CAREER: Advancing Secondary Mathematics Teachers' Quantitative Reasoning

科学、技术、工程和数学[STEM]以及STEM教育研究人员和政策文件指示各级数学教育工作者加强对定量推理的重视，以便学生为继续学习数学和其他STEM领域做好准备。通常，教师没有做好充分的准备来支持学生的定量推理。该项目产生的产品满足了对服务前具体材料的需求，这些材料体现了定量推理领域的研究基础知识。可访问的研究和教育产品集合为改变未来数学教师的定量推理提供了一个模型程序，可在全国其他机构采用。此外，早期职业学者在数学教育方面的支持将增加国家解决未来数学教育问题的能力。通过调查职前中学数学教师在包括函数和代数在内的中学数学概念背景下的定量推理，推进推理解决了教师教育材料的缺乏。该项目扩展了先前在定量推理方面的研究，以开发差异化的教学经验和课程，以支持未来教师的定量推理并产生他们知识的转变。三个相互关联的研究问题指导了该项目：(i)定量推理的哪些方面为未来教师对主要中学数学概念（如函数和代数）的理解提供了支持？（ii）在教授和学习函数和代数等主要中学数学概念的背景下，教学如何支持未来教师的定量推理？（iii）未来教师在进入职前项目时的理解是如何支持或抑制他们的定量推理的？推进推理通过制定一个迭代，多阶段的研究来解决这些问题，200名未来的教师参加了为期5年的中学数学教育内容课程。研究的主要阶段实施了一系列课堂设计实验，以产生关于未来教师定量推理的核心方面的知识和支持这种推理的教学经验。通过从课堂环境中汲取这些知识，推进推理提供了基于研究和实践驱动的可交付成果，从而改善了数学的教与学。

Science, Technology, Engineering and Mathematics [STEM] and STEM education researchers and policy documents have directed mathematics educators at all levels to increase emphasis on quantitative reasoning so that students are prepared for continued studies in mathematics and other STEM fields. Often, teachers are not sufficiently prepared to support their students' quantitative reasoning. The products generated by this project fill a need for concrete materials at the pre-service level that embody research-based knowledge in the area of quantitative reasoning. The accessible collection of research and educational products provides a model program for changing prospective mathematics teachers' quantitative reasoning that is adoptable at other institutions across the nation. Additionally, the support of early CAREER scholars in mathematics education will add to the capacity of the country to address issues in mathematics education in the future. Advancing Reasoning addresses the lack of materials for teacher education by investigating pre-service secondary mathematics teachers' quantitative reasoning in the context of secondary mathematics concepts including function and algebra. The project extends prior research in quantitative reasoning to develop differentiated instructional experiences and curriculum that support prospective teachers' quantitative reasoning and produce shifts in their knowledge. Three interrelated research questions guide the project: (i) What aspects of quantitative reasoning provide support for prospective teachers' understanding of major secondary mathematics concepts such as function and algebra? (ii) How can instruction support prospective teachers' quantitative reasoning in the context of the teaching and learning of major secondary mathematics concepts such as function and algebra? (iii) How do the understandings prospective teachers hold upon entering a pre-service program support or inhibit their quantitative reasoning? Advancing Reasoning addresses these questions by enacting an iterative, multi-phase study with 200 prospective teachers enrolled in a secondary mathematics education content course over 5 years. The main phase of the study implements a series of classroom design experiments to produce knowledge on central aspects of prospective teachers' quantitative reasoning and the instructional experiences that support such reasoning. By drawing this knowledge from a classroom setting, Advancing Reasoning contributes research-based and practice-driven deliverables that improve the teaching and learning of mathematics.