International Electronic Journal of Mathematics Education

International Electronic Journal of Mathematics Education
On the Role of Imagination in the Use of History in Mathematics Education
APA
In-text citation: (De Vittori, 2021)
Reference: De Vittori, T. (2021). On the Role of Imagination in the Use of History in Mathematics Education. International Electronic Journal of Mathematics Education, 16(3), em0660. https://doi.org/10.29333/iejme/11296
AMA
In-text citation: (1), (2), (3), etc.
Reference: De Vittori T. On the Role of Imagination in the Use of History in Mathematics Education. INT ELECT J MATH ED. 2021;16(3), em0660. https://doi.org/10.29333/iejme/11296
Chicago
In-text citation: (De Vittori, 2021)
Reference: De Vittori, Thomas. "On the Role of Imagination in the Use of History in Mathematics Education". International Electronic Journal of Mathematics Education 2021 16 no. 3 (2021): em0660. https://doi.org/10.29333/iejme/11296
Harvard
In-text citation: (De Vittori, 2021)
Reference: De Vittori, T. (2021). On the Role of Imagination in the Use of History in Mathematics Education. International Electronic Journal of Mathematics Education, 16(3), em0660. https://doi.org/10.29333/iejme/11296
MLA
In-text citation: (De Vittori, 2021)
Reference: De Vittori, Thomas "On the Role of Imagination in the Use of History in Mathematics Education". International Electronic Journal of Mathematics Education, vol. 16, no. 3, 2021, em0660. https://doi.org/10.29333/iejme/11296
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: De Vittori T. On the Role of Imagination in the Use of History in Mathematics Education. INT ELECT J MATH ED. 2021;16(3):em0660. https://doi.org/10.29333/iejme/11296

Abstract

Based on an experiment carried out with 10- to 11-year-old pupils, this paper questions the place of imagination in a class activity using the history of mathematics. The study focuses on three groups of pupils who were offered three variants of the same activity based on base-60 counting (our time measurement system inherited from the Babylonians). To identify differences and similarities between the three scenarios, a quantitative analysis, using a Principal Component Analysis (PCA), was carried out on the basis of the pupils’ productions and a questionnaire. The approach remains exploratory, but it seems to indicate that imagination plays a relevant role in sessions using history of mathematics.

