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首页> 外文期刊>Journal of computers in mathematics and science teaching >Developing Students' Representational Fluency Using Virtual and Physical Algebra Balances
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Developing Students' Representational Fluency Using Virtual and Physical Algebra Balances

机译：利用虚拟和物理代数天平培养学生的代表性流利度

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Both virtual and physical manipulatives are reported as effective learning tools when used with different groups of students in a variety of contexts to learn mathematical content. The use of multiple representations and the flexibility to translate among those representational forms facilitates students' learning and has the potential to deepen their understanding. This classroom project involved two groups of third-grade students in a week-long unit focusing on algebraic relationships. The purpose of the unit was to engage students with different algebraic models and encourage students to use informal strategies to represent their relational thinking. The paper highlights examples of these student representations as evidence of the children's developing algebraic thinking. Result from the pre and posttest measures showed that students in the physical and virtual manipulative environments gained significantly in achievement and showed flexibility in translating and representing their understanding in multiple representations: manipulative model, pictorial, numeric, and word problems. The researchers recorded field notes, interviewed students, and videotaped class sessions in order to identify unique features of the learning environments. The virtual environment had unique features that promoted student thinking such as: (a) explicit linking of visual and symbolic modes; (b) guided step-by-step support in algorithmic processes; and (c) immediate feedback and self-checking system. In the physical environment, some unique features were: (a) tactile features; (b) opportunities for invented strategies; and (c) mental mathematics. These results show that although the different manipulative models had different features, both the physical and virtual environments were effective in supporting students' learning and encouraging relational thinking and algebraic reasoning.
机译：当在各种情况下与不同组的学生一起使用以学习数学内容时，虚拟和物理操作都被认为是有效的学习工具。使用多种表示形式以及在这些表示形式之间进行翻译的灵活性可以促进学生的学习，并有可能加深他们的理解。这个课堂项目由两组三年级学生组成，为期一周，主要研究代数关系。该单元的目的是让具有不同代数模型的学生参与进来，并鼓励学生使用非正式策略来表达他们的关系思维。该论文重点介绍了这些学生表现形式的例子，作为孩子们发展代数思维的证据。测验前和测验后的结果表明，在物理和虚拟操作环境中的学生在学习成绩上取得了显著成绩，并且在翻译和表达他们对多种模式的理解方面表现出灵活性：操作模型，图形，数字和单词问题。研究人员记录了现场笔记，接受采访的学生和录制的课堂视频，以识别学习环境的独特特征。虚拟环境具有促进学生思考的独特功能，例如：（a）视觉和符号模式的明确链接； （b）在算法过程中的逐步指导； （c）立即反馈和自我检查系统。在物理环境中，一些独特的特征是：（a）触觉特征； （b）发明策略的机会； （c）心理数学。这些结果表明，尽管不同的操纵模型具有不同的功能，但物理和虚拟环境都可以有效地支持学生的学习，并鼓励关系思维和代数推理。

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