Many randomized controlled experiments in the classroom have found that mathematics learning is improved dramatically when practice problems of one kind are distributed across multiple assignments (spaced) and mixed with other kinds of problems (interleaved). In two studies, we investigated students' knowledge of spacing and interleaving. In Study 1, 193 undergraduates designed learning schedules for a hypothetical math class. In Study 2, 175 undergraduates selected from among five hypothetical schedules in response to a variety of questions, provided reasons for their selections, and rated the utility of spacing and interleaving. In both studies, most participants incorrectly judged schedules with minimal degrees of spacing and interleaving to be most effective. Also, schedules with more spacing and interleaving were perceived as more difficult, less enjoyable, and less common. Participants' ratings of utility revealed mixed perspectives on spacing and an underappreciation of interleaving. Altogether, these findings demonstrate that most students fail to recognize the benefits of spaced and interleaved practice. Further, by identifying specific ways in which their beliefs about spacing and interleaving fall short, we reveal opportunities to reshape students' beliefs to foster these effective learning techniques. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

中文翻译：

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安排数学练习：学生对间距和交错的认识不足。

课堂上的许多随机对照实验发现，当一种练习题分布在多个作业中（间隔）并与其他类型的问题混合（交错）时，数学学习会显着提高。在两项研究中，我们调查了学生对间隔和交错的知识。在研究 1 中，193 名本科生为假设的数学课设计了学习时间表。在研究 2 中，175 名本科生从五个假设的日程表中选择了回答各种问题，提供了他们选择的理由，并对间隔和交错的效用进行了评价。在这两项研究中，大多数参与者都错误地判断间隔和交错程度最小的日程安排是最有效的。还，具有更多间隔和交错的时间表被认为更困难，更不愉快，更不常见。参与者对效用的评分揭示了对间距的不同看法和对交错的低估。总之，这些发现表明，大多数学生没有认识到间隔和交错练习的好处。此外，通过确定他们对间隔和交错的信念不足的具体方式，我们揭示了重塑学生信念以培养这些有效学习技巧的机会。（PsycInfo 数据库记录 (c) 2022 APA，保留所有权利）。这些发现表明，大多数学生没有认识到间隔和交错练习的好处。此外，通过确定他们对间隔和交错的信念不足的具体方式，我们揭示了重塑学生信念以培养这些有效学习技巧的机会。（PsycInfo 数据库记录 (c) 2022 APA，保留所有权利）。这些发现表明，大多数学生没有认识到间隔和交错练习的好处。此外，通过确定他们对间隔和交错的信念不足的具体方式，我们揭示了重塑学生信念以培养这些有效学习技巧的机会。（PsycInfo 数据库记录 (c) 2022 APA，保留所有权利）。