Artificial Intelligence Techniques in Software Design for Mathematics Education

  1. Lagrange, Jean-Baptiste
  2. Richard, Philippe R.
  3. Vélez, María Pilar
  4. Van Vaerenbergh, Steven
Libro:
Handbook of Digital Resources in Mathematics Education

Editorial: Springer

ISSN: 2197-1951 2197-196X

ISBN: 9783030950606 9783030950606

Año de publicación: 2023

Páginas: 1-31

Tipo: Capítulo de Libro

DOI: 10.1007/978-3-030-95060-6_37-1 GOOGLE SCHOLAR lock_openAcceso abierto editor

Objetivos de desarrollo sostenible

Resumen

This chapter presents a state of the art in the design of digital environments for mathematics education, with a particular focus on artificial intelligence techniques. A review of the work done in this area over the last few decades highlights current challenges and distinguishes between symbolic approaches and machine learning. About symbolic approaches, we review automatic reasoning tools in geometry and their potential. We also consider the design and research work around the Casyopée environment and the use of logic programming in the QED-Tutrix intelligent tutoring system. With respect to machine learning, four classes of techniques constitute contemporary AI in computer science. Two examples are discussed: a deep learning system of monument analysis for learning situations in mathematics, technology and art, and a computer classroom simulator that provides a new approach to training teachers. (Fuente: Springer)

