Pathways to Conceptual Knowledge of Decimals

数学能力对于在STEM领域取得成功至关重要，但对许多美国学生来说仍然是一个挑战，特别是对小数和十进制算术的理解能力。本项目旨在测试优化习题是否能提高学生对小数的理解能力。目前，学生收到的某些类型的习题比其他类型的习题更频繁，这种情况可能会限制和干扰学生对小数的牢固理解的发展。本课题旨在探讨提供均衡分布且即时反馈的习题是否能提高中学生的小数和十进制算术知识。该项目包括对六年级和七年级学生的三个短期干预研究。研究一将重点放在十进制算术上，并测试完成即时反馈的平衡练习题是否会提高学生的程序性知识。研究人员将比较平衡的十进制算术练习题与即时反馈、反映教科书中典型练习题的不平衡练习题以及日常活动的有效性。研究2将侧重于十进制数量级知识，并测试从平衡实践中获得的即时反馈的程序性知识是否会进一步提高概念知识，以及是否需要额外的脚手架。研究人员将比较有准确性反馈的平衡练习、有准确性反馈和概念提示的平衡练习和没有反馈的平衡练习的效果。研究3将结合研究1和研究2的干预措施，以检验提高学生对十进制数量级的概念知识是否会从随后的十进制算术干预中获得更大的收益，包括平衡的实践问题和即时反馈。总之，这些研究将通过平衡的实践问题分布，提供有关发展十进制知识的认知过程的见解。此外，这些发现有望为大规模的学校干预奠定基础，这些干预旨在通过教学材料中易于扩展的因素——实践问题的分布——来改善儿童的数学成绩。本项目由美国国家科学基金会EDU核心研究（ECR）项目支持。ECR项目强调在该领域产生基础知识的基础STEM教育研究。投资在至关重要、广泛和持久的关键领域：STEM学习和STEM学习环境，扩大STEM参与，以及STEM劳动力发展。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Mathematics proficiency is essential for success in STEM fields, but remains a challenge for many US students, particularly proficiency in understanding decimals and decimal arithmetic. The project aims to test whether optimizing practice problems can improve students’ competency with and understanding of decimals. Currently, students receive certain types of practice problems more frequently than other types of practice problems, an occurrence that may limit as well as interfere with students’ development a robust understanding of decimals. This project investigates whether providing balanced distributions of practice problems with immediate feedback can improve students’ knowledge of decimals and decimal arithmetic in middle school.The project includes three short-term intervention studies with 6th and 7th grade students. Study 1 will focus on decimal arithmetic and test whether completing balanced practice problems with immediate feedback will improve students’ procedural knowledge. The researchers will compare the effectiveness of balanced decimal arithmetic practice problems with immediate feedback, unbalanced practice problems that reflect typical practice problems presented in textbooks, and business-as-usual activities. Study 2 will focus on decimal magnitude knowledge and test whether procedural knowledge developed from balanced practice with immediate feedback will further improve conceptual knowledge, and whether additional scaffolding is needed. The researchers will compare effects of balanced practice with accuracy feedback, balanced practice with accuracy feedback and conceptual prompts, and balanced practice with no feedback. Study 3 will combine the interventions from Studies 1 and 2 to examine whether boosting students’ conceptual knowledge of decimal magnitudes leads to greater benefits from a subsequent decimal arithmetic intervention involving balanced practice problems with immediate feedback. Together, these studies will provide insight into the cognitive processes involved in developing decimal knowledge through balanced practice problem distributions. Further, the findings promise to set the foundation for large-scale school-based interventions aimed at improving children’s mathematical outcomes via an easily malleable factor in instructional materials – distributions of practice problems.This project is supported by NSF’s EDU Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field. Investments are made in critical areas that are essential, broad, and enduring: STEM learning and STEM learning environments, broadening participation in STEM, and STEM workforce development.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.