Collaborative Proposal: Mathematical Modeling With Cultural and Community Contexts

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。来自亚利桑那大学的一组调查人员将对亚利桑那州和华盛顿州不同小学的数学建模教学进行研究。数学建模技能是基础，因为它们通过分析、表示、解释和修订将核心数学思想与现实世界的经验联系起来。数学建模还支持数学中持久的理解和实践，例如解决问题和泛化。虽然数学建模在中学教育中有很强的传统，但大学和职业准备标准的内容增加需要在小学介绍建模。为了满足这一需求，研究人员将：(a)提高3至5年级数学建模教学的基础知识；(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，并借鉴学生的经验和相关的文化和社区背景；(c)制定一套有效和可靠的措施来评估与数学建模相关的教师和学生的学习成果。该项目由EHR核心研究计划资助，该计划支持推进STEM学习研究文献的基础研究，并对正式和非正式环境中的教育产生影响。本项目将以混合方法、多层次设计实验方式进行。在为期三年的项目中，研究人员将与亚利桑那州和华盛顿州的教师团队一起反复开发和完善一个专业发展模型，这些教师在文化和语言多样化的高贫困学校工作。研究人员将测量该模型对数学教学和学生学习的潜在影响。设计数学建模任务的建议工作是基于渐进式形式化现实数学教育（RME）的原则，这表明环境对支持学生学习数学建模很重要。该模型整合了数学建模的教与学研究，以及基于文化和社区的知识基金在数学教与学中的作用研究。当学生完成建模任务时，他们将产生包含推理和思考证据的工件。他们还将通过与共同核心相一致的国家级标准化数学评估措施进行评估。教师将适应数学建模任务，围绕这些任务设计课程，并迭代地改进一套可重用的工具来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培训条件教师课堂上的学生学习情况与可比的非培训条件课堂上的学生学习情况。由于目前在3-5年级很少有教师使用数学建模教学，因此不采用教师比较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，来检查他们的理解和实践随时间的变化。

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.