Contextualize to Learn: Preparing Faculty Toward Math Contextualization for Student Success in Advanced Technological Education

在国家科学、技术、工程和数学(STEM)的成熟和新兴技术领域，数学能力是教育和职业成功的基石。与此同时，对于在社区和技术学院攻读高级技术课程学位和认证的学生来说，完成课程和掌握数学仍然是他们的主要奋斗领域。基于一项试点研究的结果，由大学研究人员和两年制学院的教职员工和机构研究人员组成的研究小组将调查情境化数学的适应、实施和结果。情境化数学是一种很有前途的教学方法，旨在通过将数学与工作场所的学术/职业内容和应用程序联系起来，改善数学的教学和学习。这项混合方法研究结合了定量和定性方法，考察了教师的专业发展、情境数学在课堂上的适应和实施，以及情境数学对学生在先进制造、工程技术、生物技术、建筑技术和交通技术领域的教育和职业成就的影响。采用趋同的平行混合方法设计，这项有针对性的研究性研究旨在调查教师对情境数学的投入和专业发展及其对学生的影响。本文考察了两个关键领域：a)通过教师发展和实践社区发展教师专业知识，b)通过动量理论的视角对学生的结果产生的临时和长期影响，这是社区大学生成功的模式。通过深入访谈收集的定性数据将使用不断比较的方法进行分析，以评估数据类别的数据饱和度和稳定性。量化数据包括行政记录、调查和课堂观察。调查将使用探索性和验证性因素分析进行试点和验证。课堂观察数据将使用社会网络分析进行分析。为了调整学生的前处理特征以建立均衡的对照小组，本研究将倾向分数匹配应用于地址选择偏差(参加情境化数学课程的注册)。路径分析将被用来评估情境化数学的治疗效果以及情境化数学工作的潜在因果路径(例如，增加的认知、元认知和动机动量)。收敛分析将检验不同数据源的结果在多大程度上聚合、分散和/或在研究的教职员工和学生线索之间建立联系。因此，这项研究将提供一个复杂而细微的理解，以了解教师发展、在课堂上适应和实施情境化数学之间的关系，以及情境化数学对教学、学习和职业成功的影响。

Competency in mathematics is the cornerstone of educational and career success in the Nation's established and emerging technical fields in Science, Technology, Engineering, and Mathematics (STEM). At the same time, completing courses and mastering mathematics remain major areas of struggle for students who are pursuing degrees and certification in advanced technological programs at community and technical colleges. Building on findings from a pilot study, the research team composed of university researchers and faculty and institutional researchers at 2-year colleges will investigate the adaptation, implementation, and outcomes of contextualized mathematics, a promising instructional approach designed to improve teaching and learning mathematics by connecting mathematics with academic/occupational content and applications in the workplace. Integrating quantitative and qualitative approaches, the mixed methods research study examines faculty professional development, adaptation and implementation of contextualized mathematics in the classroom, and the impact of contextualized mathematics on students' educational and career outcomes in advanced manufacturing, engineering technology, biotechnology, construction technology, and transportation technology. Using a convergent parallel mixed methods design, this targeted research study is designed to investigate faculty engagement with and professional development around contextualized mathematics and its impact on students. Two critical areas are examined: a) the development of faculty expertise through faculty development and communities of practice, and b) the interim and longer-term impact on student outcomes through the lens of momentum theory, a model of community college student success. Qualitative data collected by in-depth interviews will be analyzed using the constant comparative method to assess data saturation and stability of data categories. Quantitative data include administrative records, surveys, and classroom observations. Surveys will be piloted and validated using exploratory and confirmatory factor analyses. Classroom observation data will be analyzed using social network analysis. In order to adjust for pre-treatment characteristics of students for establishing balanced comparison groups, the research study applies propensity score matching to address selection bias (enrollment in contextualized mathematics courses). Path analysis will be used to estimate the treatment effect of contextualized mathematics and the potential causal pathways through which contextualized mathematics works (e.g., increased cognitive, metacognitive, and motivational momentum). Convergent analysis will examine the extent to which and the ways in which results from different data sources converge, diverge, and/or connect within and across faculty and student threads of the research. Accordingly, the study will provide a complex and nuanced understanding of the relationships among faculty development, adaptation and implementation of contextualized mathematics in the classroom, and the impact of contextualized mathematics on teaching, learning, and career success.