Investigating Relationships Between Mathematical Knowledge for Teaching and High-Leverage Teaching Practices

该提案是根据EHR核心研究（ECR）项目公告NSF 15-509提交的。STEM教育基础研究ECR项目为重要、广泛和持久的关键研究领域提供资金。EHR寻求有助于在以下重点领域综合、建立和/或扩大研究基础的提案：STEM学习、STEM学习环境、STEM劳动力发展和扩大STEM参与。ECR项目的特点是强调积累有力的证据，为以下方面的努力提供信息：(a)理解，(b)建立理论来解释，(c)提出干预（和创新）措施，以解决STEM兴趣、教育、学习和参与方面的持续挑战。拟议的研究将检查STEM学习环境和STEM劳动力发展。拟议的项目将使用与实习教师的模拟来探索职前教师的数学教学知识（MKT）与他们在K-6数学课程涵盖的内容领域（例如，数字运算和区域）中促进学生学习的能力之间的关系。这项研究将达到三个目的。这将有助于建立数学教学知识与学生教师引导和解释学生思维能力之间关系的基础知识和理论。它将为该领域提供关于设计选择对评估MKT和hlp的模拟效用的影响的初步发现，以及对培养数学知识发展的模拟效用的关键见解。最后，它将通过开发实际模拟，包括实施材料，有助于职前教师的培训，可用于评估和提高职前教师的市场营销能力。

This proposal was submitted in response to EHR Core Research (ECR) program announcement NSF 15-509. The ECR program of fundamental research in STEM education provides funding in critical research areas that are essential, broad and enduring. EHR seeks proposals that will help synthesize, build and/or expand research foundations in the following focal areas: STEM learning, STEM learning environments, STEM workforce development, and broadening participation in STEM. The ECR program is distinguished by its emphasis on the accumulation of robust evidence to inform efforts to (a) understand, (b) build theory to explain, and (c) suggest interventions (and innovations) to address persistent challenges in STEM interest, education, learning, and participation.The proposed research will examine STEM learning environments and STEM workforce development. The proposed project will use simulations with student teachers to explore the relationship between preservice teachers' mathematics knowledge for teaching (MKT) and their ability to promote student learning in a sample of the content areas covered in K-6 mathematics curriculum (e.g., number operations, and area).This research will accomplish three aims. It will contribute to foundational knowledge and theory about the relationships between mathematical knowledge for teaching and student teachers skill with eliciting and interpreting student thinking. It will provide the field with initial findings about the impact of design choices on the utility of a simulation for assessing MKT and HLPs, as well as critical insights on the utility of the simulation for nurturing the development of mathematical knowledge. Finally, it will contribute to the training of preservice teachers by developing actual simulations, including materials for implementing, which can be used to assess and enhance the MKT of preservice teachers.