Using Digital Images to Teach Abstract Math and Inspire Students towardsCareers in Computer Science and Engineering
Victor Mejia, Jessica Alvarenga, Jianyu Dong, Huiping Guo, Israel Hernandez, Eun-Young Kang, Phanit Pollavith, Adriana Trejo, Nancy Warter-Perez · 2020
mathematical concepts are often difficult for high school students to understand.Students are often adept at learning how to solve specific math problems but have a difficult time understanding how they can relate to the real world.In response to this, math teachers try to come up with engaging, real-world examples to not only allow students to better understand abstract mathematical concepts but also to reinforce their comprehension.These real-world examples must meet state standards and should be designed to increase students' interest in science and engineering.Image processing is a real-world example of engineering that students easily relate to because of their familiarity with cell phones, video game consoles, cameras, and computers.1,2 This paper presents a collection of different demonstrations and hands-on activities that were developed to help students learn about digital images while reinforcing their understanding of abstract mathematical concepts such as matrices and functions.Through the IMPACT LA GK-12 Program, Improving Minority Partnerships and Access through CISE (Computer & Information Science & Engineering)-related Teaching, three graduate fellows were paired with three different high school math teachers and were successfully able to engage students in their graduate research through these demonstrations and hands-on activities.Through the IMPACT LA Program, graduate student fellows become educators, thus bridging the gap between abstract math and real-world engineering by bringing graduate student research into the classroom.The three different areas of research that were brought into the classrooms are: computer vision and object tracking, information security and digital watermarking, and telescopes and deep-space exploration.How can a computer track moving objects in a video?How can you detect if a video has been tampered with?How are pictures sent on your cell phone or from the Hubble Space Telescope?These are some of the research-related questions that students were able to explore through demonstrations and hands-on activities.This paper is organized as follows.Section 2 describes the IMPACT LA Program and its goals.Section 3 introduces the fellows' research in computer vision and object tracking, information security and digital watermarking, and space telescopes and deep-space exploration.Section 4 describes the mathematical concepts the high school math students were learning when these demonstrations and activities were done and presents the mathematical background needed to understand them.Section 5 presents the demonstrations that were used.It first describes the multimedia that was used to introduce students to space and satellites, and then presents the science and engineering tools used to introduce students to digital images and object trajectories.Section 6 describes two different hands-on activities used, digital image decoding and assembly of macroblocks, along with an explanation of how the activities reinforce concepts of matrices and algebraic functions.Students' evaluations of the hands-on activities are also presented that demonstrate students' understanding of abstract math concepts.Finally, section 7 presents preand post-assessment data that demonstrate noteworthy improvements in attitudes of students towards computer science and engineering, respectively.Page 22.1613.2