Comparison as a Social Practice in the Analysis of Chaotic Phenomena: the Case of the Double Pendulum

While scholars have proposed incorporating the study of complex phenomena such as chaotic systems in high school and undergraduate-level curricula, the literature on this topic is scant and has focused mostly on the analysis of mathematical models—and often only on certain populations, such as gifte...

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Vydané v:	International journal of science and mathematics education Ročník 22; číslo 1; s. 101 - 120
Hlavní autori:	Hernández-Zavaleta, Jesús E., Preciado Babb, Armando Paulino, Cantoral, Ricardo
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Singapore Springer Nature Singapore 01.01.2024 Springer Nature B.V
Predmet:	Advanced Courses Algorithms Behavior Calculus Chaos theory Cognitive Processes Computer Use Data Analysis Dynamical systems Education Educational Benefits Engineering Education Epistemology Equations (Mathematics) Graphing Calculators High School Students Influence of Technology Learner Engagement Mathematical Applications Mathematical Concepts Mathematical Formulas Mathematical models Mathematics Achievement Mathematics Education Mathematics Instruction Mechanics (Physics) Motion Professional Development Science Education Secondary School Mathematics Secondary schools Students Chaos Socio-epistemology Modeling Complexity High school
ISSN:	1571-0068, 1573-1774
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Abstract	While scholars have proposed incorporating the study of complex phenomena such as chaotic systems in high school and undergraduate-level curricula, the literature on this topic is scant and has focused mostly on the analysis of mathematical models—and often only on certain populations, such as gifted students. We report in this manuscript an exploratory study involving 16 high school students engaged in a task-based interview. Consistent with the socio-epistemological theory in mathematics education, the task was informed by an analysis of the social practices around the historical development of the study of chaotic phenomena. An analysis of students’ descriptions and justifications revealed key features of comparison as a mathematical type of practice involved in the study of chaotic behavior, which differs from common school mathematical practices. We conclude with implications relevant to socio-epistemological theory in mathematics education and suggestions to incorporate the study of chaotic phenomena and dynamic systems in formal education.
AbstractList	While scholars have proposed incorporating the study of complex phenomena such as chaotic systems in high school and undergraduate-level curricula, the literature on this topic is scant and has focused mostly on the analysis of mathematical models—and often only on certain populations, such as gifted students. We report in this manuscript an exploratory study involving 16 high school students engaged in a task-based interview. Consistent with the socio-epistemological theory in mathematics education, the task was informed by an analysis of the social practices around the historical development of the study of chaotic phenomena. An analysis of students’ descriptions and justifications revealed key features of comparison as a mathematical type of practice involved in the study of chaotic behavior, which differs from common school mathematical practices. We conclude with implications relevant to socio-epistemological theory in mathematics education and suggestions to incorporate the study of chaotic phenomena and dynamic systems in formal education. While scholars have proposed incorporating the study of complex phenomena such as chaotic systems in high school and undergraduate-level curricula, the literature on this topic is scant and has focused mostly on the analysis of mathematical models—and often only on certain populations, such as gifted students. We report in this manuscript an exploratory study involving 16 high school students engaged in a task-based interview. Consistent with the socio-epistemological theory in mathematics education, the task was informed by an analysis of the social practices around the historical development of the study of chaotic phenomena. An analysis of students’ descriptions and justifications revealed key features of comparison as a mathematical type of practice involved in the study of chaotic behavior, which differs from common school mathematical practices. We conclude with implications relevant to socio-epistemological theory in mathematics education and suggestions to incorporate the study of chaotic phenomena and dynamic systems in formal education.
