Teaching and Learning Algebraic Thinking Across the Middle Grades: A Research-based Approach Using PhET Interactive Simulations

探索研究K-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pre -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。技术的广泛、高质量使用具有巨大的潜力，可以改变当今的数学课堂，并使所有学生都能对数学形成牢固的概念理解。目前严峻的挑战限制了这种潜力的实现，69%的美国八年级学生在国家研究中的得分低于熟练水平。在这个为期3年的探索研究K-12全面研究与开发项目中，“中学阶段的代数思维教学：基于研究的PhET互动模拟方法”，科罗拉多大学博尔德分校的PhET互动模拟小组与南佛罗里达大学圣彼得堡分校和佛罗里达州立大学的数学教育研究人员合作，解决以下三个核心挑战：1)学生在使用技术时不进行真正的数学思考的倾向；2)教师倾向于不制定有效的教学方法；3)由于各种障碍，教师没有采用有效的技术。这种合作的努力使用丰富的、探索性的、互动的模拟和相关的教学材料作为快速进步的途径，重点是提高6-9年级学生的代数思维。该项目旨在使教师能够充分利用交互式模拟的好处，提高学生的参与度和数学学习，将技术从边缘转移到教学的核心部分。该项目将回答关键的研究问题，例如：交互式模拟的设计如何产生教学上的生产性使用；如何最好地组织模拟教学，以支持数学概念的学习和数学实践的参与；如何使模拟教学对教师具有吸引力、可行性和有效性；最后，基于模拟的教学如何影响学生的学习。同时，该项目将为教师和学生提供一个开放的教育资源集合。这些资源将包括15个基于研究的、学生测试的代数思维教学模拟，相关的教学支持材料，以及有效实施的教师专业发展资源。基于每年使用PhET的7500万次？通过科学模拟，我们期望这些资源能够改变数百万学生和数千名教师的数学教学。这个项目将采用多种研究方法来解决这些问题。研究人员将使用来自不同小组的6-9年级学生的个人访谈，因为他们使用15个新的模拟来检查可用性，参与度和成就，并确定刺激生产性使用的设计方法。与此同时，在科罗拉多州和佛罗里达州进行的以课堂为基础的研究将调查如何将模拟与教学材料和教师指导相结合，以吸引学生群体参与探究，促进对重要数学思想的丰富讨论，并促进在“共同核心州数学标准”中的成就。该项目将采用迭代设计和开发过程，涉及对包括数学教学质量在内的各种措施进行定性和定量分析。最后，一项试点研究和对教师PD支持的评估将检验教师实施创新的可行性和保真度，以及对学生学习的影响。

The Discovery Research K-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. Widespread, high-quality use of technology has great potential to transform today's mathematics classrooms and enable all students to develop a robust conceptual understanding of mathematics. Critical challenges are currently limiting the realization of this potential, and 69% of US Grade 8 students are scoring below proficient in national studies. In this 3-year Discovery Research K-12 Full Research and Development project, Teaching and Learning Algebraic Thinking Across the Middle Grades: A Research-based Approach Using PhET Interactive Simulations, the PhET Interactive Simulations group at the University of Colorado Boulder is partnering with mathematics education researchers at the University of South Florida St. Petersberg and Florida State University to address three central challenges, as follows: 1) the tendency for students to not engage in real mathematical thinking as they use technologies; 2) the tendency for teachers to not enact pedagogically-effective approaches; and 3) the lack of adoption of effective technologies by teachers due to a variety of barriers. This collaborative effort uses rich, exploratory, interactive simulations and associated instructional materials as a pathway for making rapid progress and focuses on advancing algebraic thinking in Grades 6-9. This project seeks to enable teachers to fully-leverage the benefits of interactive simulations to advance student engagement and learning of mathematics, moving technology from the margins to a core part of instruction. The project will answer critical research questions, such as: how the design of an interactive simulation can generate pedagogically-productive use; how instruction with simulations can be best structured to support learning of mathematical concepts and engagement in mathematical practices; how sim-based instruction can be made attractive, feasible and effective for teachers; and finally, how student learning is impacted by sim-based instruction. At the same time, this project will produce a collection of open educational resources for teachers and students. These resources will include 15 research-based, student-tested simulations for teaching and learning of algebraic thinking, associated instructional support materials, and teacher professional development resources for effective implementation. Based on the 75 million uses per year of PhET?s science simulations, we expect these resources to transform mathematics instruction for millions of students and thousands of teachers. This project will employ a variety of research methods to approach these questions. Researchers will use individual interviews from a diverse group of Grades 6-9 students as they use the 15 new simulations to examine usability, engagement, and achievement and to identify design approaches that stimulate productive use. In parallel, classroom-based studies in Colorado and Florida will investigate ways in which simulations can be combined with instructional materials and teacher facilitation to engage groups of students in inquiry, promote rich discussions of important mathematical ideas, and advance achievement in the Common Core State Standards for Mathematics. The project will employ an iterative design and development process involving qualitative and quantitative analysis of diverse measures including the quality of mathematical instruction. Finally, a pilot study and an evaluation of teacher PD supports will examine the feasibility and fidelity with which teachers implement the innovation, and the impact on student learning.