Pathways to Conceptual Knowledge of Decimals

数学熟练程度是在STEM领域取得成功的关键，但对许多美国学生来说仍然是一个挑战，特别是在理解小数和十进制算术方面的熟练程度。本研究旨在测试优化练习题是否能提高学生对小数的理解能力。目前，学生接受某些类型的练习问题比其他类型的练习问题更频繁，这种情况可能会限制和干扰学生对小数的强大理解。本研究以六、七年级学生为研究对象，探讨提供均衡分布的即时反馈练习题是否能提高学生的小数和小数算术知识。研究1将集中在十进制算术和测试是否完成平衡的实践问题与即时反馈将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问题与即时反馈的有效性，反映教科书中典型练习问题的不平衡练习问题，以及照常活动。研究2将侧重于小数数量级的知识和测试是否从平衡的实践与即时反馈开发的程序性知识将进一步提高概念性知识，以及是否需要额外的脚手架。研究人员将比较平衡练习与准确性反馈，平衡练习与准确性反馈和概念提示，以及平衡练习没有反馈的效果。研究3将结合联合收割机的干预措施，从研究1和2，以检查是否提高学生的概念知识的小数量导致更大的好处，从随后的十进制算术干预，涉及平衡的实践问题，即时反馈。总之，这些研究将提供深入了解通过平衡的实践问题分布发展十进制知识的认知过程。此外，研究结果有望为大规模的校本干预奠定基础，旨在通过教学材料中一个容易延展的因素-实践问题的分布来改善儿童的数学成果。ECR计划强调基础STEM教育研究，产生该领域的基础知识。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响力审查标准进行评估，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.