Author	Preciado Babb, Armando Paulino Hernández-Zavaleta, Jesús E. Cantoral, Ricardo
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References	EnglishLDComplex systems in the elementary and middle school mathematics curriculum: A focus on modeling. Festschrift in Honor of Gunter TornerThe Montana Mathematics Enthusiast20073139156 Ghys, É. (2015). The butterfly effect. In S. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education (pp. 19–39). Springer. https://doi.org/10.1007/978-3-319-12688-3_6 Jaloveczki, J. (2014). Studying non-linear phenomena in high school workshop (Unpublished doctoral dissertation). Universitas Budapestinensis de Rolando Eotvos Nominata. DeleanuDThe dynamics of a double pendulum: Classic and modern approachAnnals of “Dunarea de Jos” University of Galati, Mathematics: Fascicle II, Physics, Theoretical Mechanics2011342203211 MayRBiological populations with nonoverlapping generations: Stable points, stable cycles, and chaosScience1974186416464564710.1126/science.186.4164.645 NemirovskyRStudents making sense of chaotic behaviourInteractive Learning Enviroments19933315117510.1080/1049482930030301 BuendíaGCorderoFPrediction and the periodical aspect as generators of knowledge in a social practice frameworkEducational Studies in Mathematics200558329933310.1007/s10649-005-2295-5 Barrow-GreenJPoincaré and the three body problem1997American Mathematical Society Kasmer, L. (2008). The role of prediction in the teaching and learning of algebra (Unpublished doctoral dissertation). Western Michigan University. Strogatz, S. (1994). Non linear dynamics and chaos with applications to physics, biology, chemistry, and engineering. Perseus Books. RoeJdeForestRJamshidiSMathematics for sustainability2018Springer10.1007/978-3-319-76660-7 LambRCavagnettoAAkmalTExamination of the nonlinear dynamic systems associated with science student cognition while engaging in science information processingInternational Journal of Science and Mathematics Education20161418720510.1007/s10763-014-9593-2 Caballero Pérez, M. (2018). Causalidad y temporización entre jóvenes de bachillerato. La construcción de la noción de variación y el desarrollo del pensamiento y lenguaje variacional [Causality and timing among high school students. The construction of the notion of variation and the development of variational thought and language] (Unpublished doctoral dissertation). Mathematics Education Department, Cinvestav IPN. Fallas Soto, R. (2019). Variación acotada y predicción. Prácticas socialmente compartidas en la significación de la existencia y unicidad de la solución de la ecuación diferencial [Bounded variation and prediction. Socially shared practices in the significance of the existence and uniqueness of the solution of the differential equation] (Unpublished doctoral dissertation). Cinvestav IPN. DevaneyRLFractal patterns and chaos gamesThe Mathematics Teacher200498422823310.5951/MT.98.4.0228 CochoGCiencia-humanismo-sociedad: De los sistemas complejos a la imaginación heterodoxa2017C3 Editorial Hernández Zavaleta, J. E. (2019). Elementos para el desarrollo del pensamiento y lenguaje variacional entre estudiantes de bachillerato: el caso de “lo erratico” [Elements for the development of variational thought and language among high school students: The case of "the erratic"] (Unpublished doctoral dissertation). Mathematics Education Department, Cinvestav, IPN. RenertMDavisBEcological sustainability and mathematics education: Integrally connectedJournal of Integral Theory and Practice20127194 CanuMde HossonCDuqueMStudents’ understanding of equilibrium and stability: The case of dynamic systemsInternational Journal of Science and Mathematics Education20161410112310.1007/s10763-014-9565-6 DevaneyRA first course in chaotic dynamical systems: Theory and experiments1992Addison-Wesley LorenzEThe essence of chaos1993University of Washington Press10.4324/9780203214589 JaloveczkiJStudying non-linear and chaotic phenomena in high schoolPhysics Competitions20111312937 ButeauCMullerEMarshallNWhen a university mathematics department adopted core mathematics courses of an unintentionally constructionist nature: Really?Digital Experiences in Mathematics Education20151213315510.1007/s40751-015-0009-x DavisBSumaraDLuce-KaplerREngaging minds: Cultures of