ABSTRACT

Researchers have emphasized the importance of characterizing students’ abilities to coordinate changes in covarying quantities. In this paper, we characterize three undergraduate students’ coordination of covarying quantities’ amounts of change during a teaching experiment. We adopt Piagetian notions of figurative and operative thought to describe the extent their meanings for covariational relationships are constrained to or supported by their partitioning activity – the mental and physical actions associated with constructing accruals in quantities’ magnitudes. Our analysis suggests that students’ construction of amounts of change is constrained by figurative partitioning activity that requires carrying out or emulating particular actions on perceptually available material. In contrast, operative partitioning activity supports the students’ transformation and (anticipated) regeneration of partitioning activity in order to conceive equivalent covariational relationships among various situations and representational systems. We conclude by discussing how documenting these distinctive meanings contributes to extant literature on covariational reasoning and, more broadly, the theorization of mathematical concept construction.

摘要

研究人员强调了描述学生协调共变量变化的能力的重要性。在本文中，我们描述了三个本科生在教学实验中对协变量变化量的协调。我们采用 Piagetian 的比喻和操作思想的概念来描述它们对协变关系的意义受到其划分活动的限制或支持的程度– 与构建数量级应计项目相关的心理和生理活动。我们的分析表明，学生对变化量的构建受到需要对感知可用材料执行或模仿特定动作的比喻性划分活动的限制。相比之下，操作分区活动支持学生的转换和（预期的）分区活动的再生，以构想各种情况和表征系统之间的等效协变关系。我们最后讨论了记录这些独特的含义如何有助于现有的关于协变推理的文献，更广泛地说，是数学概念构建的理论化。