Place value understanding requires the same activity that students use when developing fractional and algebraic reasoning, making this understanding foundational to mathematics learning. However, many students engage successfully in mathematics classrooms without having a conceptual understanding of place value, preventing them from accessing mathematics that is more sophisticated later. The purpose of this exploratory study is to investigate how upper elementary students’ unit coordination related to difficulties they experience when engaging in place value tasks. Understanding place value requires that students coordinate units recursively to construct multi-digit numbers from their single-digit number understandings through forms of unit development and strategic counting. Findings suggest that students identified as low-achieving were capable of only one or two levels of unit coordination. Furthermore, these students relied on inaccurate procedures to solve problems with millennial numbers. These findings indicate that upper elementary students identified as low-achieving are not to yet able to (de)compose numbers effectively, regroup tens and hundreds when operating on numbers, and transition between millennial numbers. Implications of this study suggest that curricula designers and statewide standards should adopt nuances in unit coordination when developing tasks that promote or assess students’ place value understanding.

中文翻译：

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位值理解的组成部分：在提供干预时针对数学困难

位值理解需要学生在开发分数和代数推理时使用的相同活动，使这种理解成为数学学习的基础。然而，许多学生在没有对位值概念性理解的情况下成功地参与了数学课堂，从而阻止他们接触到更复杂的数学。这项探索性研究的目的是调查高年级学生的单元协调如何与他们在参与地方价值任务时遇到的困难相关。理解位值要求学生递归地协调单位，通过单位发展和战略计数的形式，从他们对一位数的理解中构造多位数字。调查结果表明，被认定为成绩不佳的学生只能进行一到两个级别的单元协调。此外，这些学生依靠不准确的程序来解决千禧一代数字的问题。这些发现表明，被认定为成绩不佳的高年级学生还不能有效地（分解）数字，在处理数字时重新组合成百上千，以及在千禧一代数字之间过渡。本研究的意义表明，在制定促进或评估学生位值理解的任务时，课程设计者和全州标准应该在单元协调中采用细微差别。这些发现表明，被认定为成绩不佳的高年级学生还不能有效地（分解）数字，在处理数字时重新组合成百上千，以及在千禧一代数字之间过渡。本研究的意义表明，在制定促进或评估学生位值理解的任务时，课程设计者和全州标准应该在单元协调中采用细微差别。这些发现表明，被认定为成绩不佳的高年级学生还不能有效地（分解）数字，在处理数字时重新组合成百上千，以及在千禧一代数字之间过渡。本研究的意义表明，在制定促进或评估学生位值理解的任务时，课程设计者和全州标准应该在单元协调中采用细微差别。