education and practices of teaching2015Taylor & Francis10.4324/9781315695891 Moreno Durazo, A. (2018). Principios del pensamiento matemático: el principio estrella en la práctica médica. El uso de la pequeña variación en el diagnóstico y el tratamiento de enfermedades cardiacas [Principles of mathematical thought: the star principle in medical practice. The use of small variation in the diagnosis and treatment of cardiac diseases] (Unpublished doctoral dissertation). Cinvestav–IPN. PoincaréHSur la stabilité du systéme solaire [On the stability of the solar system]Scient1898204538547 KimOKKasmerLUsing “prediction” to promote mathematical reasoningMathematics Teaching in the Middle School200712629429910.5951/MTMS.12.6.0294 StarkJHardyKChaos: Useful at last?Science200330156371192119310.1126/science.1087822 GleickJChaos: Making a new science1989Viking Cantoral, R. (2016). Teoría socioepistemológica de la matemática educativa. Estudios sobre construcción social del conocimiento matemático [Socioepistemological theory of educational mathematics. Studies on the social construction of mathematical knowledge] (2nd ed.). Gedisa. Cantoral, R. (2019a). Caminos del saber: Pesamiento y lenguaje variacional [Ways of knowing: Weighing and variational language]. Gedisa. Reyes-Gasperini, D. (2016). Empoderamiento docente y sociepistemología [Teacher empowerment and sociepistemology]. Gedisa. Gobierno del Distrito Federal, Secretaría de Desarrollo Social del Distrito Federal, & Instituto de Educación Media Superior del Distrito Federal (Eds.). (2006). Programas de estudio de Matemáticas [Mathematics study programs]. Corporación Méxicana de Impresión, S.A. de C.V. Maher, C. A., & Sigley, R. (2020). Task-based interview in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_147 Hernández ZavaletaJECantoralRCaracterización de prácticas asociadas con la predicción en el enfrentamiento con lo errático: Un estudio sociepistemológico [Characterization of practices associated with prediction in coping with the erratic: A socioepistemological study]Transformación2018142177189 HurfordASriramanBEnglishLComplexity theories and theories of learning: Literature reviews and synthesesTheories of mathematics education: Seeking new frontiers2010Springer56758910.1007/978-3-642-00742-2_54 SinnREcosystem simulations and chaos on the graphing calculatorThe Mathematics Teacher2007101316717510.5951/MT.101.3.0167 CharmazKConstructing grounded theory2006SAGE CapraFThe web of life: A new scientific understanding of living systems1996Anchor CantoralRMoreno-DurazoACaballero-PérezMSocio-epistemological research on mathematical modeling: An empirical approach to teaching and learningZDM2018501778910.1007/s11858-018-0922-8 PeitgenH-OJürgensHSaupeDFractals for the classroom1991Springer-Verlag PoincaréHLes méthodes nouvelles de la mécanique céleste1892Gauthier-Villars et fils DevaneyRChoateJChaos: A tool kit of dynamics activities2000Key Curriculum Press DugdaleSNewton’s method for square root: A spreadsheet investigation and extension into chaosThe Mathematics Teacher199891757658510.5951/MT.91.7.0576 Cantoral, R. (2019b). Socioepistemology in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. Springer. https://doi.org/10.1007/978-3-319-77487-9_100041-1 MayRSimple mathematical models with very complicated dynamicsNature197626145946710.1038/261459a0 GlaserBStraussAThe discovery of grounded theory: Strategies for qualitative research20127Aldine transaction LorenzEDeterministic nonperiodic flowJournal of Atmospheric Sciences196320213014110.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 LimKBuendíaGKimO-KCorderoFKasmerLThe role of prediction in the teaching and learning of mathematicsInternational Journal of Mathematical Education in Science and Technology201041559560810.1080/00207391003605239 BedfordCWThe case for chaosThe Mathematics Teacher199891427628110.5951/MT.91.4.0276 ThornbergRInformed grounded theoryScandinavian Journal of Educational Research201256324325910.1080/00313831.2011.581686 Feurzeig, W., Horwitz, P., & Boulanger, A. (1989). Advanced mathematics from an elementary viewpoint: Chaos, fractal geometry, and nonlinear systems. In E. Kaltofen, & S. Watt (Eds.), Computers and mathematics (pp. 240–249). Springer. https://doi.org/10.1007/978-1-4613-9647-5_28 