Investigating Proportional Relationships from Two Perspectives (InPReP2)

从两个角度研究比例关系（InPReP2）

• 批准号: 1420307
• 负责人: Andrew Izsak
• 金额: $ 133.12万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2018-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1420307&HistoricalAwards=false
• 关键词: Investigating; Proportional; Relationships; Two; Perspectives

Strengthening middle school mathematics education is as urgent as any challenge facing STEM education in the United States. Ratios and proportional relationships are a critical foundation for mathematics and science, yet they pose perennial challenges for students and teachers. Investigating Proportional Relationships from Two Perspectives (InPReP2) will examine how future teachers develop understandings of proportional relationships in mathematics courses they take as part of their preparation programs. The project will collect data in teacher preparation courses and through interviews during which future teachers solve problems about proportional relationships. The courses and interviews will be based on a potentially transformative approach to ratio and proportional relationships, which has been overlooked by past research. The project will also conduct a study comparing how preservice middle grades and secondary grades mathematics teachers at the University of Georgia (UGA) and Kennesaw State University (KSU) reason about proportional relationships. Discoveries about what is easier and what is harder for future teachers to learn will be used to identify key targets for instruction that better prepare future teachers to help their students with critical, yet difficult, middle grades mathematics. Past research suggests teachers' difficulties with proportional relationships, covariation, and multiplicative relationships are likely to have roots deep in the multiplicative conceptual field, yet this same research has not examined those roots directly. InPReP2 will examine how preservice middle school teachers' capacities to reason about multiplication and division in terms of quantities support and constrain their facility with proportional relationships. InPReP2 will also investigate proportional relationships based on two complementary perspectives, one that makes covariation visually explicit with double number lines and one that makes multiplicative relationships between quantities visually explicit with strip diagrams. The central hypothesis for InPReP2 is that the two perspectives may facilitate both key features of proportional relationships and open new pathways that make subsequent topics more accessible. InPReP2 will investigate methods that coordinate detailed case studies with recent advances surveying multiplicative reasoning in large, national samples. InPReP2 will also examine in both clinical and experimental settings how different initial strengths and weaknesses with multiplicative reasoning affect how future teachers make sense of the two perspectives on proportions and applications. InPReP2 results about multiplicative reasoning will inform improved teacher education and professional development content courses that prepare teachers across the nation for standards that emphasize sense making with quantities. Teachers with an understanding of proportional relationships in terms of quantities will be better prepared to support their students' reasoning about co-variation and multiplicative relationships, which is fundamental to college readiness. InPReP2 methods will advance STEM education research by investigating how Diagnostic Classification Models, in combination with measures of reasoning, can be used to coordinate surveys of large samples with detailed case-studies of small samples. Such methods have broad implications for generating generalizable findings about learning in complex, multi-faceted domains. InPReP2 will integrate training of new mathematics education researchers and teacher educators into all aspects of the project.

加强中学数学教育与美国STEM教育面临的挑战一样紧迫。比率和比例关系是数学和科学的重要基础，但也给学生和教师带来了长期的挑战。从两个角度调查比例关系（InPReP2）将研究未来的教师如何在他们作为准备计划的一部分的数学课程中发展对比例关系的理解。该项目将在教师培训课程中收集数据，并通过对未来教师的访谈来解决比例关系问题。课程和访谈将基于一种潜在的变革性方法来研究比例和比例关系，这一点被过去的研究所忽视。该项目还将进行一项研究，比较佐治亚大学（UGA）和肯尼索州立大学（KSU）的职前初中和初中数学教师如何理解比例关系。对于未来的教师来说，什么容易学，什么难学的发现将用于确定教学的关键目标，从而更好地为未来的教师做好准备，帮助他们的学生学习关键但困难的初中数学。过去的研究表明，教师在比例关系、共变和乘法关系方面的困难可能深深植根于乘法概念领域，但同样的研究并没有直接检查这些根源。InPReP2将考察职前中学教师在数量方面推理乘法和除法的能力如何支持和限制他们在比例关系方面的能力。InPReP2还将研究基于两个互补视角的比例关系，一个是通过双数轴使共变可视化地显化，另一个是通过条形图使数量之间的乘法关系可视化地显化。InPReP2的中心假设是，这两个视角可能促进比例关系的关键特征，并开辟新的途径，使后续主题更容易理解。InPReP2将研究将详细案例研究与在大型国家样本中调查乘法推理的最新进展相协调的方法。InPReP2还将在临床和实验环境中研究乘法推理的不同初始优势和劣势如何影响未来教师如何理解比例和应用的两种观点。InPReP2关于乘法推理的结果将为改进教师教育和专业发展内容课程提供信息，使全国的教师为强调用数量来理解意义的标准做好准备。理解数量方面的比例关系的教师将更好地准备支持他们的学生关于共变和乘法关系的推理，这是大学准备的基础。InPReP2方法将通过研究如何使用诊断分类模型与推理方法相结合来协调大样本调查和小样本的详细案例研究，从而推进STEM教育研究。这些方法对于在复杂的、多方面的领域中产生关于学习的可推广的发现具有广泛的意义。InPReP2将把对新的数学教育研究人员和教师教育工作者的培训纳入项目的各个方面。