Cultivating intelligence through mathematical language
This paper sets out different contexts where mathematics helps create a thinking and reasoning habit, with special emphasis on problem solving. Intelligence is thought to be connected to problem solving ability and so we are interested in the relation- ship between intelligence and mathemat- ical problem solving. These problems will be posed in a broad sense, not just consid- ering classical written problems but also problems that appear in situations such as chess, magic tricks, and board games. These settings motivate students better, solving them requires different approaches, and they relate to other fields of knowledge. This paper reports on our experience of posing problems and reasoning with gifted students through magic tricks based on mathemati- cal ideas and we give some examples of the activities we have done with them. We also present recreational mathematics as a dis- cipline that promotes student motivation and increases curiosity and inquiry. We show some ideas from Miguel De Guzmán, Martín Gardner, and Raymond Smullyan that have been used in different frameworks. We de- scribe some games that have been shown to be useful tools for creating reasoning schemas, presenting the particular case of chess as an educational tool. Finally, we set out some conclusions about the introduction of new materials, methods, and ideas for solving problems and we formulate a proposal for continuing this work and applying it in the classroom.
Please, cite this article as follows: Blasco, F. (2021). El cultivo de la inteligencia a través del lenguaje matemático | Cultivating intelligence through ematical language. Revista Española de Pedagogía, 79 (278), 59-75. https://doi.org/10.22550/REP79-1-2021-07
Aciego, R., García, L., & Betancort, M. (2012). The benefits of chess for the intellectual and social-emotional enrichment in school-children. The Spanish Journal of Psychology, 15 (2), 551-559. doi: https://doi. org/10.5209/rev_SJOP.2012.v15.n2.38866
Álvarez, V., Fernández, P., & Márquez, M. A. (2002). Cartomagia matemática y cartoteoremas magicos [Mathematical cartomagic and magic carto-theorems]. La Gaceta de la RSME, 5 (3), 711-735.
Bachet, C. G. (1884). Problèmes plaisants & delectables qui se font par les nombres [Pleasant & delectable problems that are done with numbers]. Librería Gauthier-Villars. https://archive.org/details/problmesplaisan00labogoog (Original work published 1612)
Barrett, D. C., & Fish, W. W. (2011). Our move: Using chess to improve math achievement for students who receive special education services. International Journal of Special Education, 26, 181-193.
Benjamin, A., & Shermer, M. (2006). Secrets of mental math: The mathemagician’s guide to lightening calculation and amazing math tricks. Crown Publishing Group.
Blasco, F. (2016). Matemagia. Los mejores trucos para entender los números [Mathemagics. The best tricks for understanding numbers]. Editorial Ariel.
Bouton, C. L. (1901). Nim, a game with a complete mathematical theory. Annals of Mathematics, 3 (1 /4), 35-39.
Bragg, L. (2007). Students' conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma. Mathematics Education Research Journal, 19, 29-44. https://doi.org/10.1007/BF03217448
Bragg, L. A. (2012). Testing the effectiveness of mathematical games as a pedagogical tool for children’s learning. International Journal of Science and Mathematics Education, 10, 1445-1467. https://doi.org/10.1007/ s10763-012-9349-9
Carroll, L. (2002). Un cuento enmarañado [A tangled tale]. Editorial Nivola. (Original work published 1885)
Carroll, L. (2014). Problemas de almohada [Pillow problems]. Editorial Nivola. (Original work published 1895)
Congreso de los Diputados (2014). Proposición no de Ley sobre la implantación y fomento de la práctica del ajedrez en escuelas y espacios públicos y su promoción como deporte [Non-legislative proposal on the implementation and encouragement of the practice of chess in schools and public spaces and its promotion as a sport]. (161/002598). https://bit.ly/38vL31Q
Coto, A. (2010). La aventura del cálculo [The adventure of calculus]. Editorial EDAF.
De Guzmán, M. (1984). Cuentos con cuentas [Stories with sums]. Editorial Labor.
Duran, M. (2017). La magia, centre del projecte extracurricular per a estudiants d’altes capacitats [Magic, centre of the extracurricular project for students with high abilities]. https://bit.ly/3lnDG1V
European Parliament (2012). Declaration of the European Parliament of 15 March 2012 on the introduction of the programme ‘Chess in School’ in the educational systems of the European Union. https://bit.ly/3ltmp7q
Gardiner, G. C. (2018). Learning chess and the development of cognitive thinking in Queensland primary schools: An exploratory study [Doctoral dissertation, University of Southern Queensland]. https://eprints.usq.edu.au/36711/
Gardner, M. (1994). My best mathematics and logical puzzles. Dover.
