Pathways to Conceptual Knowledge of Decimals

精通数学对于STEM领域的成功至关重要，但对许多美国学生来说，这仍然是一个挑战，特别是对理解小数和小数算术的熟练程度。该项目旨在测试优化练习题是否可以提高学生的小数能力和理解。目前，学生收到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健理解。本研究以六、七年级学生为研究对象，以三个短期干预研究为研究对象，探讨以即时反馈方式提供均衡的习题分布，是否能提高中学生的小数和小数算术知识。研究一将重点放在十进制算术上，并测试用即时反馈完成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十进制算术练习问题与即时反馈、反映教科书中典型练习问题的不平衡练习问题以及一切照常活动的有效性。研究2将重点放在小数量级知识上，并测试从平衡练习和即时反馈中发展出来的程序性知识是否会进一步提高概念性知识，以及是否需要额外的支架。研究人员将比较平衡练习和准确反馈的效果，平衡练习和精确反馈和概念提示的效果，以及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，考察提高学生对小数大小的概念性知识是否会从随后的十进制算术干预中获得更大的好处，这些干预涉及带有即时反馈的平衡练习问题。总之，这些研究将提供对通过平衡练习问题分布来发展十进制知识所涉及的认知过程的洞察。此外，这些发现有望为大规模的学校干预奠定基础，旨在通过教材中一个容易伸展的因素-练习问题的分配-来改善儿童的数学成绩。该项目得到了NSF的EDU核心研究(ECR)计划的支持。ECR计划强调基础STEM教育研究，以产生该领域的基础知识。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，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.