Mathematics word problems provide students with an opportunity to apply what they are learning in their mathematics classes to the world around them. However, students often neglect their knowledge of the world and provide nonsensical responses (e.g., they may answer that a school needs 12.5 buses for a field trip). This study examined if the question design of word problems affects students' mindset in ways that affect subsequent sense‐making. The hypothesis was that rewriting standard word problems to introduce inherent uncertainty about the result would be beneficial to student performance and sense‐making because it requires students to reason explicitly about the context described in the problem. Middle school students (N = 229) were randomly assigned to one of three conditions. In the standard textbook condition, students solved a set of six word problems taken from current textbooks. In the modified yes/no condition, students solved the same six problems rewritten so the solution helped answer a “yes” or “no” question. In the disfluency control condition, students solved the standard problems each rewritten in a variety of fonts to make them look unusual. After solving the six problems in their assigned condition, all students solved the same three “problematic” problems designed to assess sense‐making. Contrary to predictions, results showed that students in the modified yes/no condition solved the fewest problems correctly in their assigned condition problem set. However, consistent with predictions, they subsequently demonstrated more sense‐making on the three problematic problems. Results suggest that standard textbook word problems may be able to be rewritten in ways that mitigate a “senseless” mindset.

中文翻译：

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问题设计影响学生对数学单词问题的理解

数学单词问题为学生提供了将他们在数学课上学到的知识应用到周围世界的机会。然而，学生经常忽视他们对世界的了解并提供荒谬的回答（例如，他们可能会回答学校需要 12.5 辆公共汽车进行实地考察）。本研究考察了单词问题的问题设计是否以影响后续意义构建的方式影响学生的思维方式。假设是重写标准单词问题以引入对结果的固有不确定性将有利于学生的表现和意义构建，因为它要求学生对问题中描述的上下文进行明确的推理。中学生（N = 229) 被随机分配到三个条件之一。在标准教科书条件下，学生解决了一组从当前教科书中提取的六个单词问题。在修改后的是/否条件下，学生解决了重写的相同六个问题，因此该解决方案有助于回答“是”或“否”问题。在不流畅控制条件下，学生们解决了标准问题，每个问题都用各种字体重写，使它们看起来不寻常。在分配的条件下解决了六个问题后，所有学生都解决了相同的三个旨在评估意义构建的“问题”问题。与预测相反，结果表明，修改是/否条件下的学生在他们指定的条件问题集中正确解决的问题最少。然而，与预测一致，他们随后在三个有问题的问题上表现出更多的意义。结果表明，标准的教科书单词问题可能能够以减轻“无意义”心态的方式重写。