Math Snacks Early Algebra: Using Games and Inquiry to Help Students Transition from Number to Variable

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，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。许多美国学生进入大学时没有在高等数学和科学课程中取得成功所必需的代数背景，因此无法从事许多有回报的职业。通常情况下，这个问题可以追溯到4-6年级的早期代数，在学生理解基本概念和提出问题的原因之前，他们被介绍给抽象的公式。由于准备不足，许多学生在面对抽象代数时对数学敬而远之。没有数学，学生就不能进入STEM领域，这导致美国这些领域的劳动力被削弱。在这个为期4年的完整研究和开发项目中，来自新墨西哥州立大学的跨学科研究小组将在他们成功使用游戏来增加学生对比例推理和分数的理解的基础上，利用数学零食早期代数：使用游戏来帮助学生从数字过渡到变量。他们将开发游戏，以建立对关键早期代数主题的概念性理解。这些材料将在网上以英文和西班牙文免费提供。该项目将开发4-5个游戏。每个游戏将包括供学生在探究式课堂课程中使用的辅助材料，以及为教师提供的基于网络的专业发展工具。大多数学生不了解变量在数学中的各种不同用法：要解的未知数、相关量、数的一般性质以及其他用途。代数课程往往强调运算规则，较少花时间在基本思想上。学生们认为变量是令人困惑的新材料，而不是理解数字的捷径，或者是分析有趣问题的强大工具。这阻碍了学生以后对STEM课程和职业的兴趣和进步。这一研发项目的智力价值包括开发了一种学习代数关键基本概念的新方法，进一步调查了游戏和技术在学习抽象数学概念方面的负担，以及更好地理解了早期代数的学习评估。这个研发项目的更广泛影响包括让学生广泛使用这些工具，以及教师可能转向有效的、有吸引力的、以探究为基础的数学教学法。开发将从对早期代数思维和学习的现有研究开始，并经过一个迭代过程，包括设计、在NMSU学习游戏实验室的测试、教室测试，然后返回设计。然后，该项目将研究开发的材料对学生理解和课堂学习环境的影响。将采用定性和定量相结合的方法。研究人员将使用与NAEP(国家教育进步评估)和其他标准测试相一致的定制测量方法，对教师和学生进行采访和观察，并嵌入关于游戏使用频率和程度的数据收集和自我报告。在之前的两个试点研究之后，在最后一年，将对50名教师和他们的学生进行延迟干预研究。数学零食团队已经与PBS、GlassLabs、BrainPOP和其他公司建立了游戏和材料分发的现有合作伙伴关系。该项目的学术成果将通过会议和研究出版物分享。

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.Many U.S. students enter college without the necessary background in algebra to be successful in advanced mathematics and science courses, and are thereby blocked from many rewarding careers. Oftentimes, the problem goes back to early algebra in grades 4-6, where students are introduced to abstract formulations before they understand the underlying ideas and the reasons for the questions being asked. As a result of inadequate preparation many students turn away from mathematics when faced with abstract algebra. Without mathematics, students are not able to enter the STEM field which results in a weakened workforce in these fields in the United States. In this 4-year Full Research and Development project, Math Snacks Early Algebra: Using Games and Inquiry to Help Students Transition from Number to Variable, the interdisciplinary research group from New Mexico State University will build on their success in using games to increase students' understanding of proportional reasoning and fractions. They will develop games to build conceptual understanding of key early algebra topics. The materials will be freely accessible on the web in both English and Spanish. The project will develop 4-5 games. Each game will include supporting materials for use by students in inquiry-based classroom lessons, and web-based professional development tools for teachers. Most students do not understand the variety of distinct ways that variables are used in mathematics: unknowns to be solved for, related quantities, general properties of numbers, and other uses. Algebra courses often emphasize the rules of manipulation, with less time spent on the underlying ideas. Students see variables as confusing new material, rather than as shortcuts for making sense of numbers, or as powerful tools for analyzing interesting problems. This hinders students' later interest and progress in STEM courses and careers.The intellectual merit for this R & D project includes the development of a new way to learn key underlying concepts in algebra, further investigation of the affordances of games and technology in learning abstract mathematical concepts, and a better understanding of learning assessment in early algebra. The broader impact for this R & D project includes making these tools widely available to students, and the potential shift of teachers towards effective mathematical pedagogy that is engaging and inquiry-based. Development will begin with existing research on early algebraic thinking and learning, and proceed through an iterative process involving design, testing in the NMSU Learning Games Lab, testing in classrooms, and back to design. The project will then study the effect of the developed materials on student understanding and on classroom learning environments. Qualitative and quantitative measures will be used. Researchers will use a custom measure aligned with NAEP (National Assessment of Educational Progress) and other standard tests, interviews and observations with teachers and students, and embedded data collection and self-reports on frequency and extent of game usage. After two earlier pilot studies, in the final year a delayed intervention study will be conducted with 50 teachers and their students. The Math Snacks team has existing partnerships for distribution of games and materials with PBS, GlassLabs, BrainPOP, and others. Academic findings of the project will be shared through conferences and research publications.