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Components of Place Value Understanding: Targeting Mathematical Difficulties When Providing Interventions

机译：地方价值理解的组成部分：提供干预措施时针对数学难题

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摘要

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.
机译：对位值的理解需要与学生在发展分数和代数推理时使用的相同活动，从而使这种理解成为数学学习的基础。但是，许多学生在没有对场所价值的概念理解的情况下成功地进入了数学课堂，从而阻止了他们以后学习更复杂的数学。这项探索性研究的目的是调查上级小学生的单位协调与他们在从事地方价值任务时遇到的困难如何相关。理解位置价值要求学生递归地协调单位，通过对单位数字的理解，通过单元发展和战略计数的形式来构造多位数的数字。研究结果表明，被认定为学习成绩不佳的学生只能进行一两个级别的单元协调。此外，这些学生依靠不正确的程序来解决千禧年数字的问题。这些发现表明，被认定为低成就的高年级学生尚无法有效地分解数字，对数字进行运算时会重新组合数十万和数百个数字之间的过渡。这项研究的意义表明，课程设计者和州级标准在制定促进或评估学生对地方价值理解的任务时，应在单元协调中采取细微差别。

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