht, Wiener Berichte 76, 373–435 in L. Boltzmann Wissenschaftliche Abhandlungen, Vol. II, ed F. Hasenöhrl, (Leipzig Barth, 1909, reissued New York Chelsea, 1969, paper 42)
 Borg, I., & Groenen, P. (1997) Modern Multidimensional Scaling. Springer, New York. doi:10.1007/9781475727111
 Bybee, R. W. (1993). An instructional model for science education Developing Biological Literacy (Colorado Springs, CO: Biological Sciences Curriculum Study)
 Brown, D. E., & Clement, J. (1989). Overcoming misconceptions via analogical reasoning: Abstract transfer versus explanatory model construction. Instructional Science, 18, 237261.
 Chiu, M. H., & Lin, J. W. (2005). Promoting fourth graders' conceptual change of their understanding of electric current via multiple analogies. Journal of Research in Science Teaching, 42(4), 429464.
 Clough, E. E., & Driver, R. (1986). A Study of Consistency in the Use of Students' Conceptual Frameworks across Different Task Contexts. Sci. Educ., 70(4), 473.
 Day, S., Goldstone, R. L., & Hills, T. (2010). The effects of similarity and individual differences on comparison and transfer. In Proceedings of the ThirtySecond Annual Conference of the Cognitive Science Society (pp. 465470).
 DiCiccio, T. J., & Efron, B. (1996). Bootstrap confidence intervals. Statistical Science 11(3), 189228.
 Di Paola, B., Battaglia, O. R., & Fazio, C. (2016). NonHierarchical Clustering to Analyse an OpenEnded Questionnaire on Algebraic Thinking. South African Journal of Education, 36, 113.
 Duit, R. (1991). On the role of analogies and metaphors in learning science. Science education, 75(6), 649672.
 Duit, R. & Glynn, S. (1996). Mental Modelling in Research in Science Education in Europe, edited by G. Welford, J. Osborne and P. Scott, (Falmer, London,England), p. 166.
 Duit, R., & Glynn, S. (1996). Mental modelling. Research in science education in Europe, 166176.
 Duit, R. Gropengieber, H., & Kattmann, U. (2005). Toward science education research that is relevant for improving practice: The model of educational reconstruction, in HE Fisher (ed), Developing Standard in Research on Science Education (London, UK: Taylor and Francis) pp. 19.
 Dupin, J. J., & Johsua, S. (1989). Analogies and "modeling analogies" in teaching: Some examples in basic electricity. Science Education, 73, 207224.
 Ericsson, K. A., & Simon, H. A. (1998). How to study thinking in everyday life: Contrasting think aloud protocols with descriptions and explanations of thinking. Mind Cult. Act., 5, 178.
 Etkina, E. (2014). Helping our students learn physics and think like scientists Teaching and Learning Physics Today: Challenges? Benefits? ed W. Kaminski and M. Michelini (Udine, Italy: Lithostampa) pp. 63
 Everitt, B. S., Landau, S., Leese, M., & Stahl, D. (2011). Cluster Analysis. John Wiley & Sons Ltd., Chichester.
 Fazio, C., Guastella, I., & Tarantino, G. (2007). The elastic body model: A pedagogical approach integrating real time measurements and modelling activities. Eur. J. Phys., 28(5), 991.
 Fazio, C., Guastella, I., SperandeoMineo, R. M., & Tarantino, G. (2008). Modelling mechanical wave propagation: guidelines and experimentation of a teaching learning sequence. Int. J. Sci. Educ., 30(11), 1491.
 Fazio, C., & Spagnolo, F. (2008). Conceptions on modelling processes in Italian high school prospective mathematics and physics teachers. S. Afr. J. Educ., 28, 469.
 Fazio, C, Di Paola, B., & Guastella, I. (2012). Prospective elementary teachers' perceptions of the processes of modeling: A case study. Phys. Rev. ST Phys. Educ., Res. 8 010110.
 Fazio, C., Battaglia, O. R., & Guastella, I. (2012). Two experiments to approach the Boltzmann factor: chemical reaction and viscous flow. Eur. J. Phys., 33, 359.
 Fazio, C., Battaglia, O. R., & Di Paola, B. (2013). Investigating the quality of mental models deployed by undergraduate engineering students in creating explanations: the case of thermally activated phenomena. Phys. Rev. ST Phys. Educ., Res. 9 020101.
