Linking Mathematical Operations and Their Applications

这个项目的主要目标是制作原型材料，使学生能够更好地将算术的数学运算与他们的应用程序联系起来。试用材料的目标受众将是中等或低于平均水平的中学生，在某些情况下也适用于更年轻或更有能力的学生。第二个目标将是探索在课程中涉及自然环境的方法，而不是传统的“故事”问题。这个项目的理论基础是基于最近的一项研究，该研究表明，许多中学生处理数学故事问题的策略并不是基于运算的可能含义，数学故事问题是算术运算最常见的学校应用形式。虽然这些策略中的一些可能会在许多整数的一步故事问题上取得成功，但它们在涉及分数或小数的多步问题上的使用不太可能给出正确的解决方案。该项目将在中学生中开发和实地测试材料，以更加强调对操作的意义。这些材料的结果应该会改善学生在学校和自然环境中应用手术的方法。教师、监督员、出版商、心理学家和主题专家将被要求帮助确保材料具有最大的可用性。传播计划包括向课本出版商分发材料，为他们的教科书中的此类课程提供原型和研究支持。

The primary objective of this project is to produce prototypical materials which will better enable students to link the mathematical operations of arithmetic with their applications. The target audience for the materials tryout will be average and below average middle school students, and in some cases adapted and given to younger or more able students as well. A secondary objective will be to explore means of involving natural settings, rather than the traditional "story" problems, in the lessons. The rationale for this project is based on recent research which suggests that many middle school students approach mathematical story problems, the most common school form of applications of the arithmetic operations, with strategies that are not based on possible meanings for the operations. Although some of these strategies may give success on many one-step story problems with whole numbers, their use with multi-step problems involving fractions or decimals is unlikely to give correct solutions. This project will develop and field test with middle school students, materials to give a greater emphasis to meanings for the operations. The outcome from the materials should provide improvement in the students' approaches to applications of the operations, both in school and in natural settings. Teachers, supervisors, publishers, psychologists, and subject-matter experts will be called on to help insure that the materials have maximum usability. Dissemination plans include distribution of the materials to text publishers, to give them prototypes and research support for such lessons in their textbooks.