References

  • Archambault, A., & Venet, M. (2007). Le développement de l’imagination selon Piaget et Vygotsky: d’un acte spontané à une activité consciente [The development of the imagination according to Piaget and Vygotsky: from a spontaneous act to a conscious activity]. Revue des sciences de l’éducation, 33(1), 5-24. https://doi.org/10.7202/016186ar
  • Beavers, A. S., Lounsbury, J. W., Richards, J. K., Huck, S. W., Skolits, G. J., & Esquivel, S. L. (2013). Practical considerations for using exploratory factor analysis in educational research. Practical Assessment, Research & Evaluation, 18(6), 1-13. https://doi.org/10.7275/qv2q-rk76
  • Blum, W., Artigue, M., Mariotti, M. A., Sträßer, R., & Van den Heuvel-Panhuizen, M. (2019). European traditions in didactics of mathematics. Springer International Publishing Imprint, Springer. https://doi.org/10.1007/978-3-030-05514-1
  • Bütüner, S. Ö. (2015a). Impact of using history of mathematics on students mathematics attitude: A meta-analysis study. European Journal of Science and Mathematics Education, 3(4), 337-349. https://doi.org/10.30935/scimath/9442
  • Bütüner, S. Ö. (2015b). Using history of mathematics to teach volume formula of frustum pyramids: Dissection method. Universal Journal of Educational Research, 3(12), 1034‑1048. https://doi.org/10.13189/ujer.2015.031213
  • Bütüner, S. Ö., & Baki, A. (2020). The use of history of mathematics in the mathematics classroom: An action study. International Journal of Education in Mathematics, Science and Technology (IJEMST), 8(2), 92-117. https://doi.org/10.46328/ijemst.v8i2.843
  • Clark, K. M., Kjeldsen, T. H., Schorcht, S., & Tzanakis, C. (2019). History of mathematics in mathematics education – An overview. Mathematica Didactica, 42(1), 1-26. https://doi.org/10.1007/978-3-319-73924-3_1
  • Clark, K. M., Kjeldsen, T. H., Schorcht, S., & Tzanakis, C. (Eds.). (2018). Mathematics, education and history, Towards a harmonious partnership. Springer. https://doi.org/10.1007/978-3-319-73924-3
  • D’Amato, M. (2007). L’imaginaire proposé par les jeux vidéo [The imaginary offered by video games]. Le Télémaque, 32(2), 73-82. https://doi.org/10.3917/tele.032.0073
  • De Vittori, T. (2018). Analyzing the use of history in mathematics education: Issues and challenges around Balacheff’s cKȼ model. Educational Studies in Mathematics, 99(2), 125-136. https://doi.org/10.1007/s10649-018-9831-6
  • Egan, K. (1992). Imagination in teaching and learning. University of Chicago. https://doi.org/10.7208/chicago/9780226244136.001.0001
  • Egan, K., Bullock, S., & Chodakowski, A. (2016). Learning to teach, imaginatively: Supporting the development of new teachers through cognitive tools. McGill Journal of Education, 51(3), 999-1012. https://doi.org/10.7202/1039625ar
  • Fauvel, J. (1991). Using history in mathematics education. For the Learning of Mathematics, 11(2), 3-6.
  • Fauvel, J., & van Maanen, J. (Eds.). (2002). History in mathematics education: The ICMI study, New ICMI Study Series (vol. 6), Springer. https://doi.org/10.1007/0-306-47220-1
  • Fried, M. N., Guillemette, D., & Jahnke, H. N. (2016). Theoretical and/or conceptual frameworks for integrating history in mathematics education. In L. Radford, F. Furinghetti, & T. Hausberger (Eds.), Proceedings of the 2016 ICME Satellite Meeting of the International Study Group on the Relations Between the History and Pedagogy of Mathematics (pp. 211-230). IREM de Montpellier. https://hal.archives-ouvertes.fr/HPM2016
  • Furinghetti, F. (1997). History of mathematics, mathematics education, school practice: Case studies in linking different domains. For the Learning of Mathematics, 17(1), 55-61.
  • Gajdamaschko, N. (2006). Theoretical concerns: Vygotsky on imagination development. Educational Perspectives, 39(2), 34-40.
  • Gras, R. (1992). L’analyse des données : une méthodologie de traitement de questions de didactique [Data analysis: a method for the processing of didactic questions]. Recherches en Didactique des Mathématiques, 12(1), 59-72. https://revue-rdm.com/1992/l-analyse-des-donnees/
  • Gulikers, I., & Blom, K. (2001) “A historical angle”, a survey of recent literature on the use and value of history in geometrical education. Educational Studies in Mathematics, 47(2), 223-258. https://doi.org/10.1023/A:1014539212782
  • Hadzigeorgiou, Y. (2014). Imagination and learning science. In R. Gunstone (Ed.), Encyclopedia of science education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6165-0_465-2
