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Compartmentalisation of Mathematical Sectors: The Case of Continuous Probability Distributions and Integrals
International Journal of Research in Undergraduate Mathematics Education Pub Date : 2021-05-20 , DOI: 10.1007/s40753-021-00143-y
Thomas Hausberger , Charlotte Derouet , Reinhard Hochmuth , Gaetan Planchon

This paper investigates the phenomenon of compartmentalisation of knowledge in the teaching and learning of continuous probability distributions and integral calculus at the secondary-tertiary transition in France. Using the Anthropological Theory of the Didactic (ATD), and in particular the key notion of praxeology, we investigate in which sense those two sectors may be described as compartmentalised in current textbooks. We then study, by means of a questionnaire, the educational effects of the compartmentalisation: do students’ difficulties in completing “bridging tasks” (tasks that require to relate the two sectors) reflect the partial disconnections revealed by the praxeological analyses? The key notion of ostensive, combined with the role played by the technology in the sense of ATD, is used to interpret the data. Altogether, this study sheds light on the deficit of cognitive flexibility required to change mathematical sectors, which is understood as a result of deficient praxeologies developed within the institutions.



中文翻译:

数学部门的区间化:连续概率分布和积分的情况

本文研究了在法国二次-三次转型中连续概率分布和积分演算的教与学中知识分隔的现象。使用教学法的人类学理论(ATD),尤其是人类行为学的关键概念,我们研究了在当前教科书中这两个领域在何种意义上被描述为分隔的。然后,我们通过问卷调查划分的教育效果:学生在完成“桥接任务”(要求将两个部门联系起来的任务)方面的困难是否反映了人类行为学分析所揭示的部分脱节?表观性的关键概念与该技术在ATD方面的作用相结合,用于解释数据。共,

更新日期:2021-05-20
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