Children's Understanding of Functions in Grades K-2

儿童理解函数项目的研究人员正在研究K-2年级的幼儿如何理解数学概念，这些概念是发展代数思维的基础。 达特茅斯的马萨诸塞州大学和塔夫茨大学的研究人员正在努力开发一种描述代数概念如何发展的学习轨迹。 大多数研究都集中在小学高年级和中学阶段的学生发展，但本项目将增加有关小学早期学习者的信息。该项目的研究方法使用教学实验，使研究人员直接与学生交谈，因为他们探索代数思想。 他们探索学生如何思考和发展相关的概念，协变，函数的表示，变量之间的关系，和泛化。 研究人员设计了一些任务，帮助学生解释他们的想法，并解决一些量变化而另一些量不变的问题。 他们正在分析视频和学生的书面作业，因为他们建立了关于代数思维发展的案例研究。 对这一探索性项目的外部评估是其咨询委员会的职责之一，该项目将年幼儿童的代数思维与年长儿童的记录联系起来。 这个过程使他们能够建立一个关于学生代数思维发展的循证学习轨迹。 这项研究的成果可以用来建立课程和课程，这些课程和课程与学生在发展过程中的各个阶段所知道和可以学到的东西保持一致。 通过专业出版物和DRK-12资源网络，不仅向研究人员，而且向从业人员传播项目的调查结果、任务和录像。

The researchers in the Children's Understanding of Functions project are studying how young children in grades K-2 understand mathematical concepts that are foundational for developing algebraic thinking. Researchers at University of Massachusetts at Dartmouth and Tufts University are contributing to an ongoing effort to develop a learning trajectory that describes how algebraic concepts are developed. Most research has focused on student development at the upper elementary and middle school levels, but this project will add information about early elementary learners. The project's research methodology uses teaching experiments which allow researchers to talk directly to students as they explore algebraic ideas. They explore how students think about and develop concepts related to covariation, representations of functions, relationships among variable, and generalization. Researchers have designed tasks that help students explain their thinking and solve problems where some quantities vary and others are constant. They are analyzing videos and students' written work as they build case studies about the development of algebraic thinking. External evaluation of this exploratory project is one of the responsibilities of its advisory board.This project is connecting the algebraic thinking of younger children to what has been documented for older children. This process enables them to build an evidence-based learning trajectory about students' development of algebraic thinking. The products of this research can be used to build curricula and lessons that are aligned with what students know and can learn at various points in their development. Project findings, tasks and videos are being disseminated not only to researchers, but also to practitioners through professional publications and the DRK-12 Resource Network.