  • Hadzigeorgiou, Y., Klassen, S., & Klassen, C. F. (2012). Encouraging a “romantic understanding” of science: The effect of the nikola tesla story. Science & Education, 21(8), 1111‑1138. https://doi.org/10.1007/s11191-011-9417-5
  • Hansson, L., Hansson, Ö., Juter, K., & Redfors, A. (2020). Curriculum emphases, mathematics and teaching practices: Swedish upper-secondary physics teachers’ views. International Journal of Science and Mathematics, 19, 499-515. https://doi.org/10.1007/s10763-020-10078-6
  • Harris, P. L. (2002). Penser à ce qui aurait pu arriver si... [Think about what could have happened if...]. Enfance, 54(3), 223-240. https://doi.org/10.3917/enf.543.0223
  • Hawkey, K. (2004). Narrative in classroom history. Curriculum Journal, 15(1), 35-44. https://doi.org/10.1080/1026716032000189461
  • Heiede, T. (1992). Why teach history of mathematics? The Mathematical Gazette, 76(475), 151-157. https://doi.org/10.2307/3620388
  • Husson, F., Lê, S., & Pagès, J. (2016). Analyse de données avec R [Data analysis with R]. Presses Universitaires de Rennes.
  • Jankvist, U. T. (2009). A categorization of the “whys” and “hows” of using history in mathematics education. Educational Studies in Mathematics, 71(3), 235-261. https://doi.org/10.1007/s10649-008-9174-9
  • Kotsopoulos, D., & Cordy, M. (2009). Investigating imagination as a cognitive space for learning mathematics. Educational Studies in Mathematics, 70, 259-274. https://doi.org/10.1007/s10649-008-9154-0
  • Lê, S., Josse, J., & Husson, F. (2008). FactoMineR: An R package for multivariate analysis. Journal of Statistical Software, 25(1), 1-18. https://doi.org/10.18637/jss.v025.i01
  • Lemondis, C. (2016). The use of history of mathematics in mathematics education, MENON ©online Journal of Educational Research, 2nd thematic issue, May, 2016. http://www.edu.uowm.gr/site/node/526
  • Nawani, J., Kotzebue, L., Rixius, J., Graml, M., & Neuhaus, B. (2018). Teachers’ use of focus questions in German biology classrooms: A video-based naturalistic study. International Journal of Science and Mathematics, 16, 1431-1451. https://doi.org/10.1007/s10763-017-9837-z
  • Nemirovsky, R., & Ferrara, F. (2009). Mathematical imagination and embodied cognition. Educational Studies in Mathematics, 70(2), 159‑174. https://doi.org/10.1007/s10649-008-9150-4
  • Nielsen, T. W., Fitzgerald, R., & Fettes, M. (Eds.). (2010). Imagination in educational theory and practice: A many-sided vision. Cambridge Scholars Pub.
  • Paixão, G. M., & Borges, F. T. (2018). Imagination and educational curriculum: A literature review. Psicologia: Teoria e Pesquisa, 34, e34310. https://doi.org/10.1590/0102.3772e34310
  • Piaget, J. (1972). La formation du symbole chez l’enfant. Imitation, jeu et rêve, image et représentation [The formation of the symbol in childhood. Imitation, play and dream, image and representation]. Delachaux et Niestlé.
  • Proust, C. (2008). Quantifier et calculer : usages des nombres à Nippur [Quantifying and calculating: uses of numbers in Nippur]. Revue d’Histoire des Mathématiques, 14, 143-209. http://www.numdam.org/item/RHM_2008__14_2_143_0/
  • R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna.
  • Sauvageot, A. (2002). Imaginaire (structures et mécanismes de l’). In A. Mucchielli (Ed.), Dictionnaire des méthodes qualitatives en sciences humaines et sociales [Dictionary of qualitative methods in the humanities and social sciences]. Armand Colin.
  • Schoenfeld, A. H. (2020). On meaningful, researchable, and generative questions. International Journal of Science and Mathematics Education, 18, 67-82. https://doi.org/10.1007/s10763-020-10068-8
  • Staus, N. L., Lesseig, K., Lamb, R., Falk, J., & Dierking, L. (2020). Validation of a measure of STEM interest for adolescents. International Journal of Science and Mathematics, 18, 279-293. https://doi.org/10.1007/s10763-019-09970-7
  • Vygotsky, L. S. (2004). Imagination and creativity in childhood. Journal of Russian and East European Psychology, 42(1), 7-97. https://doi.org/10.1080/10610405.2004.11059210
  • Wang, K., Wang, X., Li, Y., & Rugh, M. S. (2018). A framework for integrating the history of mathematics into teaching in Shanghai. Educational Studies in Mathematics, 98(1), 135-155. https://doi.org/10.1007/s10649-018-9811-x

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