New Challenge for Initial Training of Mathematics Teachers: The Planning Phase of Mathematics Distance Learning
DOI:
https://doi.org/10.19173/irrodl.v22i3.5525Keywords:
distance learning, planning, preservice teachers, conceptual understanding, mathematicsAbstract
The scientific literature identifies five challenges related to training teachers: the basics of the constructivist approach, the problematization of mathematical knowledge to be taught, the promotion of interdisciplinarity, the use of digital pedagogical resources in planning teaching, and new skills to be developed due to the arrival of artificial intelligence. Considering the COVID-19 pandemic, it is appropriate to consider a sixth challenge, notably, training teachers capable of delivering mathematical distance learning courses focused on students’ conceptual understanding. It therefore is necessary to link the stakes of initial training with that of distance learning, which can enhance conceptual understanding. Linking the need to construct knowledge among students with technological tools used for distance learning allows new challenges faced in the planning of mathematics teaching to be highlighted. These new challenges give rise to the anticipation genesis that helps in situating the planning of mathematics teaching between three variables: artifact variables, arrangement variables, and variables related to the nature of the data to be used. These variables are a major asset for the training of the preservice mathematics teacher. Their study in this article allows us to recognize that the choice of technological tools to be used in mathematics distance learning depends greatly on the conceptual analysis of the mathematical knowledge to be taught. This study shows that it is important to rethink and question distance learning for each mathematical concept.
References
Adler, J. (2010). La conceptualisation des ressources. Apports pour la formation des professeurs de mathématiques [Conceptualizing resources. Contributions to the training of mathematics teachers]. In G. Gueudet & L. Trouche (Eds.), Ressources vives. Le travail documentaire des professeurs en mathématiques (pp. 23–37). Presses Universitaires de Rennes et INRP.
Balhan, K., Gerard, I., Ngan, G. N., & Schneider, M. (2019). Une dimension particulière de la réflexivité: “les mathématiques comme problème professionnel” à la base d’un dispositif de formation initiale en didactique des mathématiques [A particular dimension of reflexivity: "mathematics as a professional problem" at the basis of an initial training program in mathematics education]. Canadian Journal of Science, Mathematics and Technology Education, 19(2), 1–13. https://doi.org/10.1007/s42330-018-0035-y
Ben-Zvi, D., & Makar, K. (2016). International perspectives on the teaching and learning of statistics. In D. Ben-Zvi & K. Makar (Eds.), The teaching and learning of statistics (pp. 1–10). Springer.
Bergeron, L. (2016). La planification de l’enseignement et la gestion pédagogique de la diversité des besoins des élèves en classe ordinaire: une recherche collaborative au primaire [Teaching planning and pedagogical management of students' diverse needs in the regular classroom: collaborative research in the elementary school]. Thèse de doctorat. Université du Québec à Trois-Rivières. http://depot-e.uqtr.ca/id/eprint/8015/
Brousseau, G. (1998). Théorie des situations didactiques [The theory of didactical situations]. La pensée sauvage.
Brown, S., Race, R., & Bull, J. (1999). Computer-assisted assessment in higher education. Koganm.
Cabon, P., Delgoulet, C., & Valot, C. (2014). Quelques approches du processus d’anticipation en ergonomie: de l’individu à l’organisation [Some approaches to the anticipation process in ergonomics: from the individual to the organization]. In E. Siéroff, E. Drozda-Senkowska, A. M. Ergis, & S. Moutier (Eds.), Psychologie de l’anticipation (pp. 37–55). Armand Colin.
Chinnappan, M. (2006). Using the productive pedagogies framework to build a community of learners online in mathematics education. Distance Education, 27(3), 355–369. https://doi.org/10.1080/01587910600940430
Cho, M. H., & Heron, M. L. (2015). Self-regulated learning: The role of motivation, emotion, and use of learning strategies in students’ learning experiences in a self-paced online mathematics course. Distance Education, 36(1), 80–99. https://doi.org/10.1080/01587919.2015.1019963
Clerc, A., & Martin, D. (2011). L’étude collective d’une leçon, une démarche de formation pour développer et évaluer la construction des compétences professionnelles des futurs enseignants [The collective study of a lesson, a training approach to develop and evaluate the construction of professional skills of preservice teachers]. Revue internationale de pédagogie de l’enseignement supérieur, 27(2), 2–13. https://doi.org/10.4000/ripes.514
Clift, R., & Brady, P. (2005). Research on methods courses and field experiences. In M. Cochran-Smtih & K. Zeichner (Eds.), Studying teacher education: The report of the AERA panel on research and teacher education (pp. 309–424). American Educational Research Association.
