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

探索研究K-12计划(DRK-12)旨在通过研究和开发创新资源、模型和工具，显著提高K-12学生和教师在科学、技术、工程和数学(STEM)方面的学习和教学。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努力的基础上，这些研究和开发工作为拟议的项目提供了理论和经验证明。广泛、高质量地使用技术具有巨大的潜力，可以改变当今的数学课堂，使所有学生都能够对数学产生强有力的概念理解。严峻的挑战目前限制了这一潜力的实现，69%的美国八年级学生在国家学习中的得分低于熟练程度。在这个为期3年的发现研究K-12完整的研究和开发项目中，科罗拉多大学博尔德大学的PHET交互模拟小组正在与南佛罗里达大学圣彼得堡大学和佛罗里达州立大学的数学教育研究人员合作，共同应对如下三个主要挑战：1)学生在使用技术时不参与真正的数学思维的倾向；2)教师没有制定有效的教学方法的倾向；3)由于各种障碍，教师缺乏采用有效的技术。这一合作努力使用丰富的、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，并专注于促进6-9年级的代数思维。该项目旨在使教师能够充分利用交互模拟的好处，促进学生参与和学习数学，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成果；模拟教学如何才能得到最佳的结构，以支持数学概念的学习和参与数学实践；如何使基于模拟的教学对教师有吸引力、可行和有效；以及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产生一个开放的教育资源集合。这些资源将包括15个以研究为基础的、经过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Phet？S科学模拟每年7500万次的使用，我们预计这些资源将改变数百万学生和数以千计的教师的数学教学。本项目将采用多种研究方法来探讨这些问题。研究人员将使用不同的6-9年级学生群体的个人访谈，他们使用15个新的模拟来检查可用性、参与度和成就，并确定刺激生产使用的设计方法。与此同时，科罗拉多州和佛罗里达州的课堂研究将调查如何将模拟与教学材料和教师促进相结合，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，并促进数学共同核心州立标准的成就。该项目将采用迭代设计和开发过程，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，一项初步研究和对教师PD支持的评估将检验教师实施创新的可行性和忠诚度，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.