Referencias bibliográficas

  • Arsac G (1987) L’origine de la démonstration: essai d’épistémologie didactique [the origin of the demonstration: essay on didactic epistemology]. Publications mathématiques et informatique de Rennes 5:1–45
  • Asif R, Merceron A, Ali SA, Haider NG (2017) Analyzing undergraduate students’ performance using educational data mining. Comput Educ 113:177–194. https://doi.org/10.1016/j.compedu.2017.05.007
  • Balacheff N (1994) Didactique et intelligence artificielle. Recherches en didactique des mathématiques 14(1):9–42
  • Barredo Arrieta A, Díaz-Rodríguez N, del Ser J, Bennetot A, Tabik S, Barbado A, Garcia S, Gil-Lopez S, Molina D, Benjamins R, Chatila R, Herrera F (2020) Explainable artificial intelligence (XAI): concepts, taxonomies, opportunities and challenges toward responsible AI. Inf Fusion 58:82–115. https://doi.org/10.1016/j.inffus.2019.12.012
  • Botana F, Recio T (2004) Towards solving the dynamic geometry bottleneck via a symbolic approach. In: International workshop on automated deduction in geometry. Springer, Berlin, Heidelberg, pp 92–110
  • Butler D, Jackiw N, Laborde JM, Lagrange JB, Yerushalmy M (2010) Design for transformative practices. In: Mathematics education and technology-rethinking the terrain. Springer, Boston, MA, pp 425–437
  • Carbonell J (1970) AI in CAI: an artificial-intelligence approach to computer-assisted instruction. IEEE Trans. Man-Machine Systems 11(4):190–202. https://doi.org/10.1109/tmms.1970.299942
  • Carlson M, Jacobs S, Coe E, Larsen S, Hsu E (2002) Applying covariational reasoning while modeling dynamic events: a framework and a study. J Res Math Educ 33(5):352. https://doi.org/10.2307/4149958
  • Emprin F (2022) Modeling practices to design computer simulators for trainees’ and mentors’ education. In: Richard PR, Vélez PM, Vaerenbergh VS (eds) Mathematics education in the age of artificial intelligence: how artificial intelligence can serve mathematical human learning, Mathematics education in the digital era, 17. Springer, pp 319–341. https://doi.org/10.1007/978-3-030-86909-0_14
  • Falcade R, Laborde C, Mariotti MA (2007) Approaching functions: Cabri tools as instruments of semiotic mediation. Educ Stud Math 66(3):317–333. https://doi.org/10.1007/s10649-006-9072-y
  • Fayek HM, Lech M, Cavedon L (2017) Evaluating deep learning architectures for speech emotion recognition. Neural Netw 92:60–68. https://doi.org/10.1016/j.neunet.2017.02.013
  • Font L, Gagnon M, Leduc N, Richard PR (2022) Intelligence in QED-Tutrix: balancing the interactions between the natural intelligence of the user and the artificial intelligence of the tutor software. In: Richard PR, Vélez PM, Vaerenbergh VS (eds) Mathematics education in the age of artificial intelligence: how artificial intelligence can serve mathematical human learning, Mathematics education in the digital era, 17. Springer, pp 45–76. https://doi.org/10.1007/978-3-030-86909-0
  • Ganesalingam M, Gowers WT (2016) A fully automatic theorem prover with human-style output. J Autom Reason 58(2):253–291. https://doi.org/10.1007/s10817-016-9377-1
  • Howson AG, Wilson B, International Commission on Mathematical Instruction (1990) School mathematics in the 1990s. Cambridge University Press
  • Hoyles C, Lagrange JB (2010) Mathematics education and technology-rethinking the terrain: the 17th ICMI study, New ICMI study series, 13. Springer
  • Jankvist UT, Misfeldt M, Aguilar MS (2019) What happens when CAS procedures are objectified ? —the case of “solve” and “desolve”. Educ Stud Math 101(1):67–81. https://doi.org/10.1007/s10649-019-09888-5
  • Jarvis D., Dreise K., Buteau C., LaForm-Csordas S., Doran C., & Novoseltsev A. (2022) CAS use in university mathematics teaching and assessment: applying Oates’ taxonomy for integrated technology. In: Richard, P. R., Vélez, P. M., & Vaerenbergh, V. S.Mathematics education in the age of artificial intelligence: how artificial intelligence can serve mathematical human learning (Mathematics education in the digital era, 17) (pp. 283–317). Springer https://doi.org/10.1007/978-3-030-86909-0_13
  • Kafetzopoulos G, Psycharis G (2022) Conceptualization of function as a covariational relationship between two quantities through modeling tasks. J Math Behav 67. https://doi.org/10.1016/j.jmathb.2022.100993
  • Koncel-Kedziorski R, Hajishirzi H, Sabharwal A, Etzioni O, Dumas Ang S (2015) Parsing algebraic word problems into equations. Trans Assoc Comput Linguist 3:585–597
  • Kovács Z, Parisse B (2015) Giac GeoGebra -Improved Gröbner Basis Computations. In: Computer algebra and polynomials, Gutierrez J, et. al. (Eds.), Lect Notes Comput Sci 8942:126–138. https://doi.org/10.1007/978-3-319-15081-97
  • Kovács Z, Recio T, Vélez MP (2022) Automated reasoning tools with GeoGebra: what are they? What are they good for? In: Richard PR, Vélez PM, Vaerenbergh VS (eds) Mathematics education in the age of artificial intelligence: how artificial intelligence can serve mathematical human learning, Mathematics education in the digital era, 17. Springer, pp 23–44
