While conceptual understanding of properties, operations, and the base-ten number system is certainly associated with the ability to access math facts fluently, the role of math fact memorization to promote conceptual understanding remains contested. In order to gain insight into this question, this study looks at the results when one of three elementary schools in a school district implements mandatory automaticity drills for 10 minutes each day while the remaining two elementary schools, with the same curriculum and very similar demographics, do not. This study looks at (a) the impact that schoolwide implementation of automaticity drills has on schoolwide computational math skills as measured by the ITBS and (b) the relationship between automaticity and conceptual understanding as measured by statewide standardized testing. The results suggest that while there may be an association between automaticity and higher performance on standardized tests, caution should be taken before assuming there are benefits to promoting automaticity drills. These results are consistent with those that support a process-driven approach to automaticity based on familiarity with properties and strategies associated with the base-ten number system; they are not consistent with those that support an answer-driven approach to automaticity based on memorization of answers.

中文翻译：

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在基于概念的小学数学教学中对自动性的全区研究

虽然对属性、运算和十进制数字系统的概念理解肯定与流利地访问数学事实的能力相关，但数学事实记忆在促进概念理解方面的作用仍然存在争议。为了深入了解这个问题，本研究考察了以下结果：一个学区的三所小学中的一所每天实施 10 分钟的强制性自动练习，而其余两所具有相同课程和非常相似的人口统计数据的小学，不要。本研究着眼于 (a) 全校实施自动性练习对 ITBS 衡量的全校计算数学技能的影响，以及 (b) 全州标准化测试衡量的自动性与概念理解之间的关系。结果表明，虽然自动化程度与标准化测试中的更高表现之间可能存在关联，但在假设促进自动化练习有好处之前，应谨慎行事。这些结果与基于对与基数 10 数字系统相关的属性和策略的熟悉程度而支持流程驱动的自动化方法的结果一致；它们与支持基于答案记忆的答案驱动的自动化方法的方法不一致。这些结果与基于对与基数 10 数字系统相关的属性和策略的熟悉程度而支持流程驱动的自动化方法的结果一致；它们与支持基于答案记忆的答案驱动的自动化方法的方法不一致。这些结果与基于对与基数 10 数字系统相关的属性和策略的熟悉程度而支持流程驱动的自动化方法的结果一致；它们与支持基于答案记忆的答案驱动的自动化方法的方法不一致。