Cohan, A., & Honigsfeld, A. (2006). Incorporating “lesson study” in teacher preparation. The Educational Forum, 71(1), 81–82. https://doi.org/10.1080/00131720608984570
CSE: Conseil supérieur de l’éducation. (2020). Éduquer au numérique: Rapport sur l’état et les besoins de l’éducation 2018–2020 [Educating digitally: a report on the state and needs of education 2018-2020]. Québec, Le Conseil. https://www.cse.gouv.qc.ca/publications/eduquer-au-numerique-50-0534/#:~:text=Dans%20son%20rapport%20sur%20l,pour%20le%20syst%C3%A8me%20d’%C3%A9ducation
DeBlois, L. (2012). De l’ancien élève à l’enseignant. Quel parecours [From former student to teacher. What a path]. In J. Proulx, C. Corriveau, & H. Squalli (Eds.), Formation mathématique pour l’enseignement des mathématiques (pp. 313–320). Presses de l’Université du Québec.
DeBlois, L., & Squalli, H. (2002). Implication de l’analyse de productions d’élèves dans la formation des maitres du primaire [Implication of the analysis of students' productions in the training of primary school teachers ]. Educational Studies in Mathematics, 50(2), 212–237. https://www.jstor.org/stable/3483299?seq=1
Diallo, P. (2005). Savoir-enseigner et approche constructiviste des apprentissages en formation initiale des maîtres: Les paramètres du développement professionnel dans les productions étudiantes des futurs enseignants Franco-Ontariens [Knowing how to teach and the constructivist approach to learning in initial teacher training: The parameters of professional development in the productions of preservice Franco-Ontarian teachers]. Canadian Journal of Educational Administration and Policy, 39, 1–15. https://cdm.ucalgary.ca/index.php/cjeap/article/view/42719
Djeumeni, M. (2015). La formation pratique des enseignants au Cameroun [Practical teacher training in Cameroon]. Formation et profession, 23(3), 169–180. https://doi.org/10.18162/fp.2015.a77
Drijvers, P., ... Nongni, G., ... et Rodrigues, A. (2019). Transitions Toward Digital Resources: Change, Invariance, and Orchestration. In: Trouche L., Gueudet G., Pepin B. (eds) The 'Resource' Approach to Mathematics Education. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-20393-1_12
Dumouchel, G., & Karsenti, T. (2013). Les compétences informationnelles relatives au Web des futurs enseignants québécois et leur préparation à les enseigner: résultats d’une enquête [Computer/Internet skills of preservice teachers in Québec and their readiness to teach them: survey results]. Éducation et Francophonie, 41(1), 7–29. https://doi.org/10.7202/1015057ar
Farrús, M., & Costa-jussà, M. R. (2013). Automatic evaluation for e-learning using latent semantic analysis: A use case. International Review of Research in Open and Distributed Learning, 14(1), 239–254. https://doi.org/10.19173/irrodl.v14i1.1389
Francis, K., & Jacobsen, M. (2013). Synchronous online collaborative professional development for elementary mathematics teachers. The International Review of Research in Open and Distributed Learning, 14(3), 319–343. https://doi.org/10.19173/irrodl.v14i3.1460
Gattuso, L. (1993). Les conceptions personnelles au sujet de l’enseignement des mathématiques et leur reflet dans la pratique: Un essai d’autoanalyse [Personal conceptions about mathematics education and their reflection in practice: An attempt at self-analysis]. [Doctoral dissertation, Université de Montréal]. https://www.elibrary.ru/item.asp?id=5685147
Gueudet, G., & Trouche, L. (2008). Du travail documentaire des enseignants: Genèses, collectifs, communautés. Le cas des mathématiques [On teachers' documentary work: Geneses, collectives, communities. The case of mathematics]. Éducation et Didactique, 2(3), 7–33. https://doi.org/10.4000/educationdidactique.342
Gueudet, G., & Trouche, L. (2010). Des ressources aux documents, travail du professeur et genèses documentaires [From resources to documents, teacher's work and documentary genesis]. In G. Gueudet & L. Trouche (Eds.), Ressources vives. Le travail documentaire des professeurs en mathématiques (pp. 57–74). Presses Universitaires de Rennes et INRP.
