Collaborative Proposal: Mathematical Modeling With Cultural and Community Contexts

该提案是针对电子病历核心研究(ECR)计划公告NSF 15-509而提交的。ECR STEM教育基础研究计划为关键的研究领域提供资金，这些领域是基本的、广泛的和持久的。EHR寻求的建议将有助于综合、建立和/或扩大以下重点领域的研究基础：STEM学习、STEM学习环境、STEM劳动力发展和扩大STEM的参与。ECR项目的特点是强调积累可靠的证据，为以下工作提供信息：(A)理解，(B)建立解释理论，(C)提出干预措施(和创新)，以解决STEM兴趣、教育、学习和参与方面的持续挑战。来自亚利桑那大学的一组调查人员将在亚利桑那州和华盛顿州的不同小学课堂上对数学建模的教学和学习进行研究。数学建模技能是基础性的，因为他们通过分析、表示、解释和修改将核心数学思想与现实世界的经验联系起来。数学建模还支持对数学的持久理解和实践，例如解决问题和推广。虽然数学建模在中学教育中有着深厚的传统，但随着大学和职业准备标准内容的增加，需要在小学引入建模知识。为了满足这一需求，研究人员将：(A)在三年级到五年级提高数学建模教学和学习的基础知识；(B)完善创新的专业发展计划，以提高教师对数学建模的理解和实践，利用学生的经验以及相关的文化和社区背景；以及(C)制定一套有效和可靠的衡量标准，以评估教师和学生与数学建模相关的学习成果。该项目由EHR核心研究计划资助，该计划支持基础研究，推动STEM学习的研究文献，并对正式和非正式环境下的教育产生影响。本项目将以混合方法、多层次设计进行实验。在三个项目年中，研究人员将与亚利桑那州和华盛顿州的一批教师一起，反复开发和完善一种专业发展模式，这些教师在人口文化和语言多样化的高贫困学校工作。研究人员将衡量该模型对数学教学和学生学习的潜在影响。所提出的设计数学建模任务的工作是基于渐进式形式化现实数学教育(RME)的原则，该原则表明上下文对于支持学生学习数学建模很重要。该模式整合了关于数学建模教学的研究，以及关于文化和社区知识基金在数学教学中的作用的研究。当学生在建模任务中工作时，他们将产生包括推理和思考证据的人工制品。它们还将通过共同核心协调一致的国家级标准化数学评估措施进行评估。教师将调整数学建模任务，围绕这些任务设计课程，并反复改进一套可重复使用的工具，以评估学生的建模活动。为了衡量对学生学习的影响，研究人员将使用两组设计来比较在培训条件教师的教室中学习的学生与在可比较的非培训条件教室中学习的学生。由于目前很少有教师在3-5年级使用数学建模教学，因此将不会使用教师对照小组来衡量对教师学习的影响。相反，研究人员将使用参与的教师作为他们自己的对照，以检查他们在理解和实践中随着时间的推移而发生的变化。

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.A team of investigators from the University of Arizona will conduct research on the teaching and learning of mathematical modeling in diverse elementary classrooms in Arizona and Washington. Mathematical modeling skills are foundational as they connect core mathematical ideas to real world experiences through analysis, representation, interpretation, and revision. Mathematical modeling also supports enduring understandings and practices in mathematics, such as problem solving and generalization. While mathematical modeling has a strong tradition in secondary education, the increased content of college and career readiness standards requires an introduction to modeling in elementary school. To address this need, the researchers will: (a) advance foundational knowledge on teaching and learning mathematical modeling in grades 3 through 5; (b) refine innovative professional development programs to increase teacher understanding and practice of mathematical modeling that draws on student experiences and relevant cultural and community contexts; and (c) develop a set of valid and reliable measures to evaluate teacher and student learning outcomes related to mathematical modeling. The project is funded by the EHR Core Research program, which supports fundamental research that advances the research literature on STEM learning, and has implications for education in both formal and informal settings. The project will be conducted as a mixed methods, multi-tiered design experiment. Across the three project years, researchers will iteratively develop and refine a professional development model with cohorts of teachers in Arizona and Washington who work in high poverty schools with culturally and linguistically diverse populations. The researchers will measure the potential for impact of the model on mathematics instruction and student learning. The proposed work to design mathematical modeling tasks is based on tenets of progressive formalization Realistic Mathematics Education (RME), which suggest that contexts matter for supporting student learning of mathematical modeling. The model integrates research on teaching and learning of mathematical modeling, and research on the role of culturally and community based funds of knowledge in teaching and learning mathematics. As students work on modeling tasks, they will produce artifacts that include evidence of reasoning and thinking. They will also be assessed by means of a Common Core aligned State-level Standardized Mathematics Assessment measure. Teachers will adapt mathematical modeling tasks, design lessons around those tasks, and iteratively refine a set of reusable tools for assessing students modeling activity. To measure impact on student learning, the researchers will use a two-group design to compare student learning in classrooms of training condition teachers with student learning in comparable, non-training condition classrooms. Since few teachers currently use mathematical modeling instruction in grades 3-5, a teacher comparison group to measure impact on teacher learning will not be employed. Rather, the researchers will use participating teachers as their own controls to examine changes over time in their understanding and practice.