Rich Kathryn M
American Institutes for Research, Human Services Division, Chicago, IL USA.
Digit Exp Math Educ. 2023;9(1):163-208. doi: 10.1007/s40751-022-00111-4. Epub 2022 Sep 27.
Incorporating visual representations, rather than strictly relying on symbolic representations, is a research-based strategy for supporting fraction learning. However, students must also make transitions between visual and symbolic fraction representations to apply the conceptual understanding they gained from visual representations to symbolic fraction computation. Virtual manipulatives (VMs) offer opportunities for supporting students in making these transitions, as many fraction VMs integrate visual and symbolic representations into one manipulative. Some VMs also dynamically link the representations, so learners can observe how changes to one representation impact the other. For these features to support students in transitioning among representations, teachers must orchestrate opportunities for students to use and reflect on their use of the features. This study examined how six fourth- and fifth-grade teachers orchestrated opportunities in lesson plans for students to make transitions among the visual and symbolic representations within and beyond fraction VMs. Results showed that teachers used two strategies for orchestrating these transitions: VM choice and direct teacher intervention. Implications of teachers' uses of these strategies are discussed in terms of what kinds of transition opportunities were made available to students and what professional learning experiences could be needed to support teachers in orchestrating transitions.
纳入视觉表征，而不是严格依赖符号表征，是一种基于研究的支持分数学习的策略。然而，学生还必须在视觉和符号分数表征之间进行转换，以便将他们从视觉表征中获得的概念理解应用于符号分数计算。虚拟操作工具（VMs）为支持学生进行这些转换提供了机会，因为许多分数VMs将视觉和符号表征整合到一个操作工具中。一些VMs还动态地链接这些表征，以便学习者能够观察到一种表征的变化如何影响另一种表征。为了使这些功能支持学生在不同表征之间进行转换，教师必须精心安排机会，让学生使用并反思他们对这些功能的使用。本研究考察了六位四、五年级教师如何在教案中精心安排机会，让学生在分数VMs内外的视觉和符号表征之间进行转换。结果表明，教师使用了两种策略来精心安排这些转换：VM选择和教师直接干预。将根据为学生提供了哪些类型的转换机会以及需要哪些专业学习经验来支持教师精心安排转换，来讨论教师使用这些策略的影响。
