Abstract The study reported in this article examined the ways in which new mathematics learning influences students’ prior ways of reasoning. We conceptualize this kind of influence as a form of transfer of learning called backward transfer. The focus of our study was on students’ covariational reasoning about linear functions before and after they participated in a multi-lesson instructional unit on quadratic functions. The subjects were 57 students from two authentic algebra classrooms at two local high schools. Qualitative analysis suggested that quadratic functions instruction did influence students’ covariational reasoning in terms of the number of quantities and the level of covariational reasoning they reasoned with. These results further the field’s understanding of backward transfer and could inform how to better support students’ abilities to engage in covariational reasoning.

中文翻译：

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二次函数教学的后向迁移对学生线性函数协变推理先验方法的影响

摘要 本文报道的研究考察了新数学学习影响学生先前推理方式的方式。我们将这种影响概念化为一种称为反向迁移的学习迁移形式。我们研究的重点是学生在参加关于二次函数的多课教学单元之前和之后对线性函数的协变推理。受试者是来自两所当地高中的两个真正的代数教室的 57 名学生。定性分析表明，二次函数教学确实在数量的数量和他们推理的协变推理水平方面影响了学生的协变推理。