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Illustration by S.L.Meyer |
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).
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.
In the case of JAN, a pedagogical and an epistemological problem had to be solved: What means insight in mathematical education and how can it be developed in the field? Flexible interviews and role-playing games like "I am your calculator" are rich systemic tools. The triangulation of methods (roleplay, critical exploration, thinking arithmetic – arithmetic thinking (see Arrigo “calcolo ragionato”), semi-written arithmetic, critical exploration, zone of proximal development, see Bodrova & Leong, 2015; Duckworth, 2004; Winnicott, 2002; Cuomo, 2007; Lillard, Lerner, Hopkins, Dore, Smith & Palmquist, 2012; Vygotsky, 2019) dynamizes pedagogy and research. This case analysis does not only describe developments in the here and now of JAN, but also current developments of the pedagogue.
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).
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