 Feynman, R. P. Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol. I (Reading, MA: AddisonWesley) 421.
 Feynman, R. P. (1974). Statistical Mechanics (Reading MA: Benjamin A)
 Gentner, D. (1983). Structure‐mapping: A theoretical framework for analogy. Cognitive science, 7(2), 155170.
 Gilbert, S. W. (1989). An evaluation of the use of analogy, similc and metaphor in science texts.
 Jou alof Research in Science Teaching, 26, 315327.
 Gilbert, J. K., & Boulter, C. (1998). Learning science through models and modelling. International handbook of science education ed BJ Fraser and KG Tobin (Dordrecht, The Netherlands: Kluwer Academic Publisher), pp. 53.
 Glynn, S. M. (1989). The teaching with analogies model: Explaining concepts in expository texts. In K. D. Muth (Ed.), Children's comprehension of narrative and expository text: Research into practice. Neward, DE: International Reading Association, 185 204.
 Greca, I. M., & Moreira, M. A. (2000). Mental models, conceptual models, and modeling. Int. J. Sci. Teach., 22, 1.
 Griffiths, D. J. (1988). Introduction to Electrodynamics (Upper Saddle River, NJ: PrenticeHall) p 289
 Hestenes, D. (1987). Toward a modelling theory of physics in struction. Am. J. Phys., 55, 440.
 Hestenes, D. (1992). Modelling games in the Newtonian world, Am. J. Phys. 60, 732.
 Hestenes, D. (2006). Notes for a modelling theory of science, cognition and instruction, in
 Modelling in Physics and Physics Education, edited by E. van den Berg, T. Ellermeijer, and
 O. Slooten (University of Amsterdam, the Netherlands), pp. 34.
 Horne, M. Farago, P., & Oliver, J. (1973). An experiment to measure Boltzmann’s constant. Am. J. Phys., 41, 344.
 Jacobs, H., Hees, G., & Crossley, W. P. (1948). The relationship between the emission constant and the apparent work function for various oxidecoated cathodes. Proc. IRE, 36, 1109.
 Jasien, P.G., & Oberem, G. E. (2002). Understanding of elementary concepts in heat and temperature among college students and K12 teachers. J. Chem. Educ., 79(7), 88995.
 JohnsonLaird, P. N. (1983). Mental Models: Towards a Cognitive Science of Language, Inference, and Consciousness. (Cambridge, UK: Cambridge University Press)
 JohnsonLaird, P. N. (2006). How We Reason. (Oxford, UK: Oxford University Press)
 Leisch, F. (2006). A Toolbox for KCentroids Cluster Analysis. Computational Statistics and Data Analysis, 51(2), 526544.
 Karelina, A., & Etkina, E. (2007). Acting like a physicist: Student approach study to experimental design, Phys. Rev. ST Phys. Ed. Res. 3 020106.
 Kittel, C. (1966). Introduction to Solid State Physics, 3rd ed. (New York: Wiley) pp. 246.
 Maloney, D., & Siegler, R. S. (1993). Conceptual Competition in Physics Learning Int. J. Sci. Educ., 15, 283.
 Marton, F. (1986). Phenomenography  A research approach investigating different understandings of reality. Journal of Thought, 21(2), 2849.
 MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. In: Cam, L. M. L., Neyman, J. (Eds.), Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability. University of California Press, Berkeley, CA, USA, pp. 281–297.
 Nageri, H. (1980). Transfer mittels Analogie: Lernhilfe bei der Informationsverarbeitung. In A. Scharmann & A. Hofstaetter (Eds.). DPG Fachausschu Didaktik der Physik. Vortrage der Frilhjahrstagung 1980. Gie en: 1. Physikalisches Institut, 501506.
 Olson, S., & LoucksHorsley, S. (eds) (2000). Inquiry and the National Science Education Standards: A Guide for Teaching and Learning, (Washington DC: National Academic Press Inc.).