  • Kynigos C, Lagrange JB (2013) Cross-analysis as a tool to forge connections amongst theoretical frames in using digital technologies in mathematical learning. Educ Stud Math 85(3):321–327. https://doi.org/10.1007/s10649-013-9521-3
  • Lagrange JB (2005a) Using symbolic calculators to study mathematics. The case of tasks and techniques. In: Guin D, Ruthven K, Trouche L (eds) The didactical challenge of symbolic calculators. Turning a computational device into a mathematical instrument. Springer, pp 113–135
  • Lagrange JB (2005b) Curriculum, classroom practices, and tool design in the learning of functions through technology-aided experimental approaches. Int J Comput Math Learn 10(2):143–189
  • Lagrange JB, Abboud M (2018) Environnements numériques pour l’apprentissage, l’enseignement et la formation: perspectives didactiques sur la conception et le développement. IREM de Paris, Cahiers du Laboratoire de Didactique André Revuz
  • Leduc N (2016) PhD thesis, École polytechnique de Montréal
  • Mariotti MA (2013) Le potentiel sémiotique de Casyopée. In: Postface à Halbert R, Lagrange JB, Le Bihan C, Le Feuvre B, Manens MC, Meyrier X (eds) Les fonctions: comprendre et résoudre des problèmes de la 3ème à la Terminale. L’apport d’un logiciel dédié. IREM de Rennes, pp 78–82
  • Martínez-Sevilla Á, Alonso S (2022) AI and mathematics interaction for a new learning paradigm on monumental heritage. In: Richard PR, Vélez PM, Vaerenbergh VS (eds) Mathematics education in the age of artificial intelligence: how artificial intelligence can serve mathematical human learning, Mathematics education in the digital era, 17. Springer, pp 107–136
  • Minh TK (2012) Les fonctions dans un environnement numérique d’apprentissage: étude des apprentissages des élèves sur deux ans. Can J Sci Math Technol Educ 12(3):233–258. https://doi.org/10.1080/14926156.2012.704127
  • Mitchell TM (1997) Machine learning. McGraw-Hill, New York
  • Recio T, Vélez MP (1999) Automatic discovery of theorems in elementary geometry. J Autom Reason 23:63–82
  • Recio T, Richard PR, Vélez MP (2019) Designing tasks supported by GeoGebra automated reasoning tools for the development of mathematical skills. Int J Technol Math Educ 26(2):81–89
  • Richard PR (2004) L’inférence figurale: Un pas de raisonnement discursivo-graphique. Educ Stud Math 57(2):229–263. https://doi.org/10.1023/b:educ.0000049272.75852.c4
  • Richard PR, Vélez PM, Vaerenbergh VS (2022) Mathematics education in the age of artificial intelligence: how artificial intelligence can serve mathematical human learning, Mathematics education in the digital era, 17, 1st edn. Springer
  • Roanes-Lozano E, Roanes-Macías E, Villar-Mena M (2003) A bridge between dynamic geometry and computer algebra. Math Comput Model 37(9–10):1005–1028. https://doi.org/10.1016/s0895-7177(03)00115-8
  • Robert A, Rogalski J (2002) Le système complexe et cohérent des pratiques des enseignants de mathématiques: Une double approche. Can J Sci Math Technol Educ 2(4):505–528. https://doi.org/10.1080/14926150209556538
  • Robert A, Vandebrouck F (2014) Proximités-en-acte mises en jeu en classe par les enseignants du secondaire et ZPD des élèves: analyses de séances sur des tâches complexes. Recherches en didactique des mathématiques 43(2–3):239–285
  • Roozemond DA (2004) Automated proofs using bracket algebra with Cinderella and OpenMath. In Proceedings of 9th Rhine workshop on computer algebra (RWCA 2004)
  • Saxton D, Grefenstette E, Hill F, Kohli P (2019) Analysing mathematical reasoning abilities of neural models. In: Proceedings of ICLR. In international conference on machine learning
  • Smith A, Min W, Mott BW, Lester JC (2015) Diagrammatic student models: modeling student drawing performance with deep learning. In: International conference on user modeling, adaptation, and personalization. Springer, pp 216–227
  • Tessier-Baillargeon M, Richard PR, Leduc N, Gagnon M (2017) Étude comparative de systèmes tutoriels pour l’exercice de la démonstration en géométrie. Annales de didactique et de sciences cognitives 22:93–117. https://doi.org/10.4000/adsc.716
  • Thompson PW (2011) Quantitative reasoning and mathematical modeling. In: Hatfield LL, Chamberlain S, Belbase S (eds) New perspectives and directions for collaborative research in mathematics education, WISDOMe Mongraphs, vol 1. University of Wyoming, pp 33–57
  • Turing AM (1950) Computing machinery and intelligence. Mind 49:433–460
  • Van Vaerenbergh S, Pérez-Suay A (2022) A classification of artificial intelligence systems for mathematics education. In: Richard PR, Vélez PM, Vaerenbergh VS (eds) Mathematics education in the age of artificial intelligence: how artificial intelligence can serve mathematical human learning, Mathematics education in the digital era, 17. Springer, pp 89–106
  • Vapnik V (1999) The nature of statistical learning theory. Springer
  • Wu WT (1978) On the decision problem and the mechanization of theorem-proving in elementary geometry. Sci Sinica 21:159–172
  • Zehavi N, Mann G (2011) Development process of a praxeology for supporting the teaching of proofs in a cas environment based on teachers’ experience in a professional development course. Tech Know Learn 16:153–181. https://doi.org/10.1007/s10758-011-9181-2