Improving Grades 6-8 students' mathematics achievement in modeling and problem solving through effective sequencing of instructional practices

教学研究顺序项目将为教师提供结构化和有意义的框架，以检验两种基于研究的教学策略，假设它们对数学建模和问题解决领域的数学成就产生积极影响。第一种策略是“明确关注概念”（Explicit Attention to Concepts， EAC），这是一套将学生的注意力特别吸引到数学概念上的实践，其方式超出了记忆、过程或技能应用的范围。这种策略可能包括教师要求学生将多种数学表示联系起来，比较解决策略，讨论数学推理的基本程序，或确定课程中的主要数学思想以及如何将其融入更广泛的数学领域。第二个策略，学生奋斗的机会（SOS），需要为学生提供时间和空间来理解可掌握的内容，克服困惑点，刺激个人的理解，建立毅力，并促进对挑战的开放。这种策略可能包括教师分配具有多种解决策略的问题，要求学生寻找模式并进行猜测，鼓励和促进围绕令人困惑或具有挑战性的想法进行讨论，并要求学生进行扩展的数学反应。这个项目调查了教师在数学内容教学中应用这些实践的顺序是否对学生的学习有影响。本研究建立在先前的工作基础上，该工作已经确定了EAC和SOS教学策略之间的相互作用，并将教师报告的更强的实践使用与更高的学生数学成绩联系起来。该项目将有四个主要的设计特点。首先，该项目将采用并扩展基于研究的EAC/SOS概念框架，并明确响应对相互作用的进一步研究的呼吁。其次，该项目将侧重于建模和解决问题的数学领域，这是所有中年级学生的两种复杂而关键的能力。第三，该项目将教师定位为具有所需专业知识的研究合作者。最后，该项目将利用从交叉临床试验到课堂实施的研究方法。该项目旨在确定EAC/SOS框架在设计和开发教学实践中的优势和制约因素，确定与建模和问题解决结果变化相关的学生和教师层面因素，分析教师在教学建模和问题解决方面实施EAC和SOS的情况，并将这些实施因素与学生成绩变化联系起来。并确定这两种策略的顺序是否与成就的差异有关。该项目将收集课堂观察数据，并利用现有工具对EAC和SOS策略的实际行动进行可靠和有效的评级。该研究的设计特点是随机2 x 2集群交叉试验，教师样本为80%的功率。在专业发展的背景下，该项目建立在现有的国家基础设施和与广泛学区的关系之上，旨在创建一个正式的教师-研究员联盟，以调查学习，作为项目工作的一部分。探索研究preK-12项目（DRK-12）旨在通过研究和开发创新资源、模型和工具，显著提高preK-12学生和教师对科学、技术、工程和数学（STEM）的学习和教学。DRK-12计划中的项目建立在STEM教育的基础研究和先前的研究和开发工作的基础上，为拟议的项目提供了理论和实证依据。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。

The Researching Order of Teaching project will provide structured and meaningful scaffolds for teachers in examining two research-based teaching strategies hypothesized to positively impact mathematics achievement in the areas of mathematical modeling and problem solving. The first strategy, Explicit Attention to Concepts (EAC), is a set of practices that draw students' attention specifically to mathematical concepts in ways that extend beyond memorization, procedures, or application of skills. This strategy may include teachers asking students to connect multiple mathematical representations, compare solution strategies, discuss mathematical reasoning underlying procedures, or to identify a main mathematical idea in a lesson and how it fits into the broader mathematical landscape. The second strategy, Student Opportunities to Struggle (SOS), entails providing students with time and space to make sense of graspable content, overcoming confusion points, stimulating personal sense-making, building perseverance, and promoting openness to challenge. This strategy may include teachers assigning problems with multiple solution strategies, asking students to look for patterns and make conjectures, encouraging and promoting discourse around confusing or challenging ideas, and asking students for extended mathematical responses. This project investigates whether the order in which teachers apply these practices within the teaching of mathematics content has an impact on student learning. This study builds on previous work that had identified an interaction between the EAC and SOS instructional strategies, and associated teacher reporting of stronger use of the practices with higher student mathematics achievement.The project will have four key design features. First, the project will adopt and extend the research-based EAC/SOS conceptual framework, and explicitly responds to the call for further research on the interactions. Second, the project will focus on the mathematical areas of modeling and problem solving, two complex and critical competencies for all students in the middle grades. Third, the project will position teachers as collaborators in the research with needed expertise. Finally, the project will make use of research methods from crossover clinical trials to implementation in classrooms. The project aims to identify the affordances and constraints of the EAC/SOS framework in the design and development of instructional practices, to identify student- and teacher-level factors associated with changes in modeling and problem solving outcomes, to analyze teachers' implementations EAC and SOS in teaching modeling and problem solving and to associate those implementation factors with student achievement changes, and to determine whether the ordering of these two strategies correlates with differences in achievement. The project will collect classroom observation data and make use of existing tools to obtain reliable and valid ratings of the EAC and SOS strategies in action. The design of the study features a randomized 2 x 2 cluster crossover trial with a sample of teachers for 80% power. The project builds on existing state infrastructure and relationships with a wide array of school districts in the context of professional development, and aims to create a formal Teacher-Researcher Alliance for Investigating Learning as a part of the project work.The Discovery Research preK-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.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.