Hewson, C. (2012). Can online course-based assessment methods be fair and equitable? Relationships between students’ preferences and performance within online and offline assessments. Journal of Computer Assisted Learning, 28, 288–298. https://doi.org/10.1111/j.1365-2729.2011.00473.x
Hodges, C., Moore, S., Lockee, B., Trust, T., & Bond, A. (2020, March 27). The difference between emergency remote teaching and online learning. EDUCAUSE Review. https://er.educause.edu/articles/2020/3/the-difference-between-emergency-remote-teaching-and-online-learning
Ku, H., Akarasriworn, C., Glassmeyer, D. M., Mendoza, B., & Rice, L. A. (2011). Teaching an online graduate mathematics education course for in-service mathematics teachers. Quarterly Review of Distance Education, 12(2), 135–147. https://go.gale.com/ps/anonymous?id=GALE%7CA284222195&sid=googleScholar&v=2.1&it=r&linkaccess=abs&issn=15283518&p=AONE&sw=w
Lee, J. (2014). An exploratory study of effective online learning: Assessing satisfaction levels of graduate students of mathematics education associated with human and design factors of an online course. International Review of Research in Open and Distributed Learning, 15(1), 111–132. https://doi.org/10.19173/irrodl.v15i1.1638
Legendre, R. (2005). Dictionnaire actuel de l’éducation [Current Dictionary of Education] (3rd ed.). Guérin.
Leroyer, L. (2018a). The capacity to think of transmission of knowledge from learning supports: A proposition of a conceptual model. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 203–206). ENS de Lyon.
Leroyer, L. (2018b, October 22–26). La notion de support, au centre d’un modèle des situations d’enseignement/apprentissage, ressource pour comprendre et pour faire [The notion of support, at the center of a model of teaching/learning situations, a resource for understanding and doing]. In Espace mathématique francophone 2018 (EMF). GT6: Conception, diffusion et usages des ressources (pp. 98–105). Gennevilliers, France.
Malo, A. (2000). Savoirs de formation et savoirs d’expérience: un processus de transformation [Training knowledge and experience knowledge: a process of transformation]. Éducation et Francophonie, 28(2), 216–235. http://collections.banq.qc.ca/ark:/52327/bs61547
Morin, M. P. (2008). Les connaissances mathématiques et didactiques chez les futurs maîtres du primaire: Quatre cas à l’étude [The mathematical and didactic knowledge of primary preservice teachers: Four case studies]. Canadian Journal of Education/Revue Canadienne de l’éducation, 31(3), 537–566. https://journals.sfu.ca/cje/index.php/cje-rce/article/view/3012
Ndolly, G. (2012). L’apprentissage à l’enseignement de la géométrie: analyse des pratiques de futurs enseignants en stage à l’école primaire au Gabon [Learning to teach geometry: analysis of the practices of primary pre-service teachers in Gabon]. [Doctoral dissertation, Université Laval Bibliothèque]. https://corpus.ulaval.ca/jspui/handle/20.500.11794/23261
Nongni, G. (2020). Intégration des ressources documentaires numériques dans la planification de l’enseignement de la statistique par des futurs enseignants au secondaire [Integration of digital documentary resources in the planning of statistics education by secondary preservice teachers]. [Doctoral dissertation, Université Laval]. https://corpus.ulaval.ca/jspui/handle/20.500.11794/38214
Nuangchalerm, P., Prachagool, V., & Sriputta, P. (2011). Online professional experiences in teacher preparation program: A preservice teacher study. Canadian Social Science, 7(5), 116–120. https://doi.org/10.3968/J.css.1923669720110705.298
Proulx, J., & Bednarz, N. (2010). Formation mathématique des enseignants du secondaire. Partie 1: Réflexions fondées sur une analyse des recherches [Mathematics Education for Secondary School Teachers. Part 1: Reflections based on a review of research]. Revista de Educação Matemática eTecnologica Ibero-americana, 1(1), 1–23. https://periodicos.ufpe.br/revistas/index.php/emteia/article/viewFile/2271/1833
Queiroz, T., Monteiro, C., Carvalho, L., & François, K. (2017). Interpretation of statistical data: The importance of affective expressions. Statistics Education Research Journal, 16(1), 163–180. https://iase-web.org/documents/SERJ/SERJ16(1)_Queiroz.pdf
Rabardel, P. (1995). Les hommes et les technologies: Approche cognitive des instruments contemporains [People and technology: A cognitive approach to contemporary instruments]. Armand Colin.