 Pauling, L. (1988). General Chemistry, (New York: Dover) pp. 564
 Pauling, L. (1988). General Chemistry (New York: Dover) p 551
 Pizzolato, N., Fazio, C., SperandeoMineo, R. M., & PersanoAdorno, D. (2014). Openinquiry driven overcoming of epistemological difficulties in engineering undergraduates: A case study in the context of thermal science. Physical Review Special Topics  Physics Education Research, 10, 010107.
 Prentis, J. J. (2000). Experiments in statistical mechanics Am. J. Phys., 68, 1073.
 Prentis, J. J., Andrus, A. E., & Stasevich, T. J. (1999). Crossover from the exact factor to the Boltzmann factor Am. J. Phys., 67, 508–515.
 Redish, E. F. (1994). The Implications of Cognitive Studies for Teaching Physics. Am. J. Phys., 62(6), 796.
 Reif, J. (1965). Statistical and Thermal Physics (New York: MacGrowHill)
 Rouseeuw, P. J. (1987). Silhouttes: a graphical aid to the interpretation and validation of cluster analysis, Journal of Computational and Applied Mathematics, 20, 5365.
 Salmon, W. C. (1990). Four Decades of Scientific Explanation (University of Minnesota Press, Minneapolis).
 Saxena, P., Singh, V., & Lehri, S. (2013). Evolving efficient clustering patterns in liver patient data through data mining techniques. International Journal of Computer Applications, 66(16), 2328.
 Schöredinger, E. (1967). Statistical Thermodynamics (Cambridge: Cambridge University Press)
 Shapiro, M. A. (1985). Analogies, visualization and mental processing of science stories. Paper presented to the Information Systems Division of the International Communication Association.
 SperandeoMineo, R. M., Fazio, C., & Tarantino, G. (2006). Pedagogical content knowledge development and preservice physics teacher education: a case study. Res. Sci. Educ., 36, 235.
 Streveler, R.A., Olds, B.M., Miller, R.L. and Nelson MA (2003). Using a Delphy study to identify the most difficult concepts for students to master in thermal and transport science. Proc. Of ASEE Annual Conference, Nashville, TS.
 Streveler, R. A., Litzinger, T. A., Miller, R. L., & Steif, P. S. (2008). Learning Conceptual Knowledge in the Engineering Science: Overview and Future Research Directions. J. Eng. Educ., 97(3), 27994.
 Struyf, A., Hubert, M., & Rousseeuw, P. J. (1997) Clustering in an ObjectOriented Environment. Journal of Statistical Software, 1, 130.
 Sturge, M. D., & Toh, S. B. (1999). An experiment to demonstrate the canonical distribution. Am. J.
 Phys., 67, 1129.
 Tarantino, G., Fazio, C., & SperandeoMineo, R.M. (2010). A pedagogical flight simulator for longitudinal airplane flight. Comput. Appl. Eng. Educ., 18(1), 144.
 Ugur, G., Dilber, R., Senpolat, Y., & Duzgun, B. (2012). The Effects of Analogy on Students' Understanding of Direct Current Circuits and Attitudes towards Physics Lessons. European Journal of Educational Research, 1(3), 211223.
 Hestenes, Wells. M., D., and Swackhammer, G. (1995). A modeling method for high school physics instruction. Am. J. Phys., 63, 606.
 Zeitoun. H. H. (1984). Teaching scientific analogies: A proposed model. Research in Science and Technology Education, 2, 107125.
APA 
Battaglia, O. R., Paola, B. D., & Fazio, C. (2017). Kmeans Clustering to Study How Student Reasoning Lines Can Be Modified by a Learning Activity Based on Feynman’s Unifying Approach. EURASIA Journal of Mathematics, Science and Technology Education, 13(6), 20052038. 
MLA 
Battaglia, Onofrio R., Benedetto D. Paola, and Claudio Fazio. "Kmeans Clustering to Study How Student Reasoning Lines Can Be Modified by a Learning Activity Based on Feynman’s Unifying Approach" EURASIA Journal of Mathematics, Science and Technology Education 13.6 (2017): 20052038. 
ISO 690 
BATTAGLIA, Onofrio R.; PAOLA, Benedetto D.; FAZIO, Claudio. Kmeans Clustering to Study How Student Reasoning Lines Can Be Modified by a Learning Activity Based on Feynman’s Unifying Approach. EURASIA Journal of Mathematics, Science and Technology Education, 2017, 13.6: 20052038. 
