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支架，以检查两个基于研究的教学策略，假设在数学建模和问题解决领域的数学成绩产生积极影响。第一个策略，明确注意概念（EAC），是一套做法，吸引学生的注意力，特别是数学概念的方式，超越记忆，程序，或技能的应用。 这一策略可能包括教师要求学生连接多个数学表示，比较解决方案的策略，讨论数学推理的基本程序，或确定一个主要的数学思想在一个教训，以及它如何融入更广泛的数学景观。第二个战略，学生的机会，以斗争（SOS），需要为学生提供时间和空间，使理解的内容，克服困惑点，刺激个人的意义，建设毅力，并促进开放的挑战。这一策略可能包括教师分配问题与多种解决方案的策略，要求学生寻找模式，并作出解释，鼓励和促进话语周围的混乱或具有挑战性的想法，并要求学生扩展数学的反应。本研究旨在探讨教师在数学教学内容中应用这些实践的顺序是否会对学生的学习产生影响。本研究建立在以前的工作，已经确定了EAC和SOS教学策略之间的相互作用，以及相关的教师报告更强的使用实践与更高的学生数学成绩。 首先，该项目将采用和扩展基于研究的EAC/SOS概念框架，并明确响应进一步研究相互作用的呼吁。 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项复杂而关键的能力。第三，该项目将把教师定位为研究中具有所需专业知识的合作者。 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框架在教学实践设计和开发中的启示和限制，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中的EAC和SOS实施情况，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排序是否与成绩差异相关。 该项目将收集课堂观察数据，并利用现有工具对正在实施的东非共同体和SOS战略进行可靠和有效的评级。本研究采用随机2 × 2整群交叉试验设计，样本为教师，把握度为80%。 该项目建立在现有的国家基础设施和与专业发展背景下的广泛学区的关系，并旨在创建一个正式的教师-研究人员联盟，作为项目工作的一部分。发现研究preK-12计划（DRK-12）旨在显着提高科学，技术，工程和数学（STEM）的preK-12学生和教师，通过研究和开发创新的资源，模型和工具。DRK-12项目中的项目建立在STEM教育的基础研究以及为拟议项目提供理论和经验依据的先前研究和开发工作的基础上。该奖项反映了NSF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.