Rabardel, P. (1999). Éléments pour une approche instrumentale en didactique des mathématiques [Elements for an instrumental approach in mathematics education]. Actes de L’école D’été de Didactique des Mathématiques, 2, 203–213. https://www.rabardel.fr/app/download/14429086135/1999-Rabardel-ARDM.pdf?t=1589991217
Rogers, P. L. (2009). Encyclopedia of distance learning (2nd ed.). Idea Group Inc (IGI).
Russell, M., Kleiman, G., Carey, R., & Douglas, J. (2009). Comparing self-paced and cohort-based online courses for teachers. Journal of Research on Technology in Education, 41(4), 443–466. https://doi.org/10.1080/15391523.2009.10782538
Savard, A. (2014). Enseigner à enseigner: regards croisés sur l’épistémologie et le rapport au savoir d’une professeure [Teaching to teach: crossed views on epistemology and a teacher's relationship to knowledge]. In M.-C. Bernard, A. Savard, & C. Beaucher (Eds.), Le rapport aux savoirs: une clé pour analyser les épistémologies enseignantes et les pratiques de classe. Québec: Livres en ligne du CRIRES (pp. 77–91). https://lel.crires.ulaval.ca/oeuvre/une-cle-pour-analyser-les-epistemologies-enseignantes-et-les-pratiques-de-classe
Tochon, F. (2013). Planification ouverte de l’enseignement dans une approche profonde de l’apprentissage. Le défi que les réformes en cours posent aux enseignants et aux administrations [Open planning of teaching in a deep approach to learning. The challenge that the current reforms pose to teachers and administrations]. In M. De Kesel, M. Bouhon, J.-L. Dufays, & J. Plumat (Eds.), La planification des apprentissages. Comment les enseignants des différentes disciplines programment-ils et préparent-ils leurs cours? Cadrage de la problématique (pp. 31–62). Presses universitaires de Louvain.
Trouche, L. (2007). Chapitre 1. Environnements informatisés d’apprentissage: quelle assistance didactique pour la construction des instruments mathématiques? [ Chapter 1: Computerized learning environments: what didactic assistance for the construction of mathematical instruments]. In R. Floris (Ed.), Environnements informatiques, enjeux pour l’enseignement des mathématiques: Intégrer des artefacts complexes, en faire des instruments au service de l’enseignement et de l’apprentissage (pp. 19–38). De Boeck Supérieur.
UNESCO. (2020a, March 21). COVID-19: L’UNESCO organise un webinaire sur l’éducation consacré à l’équité dans la scolarité [UNESCO organizes webinar on equity education and schooling]. https://fr.unesco.org/news/covid-19-lunesco-organise-webinaire-leducation-consacre-lequite-scolarite
UNESCO. (2020b, March 30). Webinaire sur le COVID-19: Un monde nouveau s’ouvre aux enseignants, en première ligne de l’éducation [A new world for teachers, education’s frontline workers - COVID-19 education webinar ]. https://fr.unesco.org/news/webinaire-covid-19-monde-nouveau-souvre-aux-enseignants-premiere-ligne-leducation
Vergnaud, G. (1990). La théorie des champs conceptuels [The Conceptual Fields' Theory]. Recherches en Didactique des Mathématiques, 10(2–3), 133–170. https://revue-rdm.com/2005/la-theorie-des-champs-conceptuels/
Vergnaud, G. (1994). Le rôle de l’enseignant à la lumière des concepts de schème et de champ conceptuel [The role of the teacher in light of the concepts of pattern and conceptual field]. Vingt ans de didactique des mathématiques en France, Grenoble, La Pensée Sauvage (pp. 177–191). La Pensée Sauvage éditions Grenoble.
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