Figure 1: Jan writes on the blackboard |
Figure 3: logo of the IayC |
Can we conclude that the critical method is better than testing? Piaget* was open-minded: «Or, une méthode n'est pas bonne ou mauvaise en soi. Elle ne peut être jugée qu'en fonction des problèmes qu'elle est appelée à résoudre et qui, à leur tour, sont orientés par des perspectives épistémologiques plus ou moins explicites » (cf. Piaget in Inhelder, Sinclair & Bovet, 1974, p. 35; see Duckworth, 2004. *Piaget: "However, a method is not good or bad in itself. It can only be judged according to the problems it is intended to solve, which in turn are oriented by more or less explicit epistemological perspectives").
Vygotsky (2019, p. 88-89) specifies the meaning of test methodologies as follows: "Formerly, it was believed that by using tests, we determine the mental development level with which education should reckon and whose limits it should not exceed. This procedure oriented learning toward yesterday’s development, toward developmental stages already completed. The error of this view was discovered earlier in practice than in theory. It is demonstrated most clearly in the teaching of mentally retarded children. Studies have established that mentally retarded children are not very capable of abstract thinking. From this the pedagogy of the special school drew the seemingly correct conclusion that all teaching of such children should be based on the use of concrete, look-and-do methods." From the meta-analysis of Hodgen, Foster, Marks and Brown (2018) it can be concluded that the evidence of this method is high because an ensemble of pedagogic approaches, learning forms and tools is used. The fantasy of number artists (arithmeticians) is sustained by the "poetry of possibilities" (cf. Sutton-Smith, 1986).
Future case studies will examine experiences and development work at different levels. "Sharing the video" is a promising method to explore the meaning of the experiences with the talking and acting calculator in a "video-stimulated-dialogue" (see Morgan, 2007; Nind, Kilburn, Wiles, 2015; Werfeli & Meyer, 2019; Eggenberger, 2021).
Let's recall the basic questions at IayC again: What is mental arithmetic exactly? What does "calculate like a flash" mean? What is the "calcolo ragionato"? How does mental arithmetic occur when a person solves arithmetic operations with his fingers? How do intuitions, comprehension, and competence in arithmetic operations occur when learners have little or no schemata for them?
The "I am your calculator" method positively provokes mind games from which answers to the posed questions can be generated. - The concern about transmission pedagogical methods is not discussed further (cf. Meyer, 2017). But a methodological note is presented, which differentiates the meaning of IayC.
The previous case studies and explanations described working relations in two-person situations or in the work of one teacher with two children. It turned out, despite all methodological precision, that it is difficult to recognize and overcome the linear-chronological teaching behavior (cf. Eggenberger, 2021). And this is one of the objectives of the IayC method. Walter Omar Kohan (Rio de Janeiro) shed light on this in the lecture "Paulo Freire more than (n)ever?" (cf. international conference 100 years of Paulo Freire from 15.10.2021 in Salzburg; Kohan, 2018) the following aspect. As a rule, transmission pedagogy works with the measurable concept of time of chronos. Liberating pedagogy reflects on a different concept of time, which focuses on lifetime or individual life (cf. GEMOLL: Aiòn: lifetime, life, generation, time, duration, period. Lifeless, long, unlimited time and eternity). The holistic view of life is already found in Heraclitus: "Aiòn (time) is a child, - a child at the board game; a child sitting on the throne" (B52, Heraclitus, 2007).
How can an educator free himself or herself from the dictates of Chronos? Through what does she learn to think, work, and feel with the liberating concept of time? The answer lies not in a romantic enchantment, but in the transformation of working and working relationships. Play pedagogy is a key to changing the way we work in pedagogy. This will be exemplified in the following scene looking at groups of learners.
Figure 4: IayC as a puppet play (Image: S. Meyer). |
This episode provides insight into the "I'm Your Calculator Mental Arithmetic Game." Game ideas, roles, tasks, playtime, and metacognition are developed, carried out, discussed, modified, and continued in free conversation. The IayC and the mental arithmetic game would be expressions of reciprocal maieutics and free operative conversation (cf. Dolci, 2011; Fasce & Vigilante, 2011; Piaget, abstraction réfléchissante; Meyer, 2006).
Arrigo, G. (2014). Calcolo mentale-approssimato-strumentale. Bollettino dei docenti di matematica, 68, 53-62.
Bodrova, E. & Leong, D. J. (2015). Vygotskian and Post-Vygotskian Views on Children’s Play. American Journal of Play, 7(3), 371–388.
Cargnelutti, E., Tomasetto, C. & Passolunghi, M. C. (2017). The interplay between affective and cognitive factors in shaping early proficiency in mathematics. Trends in Neuroscience and Education, 8–9, 28–36. https://doi.org/10.1016/j.tine.2017.10.002
Cuomo, N. (2007). Verso una scuola dell'emozione di conoscere. Il futuro insegnante, insegnante del futuro. Pisa: Edizioni ETS.
Dolci, D. (2011). Dal trasmettere al comunicare (Terza edizione.). Casale Monferrato (Alessandria): Sonda. Verfügbar unter: https://danilodolci.org/maieuticareciproca/
Duckworth, E. (2004). L’exploration critique dans la salle de classe. In J.-P. Bronckart & M. Gathier Thurler (Hrsg.), Transformer l’école (S. 79–98). Bruxelles : De Boeck & Larcier.