FrameMMandelbrotBFractals, graphics, and mathematics education2002Cambridge University Press Lesh, R., & Sriraman, B. (2010). Re-conceptualizing mathematics education as a design science. In B. Sriraman & L. English (Eds.), Theories of mathematics education. Advances in mathematics education (pp. 123–146). Springer. https://doi.org/10.1007/978-3-642-00742-2_14 M Canu (10363_CR10) 2016; 14 K Charmaz (10363_CR12) 2006 G Buendía (10363_CR3) 2005; 58 G Cocho (10363_CR13) 2017 R Devaney (10363_CR16) 1992 10363_CR22 10363_CR21 10363_CR24 OK Kim (10363_CR34) 2007; 12 A Hurford (10363_CR30) 2010 C Buteau (10363_CR4) 2015; 1 R Lamb (10363_CR35) 2016; 14 10363_CR53 LD English (10363_CR20) 2007; 3 F Capra (10363_CR11) 1996 JE Hernández Zavaleta (10363_CR29) 2018; 14 K Lim (10363_CR37) 2010; 41 S Dugdale (10363_CR19) 1998; 91 10363_CR49 H Poincaré (10363_CR46) 1892 CW Bedford (10363_CR2) 1998; 91 R Nemirovsky (10363_CR44) 1993; 3 (10363_CR23) 2002 R Devaney (10363_CR18) 2000 10363_CR5 10363_CR40 10363_CR6 10363_CR7 10363_CR8 B Glaser (10363_CR25) 2012 10363_CR43 B Davis (10363_CR14) 2015 10363_CR36 R May (10363_CR41) 1974; 186 R May (10363_CR42) 1976; 261 E Lorenz (10363_CR39) 1993 J Barrow-Green (10363_CR1) 1997 R Cantoral (10363_CR9) 2018; 50 RL Devaney (10363_CR17) 2004; 98 J Gleick (10363_CR26) 1989 R Sinn (10363_CR51) 2007; 101 10363_CR31 10363_CR33 J Stark (10363_CR52) 2003; 301 D Deleanu (10363_CR15) 2011; 34 E Lorenz (10363_CR38) 1963; 20 10363_CR28 M Renert (10363_CR48) 2012; 7 10363_CR27 J Roe (10363_CR50) 2018 R Thornberg (10363_CR54) 2012; 56 H-O Peitgen (10363_CR45) 1991 J Jaloveczki (10363_CR32) 2011; 13 H Poincaré (10363_CR47) 1898; 20
References_xml	– reference: Barrow-GreenJPoincaré and the three body problem1997American Mathematical Society – reference: Maher, C. A., & Sigley, R. (2020). Task-based interview in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_147 – reference: MayRSimple mathematical models with very complicated dynamicsNature197626145946710.1038/261459a0 – reference: RoeJdeForestRJamshidiSMathematics for sustainability2018Springer10.1007/978-3-319-76660-7 – reference: BedfordCWThe case for chaosThe Mathematics Teacher199891427628110.5951/MT.91.4.0276 – reference: KimOKKasmerLUsing “prediction” to promote mathematical reasoningMathematics Teaching in the Middle School200712629429910.5951/MTMS.12.6.0294 – reference: ButeauCMullerEMarshallNWhen a university mathematics department adopted core mathematics courses of an unintentionally constructionist nature: Really?Digital Experiences in Mathematics Education20151213315510.1007/s40751-015-0009-x – reference: FrameMMandelbrotBFractals, graphics, and mathematics education2002Cambridge University Press – reference: Hernández Zavaleta, J. E. (2019). Elementos para el desarrollo del pensamiento y lenguaje variacional entre estudiantes de bachillerato: el caso de “lo erratico” [Elements for the development of variational thought and language among high school students: The case of "the erratic"] (Unpublished doctoral dissertation). Mathematics Education Department, Cinvestav, IPN. – reference: PeitgenH-OJürgensHSaupeDFractals for the classroom1991Springer-Verlag – reference: Feurzeig, W., Horwitz, P., & Boulanger, A. (1989). Advanced mathematics from an elementary viewpoint: Chaos, fractal geometry, and nonlinear systems. In E. Kaltofen, & S. Watt (Eds.), Computers and mathematics (pp. 240–249). Springer. https://doi.org/10.1007/978-1-4613-9647-5_28 – reference: NemirovskyRStudents making sense of chaotic behaviourInteractive Learning Enviroments19933315117510.1080/1049482930030301 – reference: Strogatz, S. (1994). Non linear dynamics and chaos with applications to physics, biology, chemistry, and engineering. Perseus Books. – reference: Gobierno del Distrito Federal, Secretaría de Desarrollo Social del Distrito Federal, & Instituto de Educación Media Superior del Distrito Federal (Eds.). (2006). Programas de estudio de Matemáticas [Mathematics study programs]. Corporación Méxicana de Impresión, S.A. de C.V. – reference: Caballero Pérez, M. (2018). Causalidad y temporización entre jóvenes de bachillerato. La construcción de la noción de variación y el desarrollo del pensamiento y lenguaje variacional [Causality and timing among high school students. The construction of the notion