Technology's Role in Student Understanding of Mathematics in Modern Undergraduate Engineering Courses

摘要

This paper seeks to identify important implications on the use of technology in the teaching of mathematics in modern undergraduate engineering courses. These are used to create a big picture of the current situation of engineering mathematics teaching based on the developments over time. Certainly, the use of technology in engineering and mathematics is necessary in the modern world. Technology is integrated into everything engineers do, and engineering students must develop skills with learning and using various forms of technology. For mathematics, utilizing technology leads to faster and larger quantities of calculations that can be performed, which are clear advantages. However, it has been shown that the theoretical mathematical ability of modern undergraduate engineering students has mostly decreased over the decades. Part of this decline is due to the focus in classrooms on application-based teaching and using technology to perform calculations instead of allowing students to think through mathematical problems. This can lead to engineers who can crunch numbers but not solve new conceptual problems. Mathematics is a vital skillset for engineering students. Its many forms are required of students to some degree in every engineering discipline, and higher-level courses may make extensive use of mathematics. Additionally, a good mathematical ability is often needed after graduation in industry or in graduate school. Thus, it is important to foster the conceptual mathematical understanding of undergraduate engineering students for their futures. However, students often make use of technology as a "black box" in that they get an answer for a particular problem but do not understand the concepts underneath and have difficulty applying the math to different situations. Due to this, there is a need for teaching strategies which expose students to technology without replacing analytical and theoretical ability. Thus, a literature review is conducted for articles describing the role of different technologies in teaching mathematics and student understanding. The collected articles come from engineering education and mathematics education sources. Specific technologies referenced include personal graphing calculators, programming software, and Virtual Learning Environments (VLEs). The results of using these reported different technologies and methods are compared. Advantages and disadvantages for student use and understanding are discussed. From this bigger picture, it is seen that there are ways to leverage modern technology appropriately to take advantage of the speed and power of calculation but not impede conceptual understanding and learning. As technology continues to change, it is important that engineers retain the conceptual understanding so they can adapt to new tools and still solve future engineering problems. It is hoped that through this literature review, good practices for properly using technology to supplement and improve mathematics education in undergraduate engineering can be compared and expanded upon.