Interactive Online Modules and Take-Home Assignments for Inquiry-Learning to Provide First-Hand Experience in Matrix Algebra Course

数学科学(21)这个项目正在开发互动、在线模块和探究活动，以支持传统的以讲授为基础的矩阵代数课程。这些在线互动探究活动是使用数学和网络数学开发的，目的是丰富学生在矩阵代数方面的经验，并使他们在后续课程中受益。该项目是将技术融入德克萨斯大学埃尔帕索分校提供的所有数学课程的关键一步。学生将在课外完成交互式在线模块，然后在课堂上了解矩阵概念的正式定义。因此，他们将拥有理解课堂上引入的高度抽象的概念作为二手知识所需的第一手知识。智力价值：这个项目正在测试一种新的矩阵代数教学方法的有效性。在文献中有几个报告记录了在课堂时间内在矩阵代数课堂中使用基于计算机的探究性学习活动。然而，在典型的课堂时间里，经常没有足够的时间来进行这样的实验活动。本项目研究改进的学生学习与课外提供的探究性学习体验之间的关系。这个假设是，精心设计的探究活动作为带回家的作业，将给学生提供他们理解课堂上提供的抽象信息所需的第一手知识。掌握程度将通过评估工具来衡量，这些工具侧重于对矩阵代数中基本抽象概念的程序性和概念性知识。更广泛的影响：为提高学生学习抽象概念的能力提供工具将对中学后数学教育产生广泛影响。越来越多的非数学专业的学生，尤其是工程和理科专业的学生，报名参加一年级的矩阵或线性代数课程。但这些学生中的许多人还没有准备好接受这类课程中常见的高抽象程度，导致全国范围内的通过率很低。新的模块和带回家的作业将在一个网站上提供，该网站将链接到国家科学数字图书馆，以便它们可以在全国各地的项目中使用。虽然该项目的重点是矩阵代数，但材料的核心思想可以适用于数学中的其他重要主题。最后，评估工具将收集人口统计数据，以确定材料对改善不同学生群体学习的影响。由于UTEP的学生人口中超过72%是西班牙裔，这些材料将在德克萨斯州和全国快速增长的人口上进行测试。

Mathematical Sciences (21) This project is developing interactive, online modules and inquiry activities to support traditional lecture-based matrix algebra courses. These online interactive inquiry activities are being developed using Mathematica and WebMathematica, with the goal that they will both enrich students' experience in matrix algebra and benefit them in subsequent courses. This project is a pivotal step in integrating technology into all mathematics courses offered at University of Texas at El Paso. Students will work outside of class to complete interactive online modules before being exposed in the classroom to the formal definition of matrix concepts. Thus they will have the first-hand knowledge they need to understand the highly abstract concepts introduced in class as second-hand knowledge. Intellectual Merit: This project is testing the efficacy of a new way of teaching matrix algebra. There are several reports in the literature documenting the use of computer-based, inquiry-learning activities within the matrix algebra classroom during class time. However, there is often not enough time during the typical class period for such experimental activities. This project studies the relationship between improved student learning and inquiry learning experiences provided outside of class. The hypothesis is that carefully designed inquiry activities assigned as take-home will give students the first-hand knowledge they need to understand the abstract information that will be provided in the classroom. Mastery will be measured via assessment instruments that focus on both procedural and conceptual knowledge of basic abstract concepts in matrix algebra. Broader Impact: Providing tools for improving the ability of students to learn abstract concepts will have a broad impact on post-secondary mathematics education. Increasingly, non-mathematics majors, particularly engineering and science majors, enroll in first-year matrix or linear algebra courses. But many of these students are not prepared for the high level of abstraction common in such courses, leading to low pass rates nationwide. The new modules and take-home assignments will be available on a website that will be linked to the National Science Digital Library so that they can be used in programs across the country. While the project focuses on matrix algebra, the core ideas of the materials can be adapted to other important topics in mathematics. Finally, the assessment instruments will collect demographic data to determine the effects of the materials on improved learning in diverse student populations. Since UTEP has a student population that is more than 72 percent Hispanic, the materials will be tested on a rapidly-growing population in both Texas and the nation as a whole.