Collaborative Research: Algebra Instruction at Community Colleges: Validating Measures of Quality Instruction

这个STEM学习和学习环境项目旨在促进对社区大学代数教育的理解。本研究将在先前工作的基础上，进一步探讨大学代数课堂教学质量与教师数学教学知识之间的关系。这种“教学知识”是教师成为一名有效的数学教师所需要的数学理解。例如，这些知识使教师能够探索和诊断学生在数学概念上挣扎的原因，并提供有针对性的帮助。尽管社区大学在美国高等教育中扮演着至关重要的角色，但在美国，社区大学的教学能力是一个被忽视的部门。为了推进与大学前两年相关的数学教育研究，本项目将开发《社区大学代数数学知识教学评估》。该评估将确定教师在教授社区大学代数时所需的专业知识，以支持学生在思考基本数学概念方面的成长。该项目还将通过完善评估中学后数学教学质量的工具来推进先前的工作，该工具评估社区大学代数课程的高质量教学特征。这些努力将增强社区大学专上教学的研究工具，特别是在大学代数方面。由于大学代数通常是获得STEM学位的门户课程，因此该项目有可能改善STEM领域学生的招聘和成功，从而支持STEM劳动力的发展。该项目涉及四个主要机构：密歇根大学、明尼苏达大学、马里科帕社区学院区和俄勒冈州立大学。本研究的主要目标是：(1)开发、试点、实地测试、验证和推广《社区大学代数教学数学知识评估》；(2)完善《高等教育数学视频编码工具教学质量评估》中的项目，以解决数学课堂中支持多样性、公平性和包容性的教学方面的问题；(3)从理论上和经验上探索两种工具背后的结构之间的联系。该项目将采用混合方法设计，包括对人工制品的定性分析、项目开发和心理测量测试，在研究的所有阶段都有社区学院教师的投入，包括整合社区学院教师作为研究伙伴，从而为未来的研究合作建立能力。在本项目结束时，将提供两种工具，以支持提高高等教育教学质量和教师专业发展的多项努力。该项目得到了EHR核心研究计划的支持，该计划支持推进STEM学习和学习环境的基础研究，扩大STEM参与和STEM劳动力发展的工作。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This STEM Learning and Learning Environments project seeks to advance understanding of algebra education at community colleges. It will build on prior work to explore further the relationship between the quality of instruction in college algebra classes and teachers’ mathematical knowledge for teaching. This “knowledge for teaching” is the mathematical understanding that teachers need in order to be effective teachers of mathematics. For example, this knowledge enables teachers to explore and diagnose why students are struggling with a mathematical concept and provide targeted help. Despite its critical role in US higher education, instruction at community colleges is a neglected sector of instructional capacity in the United States. To advance mathematics education research related to the first two years of college, this project will develop the Mathematical Knowledge for Teaching Community College Algebra assessment. This assessment will identify the specialized knowledge that teachers need for teaching community college algebra in a way that supports student growth in thinking about fundamental mathematical concepts. The project will also advance previous work by refining the Evaluating the Quality of Instruction of Post-secondary Mathematics instrument, which assesses characteristics of high-quality instruction in community college algebra courses. These efforts will enhance the research tools available for studying post-secondary teaching at community colleges, specifically in College Algebra. Since college algebra is often a gateway course to STEM degrees, this project has the potential to improve the recruitment into and success of students in STEM fields and, thus, support STEM workforce development. The project involves four primary institutions: University of Michigan, University of Minnesota, Maricopa Community College District, and Oregon State University. The primary goals of the proposed research are to: (1) develop, pilot, field test, validate, and disseminate the Mathematical Knowledge for Teaching Community College Algebra assessment; (2) refine items in the Evaluating the Quality of Instruction of Post-secondary Mathematics video-coding instrument to address aspects of instruction that support diversity, equity, and inclusion in mathematics classrooms; and (3) theoretically and empirically explore the connection between the constructs that underlie both instruments. The project will use a mixed methods design that involves qualitative analysis of artifacts, item development, and psychometric testing, with the input of community college faculty in all the phases of the study, including integrating community college faculty as research associates, and thus building capacity for future research collaborations. At the conclusion of this project, two instruments will be available to support multiple efforts to advance the quality of instruction in postsecondary settings and the professional development of instructors. This project is supported by the EHR Core Research program, which supports work that advances fundamental research on STEM learning and learning environments, broadening participation in STEM, and STEM workforce development.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.