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

University Of Texas At El Paso, El Paso TX

Investigators

Abstract

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.