Eggenberger, D. (2021). „Ich bin dein Taschenrechner“ (IbdT) - Kritische Exploration und Rollenspiel. Masterarbeit. Zürich: Interkantonale Hochschule für Heilpädagogik. Zugriff am 03.11.2021. Verfügbar unter: https://zenodo.org/record/5638606#.YYJD7xwxmUl
Fasce, P. & Vigilante, A. (Hrsg.). (2011). Danilo Dolci e l’educarsi maieutico. Educazione Democratica, 2. Günter, M. (2003). Psychotherapeutische Erstinterviews mit Kindern. Winnicotts Squiggletechnik in der Praxis. Stuttgart: Klett-Cotta.
Heraklit. (2007). Fragmente (14. Aufl.). Zürich: Artemis & Winkler.
Hodgen, J., Foster, C., Marks, R. & Brown, M. (2018). Evidence for Review of Mathematics Teaching: Improving Mathematics in Key Stages Two and Three: Evidence Review. London: Education Endowment Foundation. Verfügbar unter: https://educationendowmentfoundation.org.uk/evidence-summaries/evidencereviews/ improving-mathematics-in-key-stages-two-and-three/
Ingenkamp, K. & Lissmann, U. (2005). Lehrbuch der pädagogischen Diagnostik (5. völlig neu überarbeitete Aufl.). Weinheim: Beltz.
Inhelder, B., Sinclair, H., Bovet, M. (1974). Apprentissage et structures de la connaissance. Paris: Presses Universitaires de France.
Kohan, W. O. (2021, Oktober 15). “Paulo Freire more than (n)ever?”. Vortrag, hybrid gehalten auf der Internationalen Tagung 100 Jahre Paulo Freire, Salzburg (AT). Zugriff am 15.10.2021. Verfügbar unter: http://paulofreire100jahre.sbg.ac.at/
Mannoni, B. (1978). Mathe-Unterricht - Man ist schliesslich nicht zum Spass da! In M. Mannoni (Hrsg.), Ein Ort zum Leben. Die Kinder von Bonneuil (S. 80–99). Frankfurt a.M.: Syndikat.
Meyer, S. (2006). Das flexible Interview. Zugriff am 20.1.2019. Verfügbar unter: https://www.interview.hfh.ch/
Moreno, J. L. (2007a). Kanon der Kreativität und Analyse der Kreativitätscharta. In H.G. Petzold & I. Orth (Hrsg.), Die neuen Kreativitätstheorien. Handbuch der Kunsttherapie. Theorie und Praxis (4. Aufl., Bände 1-II, Band I, S. 187–188). Bielefeld und Locarno: Edition Sirius.
Moreno, J. L. (2007b). Theorie der Spontaneität-Kreativität. In H.G. Petzold & I. Orth (Hrsg.), Die neuen Kreativitätstheorien. Handbuch der Kunsttherapie. Theorie und Praxis (4. Aufl., Bände 1-II, Band I, S. 189–202). Bielefeld und Locarno: Edition Sirius.
Morgan, A. (2007). Using video‐stimulated recall to understand young children's perceptions of learning in classroom settings. European Early Childhood Education Research Journal, 15(2), 213-226.
Nind, M., Kilburn, D., Wiles, R. (2015). Using video and dialogue to generate pedagogic knowledge: teachers, learners and researchers reflecting together on the pedagogy of social research methods. International Journal of Social Research Methodology, 1-16.
Piaget, J. (1967). Le jugement et le raisonnement chez l'enfant (6ème édition). Neuchâtel: Delachaux et Niestlé.
van Oers, B., Wardekker, W., Elbers, E. & van der Veer, R. (2008). The Transformation of Learning. Advances in Cultural-Historical Activity Theory. New York: Cambridge University Press.
Roth, W.-M., Walshaw, M. (2019). Affect and emotions in mathematics education: toward a holistic psychology of mathematics education. Educational Studies in Mathematics, 102(1), 111–125. https://doi.org/10.1007/s10649-019-09899-2
Shakespeare, W. (2012). A Midsummer Night's Dream. Ein Sommernachtstraum. Stuttgart: Philipp Reclam jun.
Smith, P. K. & Roopnarine, J. L. (Hrsg.). (2018). The Cambridge Handbook of Play: Developmental and Disciplinary Perspectives. Cambridge, United Kingdom ; New York, NY: Cambridge University Press.
Storch, M. (1996, 27. 09). Kreativität und Psychodrama. Vortrag gehalten auf der 53. Psychotherapie-Seminar vom 22. bis 27. September 1996, Freudenstadt.
Sutton-Smith, B. & S. (1986). Hoppe, hoppe Reiter...Die Bedeutung von Kinder-Eltern-Spielen. München: Piper.
Vygotsky, L.S. (2019). Mind in Society. Cambridge MA: Harvard University Press. Kindle-Version.
Wang, C. C. (2006). Youth Participation in Photovoice as a Strategy for Community Change. Journal of Community Practice, 14(1–2), 147–161. Routledge. https://doi.org/10.1300/J125v14n01_09
Werfeli, B. & Meyer, S. (2019). Flexible Interviews besprechen. Fallstudie und Reflexion des flexiblen Interviews mit Hilfe von «sharing the video». Interkantonale Hochschule für Heilpädagogik. Zugriff am 21.5.2019. Verfügbar unter: http://www.interview.hfh.ch/page005.htm
Winnicott, D. W. (2002). Vom Spiel zur Kreativität (10. Aufl.). Stuttgart: Klett-Cotta.
Zaslavsky, C. (1994). Fear of Math. How to get over it and get on with your life. New Brunswick: Rutgers University Press.