of variation and the development of variational thought and language] (Unpublished doctoral dissertation). Mathematics Education Department, Cinvestav IPN. – reference: ThornbergRInformed grounded theoryScandinavian Journal of Educational Research201256324325910.1080/00313831.2011.581686 – reference: Cantoral, R. (2019a). Caminos del saber: Pesamiento y lenguaje variacional [Ways of knowing: Weighing and variational language]. Gedisa. – reference: Reyes-Gasperini, D. (2016). Empoderamiento docente y sociepistemología [Teacher empowerment and sociepistemology]. Gedisa. – reference: StarkJHardyKChaos: Useful at last?Science200330156371192119310.1126/science.1087822 – reference: JaloveczkiJStudying non-linear and chaotic phenomena in high schoolPhysics Competitions20111312937 – reference: Fallas Soto, R. (2019). Variación acotada y predicción. Prácticas socialmente compartidas en la significación de la existencia y unicidad de la solución de la ecuación diferencial [Bounded variation and prediction. Socially shared practices in the significance of the existence and uniqueness of the solution of the differential equation] (Unpublished doctoral dissertation). Cinvestav IPN. – reference: PoincaréHSur la stabilité du systéme solaire [On the stability of the solar system]Scient1898204538547 – reference: Lesh, R., & Sriraman, B. (2010). Re-conceptualizing mathematics education as a design science. In B. Sriraman & L. English (Eds.), Theories of mathematics education. Advances in mathematics education (pp. 123–146). Springer. https://doi.org/10.1007/978-3-642-00742-2_14 – reference: Jaloveczki, J. (2014). Studying non-linear phenomena in high school workshop (Unpublished doctoral dissertation). Universitas Budapestinensis de Rolando Eotvos Nominata. – reference: DugdaleSNewton’s method for square root: A spreadsheet investigation and extension into chaosThe Mathematics Teacher199891757658510.5951/MT.91.7.0576 – reference: Hernández ZavaletaJECantoralRCaracterización de prácticas asociadas con la predicción en el enfrentamiento con lo errático: Un estudio sociepistemológico [Characterization of practices associated with prediction in coping with the erratic: A socioepistemological study]Transformación2018142177189 – reference: GlaserBStraussAThe discovery of grounded theory: Strategies for qualitative research20127Aldine transaction – reference: DevaneyRChoateJChaos: A tool kit of dynamics activities2000Key Curriculum Press – reference: BuendíaGCorderoFPrediction and the periodical aspect as generators of knowledge in a social practice frameworkEducational Studies in Mathematics200558329933310.1007/s10649-005-2295-5 – reference: MayRBiological populations with nonoverlapping generations: Stable points, stable cycles, and chaosScience1974186416464564710.1126/science.186.4164.645 – reference: DavisBSumaraDLuce-KaplerREngaging minds: Cultures of education and practices of teaching2015Taylor & Francis10.4324/9781315695891 – reference: CanuMde HossonCDuqueMStudents’ understanding of equilibrium and stability: The case of dynamic systemsInternational Journal of Science and Mathematics Education20161410112310.1007/s10763-014-9565-6 – reference: SinnREcosystem simulations and chaos on the graphing calculatorThe Mathematics Teacher2007101316717510.5951/MT.101.3.0167 – reference: Ghys, É. (2015). The butterfly effect. In S. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education (pp. 19–39). Springer. https://doi.org/10.1007/978-3-319-12688-3_6 – reference: Cantoral, R. (2019b). Socioepistemology in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. Springer. https://doi.org/10.1007/978-3-319-77487-9_100041-1 – reference: LimKBuendíaGKimO-KCorderoFKasmerLThe role of prediction in the teaching and learning of mathematicsInternational Journal of Mathematical Education in Science and Technology201041559560810.1080/00207391003605239 – reference: DevaneyRA first course in chaotic dynamical systems: Theory and experiments1992Addison-Wesley – reference: Moreno Durazo, A. (2018). Principios del pensamiento matemático: el principio estrella en la práctica médica. El uso de la pequeña variación en el diagnóstico y el tratamiento de enfermedades cardiacas [Principles of mathematical thought: the star principle in medical practice. The use of small variation in the diagnosis and treatment of cardiac diseases] (Unpublished doctoral dissertation). Cinvestav–IPN. – reference: LorenzEDeterministic nonperiodic flowJournal of Atmospheric Sciences196320213014110.