Simulation-Based Inquiry-Oriented Linear Algebra

招募和培训科学、技术、工程和数学（STEM）领域的学生是一个公认的国家劳动力需求和关键挑战。由于数学是所有STEM学科的基础部分，因此本科学生在数学方面的成功是应对这一挑战的关键因素。线性代数是STEM学科学生的重要过渡课程，因为它在数学内部具有统一的力量，并且在数学之外的领域具有适用性。因此，在学生发展的这个阶段，有效的指导是至关重要的。该项目的重点将是通过将技术与几种学习理论和应用相结合，从而产生新的研究成果和课程资源，从而改善线性代数的教学、学习和学生的成功。该项目将利用研究者之前在面向探究的线性代数（IOLA）方面的研究和课程开发，以及在基于技术的学习方面的专业知识，探索课程设计与技术设计理论和实践的统一。该项目的目标是：(1)创建一个数字平台，为学生提供IOLA课程的虚拟体验；(2)记录使用游戏平台（IOLA- g）学习的便利和限制，并与经验丰富的IOLA教师面对面教学进行比较；(3)比较不同的数字游戏形式，确定哪种形式最有利于探究性学习；(4)利用从(1)、(2)和(3)中获得的知识，通过开发的技术改善学生的学习，并反射性地增强现有的IOLA课程和教师支持资源。项目团队将在学生参与数字平台的同时调查学生的数学活动和学习情况，并将利用这一见解进一步改进设计。基于先前在线性代数的学习和教学方面的研究成果以及基于游戏的学习（GBL）方面的专业知识，该团队将设计IOLA- g来模仿现有IOLA课程的以问题为中心的方法，并将通过在整个项目中与学生进行教学实验来迭代地完善这个平台。该项目还将探索GBL在多大程度上可以提供一种动态的方法来解决班级规模较大对教师实施探究性课程的限制。此外，作为创建资源技术过程的一部分，研究人员将采用混合方法，将基于游戏的学习设计、课程设计理论和基于探究的学习研究相结合，探索以下研究问题：与仅使用面对面的IOLA课程相比，使用IOLA- g的学生参与的数学实践和学生发展的概念理解是什么？在制定探究性课程方面，不同的游戏环境有什么优势和限制？该项目的影响将包括对STEM学科学生的学习，知识，能力和整体成功的积极影响，这将导致加强美国在STEM领域的劳动力需求。

A well-established National workforce need and critical challenge is to recruit and train students in Science, Technology, Engineering and Mathematics (STEM) fields. Since mathematics is a fundamental part of all STEM disciplines, success of undergraduate students in mathematics is a crucial ingredient to address this challenge. Linear algebra is a vital transition course for students in the STEM disciplines because of its unifying power within mathematics and its applicability to areas outside of mathematics. Accordingly, effective instruction at this stage in students' development is paramount. The focus of this project will be to improve teaching, learning, and student success in linear algebra by incorporating a blending of technology and several learning theories and applications to lead to new research results and production of curriculum resources. This project will leverage the investigators' previous research and curriculum development in Inquiry-Oriented Linear Algebra (IOLA) and expertise in Technology Based Learning to explore the unification of curriculum design and technology design theories and practices.The goals of the project are to: (1) create a digital platform that will equip students with a virtual experience of a version of the IOLA curriculum; (2) document the affordances and constraints for learning using a game platform (IOLA-G) in comparison to face-to-face instruction by experienced IOLA instructors; (3) compare different digital gaming formats to determine which are most conducive to inquiry-oriented learning; and (4) use the knowledge gained from (1), (2), and (3) to improve student learning through the developed technology, and, reflexively, to enhance the existing IOLA curriculum and teacher support resources. The project team will investigate students' mathematical activity and learning while the students are engaged with the digital platform and will use this insight to inform further refinement of design. Building on prior research efforts in the learning and teaching of linear algebra and expertise in Game Based Learning (GBL), the team will design IOLA-G to mimic the problem-centered approach of the existing IOLA curriculum and will iteratively refine this platform through teaching experiments with students throughout the project. The project also will explore the extent to which GBL can provide a dynamic approach to addressing the constraints that larger class sizes place on instructors' implementation of inquiry-oriented curricula. In addition to, and as part of the process of, creating the resource technology, the investigators will incorporate a mixed methods approach with a blending of game-based learning design, curriculum design theory, and research from inquiry-based learning to explore the following research questions: What are the mathematical practices that students engage in and the conceptual understandings students develop using IOLA-G compared to when using only the face-to-face IOLA curriculum? What are the affordances and constraints of different game environments in terms of enacting an inquiry-oriented curriculum? The impact of the project will include the positive effects on STEM discipline student learning, knowledge, abilities, and overall success, which will lead to strengthening United States workforce needs in STEM areas.