Gardner, M. (2008). Origami, Eleusis, and the Soma Cube. Martin Gardner’s Mathematical Diversions. Cambridge University Press.
Gobet, F., & Campitelli, G. (2006). Education and chess: A critical review. In T. Redman (Ed.), Chess and Education: Selected Essays from the Koltanowski Conference (pp. 124-143). University of Texas at Dallas.
Jankovic, A., & Novak, I. (2019). Chess as a powerful educational tool for successful people. In D. Tipuric´ & D. Hruška (Ed.), 7th International OFEL Conference on Governance, Management and Entrepreneurship: Embracing Diversity in Organisations. April 5th - 6th, 2019, Dubrovnik, Croatia, Governance Research and Development Centre (CIRU) (pp. 425-441). http://hdl.handle.net/10419/196101
Jerrim, J., Macmillan, L., Micklewright, J., Sawtell, M., & Wiggins, M. (2017). Does teaching children how to play cognitively demanding games improve their educational attainment? Evidence from a randomised controlled trial of chess instruction in England. Journal of Human Resources, 53 (4), 993-1021. https://doi.org/10.3368/jhr.53.4.0516.7952r
Khosrorad, R., Kouhbanani, S. S., & Sanii, A. (2014). Chess training for improving executive functions and mathematics performance of students with mathematics disorders. International Journal of Educational Investigations, 1 (1), 283-295.
Machargo, J., García, D., Ramos, S., & Luján, (2002). Ajedrez como recurso educativo para el desarrollo psicológico [Chess as an educational resource for psychological development]. Evaluación e Intervención Psicoeducativa: Revista Interuniversitaria de Psicología de la Educación, 8-9, 111-127.
Polya, G. (1965). Cómo plantear y resolver problemas [How to pose and solve problems]. Editorial Trillas.
Puig Adam, P. (1951). Valor formativo de las matemáticas en la enseñanza secundaria [The educational value of mathematics in secondary education]. https://www.ucm.es/data/cont/media/www/pag-81684/conferencias1.pdf
Quintero, R. (2006). El truco de m pilas de Gergonne y el sistema de numeración de base m [The Gergonne m-pile trick and the base m counting system]. Boletín de la Asociación Matemática Venezolana, 13 (2), 165-176.
Rupérez, J. A., & García, M. (2010). Graduación de la dificultad en el Cubo Soma (I) [Graduation of difficulty in the Cube Soma (I)]. Números. Revista de Didáctica de las Matemáticas, 75, 165-173. https://mdc.ulpgc.es/cdm/singleitem/collection/numeros/id/768/rec/3
Sala, G., & Gobet, F. (2016). Do the benefits of chess instruction transfer to academic and cognitive skills? A meta-analysis. Educational Research Review, 18, 46-57. http://dx.doi.org/10.1016/j.edurev.2016.02.002
Sala, G., & Gobet, F. (2017). Does far transfer exist? Negative evidence from chess, music, and working memory training. Current Directions in Psychological Science, 26 (6), 515-520. https://doi.org/10.1177%2F0963721417712760
Santaló, L. A. (1966). La matemática en la edu- cación [Mathematics in education]. Editorial Docencia.
Scholz, M., Niesch, H., Steffen, O., Ernst, B., Loeffler, M., Witruk, E., & Schwarz, H. (2008). Impact of chess training on mathematics performance and concentration ability of children with learning disabilities. International Journal of Special Education, 23 (3), 138-148.
Senado de España (1995). Expedientes relacionados con expediente 662/000126 [Files related to file 662/000126]. Retrieved from https://bit.ly/3hihRQ8
Singmaster, D. (1981). Notas sobre el cubo de Rubik [Notes on the Rubik’s Cube]. Editorial Altalena.
Storey, K. (2010). Teaching beginning chess skills to students with disabilities. Preventing School Failure: Alternative Education for Children and Youth, 44, 45-40. https://doi.org/10.1080/10459880009599782
Subia, G., Amaranto, J., Amaranto, J., Bustamante, J., & Damaso, I. (2019). Chess and mathematics performance of college players: An exploratory analysis. Open Access Library Journal, 6, e5195. https://doi.org/10.4236/oalib.1105195
Fernando Blasco is an Associate Professor at the Universidad Politécnica de Madrid (UPM). He took his undergraduate degree and doctorate in mathematics at the Universidad Complutense de Madrid. His main research interest is the frontier between non-formal education and scientific outreach. He is a member of the Committee for Raising Public Awareness of Mathematics of the European Mathematical Society and President of the Outreach Committee of the Royal Spanish Mathematical Society. He collaborates on various projects for promoting STEM disciplines.