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 – reference: Cantoral, R. (2016). Teoría socioepistemológica de la matemática educativa. Estudios sobre construcción social del conocimiento matemático [Socioepistemological theory of educational mathematics. Studies on the social construction of mathematical knowledge] (2nd ed.). Gedisa. – reference: CharmazKConstructing grounded theory2006SAGE – reference: HurfordASriramanBEnglishLComplexity theories and theories of learning: Literature reviews and synthesesTheories of mathematics education: Seeking new frontiers2010Springer56758910.1007/978-3-642-00742-2_54 – reference: PoincaréHLes méthodes nouvelles de la mécanique céleste1892Gauthier-Villars et fils – reference: GleickJChaos: Making a new science1989Viking – reference: CapraFThe web of life: A new scientific understanding of living systems1996Anchor – reference: CochoGCiencia-humanismo-sociedad: De los sistemas complejos a la imaginación heterodoxa2017C3 Editorial – reference: EnglishLDComplex systems in the elementary and middle school mathematics curriculum: A focus on modeling. Festschrift in Honor of Gunter TornerThe Montana Mathematics Enthusiast20073139156 – reference: DevaneyRLFractal patterns and chaos gamesThe Mathematics Teacher200498422823310.5951/MT.98.4.0228 – reference: LorenzEThe essence of chaos1993University of Washington Press10.4324/9780203214589 – reference: CantoralRMoreno-DurazoACaballero-PérezMSocio-epistemological research on mathematical modeling: An empirical approach to teaching and learningZDM2018501778910.1007/s11858-018-0922-8 – reference: DeleanuDThe dynamics of a double pendulum: Classic and modern approachAnnals of “Dunarea de Jos” University of Galati, Mathematics: Fascicle II, Physics, Theoretical Mechanics2011342203211 – reference: Kasmer, L. (2008). The role of prediction in the teaching and learning of algebra (Unpublished doctoral dissertation). Western Michigan University. – reference: LambRCavagnettoAAkmalTExamination of the nonlinear dynamic systems associated with science student cognition while engaging in science information processingInternational Journal of Science and Mathematics Education20161418720510.1007/s10763-014-9593-2 – reference: RenertMDavisBEcological sustainability and mathematics education: Integrally connectedJournal of Integral Theory and Practice20127194 – ident: 10363_CR6 – ident: 10363_CR49 – volume: 3 start-page: 151 issue: 3 year: 1993 ident: 10363_CR44 publication-title: Interactive Learning Enviroments doi: 10.1080/1049482930030301 – start-page: 567 volume-title: Theories of mathematics education: Seeking new frontiers year: 2010 ident: 10363_CR30 doi: 10.1007/978-3-642-00742-2_54 – volume-title: Chaos: A tool kit of dynamics activities year: 2000 ident: 10363_CR18 – volume: 91 start-page: 576 issue: 7 year: 1998 ident: 10363_CR19 publication-title: The Mathematics Teacher doi: 10.5951/MT.91.7.0576 – volume: 261 start-page: 459 year: 1976 ident: 10363_CR42 publication-title: Nature doi: 10.1038/261459a0 – volume: 50 start-page: 77 issue: 1 year: 2018 ident: 10363_CR9 publication-title: ZDM doi: 10.1007/s11858-018-0922-8 – ident: 10363_CR31 – volume-title: Engaging minds: Cultures of education and practices of teaching year: 2015 ident: 10363_CR14 doi: 10.4324/9781315695891 – volume-title: Les méthodes nouvelles de la mécanique céleste year: 1892 ident: 10363_CR46 – ident: 10363_CR7 – volume-title: Fractals for the classroom year: 1991 ident: 10363_CR45 – volume: 98 start-page: 228 issue: 4 year: 2004 ident: 10363_CR17 publication-title: The Mathematics Teacher doi: 10.5951/MT.98.4.0228 – ident: 10363_CR36 doi: 10.1007/978-3-642-00742-2_14 – volume: 56 start-page: 243 issue: 3 year: 2012 ident: 10363_CR54 publication-title: Scandinavian Journal of Educational Research doi: 10.1080/00313831.2011.581686 – ident: 10363_CR21 – ident: 10363_CR8 doi: 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Title	Comparison as a Social Practice in the Analysis of Chaotic Phenomena: the Case of the Double Pendulum
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