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

通过有效的教学实践排序，提高 6-8 年级学生在建模和解决问题方面的数学成绩

• 批准号: 1907840
• 负责人: Joe Champion
• 金额: $ 296.38万
• 依托单位: Boise State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1907840&HistoricalAwards=false
• 关键词: Improving; Grades; students; mathematics; achievement

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.

《教学项目研究顺序》将为教师检验两种研究性教学策略提供有结构和有意义的支架，这两种策略被假设为在数学建模和问题解决领域对数学成绩产生积极影响。第一种策略是明确注意概念(EAC)，这是一套让学生特别注意数学概念的练习，其方式超越了记忆、程序或技能的应用。这种策略可以包括教师要求学生连接多个数学表示法，比较解决策略，讨论潜在的数学推理程序，或者识别一节课中的主要数学思想，以及它如何适应更广泛的数学图景。第二个战略，学生奋斗的机会(SOS)，需要为学生提供时间和空间，让他们理解可掌握的内容，克服困惑，激发个人理性，培养毅力，并促进对挑战的开放。这一策略可能包括：教师布置具有多种解决策略的问题，要求学生寻找模式并进行猜测，鼓励和促进围绕困惑或具有挑战性的想法的讨论，以及要求学生做出扩展的数学回答。这个项目调查教师在数学教学中应用这些实践的顺序是否会对学生的学习产生影响。这项研究建立在以前工作的基础上，这些工作已经确定了EAC和SOS教学策略之间的互动，以及相关教师报告了更多地使用实践与学生更高的数学成绩。该项目将有四个关键的设计特征。首先，该项目将采用和扩展以研究为基础的EAC/SOS概念框架，并明确响应对相互作用进行进一步研究的呼吁。其次，该项目将侧重于建模和解决问题的数学领域，这是所有中等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框架在设计和开发教学实践方面的启示和限制，确定与建模和问题解决结果变化相关的学生和教师层面的因素，分析教师在教学建模和问题解决中实施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绩差异有关。该项目将收集课堂观察数据，并利用现有工具，获得对实施中的东非共同体和SOS战略的可靠和有效评级。这项研究的设计特点是随机的2×2群交叉试验，样本为80%的教师。该项目建立在现有的国家基础设施和与专业发展背景下广泛的学区的关系的基础上，旨在创建一个正式的教师-研究人员学习调查联盟，作为项目工作的一部分。探索研究预科-12项目(DRK-12)旨在通过研究和开发创新资源、模型和工具，显著提高预科-12年级学生和教师的科学、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经验上的证明。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Frustration: Analyzing a Card Game with Probability

挫败感：用概率分析纸牌游戏

• 发表时间: 2022
• 期刊: Mathematics Teacher
• 作者: Derrick, J.;Champion, J.;Uriarte, R.
• 通讯作者: Uriarte, R.

A validation argument for the Priorities for Mathematics Instruction (PMI) survey.

数学教学优先事项 (PMI) 调查的验证论证。

• 发表时间: 2021
• 期刊: USA.
• 作者: Carney, M. B.;Champion, J.;Crawford, A.
• 通讯作者: Crawford, A.

The role of a boundary object in a study of middle grades mathematics instruction

边界对象在中学数学教学研究中的作用

• 发表时间: 2022
• 期刊: Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
• 作者: Crawford, A.;Carney, M.;Champion, J.;Schmidt, M.
• 通讯作者: Schmidt, M.

Struggling with struggle: Implications for students with diverse cognitive resources [Brief research report]

挣扎中挣扎：对拥有多样化认知资源的学生的启示[简要研究报告]

• 发表时间: 2021
• 期刊: USA.
• 作者: Crawford, A.

Building Mathematics Professional Development With an Explicit Attention to Concepts and Student Opportunities to Struggle Framework

建立数学专业发展，明确关注概念和学生奋斗机会的框架

• DOI: 10.5951/mte.2021.0030
• 发表时间: 2023
• 期刊: Mathematics Teacher Educator
• 作者: Hughes, Gwyneth;Carney, Michele B.;Champion, Joe;Yundt, Lindsey
• 通讯作者: Yundt, Lindsey